TSTP Solution File: SEU025+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 15:21:53 EDT 2024
% Result : Theorem 0.15s 0.43s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 307
% Syntax : Number of formulae : 1022 ( 96 unt; 0 def)
% Number of atoms : 3514 ( 381 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 4607 (2115 ~;2092 |; 102 &)
% ( 256 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 265 ( 263 usr; 256 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 923 ( 896 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3402,plain,
$false,
inference(avatar_sat_refutation,[],[f179,f184,f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f259,f264,f269,f274,f278,f282,f286,f295,f299,f303,f307,f321,f326,f330,f334,f338,f342,f346,f350,f354,f370,f378,f382,f386,f391,f396,f400,f404,f408,f412,f416,f420,f427,f447,f451,f455,f459,f463,f467,f471,f514,f524,f534,f538,f542,f550,f555,f560,f570,f580,f585,f591,f600,f605,f610,f614,f626,f631,f637,f641,f645,f649,f656,f662,f663,f664,f665,f666,f689,f747,f760,f764,f768,f781,f790,f795,f801,f835,f844,f848,f856,f860,f864,f868,f872,f876,f922,f926,f930,f934,f980,f984,f989,f1000,f1011,f1019,f1023,f1027,f1031,f1079,f1090,f1094,f1098,f1118,f1122,f1140,f1158,f1163,f1167,f1197,f1202,f1207,f1238,f1249,f1260,f1268,f1273,f1281,f1285,f1294,f1311,f1315,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1512,f1600,f1604,f1620,f1624,f1628,f1632,f1636,f1645,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1767,f1921,f1940,f1946,f1959,f1965,f1979,f1983,f1987,f2005,f2009,f2013,f2017,f2021,f2025,f2029,f2033,f2037,f2041,f2046,f2211,f2215,f2219,f2223,f2227,f2231,f2235,f2253,f2257,f2261,f2265,f2269,f2372,f2469,f2473,f2477,f2490,f2494,f2498,f2616,f2639,f2687,f2691,f2695,f2699,f2703,f2707,f2844,f2894,f2898,f2902,f2906,f2987,f2991,f2995,f2999,f3003,f3007,f3011,f3119,f3124,f3128,f3132,f3136,f3140,f3144,f3145,f3158,f3168,f3172,f3212,f3220,f3224,f3256,f3261,f3265,f3302,f3304,f3317,f3335,f3340,f3375,f3390,f3401]) ).
fof(f3401,plain,
( spl12_25
| ~ spl12_1
| ~ spl12_23
| ~ spl12_132 ),
inference(avatar_split_clause,[],[f1274,f1266,f284,f176,f292]) ).
fof(f292,plain,
( spl12_25
<=> relation_dom(sK0) = relation_rng(relation_composition(sK0,function_inverse(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).
fof(f176,plain,
( spl12_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f284,plain,
( spl12_23
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_23])]) ).
fof(f1266,plain,
( spl12_132
<=> ! [X0] :
( relation_dom(sK0) = relation_rng(relation_composition(X0,function_inverse(sK0)))
| ~ relation(X0)
| ~ subset(relation_rng(sK0),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_132])]) ).
fof(f1274,plain,
( ~ relation(sK0)
| relation_dom(sK0) = relation_rng(relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_23
| ~ spl12_132 ),
inference(resolution,[],[f1267,f285]) ).
fof(f285,plain,
( ! [X0] : subset(X0,X0)
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f1267,plain,
( ! [X0] :
( ~ subset(relation_rng(sK0),relation_rng(X0))
| ~ relation(X0)
| relation_dom(sK0) = relation_rng(relation_composition(X0,function_inverse(sK0))) )
| ~ spl12_132 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f3390,plain,
( spl12_255
| ~ spl12_1
| ~ spl12_23
| ~ spl12_131 ),
inference(avatar_split_clause,[],[f1261,f1258,f284,f176,f3387]) ).
fof(f3387,plain,
( spl12_255
<=> relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_255])]) ).
fof(f1258,plain,
( spl12_131
<=> ! [X0] :
( relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),X0))
| ~ relation(X0)
| ~ subset(relation_dom(sK0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_131])]) ).
fof(f1261,plain,
( ~ relation(sK0)
| relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),sK0))
| ~ spl12_23
| ~ spl12_131 ),
inference(resolution,[],[f1259,f285]) ).
fof(f1259,plain,
( ! [X0] :
( ~ subset(relation_dom(sK0),relation_dom(X0))
| ~ relation(X0)
| relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),X0)) )
| ~ spl12_131 ),
inference(avatar_component_clause,[],[f1258]) ).
fof(f3375,plain,
( spl12_254
| ~ spl12_1
| ~ spl12_23
| ~ spl12_130 ),
inference(avatar_split_clause,[],[f1250,f1247,f284,f176,f3372]) ).
fof(f3372,plain,
( spl12_254
<=> relation_rng(sK0) = relation_rng(relation_composition(function_inverse(sK0),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_254])]) ).
fof(f1247,plain,
( spl12_130
<=> ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_130])]) ).
fof(f1250,plain,
( ~ relation(sK0)
| relation_rng(sK0) = relation_rng(relation_composition(function_inverse(sK0),sK0))
| ~ spl12_23
| ~ spl12_130 ),
inference(resolution,[],[f1248,f285]) ).
fof(f1248,plain,
( ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK0),X0)) )
| ~ spl12_130 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f3340,plain,
( spl12_253
| ~ spl12_4
| ~ spl12_69
| ~ spl12_245 ),
inference(avatar_split_clause,[],[f3249,f3222,f588,f191,f3337]) ).
fof(f3337,plain,
( spl12_253
<=> sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_253])]) ).
fof(f191,plain,
( spl12_4
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f588,plain,
( spl12_69
<=> empty_set = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_69])]) ).
fof(f3222,plain,
( spl12_245
<=> ! [X0] :
( sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_245])]) ).
fof(f3249,plain,
( sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),sK5)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_245 ),
inference(forward_demodulation,[],[f3241,f590]) ).
fof(f590,plain,
( empty_set = sK5
| ~ spl12_69 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f3241,plain,
( sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),empty_set)
| ~ spl12_4
| ~ spl12_245 ),
inference(resolution,[],[f3223,f193]) ).
fof(f193,plain,
( empty(empty_set)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f3223,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) )
| ~ spl12_245 ),
inference(avatar_component_clause,[],[f3222]) ).
fof(f3335,plain,
( spl12_252
| ~ spl12_4
| ~ spl12_69
| ~ spl12_244 ),
inference(avatar_split_clause,[],[f3235,f3218,f588,f191,f3332]) ).
fof(f3332,plain,
( spl12_252
<=> sK5 = relation_composition(sK5,relation_composition(sK0,function_inverse(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_252])]) ).
fof(f3218,plain,
( spl12_244
<=> ! [X0] :
( sK5 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_244])]) ).
fof(f3235,plain,
( sK5 = relation_composition(sK5,relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_4
| ~ spl12_69
| ~ spl12_244 ),
inference(forward_demodulation,[],[f3227,f590]) ).
fof(f3227,plain,
( sK5 = relation_composition(empty_set,relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_4
| ~ spl12_244 ),
inference(resolution,[],[f3219,f193]) ).
fof(f3219,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) )
| ~ spl12_244 ),
inference(avatar_component_clause,[],[f3218]) ).
fof(f3317,plain,
( spl12_251
| ~ spl12_95
| ~ spl12_249
| ~ spl12_66
| ~ spl12_243 ),
inference(avatar_split_clause,[],[f3213,f3210,f567,f3295,f837,f3314]) ).
fof(f3314,plain,
( spl12_251
<=> relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(relation_composition(function_inverse(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_251])]) ).
fof(f837,plain,
( spl12_95
<=> relation(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_95])]) ).
fof(f3295,plain,
( spl12_249
<=> subset(relation_dom(sK0),relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_249])]) ).
fof(f567,plain,
( spl12_66
<=> relation_dom(sK0) = relation_rng(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_66])]) ).
fof(f3210,plain,
( spl12_243
<=> ! [X0] :
( ~ subset(relation_dom(sK0),relation_rng(X0))
| ~ relation(X0)
| relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_243])]) ).
fof(f3213,plain,
( ~ subset(relation_dom(sK0),relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(relation_composition(function_inverse(sK0),relation_composition(sK0,function_inverse(sK0))))
| ~ spl12_66
| ~ spl12_243 ),
inference(superposition,[],[f3211,f569]) ).
fof(f569,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ spl12_66 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f3211,plain,
( ! [X0] :
( ~ subset(relation_dom(sK0),relation_rng(X0))
| ~ relation(X0)
| relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) )
| ~ spl12_243 ),
inference(avatar_component_clause,[],[f3210]) ).
fof(f3304,plain,
( ~ spl12_23
| spl12_249 ),
inference(avatar_contradiction_clause,[],[f3303]) ).
fof(f3303,plain,
( $false
| ~ spl12_23
| spl12_249 ),
inference(resolution,[],[f3297,f285]) ).
fof(f3297,plain,
( ~ subset(relation_dom(sK0),relation_dom(sK0))
| spl12_249 ),
inference(avatar_component_clause,[],[f3295]) ).
fof(f3302,plain,
( ~ spl12_95
| ~ spl12_249
| spl12_250
| ~ spl12_65
| ~ spl12_66
| ~ spl12_242 ),
inference(avatar_split_clause,[],[f3206,f3166,f567,f557,f3299,f3295,f837]) ).
fof(f3299,plain,
( spl12_250
<=> relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),relation_composition(sK0,function_inverse(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_250])]) ).
fof(f557,plain,
( spl12_65
<=> relation_rng(sK0) = relation_dom(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_65])]) ).
fof(f3166,plain,
( spl12_242
<=> ! [X0] :
( ~ subset(relation_rng(X0),relation_dom(sK0))
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_242])]) ).
fof(f3206,plain,
( relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),relation_composition(sK0,function_inverse(sK0))))
| ~ subset(relation_dom(sK0),relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_65
| ~ spl12_66
| ~ spl12_242 ),
inference(forward_demodulation,[],[f3202,f559]) ).
fof(f559,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ spl12_65 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f3202,plain,
( ~ subset(relation_dom(sK0),relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| relation_dom(function_inverse(sK0)) = relation_dom(relation_composition(function_inverse(sK0),relation_composition(sK0,function_inverse(sK0))))
| ~ spl12_66
| ~ spl12_242 ),
inference(superposition,[],[f3167,f569]) ).
fof(f3167,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_dom(sK0))
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))) )
| ~ spl12_242 ),
inference(avatar_component_clause,[],[f3166]) ).
fof(f3265,plain,
( spl12_248
| ~ spl12_115
| ~ spl12_241 ),
inference(avatar_split_clause,[],[f3177,f3162,f1029,f3263]) ).
fof(f3263,plain,
( spl12_248
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_248])]) ).
fof(f1029,plain,
( spl12_115
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_115])]) ).
fof(f3162,plain,
( spl12_241
<=> relation(relation_composition(sK0,function_inverse(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_241])]) ).
fof(f3177,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(sK0,function_inverse(sK0)),X0) = X1
| ~ empty(X1) )
| ~ spl12_115
| ~ spl12_241 ),
inference(resolution,[],[f3163,f1030]) ).
fof(f1030,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl12_115 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f3163,plain,
( relation(relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_241 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f3261,plain,
( spl12_247
| ~ spl12_4
| ~ spl12_69
| ~ spl12_228 ),
inference(avatar_split_clause,[],[f3036,f2993,f588,f191,f3258]) ).
fof(f3258,plain,
( spl12_247
<=> sK5 = relation_composition(sK0,sK2(powerset(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_247])]) ).
fof(f2993,plain,
( spl12_228
<=> ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK0,sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_228])]) ).
fof(f3036,plain,
( sK5 = relation_composition(sK0,sK2(powerset(sK5)))
| ~ spl12_4
| ~ spl12_69
| ~ spl12_228 ),
inference(forward_demodulation,[],[f3028,f590]) ).
fof(f3028,plain,
( sK5 = relation_composition(sK0,sK2(powerset(empty_set)))
| ~ spl12_4
| ~ spl12_228 ),
inference(resolution,[],[f2994,f193]) ).
fof(f2994,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK0,sK2(powerset(X0))) )
| ~ spl12_228 ),
inference(avatar_component_clause,[],[f2993]) ).
fof(f3256,plain,
( spl12_246
| ~ spl12_114
| ~ spl12_241 ),
inference(avatar_split_clause,[],[f3176,f3162,f1025,f3254]) ).
fof(f3254,plain,
( spl12_246
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_246])]) ).
fof(f1025,plain,
( spl12_114
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_114])]) ).
fof(f3176,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(sK0,function_inverse(sK0))) = X1
| ~ empty(X1) )
| ~ spl12_114
| ~ spl12_241 ),
inference(resolution,[],[f3163,f1026]) ).
fof(f1026,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl12_114 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f3224,plain,
( spl12_245
| ~ spl12_105
| ~ spl12_241 ),
inference(avatar_split_clause,[],[f3175,f3162,f924,f3222]) ).
fof(f924,plain,
( spl12_105
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_105])]) ).
fof(f3175,plain,
( ! [X0] :
( sK5 = relation_composition(relation_composition(sK0,function_inverse(sK0)),X0)
| ~ empty(X0) )
| ~ spl12_105
| ~ spl12_241 ),
inference(resolution,[],[f3163,f925]) ).
fof(f925,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK5
| ~ empty(X1) )
| ~ spl12_105 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f3220,plain,
( spl12_244
| ~ spl12_104
| ~ spl12_241 ),
inference(avatar_split_clause,[],[f3174,f3162,f920,f3218]) ).
fof(f920,plain,
( spl12_104
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_104])]) ).
fof(f3174,plain,
( ! [X0] :
( sK5 = relation_composition(X0,relation_composition(sK0,function_inverse(sK0)))
| ~ empty(X0) )
| ~ spl12_104
| ~ spl12_241 ),
inference(resolution,[],[f3163,f921]) ).
