TSTP Solution File: COL003-20 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL003-20 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:45:30 EDT 2024
% Result : Unsatisfiable 103.36s 15.05s
% Output : Refutation 103.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 184
% Syntax : Number of formulae : 625 ( 11 unt; 0 def)
% Number of atoms : 1631 ( 442 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1833 ( 827 ~; 826 |; 0 &)
% ( 180 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 182 ( 180 usr; 181 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 762 ( 762 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93562,plain,
$false,
inference(avatar_sat_refutation,[],[f11,f15,f23,f32,f39,f53,f57,f110,f114,f187,f257,f262,f272,f277,f293,f298,f365,f369,f373,f377,f381,f663,f667,f671,f675,f680,f684,f1010,f1014,f1018,f1022,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1082,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1452,f3362,f6001,f6005,f6009,f6013,f6017,f6021,f6025,f6029,f6033,f6037,f6041,f6045,f6049,f6053,f6057,f6061,f6065,f6069,f6073,f8257,f12492,f13274,f13278,f13282,f13286,f13290,f13294,f13298,f13302,f13306,f13310,f13314,f13318,f13322,f13326,f13330,f13334,f13338,f13342,f13346,f13350,f13354,f18572,f26362,f26366,f26370,f26374,f26378,f26382,f26386,f26390,f26394,f26398,f26650,f26654,f26658,f26662,f31113,f38759,f38763,f38767,f38771,f38775,f43165,f43170,f43174,f43178,f43685,f43689,f48107,f48726,f48731,f48735,f49226,f49480,f49485,f49490,f49764,f50122,f50126,f57440,f57444,f57448,f57453,f57457,f57461,f57465,f57469,f57473,f57477,f57481,f57485,f57489,f57493,f57497,f58499,f58503,f58507,f58511,f58515,f58519,f58523,f58527,f58531,f58535,f58539,f58543,f58548,f58552,f58556,f58560,f58564,f58568,f58572,f58576,f58580,f58584,f58588,f58592,f58596,f58600,f58604,f71819,f87212,f93001,f93005,f93009,f93013,f93017,f93341]) ).
fof(f93341,plain,
( spl0_1
| ~ spl0_175 ),
inference(avatar_contradiction_clause,[],[f93340]) ).
fof(f93340,plain,
( $false
| spl0_1
| ~ spl0_175 ),
inference(trivial_inequality_removal,[],[f93339]) ).
fof(f93339,plain,
( apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt)
| spl0_1
| ~ spl0_175 ),
inference(superposition,[],[f10,f87211]) ).
fof(f87211,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0))
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f87210]) ).
fof(f87210,plain,
( spl0_175
<=> ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f10,plain,
( apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt))
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f8,plain,
( spl0_1
<=> apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f93017,plain,
( spl0_180
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f486,f371,f291,f93015]) ).
fof(f93015,plain,
( spl0_180
<=> ! [X0] : apply(apply(w,apply(w,apply(w,apply(w,b)))),X0) = apply(apply(w,apply(X0,apply(X0,X0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f291,plain,
( spl0_15
<=> ! [X0] : apply(apply(w,apply(w,b)),X0) = apply(X0,apply(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f371,plain,
( spl0_19
<=> ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f486,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,apply(w,b)))),X0) = apply(apply(w,apply(X0,apply(X0,X0))),X0)
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f372,f292]) ).
fof(f292,plain,
( ! [X0] : apply(apply(w,apply(w,b)),X0) = apply(X0,apply(X0,X0))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f372,plain,
( ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(X0,X1)),X1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f93013,plain,
( spl0_179
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f353,f291,f21,f93011]) ).
fof(f93011,plain,
( spl0_179
<=> ! [X0,X1] : apply(apply(apply(w,apply(w,b)),apply(b,X0)),X1) = apply(X0,apply(X0,apply(apply(b,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f21,plain,
( spl0_3
<=> ! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f353,plain,
( ! [X0,X1] : apply(apply(apply(w,apply(w,b)),apply(b,X0)),X1) = apply(X0,apply(X0,apply(apply(b,X0),X1)))
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_demodulation,[],[f341,f22]) ).
fof(f22,plain,
( ! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f341,plain,
( ! [X0,X1] : apply(X0,apply(apply(apply(b,X0),apply(b,X0)),X1)) = apply(apply(apply(w,apply(w,b)),apply(b,X0)),X1)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f22,f292]) ).
fof(f93009,plain,
( spl0_178
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f329,f291,f108,f93007]) ).