fof(f921,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK5
| ~ empty(X1) )
| ~ spl12_104 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f3212,plain,
( ~ spl12_241
| spl12_243
| ~ spl12_24
| ~ spl12_64 ),
inference(avatar_split_clause,[],[f3150,f553,f288,f3210,f3162]) ).
fof(f288,plain,
( spl12_24
<=> relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_24])]) ).
fof(f553,plain,
( spl12_64
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_64])]) ).
fof(f3150,plain,
( ! [X0] :
( ~ subset(relation_dom(sK0),relation_rng(X0))
| relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
| ~ relation(X0)
| ~ relation(relation_composition(sK0,function_inverse(sK0))) )
| ~ spl12_24
| ~ spl12_64 ),
inference(superposition,[],[f554,f289]) ).
fof(f289,plain,
( relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl12_64 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f3172,plain,
( ~ spl12_1
| ~ spl12_95
| ~ spl12_57
| spl12_241 ),
inference(avatar_split_clause,[],[f3171,f3162,f469,f837,f176]) ).
fof(f469,plain,
( spl12_57
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_57])]) ).
fof(f3171,plain,
( ~ relation(function_inverse(sK0))
| ~ relation(sK0)
| ~ spl12_57
| spl12_241 ),
inference(resolution,[],[f3164,f470]) ).
fof(f470,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl12_57 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f3164,plain,
( ~ relation(relation_composition(sK0,function_inverse(sK0)))
| spl12_241 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f3168,plain,
( ~ spl12_241
| spl12_242
| ~ spl12_24
| ~ spl12_63 ),
inference(avatar_split_clause,[],[f3149,f548,f288,f3166,f3162]) ).
fof(f548,plain,
( spl12_63
<=> ! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_63])]) ).
fof(f3149,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_dom(sK0))
| relation_dom(X0) = relation_dom(relation_composition(X0,relation_composition(sK0,function_inverse(sK0))))
| ~ relation(relation_composition(sK0,function_inverse(sK0)))
| ~ relation(X0) )
| ~ spl12_24
| ~ spl12_63 ),
inference(superposition,[],[f549,f289]) ).
fof(f549,plain,
( ! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl12_63 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f3158,plain,
( ~ spl12_240
| spl12_123
| ~ spl12_24
| ~ spl12_34 ),
inference(avatar_split_clause,[],[f3146,f340,f288,f1155,f3155]) ).
fof(f3155,plain,
( spl12_240
<=> empty(relation_composition(sK0,function_inverse(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_240])]) ).
fof(f1155,plain,
( spl12_123
<=> empty(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_123])]) ).
fof(f340,plain,
( spl12_34
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_34])]) ).
fof(f3146,plain,
( empty(relation_dom(sK0))
| ~ empty(relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_24
| ~ spl12_34 ),
inference(superposition,[],[f341,f289]) ).
fof(f341,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_34 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f3145,plain,
( spl12_24
| ~ spl12_1
| ~ spl12_23
| ~ spl12_129 ),
inference(avatar_split_clause,[],[f1239,f1236,f284,f176,f288]) ).
fof(f1236,plain,
( spl12_129
<=> ! [X0] :
( ~ subset(relation_rng(X0),relation_rng(sK0))
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_129])]) ).
fof(f1239,plain,
( ~ relation(sK0)
| relation_dom(sK0) = relation_dom(relation_composition(sK0,function_inverse(sK0)))
| ~ spl12_23
| ~ spl12_129 ),
inference(resolution,[],[f1237,f285]) ).
fof(f1237,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_rng(sK0))
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK0))) )
| ~ spl12_129 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f3144,plain,
( spl12_239
| ~ spl12_32
| ~ spl12_125 ),
inference(avatar_split_clause,[],[f1185,f1165,f332,f3142]) ).
fof(f3142,plain,
( spl12_239
<=> ! [X0,X1] :
( relation_rng(X1) = relation_composition(sK0,X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_239])]) ).
fof(f332,plain,
( spl12_32
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_32])]) ).
fof(f1165,plain,
( spl12_125
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_125])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_composition(sK0,X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_32
| ~ spl12_125 ),
inference(resolution,[],[f1166,f333]) ).
fof(f333,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_32 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f1166,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_composition(sK0,X0) = X1
| ~ empty(X0) )
| ~ spl12_125 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f3140,plain,
( spl12_238
| ~ spl12_34
| ~ spl12_125 ),
inference(avatar_split_clause,[],[f1184,f1165,f340,f3138]) ).
fof(f3138,plain,
( spl12_238
<=> ! [X0,X1] :
( relation_dom(X1) = relation_composition(sK0,X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_238])]) ).
fof(f1184,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_composition(sK0,X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_34
| ~ spl12_125 ),
inference(resolution,[],[f1166,f341]) ).
fof(f3136,plain,
( spl12_237
| ~ spl12_32
| ~ spl12_124 ),
inference(avatar_split_clause,[],[f1172,f1161,f332,f3134]) ).
fof(f3134,plain,
( spl12_237
<=> ! [X0,X1] :
( relation_rng(X1) = relation_composition(X0,sK0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_237])]) ).
fof(f1161,plain,
( spl12_124
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_124])]) ).
fof(f1172,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_composition(X0,sK0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_32
| ~ spl12_124 ),
inference(resolution,[],[f1162,f333]) ).
fof(f1162,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_composition(X0,sK0) = X1
| ~ empty(X0) )
| ~ spl12_124 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f3132,plain,
( spl12_236
| ~ spl12_34
| ~ spl12_124 ),
inference(avatar_split_clause,[],[f1171,f1161,f340,f3130]) ).
fof(f3130,plain,
( spl12_236
<=> ! [X0,X1] :
( relation_dom(X1) = relation_composition(X0,sK0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_236])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_composition(X0,sK0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_34
| ~ spl12_124 ),
inference(resolution,[],[f1162,f341]) ).
fof(f3128,plain,
( spl12_235
| ~ spl12_95
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1081,f1025,f837,f3126]) ).
fof(f3126,plain,
( spl12_235
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(sK0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_235])]) ).
fof(f1081,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(sK0)) = X1
| ~ empty(X1) )
| ~ spl12_95
| ~ spl12_114 ),
inference(resolution,[],[f838,f1026]) ).
fof(f838,plain,
( relation(function_inverse(sK0))
| ~ spl12_95 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f3124,plain,
( spl12_234
| ~ spl12_4
| ~ spl12_69
| ~ spl12_227 ),
inference(avatar_split_clause,[],[f3022,f2989,f588,f191,f3121]) ).
fof(f3121,plain,
( spl12_234
<=> sK5 = relation_composition(sK2(powerset(sK5)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_234])]) ).
fof(f2989,plain,
( spl12_227
<=> ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK2(powerset(X0)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_227])]) ).
fof(f3022,plain,
( sK5 = relation_composition(sK2(powerset(sK5)),sK0)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_227 ),
inference(forward_demodulation,[],[f3014,f590]) ).
fof(f3014,plain,
( sK5 = relation_composition(sK2(powerset(empty_set)),sK0)
| ~ spl12_4
| ~ spl12_227 ),
inference(resolution,[],[f2990,f193]) ).
fof(f2990,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK2(powerset(X0)),sK0) )
| ~ spl12_227 ),
inference(avatar_component_clause,[],[f2989]) ).
fof(f3119,plain,
( spl12_233
| ~ spl12_95
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1080,f1029,f837,f3117]) ).
fof(f3117,plain,
( spl12_233
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(sK0),X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_233])]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(sK0),X0) = X1
| ~ empty(X1) )
| ~ spl12_95
| ~ spl12_115 ),
inference(resolution,[],[f838,f1030]) ).
fof(f3011,plain,
( spl12_232
| ~ spl12_95
| ~ spl12_183 ),
inference(avatar_split_clause,[],[f2105,f2003,f837,f3009]) ).
fof(f3009,plain,
( spl12_232
<=> ! [X0] :
( sK5 = relation_dom(relation_composition(X0,function_inverse(sK0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_232])]) ).
fof(f2003,plain,
( spl12_183
<=> ! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = sK5
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_183])]) ).
fof(f2105,plain,
( ! [X0] :
( sK5 = relation_dom(relation_composition(X0,function_inverse(sK0)))
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_183 ),
inference(resolution,[],[f2004,f838]) ).
fof(f2004,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_composition(X0,X1)) = sK5
| ~ empty(X0) )
| ~ spl12_183 ),
inference(avatar_component_clause,[],[f2003]) ).
fof(f3007,plain,
( spl12_231
| ~ spl12_95
| ~ spl12_182 ),
inference(avatar_split_clause,[],[f2086,f1985,f837,f3005]) ).
fof(f3005,plain,
( spl12_231
<=> ! [X0] :
( sK5 = relation_dom(relation_composition(function_inverse(sK0),X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_231])]) ).
fof(f1985,plain,
( spl12_182
<=> ! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_182])]) ).
fof(f2086,plain,
( ! [X0] :
( sK5 = relation_dom(relation_composition(function_inverse(sK0),X0))
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_182 ),
inference(resolution,[],[f1986,f838]) ).
fof(f1986,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_dom(relation_composition(X0,X1)) = sK5
| ~ empty(X1) )
| ~ spl12_182 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f3003,plain,
( spl12_230
| ~ spl12_95
| ~ spl12_181 ),
inference(avatar_split_clause,[],[f2067,f1981,f837,f3001]) ).
fof(f3001,plain,
( spl12_230
<=> ! [X0] :
( sK5 = relation_rng(relation_composition(X0,function_inverse(sK0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_230])]) ).
fof(f1981,plain,
( spl12_181
<=> ! [X0,X1] :
( sK5 = relation_rng(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_181])]) ).
fof(f2067,plain,
( ! [X0] :
( sK5 = relation_rng(relation_composition(X0,function_inverse(sK0)))
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_181 ),
inference(resolution,[],[f1982,f838]) ).
fof(f1982,plain,
( ! [X0,X1] :
( ~ relation(X1)
| sK5 = relation_rng(relation_composition(X0,X1))
| ~ empty(X0) )
| ~ spl12_181 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f2999,plain,
( spl12_229
| ~ spl12_95
| ~ spl12_180 ),
inference(avatar_split_clause,[],[f2048,f1977,f837,f2997]) ).
fof(f2997,plain,
( spl12_229
<=> ! [X0] :
( sK5 = relation_rng(relation_composition(function_inverse(sK0),X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_229])]) ).
fof(f1977,plain,
( spl12_180
<=> ! [X0,X1] :
( sK5 = relation_rng(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_180])]) ).
fof(f2048,plain,
( ! [X0] :
( sK5 = relation_rng(relation_composition(function_inverse(sK0),X0))
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_180 ),
inference(resolution,[],[f1978,f838]) ).
fof(f1978,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK5 = relation_rng(relation_composition(X0,X1))
| ~ empty(X1) )
| ~ spl12_180 ),
inference(avatar_component_clause,[],[f1977]) ).
fof(f2995,plain,
( spl12_228
| ~ spl12_121
| ~ spl12_135 ),
inference(avatar_split_clause,[],[f1305,f1283,f1120,f2993]) ).
fof(f1120,plain,
( spl12_121
<=> ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_121])]) ).
fof(f1283,plain,
( spl12_135
<=> ! [X0] :
( ~ empty(X0)
| empty(sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_135])]) ).
fof(f1305,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK0,sK2(powerset(X0))) )
| ~ spl12_121
| ~ spl12_135 ),
inference(resolution,[],[f1284,f1121]) ).
fof(f1121,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK0,X0) )
| ~ spl12_121 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1284,plain,
( ! [X0] :
( empty(sK2(powerset(X0)))
| ~ empty(X0) )
| ~ spl12_135 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f2991,plain,
( spl12_227
| ~ spl12_120
| ~ spl12_135 ),
inference(avatar_split_clause,[],[f1304,f1283,f1116,f2989]) ).
fof(f1116,plain,
( spl12_120
<=> ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_120])]) ).
fof(f1304,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK2(powerset(X0)),sK0) )
| ~ spl12_120
| ~ spl12_135 ),
inference(resolution,[],[f1284,f1117]) ).
fof(f1117,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(X0,sK0) )
| ~ spl12_120 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f2987,plain,
( ~ spl12_226
| ~ spl12_77
| spl12_137 ),
inference(avatar_split_clause,[],[f1295,f1291,f635,f2984]) ).
fof(f2984,plain,
( spl12_226
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_226])]) ).
fof(f635,plain,
( spl12_77
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_77])]) ).
fof(f1291,plain,
( spl12_137
<=> function(relation_rng(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_137])]) ).
fof(f1295,plain,
( ~ empty(sK10)
| ~ spl12_77
| spl12_137 ),
inference(resolution,[],[f1292,f636]) ).
fof(f636,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_77 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f1292,plain,
( ~ function(relation_rng(sK10))
| spl12_137 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f2906,plain,
( spl12_225
| ~ spl12_1
| ~ spl12_183 ),
inference(avatar_split_clause,[],[f2112,f2003,f176,f2904]) ).
fof(f2904,plain,
( spl12_225
<=> ! [X0] :
( sK5 = relation_dom(relation_composition(X0,sK0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_225])]) ).
fof(f2112,plain,
( ! [X0] :
( sK5 = relation_dom(relation_composition(X0,sK0))
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_183 ),
inference(resolution,[],[f2004,f178]) ).
fof(f178,plain,
( relation(sK0)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f2902,plain,
( spl12_224
| ~ spl12_1
| ~ spl12_182 ),
inference(avatar_split_clause,[],[f2093,f1985,f176,f2900]) ).
fof(f2900,plain,
( spl12_224
<=> ! [X0] :
( sK5 = relation_dom(relation_composition(sK0,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_224])]) ).
fof(f2093,plain,
( ! [X0] :
( sK5 = relation_dom(relation_composition(sK0,X0))
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_182 ),
inference(resolution,[],[f1986,f178]) ).
fof(f2898,plain,
( spl12_223
| ~ spl12_1
| ~ spl12_181 ),
inference(avatar_split_clause,[],[f2074,f1981,f176,f2896]) ).
fof(f2896,plain,
( spl12_223
<=> ! [X0] :
( sK5 = relation_rng(relation_composition(X0,sK0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_223])]) ).
fof(f2074,plain,
( ! [X0] :
( sK5 = relation_rng(relation_composition(X0,sK0))
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_181 ),
inference(resolution,[],[f1982,f178]) ).
fof(f2894,plain,
( spl12_222
| ~ spl12_1
| ~ spl12_180 ),
inference(avatar_split_clause,[],[f2055,f1977,f176,f2892]) ).
fof(f2892,plain,
( spl12_222
<=> ! [X0] :
( sK5 = relation_rng(relation_composition(sK0,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_222])]) ).
fof(f2055,plain,
( ! [X0] :
( sK5 = relation_rng(relation_composition(sK0,X0))
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_180 ),
inference(resolution,[],[f1978,f178]) ).
fof(f2844,plain,
( spl12_221
| ~ spl12_62
| ~ spl12_119 ),
inference(avatar_split_clause,[],[f1112,f1096,f540,f2842]) ).
fof(f2842,plain,
( spl12_221
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_221])]) ).
fof(f540,plain,
( spl12_62
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_62])]) ).
fof(f1096,plain,
( spl12_119
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_119])]) ).
fof(f1112,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0) )
| ~ spl12_62
| ~ spl12_119 ),
inference(duplicate_literal_removal,[],[f1111]) ).
fof(f1111,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_62
| ~ spl12_119 ),
inference(resolution,[],[f1097,f541]) ).
fof(f541,plain,
( ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_62 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f1097,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_119 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f2707,plain,
( spl12_220
| ~ spl12_57
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1061,f1029,f469,f2705]) ).
fof(f2705,plain,
( spl12_220
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_220])]) ).
fof(f1061,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl12_57
| ~ spl12_115 ),
inference(resolution,[],[f1030,f470]) ).
fof(f2703,plain,
( spl12_219
| ~ spl12_54
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1060,f1029,f457,f2701]) ).
fof(f2701,plain,
( spl12_219
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_219])]) ).
fof(f457,plain,
( spl12_54
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_54])]) ).
fof(f1060,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl12_54
| ~ spl12_115 ),
inference(resolution,[],[f1030,f458]) ).
fof(f458,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_54 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f2699,plain,
( spl12_218
| ~ spl12_56
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1059,f1029,f465,f2697]) ).
fof(f2697,plain,
( spl12_218
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_218])]) ).
fof(f465,plain,
( spl12_56
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_56])]) ).
fof(f1059,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl12_56
| ~ spl12_115 ),
inference(resolution,[],[f1030,f466]) ).
fof(f466,plain,
( ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_56 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f2695,plain,
( spl12_217
| ~ spl12_57
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1043,f1025,f469,f2693]) ).
fof(f2693,plain,
( spl12_217
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_217])]) ).
fof(f1043,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl12_57
| ~ spl12_114 ),
inference(resolution,[],[f1026,f470]) ).
fof(f2691,plain,
( spl12_216
| ~ spl12_54
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1042,f1025,f457,f2689]) ).
fof(f2689,plain,
( spl12_216
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_216])]) ).
fof(f1042,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl12_54
| ~ spl12_114 ),
inference(resolution,[],[f1026,f458]) ).
fof(f2687,plain,
( spl12_215
| ~ spl12_56
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1041,f1025,f465,f2685]) ).
fof(f2685,plain,
( spl12_215
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_215])]) ).
fof(f1041,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl12_56
| ~ spl12_114 ),
inference(resolution,[],[f1026,f466]) ).
fof(f2639,plain,
( spl12_214
| ~ spl12_45
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1058,f1029,f402,f2637]) ).
fof(f2637,plain,
( spl12_214
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(X1),X0) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_214])]) ).
fof(f402,plain,
( spl12_45
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_45])]) ).
fof(f1058,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(X1),X0) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl12_45
| ~ spl12_115 ),
inference(resolution,[],[f1030,f403]) ).
fof(f403,plain,
( ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_45 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f2616,plain,
( spl12_213
| ~ spl12_45
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1040,f1025,f402,f2614]) ).
fof(f2614,plain,
( spl12_213
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(X1)) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_213])]) ).
fof(f1040,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(X1)) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl12_45
| ~ spl12_114 ),
inference(resolution,[],[f1026,f403]) ).
fof(f2498,plain,
( spl12_212
| ~ spl12_57
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f957,f924,f469,f2496]) ).
fof(f2496,plain,
( spl12_212
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_212])]) ).
fof(f957,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl12_57
| ~ spl12_105 ),
inference(resolution,[],[f925,f470]) ).
fof(f2494,plain,
( spl12_211
| ~ spl12_54
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f956,f924,f457,f2492]) ).
fof(f2492,plain,
( spl12_211
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_211])]) ).
fof(f956,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_54
| ~ spl12_105 ),
inference(resolution,[],[f925,f458]) ).
fof(f2490,plain,
( spl12_210
| ~ spl12_56
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f955,f924,f465,f2488]) ).
fof(f2488,plain,
( spl12_210
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_210])]) ).
fof(f955,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_56
| ~ spl12_105 ),
inference(resolution,[],[f925,f466]) ).
fof(f2477,plain,
( spl12_209
| ~ spl12_57
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f938,f920,f469,f2475]) ).
fof(f2475,plain,
( spl12_209
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_209])]) ).
fof(f938,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl12_57
| ~ spl12_104 ),
inference(resolution,[],[f921,f470]) ).
fof(f2473,plain,
( spl12_208
| ~ spl12_54
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f937,f920,f457,f2471]) ).
fof(f2471,plain,
( spl12_208
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_208])]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl12_54
| ~ spl12_104 ),
inference(resolution,[],[f921,f458]) ).
fof(f2469,plain,
( spl12_207
| ~ spl12_56
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f936,f920,f465,f2467]) ).
fof(f2467,plain,
( spl12_207
<=> ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_207])]) ).
fof(f936,plain,
( ! [X2,X0,X1] :
( sK5 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl12_56
| ~ spl12_104 ),
inference(resolution,[],[f921,f466]) ).
fof(f2372,plain,
( spl12_206
| ~ spl12_4
| ~ spl12_69
| ~ spl12_153 ),
inference(avatar_split_clause,[],[f2246,f1510,f588,f191,f2369]) ).
fof(f2369,plain,
( spl12_206
<=> sK5 = relation_composition(sK5,function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_206])]) ).
fof(f1510,plain,
( spl12_153
<=> ! [X0] :
( sK5 = relation_composition(X0,function_inverse(sK0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_153])]) ).
fof(f2246,plain,
( sK5 = relation_composition(sK5,function_inverse(sK0))
| ~ spl12_4
| ~ spl12_69
| ~ spl12_153 ),
inference(forward_demodulation,[],[f2238,f590]) ).
fof(f2238,plain,
( sK5 = relation_composition(empty_set,function_inverse(sK0))
| ~ spl12_4
| ~ spl12_153 ),
inference(resolution,[],[f1511,f193]) ).
fof(f1511,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(X0,function_inverse(sK0)) )
| ~ spl12_153 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f2269,plain,
( spl12_205
| ~ spl12_101
| ~ spl12_118 ),
inference(avatar_split_clause,[],[f1108,f1092,f866,f2267]) ).
fof(f2267,plain,
( spl12_205
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_205])]) ).
fof(f866,plain,
( spl12_101
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_101])]) ).
fof(f1092,plain,
( spl12_118
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_118])]) ).
fof(f1108,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_101
| ~ spl12_118 ),
inference(duplicate_literal_removal,[],[f1104]) ).
fof(f1104,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0))
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl12_101
| ~ spl12_118 ),
inference(resolution,[],[f1093,f867]) ).
fof(f867,plain,
( ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl12_101 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f1093,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl12_118 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f2265,plain,
( spl12_204
| ~ spl12_100
| ~ spl12_117 ),
inference(avatar_split_clause,[],[f1103,f1088,f862,f2263]) ).
fof(f2263,plain,
( spl12_204
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_204])]) ).
fof(f862,plain,
( spl12_100
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_100])]) ).
fof(f1088,plain,
( spl12_117
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_117])]) ).
fof(f1103,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl12_100
| ~ spl12_117 ),
inference(duplicate_literal_removal,[],[f1100]) ).
fof(f1100,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl12_100
| ~ spl12_117 ),
inference(resolution,[],[f1089,f863]) ).
fof(f863,plain,
( ! [X0,X1] :
( function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl12_100 ),
inference(avatar_component_clause,[],[f862]) ).
fof(f1089,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_117 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f2261,plain,
( spl12_203
| ~ spl12_33
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1064,f1029,f336,f2259]) ).
fof(f2259,plain,
( spl12_203
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_rng(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_203])]) ).
fof(f336,plain,
( spl12_33
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_33])]) ).
fof(f1064,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_rng(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_115 ),
inference(resolution,[],[f1030,f337]) ).
fof(f337,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_33 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f2257,plain,
( spl12_202
| ~ spl12_35
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1063,f1029,f344,f2255]) ).
fof(f2255,plain,
( spl12_202
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_dom(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_202])]) ).
fof(f344,plain,
( spl12_35
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_35])]) ).
fof(f1063,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_dom(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_115 ),
inference(resolution,[],[f1030,f345]) ).
fof(f345,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_35 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f2253,plain,
( spl12_201
| ~ spl12_33
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1046,f1025,f336,f2251]) ).
fof(f2251,plain,
( spl12_201
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_rng(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_201])]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_rng(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_114 ),
inference(resolution,[],[f1026,f337]) ).
fof(f2235,plain,
( spl12_200
| ~ spl12_35
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1045,f1025,f344,f2233]) ).
fof(f2233,plain,
( spl12_200
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_dom(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_200])]) ).
fof(f1045,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_dom(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_114 ),
inference(resolution,[],[f1026,f345]) ).
fof(f2231,plain,
( spl12_199
| ~ spl12_45
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f954,f924,f402,f2229]) ).
fof(f2229,plain,
( spl12_199
<=> ! [X0,X1] :
( sK5 = relation_composition(function_inverse(X0),X1)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_199])]) ).
fof(f954,plain,
( ! [X0,X1] :
( sK5 = relation_composition(function_inverse(X0),X1)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_45
| ~ spl12_105 ),
inference(resolution,[],[f925,f403]) ).
fof(f2227,plain,
( spl12_198
| ~ spl12_45
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f935,f920,f402,f2225]) ).
fof(f2225,plain,
( spl12_198
<=> ! [X0,X1] :
( sK5 = relation_composition(X0,function_inverse(X1))
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_198])]) ).
fof(f935,plain,
( ! [X0,X1] :
( sK5 = relation_composition(X0,function_inverse(X1))
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl12_45
| ~ spl12_104 ),
inference(resolution,[],[f921,f403]) ).
fof(f2223,plain,
( spl12_197
| ~ spl12_53
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f897,f858,f453,f2221]) ).
fof(f2221,plain,
( spl12_197
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_197])]) ).
fof(f453,plain,
( spl12_53
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_53])]) ).
fof(f858,plain,
( spl12_99
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_99])]) ).
fof(f897,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl12_53
| ~ spl12_99 ),
inference(resolution,[],[f859,f454]) ).
fof(f454,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_53 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f859,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl12_99 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f2219,plain,
( spl12_196
| ~ spl12_55
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f896,f858,f461,f2217]) ).
fof(f2217,plain,
( spl12_196
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_196])]) ).
fof(f461,plain,
( spl12_55
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_55])]) ).
fof(f896,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl12_55
| ~ spl12_99 ),
inference(resolution,[],[f859,f462]) ).
fof(f462,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_55 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f2215,plain,
( spl12_195
| ~ spl12_53
| ~ spl12_98 ),
inference(avatar_split_clause,[],[f878,f854,f453,f2213]) ).
fof(f2213,plain,
( spl12_195
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_195])]) ).
fof(f854,plain,
( spl12_98
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_98])]) ).
fof(f878,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl12_53
| ~ spl12_98 ),
inference(resolution,[],[f855,f454]) ).
fof(f855,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl12_98 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f2211,plain,
( spl12_194
| ~ spl12_55
| ~ spl12_98 ),
inference(avatar_split_clause,[],[f877,f854,f461,f2209]) ).
fof(f2209,plain,
( spl12_194
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_194])]) ).
fof(f877,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl12_55
| ~ spl12_98 ),
inference(resolution,[],[f855,f462]) ).
fof(f2046,plain,
( spl12_193
| ~ spl12_4
| ~ spl12_69
| ~ spl12_150 ),
inference(avatar_split_clause,[],[f1998,f1366,f588,f191,f2043]) ).
fof(f2043,plain,
( spl12_193
<=> sK5 = relation_composition(function_inverse(sK0),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_193])]) ).
fof(f1366,plain,
( spl12_150
<=> ! [X0] :
( sK5 = relation_composition(function_inverse(sK0),X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_150])]) ).
fof(f1998,plain,
( sK5 = relation_composition(function_inverse(sK0),sK5)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_150 ),
inference(forward_demodulation,[],[f1990,f590]) ).
fof(f1990,plain,
( sK5 = relation_composition(function_inverse(sK0),empty_set)
| ~ spl12_4
| ~ spl12_150 ),
inference(resolution,[],[f1367,f193]) ).
fof(f1367,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(function_inverse(sK0),X0) )
| ~ spl12_150 ),
inference(avatar_component_clause,[],[f1366]) ).
fof(f2041,plain,
( spl12_192
| ~ spl12_46
| ~ spl12_116 ),
inference(avatar_split_clause,[],[f1086,f1077,f406,f2039]) ).
fof(f2039,plain,
( spl12_192
<=> ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_192])]) ).
fof(f406,plain,
( spl12_46
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_46])]) ).
fof(f1077,plain,
( spl12_116
<=> ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_116])]) ).
fof(f1086,plain,
( ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_46
| ~ spl12_116 ),
inference(duplicate_literal_removal,[],[f1085]) ).
fof(f1085,plain,
( ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_46
| ~ spl12_116 ),
inference(resolution,[],[f1078,f407]) ).
fof(f407,plain,
( ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_46 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f1078,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_116 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f2037,plain,
( spl12_191
| ~ spl12_39
| ~ spl12_109 ),
inference(avatar_split_clause,[],[f1015,f982,f376,f2035]) ).