fof(f93007,plain,
( spl0_178
<=> ! [X0] : apply(apply(w,apply(w,apply(w,apply(w,b)))),X0) = apply(apply(apply(X0,apply(X0,X0)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f108,plain,
( spl0_8
<=> ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(apply(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f329,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,apply(w,b)))),X0) = apply(apply(apply(X0,apply(X0,X0)),X0),X0)
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f109,f292]) ).
fof(f109,plain,
( ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(apply(X0,X1),X1),X1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f93005,plain,
( spl0_177
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f315,f270,f51,f93003]) ).
fof(f93003,plain,
( spl0_177
<=> ! [X0] : apply(apply(apply(w,b),apply(apply(w,w),b)),X0) = apply(b,apply(b,apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f51,plain,
( spl0_6
<=> ! [X0,X1] : apply(X0,apply(X0,X1)) = apply(apply(apply(w,b),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f270,plain,
( spl0_13
<=> ! [X0] : apply(apply(apply(w,w),b),X0) = apply(b,apply(b,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f315,plain,
( ! [X0] : apply(apply(apply(w,b),apply(apply(w,w),b)),X0) = apply(b,apply(b,apply(b,apply(b,X0))))
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f301,f271]) ).
fof(f271,plain,
( ! [X0] : apply(apply(apply(w,w),b),X0) = apply(b,apply(b,X0))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f301,plain,
( ! [X0] : apply(apply(apply(w,b),apply(apply(w,w),b)),X0) = apply(b,apply(b,apply(apply(apply(w,w),b),X0)))
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f271,f52]) ).
fof(f52,plain,
( ! [X0,X1] : apply(X0,apply(X0,X1)) = apply(apply(apply(w,b),X0),X1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f93001,plain,
( spl0_176
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f307,f270,f108,f92999]) ).
fof(f92999,plain,
( spl0_176
<=> ! [X0] : apply(apply(w,apply(w,apply(apply(w,w),b))),X0) = apply(apply(apply(b,apply(b,X0)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f307,plain,
( ! [X0] : apply(apply(w,apply(w,apply(apply(w,w),b))),X0) = apply(apply(apply(b,apply(b,X0)),X0),X0)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f109,f271]) ).
fof(f87212,plain,
( spl0_175
| ~ spl0_12
| ~ spl0_95
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f84524,f58574,f26360,f260,f87210]) ).
fof(f260,plain,
( spl0_12
<=> ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f26360,plain,
( spl0_95
<=> ! [X0,X1] : apply(apply(w,w),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,apply(apply(b,X0),X1))),apply(apply(b,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f58574,plain,
( spl0_166
<=> ! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(w,apply(apply(b,apply(b,X1)),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f84524,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0))
| ~ spl0_12
| ~ spl0_95
| ~ spl0_166 ),
inference(forward_demodulation,[],[f84306,f261]) ).
fof(f261,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f84306,plain,
( ! [X0] : apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))))
| ~ spl0_95
| ~ spl0_166 ),
inference(superposition,[],[f58575,f26361]) ).
fof(f26361,plain,
( ! [X0,X1] : apply(apply(w,w),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,apply(apply(b,X0),X1))),apply(apply(b,X0),X1))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f26360]) ).
fof(f58575,plain,
( ! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(w,apply(apply(b,apply(b,X1)),X0)),X0)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f58574]) ).
fof(f71819,plain,
( spl0_174
| ~ spl0_19
| ~ spl0_61
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f65199,f57483,f6035,f371,f71817]) ).
fof(f71817,plain,
( spl0_174
<=> ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(apply(w,apply(w,b)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f6035,plain,
( spl0_61
<=> ! [X2,X0,X1] : apply(apply(w,apply(w,apply(apply(b,X0),X1))),X2) = apply(apply(apply(X0,apply(X1,X2)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f57483,plain,
( spl0_143
<=> ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(w,apply(w,apply(apply(b,w),b))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f65199,plain,
( ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(apply(w,apply(w,b)),X0),X0)
| ~ spl0_19
| ~ spl0_61
| ~ spl0_143 ),
inference(forward_demodulation,[],[f64796,f372]) ).
fof(f64796,plain,
( ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(apply(w,apply(b,X0)),X0),X0)
| ~ spl0_61
| ~ spl0_143 ),
inference(superposition,[],[f57484,f6036]) ).
fof(f6036,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(apply(b,X0),X1))),X2) = apply(apply(apply(X0,apply(X1,X2)),X2),X2)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f6035]) ).
fof(f57484,plain,
( ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(w,apply(w,apply(apply(b,w),b))),X0)
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f57483]) ).