fof(f2035,plain,
( spl12_191
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_191])]) ).
fof(f376,plain,
( spl12_39
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_39])]) ).
fof(f982,plain,
( spl12_109
<=> ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_109])]) ).
fof(f1015,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK1(X0)) )
| ~ spl12_39
| ~ spl12_109 ),
inference(resolution,[],[f983,f377]) ).
fof(f377,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl12_39 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f983,plain,
( ! [X0] :
( in(sK1(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl12_109 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f2033,plain,
( spl12_190
| ~ spl12_39
| ~ spl12_108 ),
inference(avatar_split_clause,[],[f1010,f978,f376,f2031]) ).
fof(f2031,plain,
( spl12_190
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_190])]) ).
fof(f978,plain,
( spl12_108
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_108])]) ).
fof(f1010,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl12_39
| ~ spl12_108 ),
inference(resolution,[],[f979,f377]) ).
fof(f979,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl12_108 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f2029,plain,
( spl12_189
| ~ spl12_93
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f976,f932,f799,f2027]) ).
fof(f2027,plain,
( spl12_189
<=> ! [X0] :
( element(sK2(sK1(X0)),X0)
| empty(X0)
| empty(sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_189])]) ).
fof(f799,plain,
( spl12_93
<=> ! [X0] :
( empty(X0)
| in(sK2(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_93])]) ).
fof(f932,plain,
( spl12_107
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_107])]) ).
fof(f976,plain,
( ! [X0] :
( element(sK2(sK1(X0)),X0)
| empty(X0)
| empty(sK1(X0)) )
| ~ spl12_93
| ~ spl12_107 ),
inference(resolution,[],[f933,f800]) ).
fof(f800,plain,
( ! [X0] :
( in(sK2(X0),X0)
| empty(X0) )
| ~ spl12_93 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f933,plain,
( ! [X0,X1] :
( ~ in(X0,sK1(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl12_107 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f2025,plain,
( spl12_188
| ~ spl12_33
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f960,f924,f336,f2023]) ).
fof(f2023,plain,
( spl12_188
<=> ! [X0,X1] :
( sK5 = relation_composition(relation_rng(X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_188])]) ).
fof(f960,plain,
( ! [X0,X1] :
( sK5 = relation_composition(relation_rng(X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl12_33
| ~ spl12_105 ),
inference(resolution,[],[f925,f337]) ).
fof(f2021,plain,
( spl12_187
| ~ spl12_35
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f959,f924,f344,f2019]) ).
fof(f2019,plain,
( spl12_187
<=> ! [X0,X1] :
( sK5 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_187])]) ).
fof(f959,plain,
( ! [X0,X1] :
( sK5 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl12_35
| ~ spl12_105 ),
inference(resolution,[],[f925,f345]) ).
fof(f2017,plain,
( spl12_186
| ~ spl12_33
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f941,f920,f336,f2015]) ).
fof(f2015,plain,
( spl12_186
<=> ! [X0,X1] :
( sK5 = relation_composition(X0,relation_rng(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_186])]) ).
fof(f941,plain,
( ! [X0,X1] :
( sK5 = relation_composition(X0,relation_rng(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_104 ),
inference(resolution,[],[f921,f337]) ).
fof(f2013,plain,
( spl12_185
| ~ spl12_35
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f940,f920,f344,f2011]) ).
fof(f2011,plain,
( spl12_185
<=> ! [X0,X1] :
( sK5 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_185])]) ).
fof(f940,plain,
( ! [X0,X1] :
( sK5 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_104 ),
inference(resolution,[],[f921,f345]) ).
fof(f2009,plain,
( spl12_184
| ~ spl12_93
| ~ spl12_103 ),
inference(avatar_split_clause,[],[f918,f874,f799,f2007]) ).
fof(f2007,plain,
( spl12_184
<=> ! [X0] :
( element(sK2(sK2(powerset(X0))),X0)
| empty(sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_184])]) ).
fof(f874,plain,
( spl12_103
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_103])]) ).
fof(f918,plain,
( ! [X0] :
( element(sK2(sK2(powerset(X0))),X0)
| empty(sK2(powerset(X0))) )
| ~ spl12_93
| ~ spl12_103 ),
inference(resolution,[],[f875,f800]) ).
fof(f875,plain,
( ! [X0,X1] :
( ~ in(X0,sK2(powerset(X1)))
| element(X0,X1) )
| ~ spl12_103 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f2005,plain,
( spl12_183
| ~ spl12_53
| ~ spl12_85 ),
inference(avatar_split_clause,[],[f816,f762,f453,f2003]) ).
fof(f762,plain,
( spl12_85
<=> ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_85])]) ).
fof(f816,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = sK5
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_53
| ~ spl12_85 ),
inference(resolution,[],[f763,f454]) ).
fof(f763,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK5 )
| ~ spl12_85 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1987,plain,
( spl12_182
| ~ spl12_55
| ~ spl12_85 ),
inference(avatar_split_clause,[],[f815,f762,f461,f1985]) ).
fof(f815,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_55
| ~ spl12_85 ),
inference(resolution,[],[f763,f462]) ).
fof(f1983,plain,
( spl12_181
| ~ spl12_53
| ~ spl12_84 ),
inference(avatar_split_clause,[],[f803,f758,f453,f1981]) ).
fof(f758,plain,
( spl12_84
<=> ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_84])]) ).
fof(f803,plain,
( ! [X0,X1] :
( sK5 = relation_rng(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_53
| ~ spl12_84 ),
inference(resolution,[],[f759,f454]) ).
fof(f759,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK5 )
| ~ spl12_84 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f1979,plain,
( spl12_180
| ~ spl12_55
| ~ spl12_84 ),
inference(avatar_split_clause,[],[f802,f758,f461,f1977]) ).
fof(f802,plain,
( ! [X0,X1] :
( sK5 = relation_rng(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_55
| ~ spl12_84 ),
inference(resolution,[],[f759,f462]) ).
fof(f1965,plain,
( spl12_179
| ~ spl12_127
| ~ spl12_178 ),
inference(avatar_split_clause,[],[f1960,f1956,f1199,f1962]) ).
fof(f1962,plain,
( spl12_179
<=> sK5 = relation_dom(function_inverse(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_179])]) ).
fof(f1199,plain,
( spl12_127
<=> sK5 = relation_rng(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_127])]) ).
fof(f1956,plain,
( spl12_178
<=> relation_rng(sK5) = relation_dom(function_inverse(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_178])]) ).
fof(f1960,plain,
( sK5 = relation_dom(function_inverse(sK5))
| ~ spl12_127
| ~ spl12_178 ),
inference(forward_demodulation,[],[f1958,f1201]) ).
fof(f1201,plain,
( sK5 = relation_rng(sK5)
| ~ spl12_127 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1958,plain,
( relation_rng(sK5) = relation_dom(function_inverse(sK5))
| ~ spl12_178 ),
inference(avatar_component_clause,[],[f1956]) ).
fof(f1959,plain,
( ~ spl12_50
| ~ spl12_38
| spl12_178
| ~ spl12_60
| ~ spl12_92 ),
inference(avatar_split_clause,[],[f797,f792,f532,f1956,f367,f424]) ).
fof(f424,plain,
( spl12_50
<=> relation(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_50])]) ).
fof(f367,plain,
( spl12_38
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_38])]) ).
fof(f532,plain,
( spl12_60
<=> ! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_60])]) ).
fof(f792,plain,
( spl12_92
<=> one_to_one(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_92])]) ).
fof(f797,plain,
( relation_rng(sK5) = relation_dom(function_inverse(sK5))
| ~ function(sK5)
| ~ relation(sK5)
| ~ spl12_60
| ~ spl12_92 ),
inference(resolution,[],[f794,f533]) ).
fof(f533,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_60 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f794,plain,
( one_to_one(sK5)
| ~ spl12_92 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f1946,plain,
( spl12_177
| ~ spl12_128
| ~ spl12_176 ),
inference(avatar_split_clause,[],[f1941,f1937,f1204,f1943]) ).
fof(f1943,plain,
( spl12_177
<=> sK5 = relation_rng(function_inverse(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_177])]) ).
fof(f1204,plain,
( spl12_128
<=> sK5 = relation_dom(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_128])]) ).
fof(f1937,plain,
( spl12_176
<=> relation_dom(sK5) = relation_rng(function_inverse(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_176])]) ).
fof(f1941,plain,
( sK5 = relation_rng(function_inverse(sK5))
| ~ spl12_128
| ~ spl12_176 ),
inference(forward_demodulation,[],[f1939,f1206]) ).
fof(f1206,plain,
( sK5 = relation_dom(sK5)
| ~ spl12_128 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1939,plain,
( relation_dom(sK5) = relation_rng(function_inverse(sK5))
| ~ spl12_176 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f1940,plain,
( ~ spl12_50
| ~ spl12_38
| spl12_176
| ~ spl12_61
| ~ spl12_92 ),
inference(avatar_split_clause,[],[f796,f792,f536,f1937,f367,f424]) ).
fof(f536,plain,
( spl12_61
<=> ! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_61])]) ).
fof(f796,plain,
( relation_dom(sK5) = relation_rng(function_inverse(sK5))
| ~ function(sK5)
| ~ relation(sK5)
| ~ spl12_61
| ~ spl12_92 ),
inference(resolution,[],[f794,f537]) ).
fof(f537,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_61 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f1921,plain,
( spl12_175
| ~ spl12_32
| ~ spl12_121 ),
inference(avatar_split_clause,[],[f1145,f1120,f332,f1919]) ).
fof(f1919,plain,
( spl12_175
<=> ! [X0] :
( sK5 = relation_composition(sK0,relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_175])]) ).
fof(f1145,plain,
( ! [X0] :
( sK5 = relation_composition(sK0,relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_32
| ~ spl12_121 ),
inference(resolution,[],[f1121,f333]) ).
fof(f1767,plain,
( spl12_174
| ~ spl12_34
| ~ spl12_121 ),
inference(avatar_split_clause,[],[f1144,f1120,f340,f1765]) ).
fof(f1765,plain,
( spl12_174
<=> ! [X0] :
( sK5 = relation_composition(sK0,relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_174])]) ).
fof(f1144,plain,
( ! [X0] :
( sK5 = relation_composition(sK0,relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_34
| ~ spl12_121 ),
inference(resolution,[],[f1121,f341]) ).
fof(f1691,plain,
( spl12_173
| ~ spl12_5
| ~ spl12_69
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1073,f1029,f588,f196,f1689]) ).
fof(f1689,plain,
( spl12_173
<=> ! [X0,X1] :
( relation_composition(sK5,X0) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_173])]) ).
fof(f196,plain,
( spl12_5
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f1073,plain,
( ! [X0,X1] :
( relation_composition(sK5,X0) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_5
| ~ spl12_69
| ~ spl12_115 ),
inference(forward_demodulation,[],[f1062,f590]) ).
fof(f1062,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(empty_set,X0) = X1
| ~ empty(X1) )
| ~ spl12_5
| ~ spl12_115 ),
inference(resolution,[],[f1030,f198]) ).
fof(f198,plain,
( relation(empty_set)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f1687,plain,
( spl12_172
| ~ spl12_15
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1071,f1029,f246,f1685]) ).
fof(f1685,plain,
( spl12_172
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK10,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_172])]) ).
fof(f246,plain,
( spl12_15
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f1071,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK10,X0) = X1
| ~ empty(X1) )
| ~ spl12_15
| ~ spl12_115 ),
inference(resolution,[],[f1030,f248]) ).
fof(f248,plain,
( relation(sK10)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f1683,plain,
( spl12_171
| ~ spl12_13
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1070,f1029,f236,f1681]) ).
fof(f1681,plain,
( spl12_171
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK9,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_171])]) ).
fof(f236,plain,
( spl12_13
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f1070,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK9,X0) = X1
| ~ empty(X1) )
| ~ spl12_13
| ~ spl12_115 ),
inference(resolution,[],[f1030,f238]) ).
fof(f238,plain,
( relation(sK9)
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f1679,plain,
( spl12_170
| ~ spl12_12
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1069,f1029,f231,f1677]) ).
fof(f1677,plain,
( spl12_170
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK8,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_170])]) ).
fof(f231,plain,
( spl12_12
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f1069,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK8,X0) = X1
| ~ empty(X1) )
| ~ spl12_12
| ~ spl12_115 ),
inference(resolution,[],[f1030,f233]) ).
fof(f233,plain,
( relation(sK8)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f1675,plain,
( spl12_169
| ~ spl12_9
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1067,f1029,f216,f1673]) ).
fof(f1673,plain,
( spl12_169
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK6,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_169])]) ).
fof(f216,plain,
( spl12_9
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f1067,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK6,X0) = X1
| ~ empty(X1) )
| ~ spl12_9
| ~ spl12_115 ),
inference(resolution,[],[f1030,f218]) ).
fof(f218,plain,
( relation(sK6)
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f1671,plain,
( spl12_168
| ~ spl12_5
| ~ spl12_69
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1055,f1025,f588,f196,f1669]) ).
fof(f1669,plain,
( spl12_168
<=> ! [X0,X1] :
( relation_composition(X0,sK5) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_168])]) ).
fof(f1055,plain,
( ! [X0,X1] :
( relation_composition(X0,sK5) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_5
| ~ spl12_69
| ~ spl12_114 ),
inference(forward_demodulation,[],[f1044,f590]) ).
fof(f1044,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,empty_set) = X1
| ~ empty(X1) )
| ~ spl12_5
| ~ spl12_114 ),
inference(resolution,[],[f1026,f198]) ).
fof(f1667,plain,
( spl12_167
| ~ spl12_15
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1053,f1025,f246,f1665]) ).
fof(f1665,plain,
( spl12_167
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK10) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_167])]) ).
fof(f1053,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK10) = X1
| ~ empty(X1) )
| ~ spl12_15
| ~ spl12_114 ),
inference(resolution,[],[f1026,f248]) ).
fof(f1663,plain,
( spl12_166
| ~ spl12_32
| ~ spl12_120 ),
inference(avatar_split_clause,[],[f1127,f1116,f332,f1661]) ).
fof(f1661,plain,
( spl12_166
<=> ! [X0] :
( sK5 = relation_composition(relation_rng(X0),sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_166])]) ).
fof(f1127,plain,
( ! [X0] :
( sK5 = relation_composition(relation_rng(X0),sK0)
| ~ empty(X0) )
| ~ spl12_32
| ~ spl12_120 ),
inference(resolution,[],[f1117,f333]) ).
fof(f1659,plain,
( spl12_165
| ~ spl12_13
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1052,f1025,f236,f1657]) ).
fof(f1657,plain,
( spl12_165
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK9) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_165])]) ).
fof(f1052,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK9) = X1
| ~ empty(X1) )
| ~ spl12_13
| ~ spl12_114 ),
inference(resolution,[],[f1026,f238]) ).
fof(f1655,plain,
( spl12_164
| ~ spl12_12
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1051,f1025,f231,f1653]) ).
fof(f1653,plain,
( spl12_164
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK8) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_164])]) ).
fof(f1051,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK8) = X1
| ~ empty(X1) )
| ~ spl12_12
| ~ spl12_114 ),
inference(resolution,[],[f1026,f233]) ).
fof(f1651,plain,
( spl12_163
| ~ spl12_9
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1049,f1025,f216,f1649]) ).
fof(f1649,plain,
( spl12_163
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK6) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_163])]) ).
fof(f1049,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK6) = X1
| ~ empty(X1) )
| ~ spl12_9
| ~ spl12_114 ),
inference(resolution,[],[f1026,f218]) ).
fof(f1645,plain,
( spl12_136
| ~ spl12_161
| ~ spl12_162
| ~ spl12_44
| ~ spl12_110 ),
inference(avatar_split_clause,[],[f991,f986,f398,f1642,f1638,f1287]) ).
fof(f1287,plain,
( spl12_136
<=> empty(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_136])]) ).
fof(f1638,plain,
( spl12_161
<=> relation(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_161])]) ).
fof(f1642,plain,
( spl12_162
<=> empty(relation_rng(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_162])]) ).
fof(f398,plain,
( spl12_44
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_44])]) ).
fof(f986,plain,
( spl12_110
<=> relation_rng(sK10) = relation_dom(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_110])]) ).
fof(f991,plain,
( ~ empty(relation_rng(sK10))
| ~ relation(function_inverse(sK10))
| empty(function_inverse(sK10))
| ~ spl12_44
| ~ spl12_110 ),
inference(superposition,[],[f399,f988]) ).
fof(f988,plain,
( relation_rng(sK10) = relation_dom(function_inverse(sK10))
| ~ spl12_110 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f399,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl12_44 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f1636,plain,
( spl12_160
| ~ spl12_32
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f900,f858,f332,f1634]) ).
fof(f1634,plain,
( spl12_160
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_160])]) ).
fof(f900,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl12_32
| ~ spl12_99 ),
inference(resolution,[],[f859,f333]) ).
fof(f1632,plain,
( spl12_159
| ~ spl12_34
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f899,f858,f340,f1630]) ).
fof(f1630,plain,
( spl12_159
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_159])]) ).
fof(f899,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl12_34
| ~ spl12_99 ),
inference(resolution,[],[f859,f341]) ).
fof(f1628,plain,
( spl12_158
| ~ spl12_32
| ~ spl12_98 ),
inference(avatar_split_clause,[],[f881,f854,f332,f1626]) ).
fof(f1626,plain,
( spl12_158
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_158])]) ).
fof(f881,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl12_32
| ~ spl12_98 ),
inference(resolution,[],[f855,f333]) ).
fof(f1624,plain,
( spl12_157
| ~ spl12_34
| ~ spl12_98 ),
inference(avatar_split_clause,[],[f880,f854,f340,f1622]) ).
fof(f1622,plain,
( spl12_157
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_157])]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl12_34
| ~ spl12_98 ),
inference(resolution,[],[f855,f341]) ).
fof(f1620,plain,
( spl12_156
| ~ spl12_34
| ~ spl12_120 ),
inference(avatar_split_clause,[],[f1126,f1116,f340,f1618]) ).
fof(f1618,plain,
( spl12_156
<=> ! [X0] :
( sK5 = relation_composition(relation_dom(X0),sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_156])]) ).
fof(f1126,plain,
( ! [X0] :
( sK5 = relation_composition(relation_dom(X0),sK0)
| ~ empty(X0) )
| ~ spl12_34
| ~ spl12_120 ),
inference(resolution,[],[f1117,f341]) ).
fof(f1604,plain,
( spl12_155
| ~ spl12_77
| ~ spl12_113 ),
inference(avatar_split_clause,[],[f1039,f1021,f635,f1602]) ).
fof(f1602,plain,
( spl12_155
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_155])]) ).
fof(f1021,plain,
( spl12_113
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_113])]) ).
fof(f1039,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_77
| ~ spl12_113 ),
inference(duplicate_literal_removal,[],[f1036]) ).
fof(f1036,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl12_77
| ~ spl12_113 ),
inference(resolution,[],[f1022,f636]) ).
fof(f1022,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_113 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1600,plain,
( spl12_154
| ~ spl12_78
| ~ spl12_112 ),
inference(avatar_split_clause,[],[f1035,f1017,f639,f1598]) ).
fof(f1598,plain,
( spl12_154
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_154])]) ).
fof(f639,plain,
( spl12_78
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_78])]) ).
fof(f1017,plain,
( spl12_112
<=> ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_112])]) ).
fof(f1035,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_78
| ~ spl12_112 ),
inference(duplicate_literal_removal,[],[f1032]) ).
fof(f1032,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl12_78
| ~ spl12_112 ),
inference(resolution,[],[f1018,f640]) ).
fof(f640,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_78 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f1018,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_112 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1512,plain,
( spl12_153
| ~ spl12_95
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f1083,f920,f837,f1510]) ).
fof(f1083,plain,
( ! [X0] :
( sK5 = relation_composition(X0,function_inverse(sK0))
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_104 ),
inference(resolution,[],[f838,f921]) ).
fof(f1376,plain,
( spl12_152
| ~ spl12_5
| ~ spl12_69
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f969,f924,f588,f196,f1374]) ).
fof(f1374,plain,
( spl12_152
<=> ! [X0] :
( sK5 = relation_composition(sK5,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_152])]) ).
fof(f969,plain,
( ! [X0] :
( sK5 = relation_composition(sK5,X0)
| ~ empty(X0) )
| ~ spl12_5
| ~ spl12_69
| ~ spl12_105 ),
inference(forward_demodulation,[],[f958,f590]) ).
fof(f958,plain,
( ! [X0] :
( sK5 = relation_composition(empty_set,X0)
| ~ empty(X0) )
| ~ spl12_5
| ~ spl12_105 ),
inference(resolution,[],[f925,f198]) ).
fof(f1372,plain,
( spl12_151
| ~ spl12_15
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f967,f924,f246,f1370]) ).
fof(f1370,plain,
( spl12_151
<=> ! [X0] :
( sK5 = relation_composition(sK10,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_151])]) ).
fof(f967,plain,
( ! [X0] :
( sK5 = relation_composition(sK10,X0)
| ~ empty(X0) )
| ~ spl12_15
| ~ spl12_105 ),
inference(resolution,[],[f925,f248]) ).
fof(f1368,plain,
( spl12_150
| ~ spl12_95
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f1082,f924,f837,f1366]) ).
fof(f1082,plain,
( ! [X0] :
( sK5 = relation_composition(function_inverse(sK0),X0)
| ~ empty(X0) )
| ~ spl12_95
| ~ spl12_105 ),
inference(resolution,[],[f838,f925]) ).
fof(f1364,plain,
( spl12_149
| ~ spl12_13
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f966,f924,f236,f1362]) ).
fof(f1362,plain,
( spl12_149
<=> ! [X0] :
( sK5 = relation_composition(sK9,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_149])]) ).
fof(f966,plain,
( ! [X0] :
( sK5 = relation_composition(sK9,X0)
| ~ empty(X0) )
| ~ spl12_13
| ~ spl12_105 ),
inference(resolution,[],[f925,f238]) ).
fof(f1360,plain,
( spl12_148
| ~ spl12_12
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f965,f924,f231,f1358]) ).
fof(f1358,plain,
( spl12_148
<=> ! [X0] :
( sK5 = relation_composition(sK8,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_148])]) ).
fof(f965,plain,
( ! [X0] :
( sK5 = relation_composition(sK8,X0)
| ~ empty(X0) )
| ~ spl12_12
| ~ spl12_105 ),
inference(resolution,[],[f925,f233]) ).
fof(f1356,plain,
( spl12_147
| ~ spl12_9
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f963,f924,f216,f1354]) ).
fof(f1354,plain,
( spl12_147
<=> ! [X0] :
( sK5 = relation_composition(sK6,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_147])]) ).
fof(f963,plain,
( ! [X0] :
( sK5 = relation_composition(sK6,X0)
| ~ empty(X0) )
| ~ spl12_9
| ~ spl12_105 ),
inference(resolution,[],[f925,f218]) ).
fof(f1352,plain,
( spl12_146
| ~ spl12_5
| ~ spl12_69
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f950,f920,f588,f196,f1350]) ).
fof(f1350,plain,
( spl12_146
<=> ! [X0] :
( sK5 = relation_composition(X0,sK5)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_146])]) ).
fof(f950,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK5)
| ~ empty(X0) )
| ~ spl12_5
| ~ spl12_69
| ~ spl12_104 ),
inference(forward_demodulation,[],[f939,f590]) ).
fof(f939,plain,
( ! [X0] :
( sK5 = relation_composition(X0,empty_set)
| ~ empty(X0) )
| ~ spl12_5
| ~ spl12_104 ),
inference(resolution,[],[f921,f198]) ).
fof(f1348,plain,
( spl12_145
| ~ spl12_15
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f948,f920,f246,f1346]) ).
fof(f1346,plain,
( spl12_145
<=> ! [X0] :
( sK5 = relation_composition(X0,sK10)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_145])]) ).
fof(f948,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK10)
| ~ empty(X0) )
| ~ spl12_15
| ~ spl12_104 ),
inference(resolution,[],[f921,f248]) ).
fof(f1344,plain,
( spl12_144
| ~ spl12_13
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f947,f920,f236,f1342]) ).
fof(f1342,plain,
( spl12_144
<=> ! [X0] :
( sK5 = relation_composition(X0,sK9)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_144])]) ).
fof(f947,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK9)
| ~ empty(X0) )
| ~ spl12_13
| ~ spl12_104 ),
inference(resolution,[],[f921,f238]) ).
fof(f1340,plain,
( spl12_143
| ~ spl12_12
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f946,f920,f231,f1338]) ).
fof(f1338,plain,
( spl12_143
<=> ! [X0] :
( sK5 = relation_composition(X0,sK8)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_143])]) ).
fof(f946,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK8)
| ~ empty(X0) )
| ~ spl12_12
| ~ spl12_104 ),
inference(resolution,[],[f921,f233]) ).
fof(f1336,plain,
( spl12_142
| ~ spl12_9
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f944,f920,f216,f1334]) ).
fof(f1334,plain,
( spl12_142
<=> ! [X0] :
( sK5 = relation_composition(X0,sK6)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_142])]) ).
fof(f944,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK6)
| ~ empty(X0) )
| ~ spl12_9
| ~ spl12_104 ),
inference(resolution,[],[f921,f218]) ).
fof(f1332,plain,
( spl12_141
| ~ spl12_32
| ~ spl12_85 ),
inference(avatar_split_clause,[],[f819,f762,f332,f1330]) ).
fof(f1330,plain,
( spl12_141
<=> ! [X0] :
( sK5 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_141])]) ).
fof(f819,plain,
( ! [X0] :
( sK5 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_32
| ~ spl12_85 ),
inference(resolution,[],[f763,f333]) ).
fof(f1328,plain,
( spl12_140
| ~ spl12_34
| ~ spl12_85 ),
inference(avatar_split_clause,[],[f818,f762,f340,f1326]) ).
fof(f1326,plain,
( spl12_140
<=> ! [X0] :
( sK5 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_140])]) ).
fof(f818,plain,
( ! [X0] :
( sK5 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_34
| ~ spl12_85 ),
inference(resolution,[],[f763,f341]) ).
fof(f1315,plain,
( spl12_139
| ~ spl12_32
| ~ spl12_84 ),
inference(avatar_split_clause,[],[f806,f758,f332,f1313]) ).
fof(f1313,plain,
( spl12_139
<=> ! [X0] :
( sK5 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_139])]) ).
fof(f806,plain,
( ! [X0] :
( sK5 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_32
| ~ spl12_84 ),
inference(resolution,[],[f759,f333]) ).
fof(f1311,plain,
( spl12_138
| ~ spl12_34
| ~ spl12_84 ),
inference(avatar_split_clause,[],[f805,f758,f340,f1309]) ).
fof(f1309,plain,
( spl12_138
<=> ! [X0] :
( sK5 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_138])]) ).
fof(f805,plain,
( ! [X0] :
( sK5 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_34
| ~ spl12_84 ),
inference(resolution,[],[f759,f341]) ).
fof(f1294,plain,
( ~ spl12_136
| spl12_137
| ~ spl12_78
| ~ spl12_110 ),
inference(avatar_split_clause,[],[f990,f986,f639,f1291,f1287]) ).
fof(f990,plain,
( function(relation_rng(sK10))
| ~ empty(function_inverse(sK10))
| ~ spl12_78
| ~ spl12_110 ),
inference(superposition,[],[f640,f988]) ).
fof(f1285,plain,
( spl12_135
| ~ spl12_93
| ~ spl12_97 ),
inference(avatar_split_clause,[],[f852,f846,f799,f1283]) ).
fof(f846,plain,
( spl12_97
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_97])]) ).
fof(f852,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK2(powerset(X0))) )
| ~ spl12_93
| ~ spl12_97 ),
inference(resolution,[],[f847,f800]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ in(X1,sK2(powerset(X0)))
| ~ empty(X0) )
| ~ spl12_97 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f1281,plain,
( spl12_134
| ~ spl12_39
| ~ spl12_93 ),
inference(avatar_split_clause,[],[f830,f799,f376,f1279]) ).