fof(f58604,plain,
( spl0_173
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f30000,f26376,f270,f260,f29,f21,f58602]) ).
fof(f58602,plain,
( spl0_173
<=> ! [X0] : apply(apply(strong_fixed_point,apply(X0,X0)),apply(X0,X0)) = apply(apply(w,apply(b,apply(w,strong_fixed_point))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f29,plain,
( spl0_4
<=> strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f26376,plain,
( spl0_99
<=> ! [X2,X0,X1] : apply(apply(w,apply(b,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(X0,apply(X1,apply(X2,X2))),apply(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f30000,plain,
( ! [X0] : apply(apply(strong_fixed_point,apply(X0,X0)),apply(X0,X0)) = apply(apply(w,apply(b,apply(w,strong_fixed_point))),X0)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_99 ),
inference(forward_demodulation,[],[f29999,f261]) ).
fof(f29999,plain,
( ! [X0] : apply(apply(w,apply(b,apply(w,strong_fixed_point))),X0) = apply(apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,apply(X0,X0))))),apply(X0,X0))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13
| ~ spl0_99 ),
inference(forward_demodulation,[],[f29998,f271]) ).
fof(f29998,plain,
( ! [X0] : apply(apply(w,apply(b,apply(w,strong_fixed_point))),X0) = apply(apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),apply(X0,X0)))),apply(X0,X0))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_99 ),
inference(forward_demodulation,[],[f29488,f22]) ).
fof(f29488,plain,
( ! [X0] : apply(apply(w,apply(b,apply(w,strong_fixed_point))),X0) = apply(apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(w,w),b)),apply(X0,X0))),apply(X0,X0))
| ~ spl0_4
| ~ spl0_99 ),
inference(superposition,[],[f26377,f31]) ).
fof(f31,plain,
( strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f26377,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(b,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(X0,apply(X1,apply(X2,X2))),apply(X2,X2))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f26376]) ).
fof(f58600,plain,
( spl0_172
| ~ spl0_10
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f11590,f6059,f185,f58598]) ).
fof(f58598,plain,
( spl0_172
<=> ! [X2,X0,X1] : apply(apply(X0,apply(apply(X1,X2),X2)),X2) = apply(apply(X0,apply(apply(w,X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f185,plain,
( spl0_10
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f6059,plain,
( spl0_67
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(w,X0))),X1) = apply(apply(X2,apply(apply(X0,X1),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f11590,plain,
( ! [X2,X0,X1] : apply(apply(X0,apply(apply(X1,X2),X2)),X2) = apply(apply(X0,apply(apply(w,X1),X2)),X2)
| ~ spl0_10
| ~ spl0_67 ),
inference(superposition,[],[f6060,f186]) ).
fof(f186,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f6060,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(w,X0))),X1) = apply(apply(X2,apply(apply(X0,X1),X1)),X1)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f6059]) ).
fof(f58596,plain,
( spl0_171
| ~ spl0_10
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f10888,f6047,f185,f58594]) ).
fof(f58594,plain,
( spl0_171
<=> ! [X0,X1] : apply(apply(X0,apply(apply(X1,X1),X1)),X1) = apply(apply(X0,apply(apply(w,w),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f6047,plain,
( spl0_64
<=> ! [X0,X1] : apply(apply(w,apply(apply(b,X1),apply(w,w))),X0) = apply(apply(X1,apply(apply(X0,X0),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f10888,plain,
( ! [X0,X1] : apply(apply(X0,apply(apply(X1,X1),X1)),X1) = apply(apply(X0,apply(apply(w,w),X1)),X1)
| ~ spl0_10
| ~ spl0_64 ),
inference(superposition,[],[f6048,f186]) ).
fof(f6048,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(b,X1),apply(w,w))),X0) = apply(apply(X1,apply(apply(X0,X0),X0)),X0)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f6047]) ).
fof(f58592,plain,
( spl0_170
| ~ spl0_2
| ~ spl0_3
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f9451,f6031,f21,f13,f58590]) ).
fof(f58590,plain,
( spl0_170
<=> ! [X0] : apply(apply(w,apply(w,apply(apply(w,w),b))),X0) = apply(apply(b,X0),apply(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f13,plain,
( spl0_2
<=> ! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f6031,plain,
( spl0_60
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,b),X0))),X1) = apply(apply(apply(X0,apply(X0,X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f9451,plain,
( ! [X0] : apply(apply(w,apply(w,apply(apply(w,w),b))),X0) = apply(apply(b,X0),apply(X0,X0))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_60 ),
inference(forward_demodulation,[],[f9192,f14]) ).