fof(f1279,plain,
( spl12_134
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_134])]) ).
fof(f830,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK2(X0)) )
| ~ spl12_39
| ~ spl12_93 ),
inference(resolution,[],[f800,f377]) ).
fof(f1273,plain,
( spl12_133
| ~ spl12_4
| ~ spl12_69
| ~ spl12_121 ),
inference(avatar_split_clause,[],[f1150,f1120,f588,f191,f1270]) ).
fof(f1270,plain,
( spl12_133
<=> sK5 = relation_composition(sK0,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_133])]) ).
fof(f1150,plain,
( sK5 = relation_composition(sK0,sK5)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_121 ),
inference(forward_demodulation,[],[f1143,f590]) ).
fof(f1143,plain,
( sK5 = relation_composition(sK0,empty_set)
| ~ spl12_4
| ~ spl12_121 ),
inference(resolution,[],[f1121,f193]) ).
fof(f1268,plain,
( ~ spl12_95
| spl12_132
| ~ spl12_64
| ~ spl12_65
| ~ spl12_66 ),
inference(avatar_split_clause,[],[f1012,f567,f557,f553,f1266,f837]) ).
fof(f1012,plain,
( ! [X0] :
( relation_dom(sK0) = relation_rng(relation_composition(X0,function_inverse(sK0)))
| ~ subset(relation_rng(sK0),relation_rng(X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK0)) )
| ~ spl12_64
| ~ spl12_65
| ~ spl12_66 ),
inference(forward_demodulation,[],[f561,f569]) ).
fof(f561,plain,
( ! [X0] :
( ~ subset(relation_rng(sK0),relation_rng(X0))
| relation_rng(function_inverse(sK0)) = relation_rng(relation_composition(X0,function_inverse(sK0)))
| ~ relation(X0)
| ~ relation(function_inverse(sK0)) )
| ~ spl12_64
| ~ spl12_65 ),
inference(superposition,[],[f554,f559]) ).
fof(f1260,plain,
( ~ spl12_95
| spl12_131
| ~ spl12_63
| ~ spl12_65
| ~ spl12_66 ),
inference(avatar_split_clause,[],[f576,f567,f557,f548,f1258,f837]) ).
fof(f576,plain,
( ! [X0] :
( relation_rng(sK0) = relation_dom(relation_composition(function_inverse(sK0),X0))
| ~ subset(relation_dom(sK0),relation_dom(X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK0)) )
| ~ spl12_63
| ~ spl12_65
| ~ spl12_66 ),
inference(forward_demodulation,[],[f572,f559]) ).
fof(f572,plain,
( ! [X0] :
( ~ subset(relation_dom(sK0),relation_dom(X0))
| relation_dom(function_inverse(sK0)) = relation_dom(relation_composition(function_inverse(sK0),X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK0)) )
| ~ spl12_63
| ~ spl12_66 ),
inference(superposition,[],[f549,f569]) ).
fof(f1249,plain,
( ~ spl12_95
| spl12_130
| ~ spl12_64
| ~ spl12_66 ),
inference(avatar_split_clause,[],[f571,f567,f553,f1247,f837]) ).
fof(f571,plain,
( ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK0))
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK0),X0))
| ~ relation(function_inverse(sK0))
| ~ relation(X0) )
| ~ spl12_64
| ~ spl12_66 ),
inference(superposition,[],[f554,f569]) ).
fof(f1238,plain,
( ~ spl12_95
| spl12_129
| ~ spl12_63
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f562,f557,f548,f1236,f837]) ).
fof(f562,plain,
( ! [X0] :
( ~ subset(relation_rng(X0),relation_rng(sK0))
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK0)))
| ~ relation(function_inverse(sK0))
| ~ relation(X0) )
| ~ spl12_63
| ~ spl12_65 ),
inference(superposition,[],[f549,f559]) ).
fof(f1207,plain,
( spl12_128
| ~ spl12_4
| ~ spl12_69
| ~ spl12_85 ),
inference(avatar_split_clause,[],[f824,f762,f588,f191,f1204]) ).
fof(f824,plain,
( sK5 = relation_dom(sK5)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_85 ),
inference(forward_demodulation,[],[f817,f590]) ).
fof(f817,plain,
( sK5 = relation_dom(empty_set)
| ~ spl12_4
| ~ spl12_85 ),
inference(resolution,[],[f763,f193]) ).
fof(f1202,plain,
( spl12_127
| ~ spl12_4
| ~ spl12_69
| ~ spl12_84 ),
inference(avatar_split_clause,[],[f811,f758,f588,f191,f1199]) ).
fof(f811,plain,
( sK5 = relation_rng(sK5)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_84 ),
inference(forward_demodulation,[],[f804,f590]) ).
fof(f804,plain,
( sK5 = relation_rng(empty_set)
| ~ spl12_4
| ~ spl12_84 ),
inference(resolution,[],[f759,f193]) ).
fof(f1197,plain,
( spl12_126
| ~ spl12_36
| ~ spl12_76 ),
inference(avatar_split_clause,[],[f632,f629,f348,f1195]) ).
fof(f1195,plain,
( spl12_126
<=> ! [X0] : element(sK5,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_126])]) ).
fof(f348,plain,
( spl12_36
<=> ! [X0] : element(sK3(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_36])]) ).
fof(f629,plain,
( spl12_76
<=> ! [X0] : sK3(X0) = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_76])]) ).
fof(f632,plain,
( ! [X0] : element(sK5,powerset(X0))
| ~ spl12_36
| ~ spl12_76 ),
inference(superposition,[],[f349,f630]) ).
fof(f630,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl12_76 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f349,plain,
( ! [X0] : element(sK3(X0),powerset(X0))
| ~ spl12_36 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f1167,plain,
( spl12_125
| ~ spl12_1
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1065,f1029,f176,f1165]) ).
fof(f1065,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) )
| ~ spl12_1
| ~ spl12_115 ),
inference(resolution,[],[f1030,f178]) ).
fof(f1163,plain,
( spl12_124
| ~ spl12_1
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1047,f1025,f176,f1161]) ).
fof(f1047,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) )
| ~ spl12_1
| ~ spl12_114 ),
inference(resolution,[],[f1026,f178]) ).
fof(f1158,plain,
( spl12_70
| ~ spl12_95
| ~ spl12_123
| ~ spl12_43
| ~ spl12_66 ),
inference(avatar_split_clause,[],[f573,f567,f394,f1155,f837,f593]) ).
fof(f593,plain,
( spl12_70
<=> empty(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_70])]) ).
fof(f394,plain,
( spl12_43
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_43])]) ).
fof(f573,plain,
( ~ empty(relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| empty(function_inverse(sK0))
| ~ spl12_43
| ~ spl12_66 ),
inference(superposition,[],[f395,f569]) ).
fof(f395,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl12_43 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f1140,plain,
( spl12_122
| ~ spl12_4
| ~ spl12_69
| ~ spl12_120 ),
inference(avatar_split_clause,[],[f1132,f1116,f588,f191,f1137]) ).
fof(f1137,plain,
( spl12_122
<=> sK5 = relation_composition(sK5,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_122])]) ).
fof(f1132,plain,
( sK5 = relation_composition(sK5,sK0)
| ~ spl12_4
| ~ spl12_69
| ~ spl12_120 ),
inference(forward_demodulation,[],[f1125,f590]) ).
fof(f1125,plain,
( sK5 = relation_composition(empty_set,sK0)
| ~ spl12_4
| ~ spl12_120 ),
inference(resolution,[],[f1117,f193]) ).
fof(f1122,plain,
( spl12_121
| ~ spl12_1
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f961,f924,f176,f1120]) ).
fof(f961,plain,
( ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_105 ),
inference(resolution,[],[f925,f178]) ).
fof(f1118,plain,
( spl12_120
| ~ spl12_1
| ~ spl12_104 ),
inference(avatar_split_clause,[],[f942,f920,f176,f1116]) ).
fof(f942,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_104 ),
inference(resolution,[],[f921,f178]) ).
fof(f1098,plain,
( spl12_119
| ~ spl12_51
| ~ spl12_57 ),
inference(avatar_split_clause,[],[f510,f469,f445,f1096]) ).
fof(f445,plain,
( spl12_51
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_51])]) ).
fof(f510,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_51
| ~ spl12_57 ),
inference(resolution,[],[f470,f446]) ).
fof(f446,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl12_51 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1094,plain,
( spl12_118
| ~ spl12_51
| ~ spl12_56 ),
inference(avatar_split_clause,[],[f509,f465,f445,f1092]) ).
fof(f509,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl12_51
| ~ spl12_56 ),
inference(resolution,[],[f466,f446]) ).
fof(f1090,plain,
( spl12_117
| ~ spl12_51
| ~ spl12_54 ),
inference(avatar_split_clause,[],[f503,f457,f445,f1088]) ).
fof(f503,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_51
| ~ spl12_54 ),
inference(resolution,[],[f458,f446]) ).
fof(f1079,plain,
( spl12_116
| ~ spl12_45
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f472,f445,f402,f1077]) ).
fof(f472,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_45
| ~ spl12_51 ),
inference(resolution,[],[f446,f403]) ).
fof(f1031,plain,
( spl12_115
| ~ spl12_49
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f504,f461,f418,f1029]) ).
fof(f418,plain,
( spl12_49
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_49])]) ).
fof(f504,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl12_49
| ~ spl12_55 ),
inference(resolution,[],[f462,f419]) ).
fof(f419,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl12_49 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f1027,plain,
( spl12_114
| ~ spl12_49
| ~ spl12_53 ),
inference(avatar_split_clause,[],[f498,f453,f418,f1025]) ).
fof(f498,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl12_49
| ~ spl12_53 ),
inference(resolution,[],[f454,f419]) ).
fof(f1023,plain,
( spl12_113
| ~ spl12_33
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f475,f445,f336,f1021]) ).
fof(f475,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_33
| ~ spl12_51 ),
inference(resolution,[],[f446,f337]) ).
fof(f1019,plain,
( spl12_112
| ~ spl12_35
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f474,f445,f344,f1017]) ).
fof(f474,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_35
| ~ spl12_51 ),
inference(resolution,[],[f446,f345]) ).
fof(f1011,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_45
| spl12_95 ),
inference(avatar_split_clause,[],[f895,f837,f402,f181,f176]) ).
fof(f181,plain,
( spl12_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f895,plain,
( ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_45
| spl12_95 ),
inference(resolution,[],[f839,f403]) ).
fof(f839,plain,
( ~ relation(function_inverse(sK0))
| spl12_95 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f1000,plain,
( ~ spl12_15
| ~ spl12_16
| spl12_111
| ~ spl12_17
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f546,f536,f256,f997,f251,f246]) ).
fof(f251,plain,
( spl12_16
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).
fof(f997,plain,
( spl12_111
<=> relation_dom(sK10) = relation_rng(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_111])]) ).
fof(f256,plain,
( spl12_17
<=> one_to_one(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f546,plain,
( relation_dom(sK10) = relation_rng(function_inverse(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_17
| ~ spl12_61 ),
inference(resolution,[],[f537,f258]) ).
fof(f258,plain,
( one_to_one(sK10)
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f989,plain,
( ~ spl12_15
| ~ spl12_16
| spl12_110
| ~ spl12_17
| ~ spl12_60 ),
inference(avatar_split_clause,[],[f544,f532,f256,f986,f251,f246]) ).
fof(f544,plain,
( relation_rng(sK10) = relation_dom(function_inverse(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_17
| ~ spl12_60 ),
inference(resolution,[],[f533,f258]) ).
fof(f984,plain,
( spl12_109
| ~ spl12_41
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f493,f449,f384,f982]) ).
fof(f384,plain,
( spl12_41
<=> ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_41])]) ).
fof(f449,plain,
( spl12_52
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_52])]) ).
fof(f493,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl12_41
| ~ spl12_52 ),
inference(resolution,[],[f450,f385]) ).
fof(f385,plain,
( ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl12_41 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl12_52 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f980,plain,
( spl12_108
| ~ spl12_48
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f492,f449,f414,f978]) ).
fof(f414,plain,
( spl12_48
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_48])]) ).
fof(f492,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl12_48
| ~ spl12_52 ),
inference(resolution,[],[f450,f415]) ).
fof(f415,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl12_48 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f934,plain,
( spl12_107
| ~ spl12_41
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f526,f522,f384,f932]) ).
fof(f522,plain,
( spl12_59
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_59])]) ).
fof(f526,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) )
| ~ spl12_41
| ~ spl12_59 ),
inference(resolution,[],[f523,f385]) ).
fof(f523,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl12_59 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f930,plain,
( spl12_106
| ~ spl12_48
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f525,f522,f414,f928]) ).
fof(f928,plain,
( spl12_106
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_106])]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl12_48
| ~ spl12_59 ),
inference(resolution,[],[f523,f415]) ).
fof(f926,plain,
( spl12_105
| ~ spl12_7
| ~ spl12_31
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f508,f461,f328,f206,f924]) ).
fof(f206,plain,
( spl12_7
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f328,plain,
( spl12_31
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_31])]) ).
fof(f508,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_7
| ~ spl12_31
| ~ spl12_55 ),
inference(forward_demodulation,[],[f505,f357]) ).
fof(f357,plain,
( empty_set = sK5
| ~ spl12_7
| ~ spl12_31 ),
inference(resolution,[],[f329,f208]) ).
fof(f208,plain,
( empty(sK5)
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f329,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f505,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = empty_set )
| ~ spl12_31
| ~ spl12_55 ),
inference(resolution,[],[f462,f329]) ).
fof(f922,plain,
( spl12_104
| ~ spl12_7
| ~ spl12_31
| ~ spl12_53 ),
inference(avatar_split_clause,[],[f502,f453,f328,f206,f920]) ).
fof(f502,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_7
| ~ spl12_31
| ~ spl12_53 ),
inference(forward_demodulation,[],[f499,f357]) ).
fof(f499,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = empty_set )
| ~ spl12_31
| ~ spl12_53 ),
inference(resolution,[],[f454,f329]) ).
fof(f876,plain,
( spl12_103
| ~ spl12_28
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f527,f522,f305,f874]) ).