fof(f14,plain,
( ! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f9192,plain,
( ! [X0] : apply(apply(w,apply(w,apply(apply(w,b),b))),X0) = apply(apply(b,X0),apply(X0,X0))
| ~ spl0_3
| ~ spl0_60 ),
inference(superposition,[],[f6032,f22]) ).
fof(f6032,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,b),X0))),X1) = apply(apply(apply(X0,apply(X0,X1)),X1),X1)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f6031]) ).
fof(f58588,plain,
( spl0_169
| ~ spl0_2
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f5695,f1108,f13,f58586]) ).
fof(f58586,plain,
( spl0_169
<=> ! [X0,X1] : apply(apply(X0,X1),apply(X1,X1)) = apply(apply(w,apply(w,apply(apply(b,b),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1108,plain,
( spl0_49
<=> ! [X2,X0,X1] : apply(apply(X0,X1),apply(X1,X2)) = apply(apply(apply(w,apply(apply(b,b),X0)),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f5695,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(X1,X1)) = apply(apply(w,apply(w,apply(apply(b,b),X0))),X1)
| ~ spl0_2
| ~ spl0_49 ),
inference(superposition,[],[f1109,f14]) ).
fof(f1109,plain,
( ! [X2,X0,X1] : apply(apply(X0,X1),apply(X1,X2)) = apply(apply(apply(w,apply(apply(b,b),X0)),X1),X2)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f58584,plain,
( spl0_168
| ~ spl0_2
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f5010,f1104,f13,f58582]) ).
fof(f58582,plain,
( spl0_168
<=> ! [X2,X0,X1] : apply(X2,apply(apply(w,X0),X1)) = apply(apply(w,apply(apply(b,apply(b,X2)),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1104,plain,
( spl0_48
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X2) = apply(X0,apply(apply(X1,X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f5010,plain,
( ! [X2,X0,X1] : apply(X2,apply(apply(w,X0),X1)) = apply(apply(w,apply(apply(b,apply(b,X2)),X0)),X1)
| ~ spl0_2
| ~ spl0_48 ),
inference(superposition,[],[f1105,f14]) ).
fof(f1105,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X2) = apply(X0,apply(apply(X1,X2),X2))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f58580,plain,
( spl0_167
| ~ spl0_2
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f5008,f1104,f13,f58578]) ).
fof(f58578,plain,
( spl0_167
<=> ! [X0,X1] : apply(X1,apply(apply(X0,X0),X0)) = apply(apply(w,apply(apply(b,apply(b,X1)),w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f5008,plain,
( ! [X0,X1] : apply(X1,apply(apply(X0,X0),X0)) = apply(apply(w,apply(apply(b,apply(b,X1)),w)),X0)
| ~ spl0_2
| ~ spl0_48 ),
inference(superposition,[],[f1105,f14]) ).
fof(f58576,plain,
( spl0_166
| ~ spl0_5
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f5005,f1104,f37,f58574]) ).
fof(f37,plain,
( spl0_5
<=> ! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f5005,plain,
( ! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(w,apply(apply(b,apply(b,X1)),X0)),X0)
| ~ spl0_5
| ~ spl0_48 ),
inference(superposition,[],[f1105,f38]) ).
fof(f38,plain,
( ! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f58572,plain,
( spl0_165
| ~ spl0_44
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f4429,f1096,f1088,f58570]) ).
fof(f58570,plain,
( spl0_165
<=> ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(w,apply(w,apply(X0,X0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1088,plain,
( spl0_44
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(X0,X1))),X1) = apply(apply(apply(w,apply(w,X0)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1096,plain,
( spl0_46
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(apply(w,apply(X0,X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f4429,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(w,apply(w,apply(X0,X0))),X0)
| ~ spl0_44
| ~ spl0_46 ),
inference(superposition,[],[f1097,f1089]) ).
fof(f1089,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(X0,X1))),X1) = apply(apply(apply(w,apply(w,X0)),X1),X1)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f1097,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(apply(w,apply(X0,X1)),X1),X1)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f58568,plain,
( spl0_164
| ~ spl0_10
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f4289,f1092,f185,f58566]) ).
fof(f58566,plain,
( spl0_164
<=> ! [X0] : apply(apply(w,w),apply(w,X0)) = apply(apply(w,apply(apply(b,w),X0)),apply(w,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1092,plain,
( spl0_45
<=> ! [X0] : apply(apply(w,w),apply(w,X0)) = apply(apply(w,apply(X0,apply(w,X0))),apply(w,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f4289,plain,
( ! [X0] : apply(apply(w,w),apply(w,X0)) = apply(apply(w,apply(apply(b,w),X0)),apply(w,X0))
| ~ spl0_10
| ~ spl0_45 ),
inference(superposition,[],[f1093,f186]) ).