fof(f305,plain,
( spl12_28
<=> ! [X0] : element(sK2(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_28])]) ).
fof(f527,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) )
| ~ spl12_28
| ~ spl12_59 ),
inference(resolution,[],[f523,f306]) ).
fof(f306,plain,
( ! [X0] : element(sK2(X0),X0)
| ~ spl12_28 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f872,plain,
( spl12_102
| ~ spl12_48
| ~ spl12_58 ),
inference(avatar_split_clause,[],[f515,f512,f414,f870]) ).
fof(f870,plain,
( spl12_102
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_102])]) ).
fof(f512,plain,
( spl12_58
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_58])]) ).
fof(f515,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl12_48
| ~ spl12_58 ),
inference(resolution,[],[f513,f415]) ).
fof(f513,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl12_58 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f868,plain,
( spl12_101
| ~ spl12_26
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f507,f461,f297,f866]) ).
fof(f297,plain,
( spl12_26
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_26])]) ).
fof(f507,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl12_26
| ~ spl12_55 ),
inference(resolution,[],[f462,f298]) ).
fof(f298,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl12_26 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f864,plain,
( spl12_100
| ~ spl12_26
| ~ spl12_53 ),
inference(avatar_split_clause,[],[f501,f453,f297,f862]) ).
fof(f501,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl12_26
| ~ spl12_53 ),
inference(resolution,[],[f454,f298]) ).
fof(f860,plain,
( spl12_99
| ~ spl12_32
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f436,f418,f332,f858]) ).
fof(f436,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_32
| ~ spl12_49 ),
inference(resolution,[],[f419,f333]) ).
fof(f856,plain,
( spl12_98
| ~ spl12_34
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f435,f418,f340,f854]) ).
fof(f435,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_34
| ~ spl12_49 ),
inference(resolution,[],[f419,f341]) ).
fof(f848,plain,
( spl12_97
| ~ spl12_28
| ~ spl12_58 ),
inference(avatar_split_clause,[],[f517,f512,f305,f846]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) )
| ~ spl12_28
| ~ spl12_58 ),
inference(resolution,[],[f513,f306]) ).
fof(f844,plain,
( spl12_70
| ~ spl12_95
| ~ spl12_96
| ~ spl12_44
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f563,f557,f398,f841,f837,f593]) ).
fof(f841,plain,
( spl12_96
<=> empty(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_96])]) ).
fof(f563,plain,
( ~ empty(relation_rng(sK0))
| ~ relation(function_inverse(sK0))
| empty(function_inverse(sK0))
| ~ spl12_44
| ~ spl12_65 ),
inference(superposition,[],[f399,f559]) ).
fof(f835,plain,
( spl12_94
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f497,f449,f348,f328,f280,f206,f833]) ).
fof(f833,plain,
( spl12_94
<=> ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_94])]) ).
fof(f280,plain,
( spl12_22
<=> ! [X0] : empty(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).
fof(f497,plain,
( ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) )
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_52 ),
inference(forward_demodulation,[],[f496,f357]) ).
fof(f496,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_52 ),
inference(forward_demodulation,[],[f495,f356]) ).
fof(f356,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl12_22
| ~ spl12_31 ),
inference(resolution,[],[f329,f281]) ).
fof(f281,plain,
( ! [X0] : empty(sK3(X0))
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f495,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0)) )
| ~ spl12_36
| ~ spl12_52 ),
inference(resolution,[],[f450,f349]) ).
fof(f801,plain,
( spl12_93
| ~ spl12_28
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f494,f449,f305,f799]) ).
fof(f494,plain,
( ! [X0] :
( empty(X0)
| in(sK2(X0),X0) )
| ~ spl12_28
| ~ spl12_52 ),
inference(resolution,[],[f450,f306]) ).
fof(f795,plain,
( ~ spl12_38
| ~ spl12_7
| spl12_92
| ~ spl12_5
| ~ spl12_7
| ~ spl12_31
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f485,f445,f328,f206,f196,f792,f206,f367]) ).
fof(f485,plain,
( one_to_one(sK5)
| ~ empty(sK5)
| ~ function(sK5)
| ~ spl12_5
| ~ spl12_7
| ~ spl12_31
| ~ spl12_51 ),
inference(forward_demodulation,[],[f484,f357]) ).
fof(f484,plain,
( ~ empty(sK5)
| ~ function(sK5)
| one_to_one(empty_set)
| ~ spl12_5
| ~ spl12_7
| ~ spl12_31
| ~ spl12_51 ),
inference(forward_demodulation,[],[f483,f357]) ).
fof(f483,plain,
( ~ function(sK5)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl12_5
| ~ spl12_7
| ~ spl12_31
| ~ spl12_51 ),
inference(forward_demodulation,[],[f473,f357]) ).
fof(f473,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl12_5
| ~ spl12_51 ),
inference(resolution,[],[f446,f198]) ).
fof(f790,plain,
( spl12_90
| ~ spl12_91
| ~ spl12_14
| ~ spl12_13
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f480,f445,f236,f241,f787,f783]) ).
fof(f783,plain,
( spl12_90
<=> one_to_one(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_90])]) ).
fof(f787,plain,
( spl12_91
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_91])]) ).
fof(f241,plain,
( spl12_14
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f480,plain,
( ~ function(sK9)
| ~ empty(sK9)
| one_to_one(sK9)
| ~ spl12_13
| ~ spl12_51 ),
inference(resolution,[],[f446,f238]) ).
fof(f781,plain,
( spl12_87
| ~ spl12_88
| ~ spl12_89
| ~ spl12_12
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f479,f445,f231,f778,f774,f770]) ).
fof(f770,plain,
( spl12_87
<=> one_to_one(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_87])]) ).
fof(f774,plain,
( spl12_88
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_88])]) ).
fof(f778,plain,
( spl12_89
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_89])]) ).
fof(f479,plain,
( ~ function(sK8)
| ~ empty(sK8)
| one_to_one(sK8)
| ~ spl12_12
| ~ spl12_51 ),
inference(resolution,[],[f446,f233]) ).
fof(f768,plain,
( spl12_86
| ~ spl12_41
| ~ spl12_47 ),
inference(avatar_split_clause,[],[f430,f410,f384,f766]) ).
fof(f766,plain,
( spl12_86
<=> ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_86])]) ).
fof(f410,plain,
( spl12_47
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_47])]) ).
fof(f430,plain,
( ! [X0] :
( subset(sK1(X0),X0)
| empty(X0) )
| ~ spl12_41
| ~ spl12_47 ),
inference(resolution,[],[f411,f385]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl12_47 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f764,plain,
( spl12_85
| ~ spl12_7
| ~ spl12_31
| ~ spl12_34 ),
inference(avatar_split_clause,[],[f374,f340,f328,f206,f762]) ).
fof(f374,plain,
( ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) )
| ~ spl12_7
| ~ spl12_31
| ~ spl12_34 ),
inference(forward_demodulation,[],[f371,f357]) ).
fof(f371,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl12_31
| ~ spl12_34 ),
inference(resolution,[],[f341,f329]) ).
fof(f760,plain,
( spl12_84
| ~ spl12_7
| ~ spl12_31
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f365,f332,f328,f206,f758]) ).
fof(f365,plain,
( ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) )
| ~ spl12_7
| ~ spl12_31
| ~ spl12_32 ),
inference(forward_demodulation,[],[f362,f357]) ).
fof(f362,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl12_31
| ~ spl12_32 ),
inference(resolution,[],[f333,f329]) ).
fof(f747,plain,
( ~ spl12_83
| ~ spl12_33
| spl12_71 ),
inference(avatar_split_clause,[],[f694,f597,f336,f744]) ).
fof(f744,plain,
( spl12_83
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_83])]) ).
fof(f597,plain,
( spl12_71
<=> relation(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_71])]) ).
fof(f694,plain,
( ~ empty(sK0)
| ~ spl12_33
| spl12_71 ),
inference(resolution,[],[f598,f337]) ).
fof(f598,plain,
( ~ relation(relation_rng(sK0))
| spl12_71 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f689,plain,
( spl12_80
| ~ spl12_31
| ~ spl12_69 ),
inference(avatar_split_clause,[],[f667,f588,f328,f647]) ).
fof(f647,plain,
( spl12_80
<=> ! [X0] :
( sK5 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_80])]) ).
fof(f667,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl12_31
| ~ spl12_69 ),
inference(forward_demodulation,[],[f329,f590]) ).
fof(f666,plain,
( ~ spl12_4
| ~ spl12_81 ),
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f657,plain,
( $false
| ~ spl12_4
| ~ spl12_81 ),
inference(resolution,[],[f652,f193]) ).
fof(f652,plain,
( ! [X0] : ~ empty(X0)
| ~ spl12_81 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f651,plain,
( spl12_81
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_81])]) ).
fof(f665,plain,
( ~ spl12_22
| ~ spl12_81 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f658,plain,
( $false
| ~ spl12_22
| ~ spl12_81 ),
inference(resolution,[],[f652,f281]) ).
fof(f664,plain,
( ~ spl12_7
| ~ spl12_81 ),
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f659,plain,
( $false
| ~ spl12_7
| ~ spl12_81 ),
inference(resolution,[],[f652,f208]) ).
fof(f663,plain,
( ~ spl12_10
| ~ spl12_81 ),
inference(avatar_contradiction_clause,[],[f660]) ).
fof(f660,plain,
( $false
| ~ spl12_10
| ~ spl12_81 ),
inference(resolution,[],[f652,f223]) ).
fof(f223,plain,
( empty(sK7)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f221,plain,
( spl12_10
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f662,plain,
( ~ spl12_19
| ~ spl12_81 ),
inference(avatar_contradiction_clause,[],[f661]) ).
fof(f661,plain,
( $false
| ~ spl12_19
| ~ spl12_81 ),
inference(resolution,[],[f652,f268]) ).
fof(f268,plain,
( empty(sK11)
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f266,plain,
( spl12_19
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).
fof(f656,plain,
( spl12_81
| spl12_82
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_58 ),
inference(avatar_split_clause,[],[f520,f512,f348,f328,f280,f206,f654,f651]) ).
fof(f654,plain,
( spl12_82
<=> ! [X1] : ~ in(X1,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_82])]) ).
fof(f520,plain,
( ! [X0,X1] :
( ~ in(X1,sK5)
| ~ empty(X0) )
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_58 ),
inference(forward_demodulation,[],[f519,f357]) ).
fof(f519,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_58 ),
inference(forward_demodulation,[],[f518,f356]) ).
fof(f518,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK3(X0)) )
| ~ spl12_36
| ~ spl12_58 ),
inference(resolution,[],[f513,f349]) ).
fof(f649,plain,
( spl12_80
| ~ spl12_7
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f438,f418,f206,f647]) ).
fof(f438,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl12_7
| ~ spl12_49 ),
inference(resolution,[],[f419,f208]) ).
fof(f645,plain,
( spl12_79
| ~ spl12_28
| ~ spl12_47 ),
inference(avatar_split_clause,[],[f428,f410,f305,f643]) ).
fof(f643,plain,
( spl12_79
<=> ! [X0] : subset(sK2(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_79])]) ).
fof(f428,plain,
( ! [X0] : subset(sK2(powerset(X0)),X0)
| ~ spl12_28
| ~ spl12_47 ),
inference(resolution,[],[f411,f306]) ).
fof(f641,plain,
( spl12_78
| ~ spl12_26
| ~ spl12_34 ),
inference(avatar_split_clause,[],[f373,f340,f297,f639]) ).
fof(f373,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl12_26
| ~ spl12_34 ),
inference(resolution,[],[f341,f298]) ).
fof(f637,plain,
( spl12_77
| ~ spl12_26
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f364,f332,f297,f635]) ).
fof(f364,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl12_26
| ~ spl12_32 ),
inference(resolution,[],[f333,f298]) ).
fof(f631,plain,
( spl12_76
| ~ spl12_69
| ~ spl12_75 ),
inference(avatar_split_clause,[],[f627,f624,f588,f629]) ).
fof(f624,plain,
( spl12_75
<=> ! [X0] : empty_set = sK3(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_75])]) ).
fof(f627,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl12_69
| ~ spl12_75 ),
inference(forward_demodulation,[],[f625,f590]) ).
fof(f625,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl12_75 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f626,plain,
( spl12_75
| ~ spl12_22
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f356,f328,f280,f624]) ).
fof(f614,plain,
( spl12_74
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_47 ),
inference(avatar_split_clause,[],[f432,f410,f348,f328,f280,f206,f612]) ).
fof(f612,plain,
( spl12_74
<=> ! [X0] : subset(sK5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_74])]) ).
fof(f432,plain,
( ! [X0] : subset(sK5,X0)
| ~ spl12_7
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_47 ),
inference(forward_demodulation,[],[f431,f357]) ).
fof(f431,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl12_22
| ~ spl12_31
| ~ spl12_36
| ~ spl12_47 ),
inference(forward_demodulation,[],[f429,f356]) ).
fof(f429,plain,
( ! [X0] : subset(sK3(X0),X0)
| ~ spl12_36
| ~ spl12_47 ),
inference(resolution,[],[f411,f349]) ).
fof(f610,plain,
( spl12_73
| ~ spl12_7
| ~ spl12_19
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f361,f328,f266,f206,f607]) ).
fof(f607,plain,
( spl12_73
<=> sK5 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_73])]) ).
fof(f361,plain,
( sK5 = sK11
| ~ spl12_7
| ~ spl12_19
| ~ spl12_31 ),
inference(forward_demodulation,[],[f359,f357]) ).
fof(f359,plain,
( empty_set = sK11
| ~ spl12_19
| ~ spl12_31 ),
inference(resolution,[],[f329,f268]) ).
fof(f605,plain,
( spl12_72
| ~ spl12_7
| ~ spl12_10
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f360,f328,f221,f206,f602]) ).
fof(f602,plain,
( spl12_72
<=> sK5 = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_72])]) ).
fof(f360,plain,
( sK5 = sK7
| ~ spl12_7
| ~ spl12_10
| ~ spl12_31 ),
inference(forward_demodulation,[],[f358,f357]) ).
fof(f358,plain,
( empty_set = sK7
| ~ spl12_10
| ~ spl12_31 ),
inference(resolution,[],[f329,f223]) ).
fof(f600,plain,
( ~ spl12_70
| spl12_71
| ~ spl12_35
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f564,f557,f344,f597,f593]) ).
fof(f564,plain,
( relation(relation_rng(sK0))
| ~ empty(function_inverse(sK0))
| ~ spl12_35
| ~ spl12_65 ),
inference(superposition,[],[f345,f559]) ).
fof(f591,plain,
( spl12_69
| ~ spl12_7
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f357,f328,f206,f588]) ).
fof(f585,plain,
( spl12_68
| ~ spl12_22
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f314,f301,f280,f583]) ).
fof(f583,plain,
( spl12_68
<=> ! [X0] : relation(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_68])]) ).
fof(f301,plain,
( spl12_27
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_27])]) ).
fof(f314,plain,
( ! [X0] : relation(sK3(X0))
| ~ spl12_22
| ~ spl12_27 ),
inference(resolution,[],[f302,f281]) ).
fof(f302,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f580,plain,
( spl12_67
| ~ spl12_22
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f309,f297,f280,f578]) ).
fof(f578,plain,
( spl12_67
<=> ! [X0] : function(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_67])]) ).
fof(f309,plain,
( ! [X0] : function(sK3(X0))
| ~ spl12_22
| ~ spl12_26 ),
inference(resolution,[],[f298,f281]) ).
fof(f570,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_66
| ~ spl12_3
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f545,f536,f186,f567,f181,f176]) ).
fof(f186,plain,
( spl12_3
<=> one_to_one(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f545,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_61 ),
inference(resolution,[],[f537,f188]) ).
fof(f188,plain,
( one_to_one(sK0)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f560,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_65
| ~ spl12_3
| ~ spl12_60 ),
inference(avatar_split_clause,[],[f543,f532,f186,f557,f181,f176]) ).
fof(f543,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_60 ),
inference(resolution,[],[f533,f188]) ).
fof(f555,plain,
spl12_64,
inference(avatar_split_clause,[],[f130,f553]) ).
fof(f130,plain,
! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f550,plain,
spl12_63,
inference(avatar_split_clause,[],[f129,f548]) ).
fof(f129,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f542,plain,
spl12_62,
inference(avatar_split_clause,[],[f152,f540]) ).
fof(f152,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f538,plain,
spl12_61,
inference(avatar_split_clause,[],[f136,f536]) ).
fof(f136,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f534,plain,
spl12_60,
inference(avatar_split_clause,[],[f135,f532]) ).
fof(f135,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f524,plain,
spl12_59,
inference(avatar_split_clause,[],[f158,f522]) ).
fof(f158,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f514,plain,
spl12_58,
inference(avatar_split_clause,[],[f159,f512]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f471,plain,
spl12_57,
inference(avatar_split_clause,[],[f153,f469]) ).
fof(f153,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f467,plain,
spl12_56,
inference(avatar_split_clause,[],[f150,f465]) ).
fof(f150,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f463,plain,
spl12_55,
inference(avatar_split_clause,[],[f149,f461]) ).
fof(f149,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f459,plain,
spl12_54,
inference(avatar_split_clause,[],[f148,f457]) ).
fof(f148,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f455,plain,
spl12_53,
inference(avatar_split_clause,[],[f147,f453]) ).
fof(f147,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f451,plain,
spl12_52,
inference(avatar_split_clause,[],[f146,f449]) ).
fof(f146,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f447,plain,
spl12_51,
inference(avatar_split_clause,[],[f139,f445]) ).
fof(f139,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f427,plain,
( spl12_50
| ~ spl12_7
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f315,f301,f206,f424]) ).
fof(f315,plain,
( relation(sK5)
| ~ spl12_7
| ~ spl12_27 ),
inference(resolution,[],[f302,f208]) ).
fof(f420,plain,
spl12_49,
inference(avatar_split_clause,[],[f156,f418]) ).
fof(f156,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f416,plain,
spl12_48,
inference(avatar_split_clause,[],[f155,f414]) ).
fof(f155,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f412,plain,
spl12_47,
inference(avatar_split_clause,[],[f154,f410]) ).
fof(f154,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f408,plain,
spl12_46,
inference(avatar_split_clause,[],[f134,f406]) ).
fof(f134,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f404,plain,
spl12_45,
inference(avatar_split_clause,[],[f133,f402]) ).
fof(f133,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f400,plain,
spl12_44,
inference(avatar_split_clause,[],[f132,f398]) ).
fof(f132,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f396,plain,
spl12_43,
inference(avatar_split_clause,[],[f131,f394]) ).
fof(f131,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f391,plain,
( spl12_42
| ~ spl12_10
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f311,f297,f221,f388]) ).
fof(f388,plain,
( spl12_42
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_42])]) ).
fof(f311,plain,
( function(sK7)
| ~ spl12_10
| ~ spl12_26 ),
inference(resolution,[],[f298,f223]) ).
fof(f386,plain,
spl12_41,
inference(avatar_split_clause,[],[f120,f384]) ).
fof(f120,plain,
! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f48,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f382,plain,
spl12_40,
inference(avatar_split_clause,[],[f145,f380]) ).
fof(f380,plain,
( spl12_40
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_40])]) ).
fof(f145,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f378,plain,
spl12_39,
inference(avatar_split_clause,[],[f144,f376]) ).
fof(f144,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,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(f370,plain,
( spl12_38
| ~ spl12_7
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f310,f297,f206,f367]) ).
fof(f310,plain,
( function(sK5)
| ~ spl12_7
| ~ spl12_26 ),
inference(resolution,[],[f298,f208]) ).
fof(f354,plain,
spl12_37,
inference(avatar_split_clause,[],[f157,f352]) ).
fof(f352,plain,
( spl12_37
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_37])]) ).
fof(f157,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f350,plain,
spl12_36,
inference(avatar_split_clause,[],[f141,f348]) ).
fof(f141,plain,
! [X0] : element(sK3(X0),powerset(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f25,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f346,plain,
spl12_35,
inference(avatar_split_clause,[],[f128,f344]) ).
fof(f128,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f342,plain,
spl12_34,
inference(avatar_split_clause,[],[f127,f340]) ).
fof(f127,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f338,plain,
spl12_33,
inference(avatar_split_clause,[],[f126,f336]) ).
fof(f126,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f334,plain,
spl12_32,
inference(avatar_split_clause,[],[f125,f332]) ).
fof(f125,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f330,plain,
spl12_31,
inference(avatar_split_clause,[],[f124,f328]) ).
fof(f124,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f326,plain,
( spl12_30
| ~ spl12_4
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f308,f297,f191,f323]) ).
fof(f323,plain,
( spl12_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_30])]) ).
fof(f308,plain,
( function(empty_set)
| ~ spl12_4
| ~ spl12_26 ),
inference(resolution,[],[f298,f193]) ).
fof(f321,plain,
spl12_29,
inference(avatar_split_clause,[],[f121,f319]) ).
fof(f319,plain,
( spl12_29
<=> ! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_29])]) ).
fof(f121,plain,
! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f307,plain,
spl12_28,
inference(avatar_split_clause,[],[f140,f305]) ).
fof(f140,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f7,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f303,plain,
spl12_27,
inference(avatar_split_clause,[],[f123,f301]) ).
fof(f123,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f299,plain,
spl12_26,
inference(avatar_split_clause,[],[f122,f297]) ).
fof(f122,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f295,plain,
( ~ spl12_24
| ~ spl12_25 ),
inference(avatar_split_clause,[],[f113,f292,f288]) ).
fof(f113,plain,
( relation_dom(sK0) != relation_rng(relation_composition(sK0,function_inverse(sK0)))
| relation_dom(sK0) != relation_dom(relation_composition(sK0,function_inverse(sK0))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( ( relation_dom(sK0) != relation_rng(relation_composition(sK0,function_inverse(sK0)))
| relation_dom(sK0) != relation_dom(relation_composition(sK0,function_inverse(sK0))) )
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f47,f85]) ).
fof(f85,plain,
( ? [X0] :
( ( relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ( relation_dom(sK0) != relation_rng(relation_composition(sK0,function_inverse(sK0)))
| relation_dom(sK0) != relation_dom(relation_composition(sK0,function_inverse(sK0))) )
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
& relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ) ) ),
inference(negated_conjecture,[],[f37]) ).
fof(f37,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(relation_composition(X0,function_inverse(X0)))
& relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f286,plain,
spl12_23,
inference(avatar_split_clause,[],[f143,f284]) ).
fof(f143,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f282,plain,
spl12_22,
inference(avatar_split_clause,[],[f142,f280]) ).
fof(f142,plain,
! [X0] : empty(sK3(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f278,plain,
spl12_21,
inference(avatar_split_clause,[],[f119,f276]) ).
fof(f276,plain,
( spl12_21
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_21])]) ).
fof(f119,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f274,plain,
spl12_20,
inference(avatar_split_clause,[],[f174,f271]) ).
fof(f271,plain,
( spl12_20
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).
fof(f174,plain,
function(sK11),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
( function(sK11)
& empty(sK11)
& relation(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f23,f108]) ).
fof(f108,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK11)
& empty(sK11)
& relation(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f269,plain,
spl12_19,
inference(avatar_split_clause,[],[f173,f266]) ).
fof(f173,plain,
empty(sK11),
inference(cnf_transformation,[],[f109]) ).
fof(f264,plain,
spl12_18,
inference(avatar_split_clause,[],[f172,f261]) ).
fof(f261,plain,
( spl12_18
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f172,plain,
relation(sK11),
inference(cnf_transformation,[],[f109]) ).
fof(f259,plain,
spl12_17,
inference(avatar_split_clause,[],[f171,f256]) ).
fof(f171,plain,
one_to_one(sK10),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f27,f106]) ).
fof(f106,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK10)
& function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f254,plain,
spl12_16,
inference(avatar_split_clause,[],[f170,f251]) ).
fof(f170,plain,
function(sK10),
inference(cnf_transformation,[],[f107]) ).
fof(f249,plain,
spl12_15,
inference(avatar_split_clause,[],[f169,f246]) ).
fof(f169,plain,
relation(sK10),
inference(cnf_transformation,[],[f107]) ).
fof(f244,plain,
spl12_14,
inference(avatar_split_clause,[],[f168,f241]) ).
fof(f168,plain,
function(sK9),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f19,f104]) ).
fof(f104,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f239,plain,
spl12_13,
inference(avatar_split_clause,[],[f167,f236]) ).
fof(f167,plain,
relation(sK9),
inference(cnf_transformation,[],[f105]) ).
fof(f234,plain,
spl12_12,
inference(avatar_split_clause,[],[f166,f231]) ).
fof(f166,plain,
relation(sK8),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
relation(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f44,f102]) ).
fof(f102,plain,
( ? [X0] : relation(X0)
=> relation(sK8) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f28]) ).
fof(f28,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f229,plain,
spl12_11,
inference(avatar_split_clause,[],[f165,f226]) ).
fof(f226,plain,
( spl12_11
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f165,plain,
relation(sK7),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,f100]) ).
fof(f100,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK7)
& empty(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f224,plain,
spl12_10,
inference(avatar_split_clause,[],[f164,f221]) ).
fof(f164,plain,
empty(sK7),
inference(cnf_transformation,[],[f101]) ).
fof(f219,plain,
spl12_9,
inference(avatar_split_clause,[],[f163,f216]) ).
fof(f163,plain,
relation(sK6),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f24,f98]) ).
fof(f98,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK6)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f214,plain,
~ spl12_8,
inference(avatar_split_clause,[],[f162,f211]) ).
fof(f211,plain,
( spl12_8
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f162,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f99]) ).
fof(f209,plain,
spl12_7,
inference(avatar_split_clause,[],[f161,f206]) ).
fof(f161,plain,
empty(sK5),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f96]) ).
fof(f96,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f204,plain,
~ spl12_6,
inference(avatar_split_clause,[],[f160,f201]) ).
fof(f201,plain,
( spl12_6
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f160,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f26,f94]) ).
fof(f94,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f199,plain,
spl12_5,
inference(avatar_split_clause,[],[f116,f196]) ).
fof(f116,plain,
relation(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f194,plain,
spl12_4,
inference(avatar_split_clause,[],[f114,f191]) ).
fof(f114,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f189,plain,
spl12_3,
inference(avatar_split_clause,[],[f112,f186]) ).
fof(f112,plain,
one_to_one(sK0),
inference(cnf_transformation,[],[f86]) ).
fof(f184,plain,
spl12_2,
inference(avatar_split_clause,[],[f111,f181]) ).
fof(f111,plain,
function(sK0),
inference(cnf_transformation,[],[f86]) ).
fof(f179,plain,
spl12_1,
inference(avatar_split_clause,[],[f110,f176]) ).
fof(f110,plain,
relation(sK0),
inference(cnf_transformation,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU025+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 29 20:58:14 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % (7409)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (7412)WARNING: value z3 for option sas not known
% 0.11/0.33 % (7413)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (7414)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)
% 0.11/0.33 % (7411)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (7415)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)
% 0.11/0.33 % (7416)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)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 % (7412)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)
% 0.11/0.35 TRYING [5]
% 0.11/0.36 % (7410)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.36 TRYING [1]
% 0.15/0.36 TRYING [6]
% 0.15/0.37 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [7]
% 0.15/0.41 % (7414)First to succeed.
% 0.15/0.42 TRYING [4]
% 0.15/0.43 % (7414)Refutation found. Thanks to Tanya!
% 0.15/0.43 % SZS status Theorem for theBenchmark
% 0.15/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.44 % (7414)------------------------------
% 0.15/0.44 % (7414)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.44 % (7414)Termination reason: Refutation
% 0.15/0.44
% 0.15/0.44 % (7414)Memory used [KB]: 2369
% 0.15/0.44 % (7414)Time elapsed: 0.094 s
% 0.15/0.44 % (7414)Instructions burned: 187 (million)
% 0.15/0.44 % (7414)------------------------------
% 0.15/0.44 % (7414)------------------------------
% 0.15/0.44 % (7409)Success in time 0.112 s
%------------------------------------------------------------------------------