fof(f1093,plain,
( ! [X0] : apply(apply(w,w),apply(w,X0)) = apply(apply(w,apply(X0,apply(w,X0))),apply(w,X0))
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f58564,plain,
( spl0_163
| ~ spl0_2
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f4186,f1088,f13,f58562]) ).
fof(f58562,plain,
( spl0_163
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(w,apply(w,apply(X0,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f4186,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(w,apply(w,apply(X0,X1))),X1)
| ~ spl0_2
| ~ spl0_44 ),
inference(superposition,[],[f1089,f14]) ).
fof(f58560,plain,
( spl0_162
| ~ spl0_2
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f3745,f1084,f13,f58558]) ).
fof(f58558,plain,
( spl0_162
<=> ! [X0,X1] : apply(apply(apply(w,apply(b,apply(b,X1))),X0),X0) = apply(X1,apply(apply(w,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1084,plain,
( spl0_43
<=> ! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f3745,plain,
( ! [X0,X1] : apply(apply(apply(w,apply(b,apply(b,X1))),X0),X0) = apply(X1,apply(apply(w,X0),X0))
| ~ spl0_2
| ~ spl0_43 ),
inference(superposition,[],[f1085,f14]) ).
fof(f1085,plain,
( ! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f58556,plain,
( spl0_161
| ~ spl0_5
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f3744,f1084,f37,f58554]) ).
fof(f58554,plain,
( spl0_161
<=> ! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(apply(w,apply(b,apply(b,X1))),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f3744,plain,
( ! [X0,X1] : apply(X1,apply(apply(w,w),X0)) = apply(apply(apply(w,apply(b,apply(b,X1))),X0),X0)
| ~ spl0_5
| ~ spl0_43 ),
inference(superposition,[],[f1085,f38]) ).
fof(f58552,plain,
( spl0_160
| ~ spl0_2
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f2995,f1067,f13,f58550]) ).
fof(f58550,plain,
( spl0_160
<=> ! [X0] : apply(b,apply(apply(w,apply(b,b)),X0)) = apply(apply(apply(w,w),b),apply(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1067,plain,
( spl0_39
<=> ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X1,X1)) = apply(X0,apply(apply(w,apply(b,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2995,plain,
( ! [X0] : apply(b,apply(apply(w,apply(b,b)),X0)) = apply(apply(apply(w,w),b),apply(X0,X0))
| ~ spl0_2
| ~ spl0_39 ),
inference(superposition,[],[f1068,f14]) ).
fof(f1068,plain,
( ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X1,X1)) = apply(X0,apply(apply(w,apply(b,X0)),X1))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f58548,plain,
( spl0_159
| ~ spl0_7
| ~ spl0_22
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f2331,f1055,f661,f55,f58545]) ).
fof(f58545,plain,
( spl0_159
<=> apply(apply(w,w),apply(b,b)) = apply(apply(w,apply(apply(w,w),apply(b,b))),b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f55,plain,
( spl0_7
<=> ! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f661,plain,
( spl0_22
<=> ! [X0] : apply(X0,apply(apply(b,X0),apply(b,X0))) = apply(apply(w,w),apply(b,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1055,plain,
( spl0_36
<=> ! [X0,X1] : apply(apply(w,X0),apply(X1,X1)) = apply(apply(w,apply(b,apply(X0,apply(X1,X1)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2331,plain,
( apply(apply(w,w),apply(b,b)) = apply(apply(w,apply(apply(w,w),apply(b,b))),b)
| ~ spl0_7
| ~ spl0_22
| ~ spl0_36 ),
inference(forward_demodulation,[],[f2330,f662]) ).
fof(f662,plain,
( ! [X0] : apply(X0,apply(apply(b,X0),apply(b,X0))) = apply(apply(w,w),apply(b,X0))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f2330,plain,
( apply(b,apply(apply(b,b),apply(b,b))) = apply(apply(w,apply(apply(w,w),apply(b,b))),b)
| ~ spl0_7
| ~ spl0_22
| ~ spl0_36 ),
inference(forward_demodulation,[],[f2267,f56]) ).
fof(f56,plain,
( ! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f2267,plain,
( apply(apply(w,apply(b,b)),apply(b,b)) = apply(apply(w,apply(apply(w,w),apply(b,b))),b)
| ~ spl0_22
| ~ spl0_36 ),
inference(superposition,[],[f1056,f662]) ).
fof(f1056,plain,
( ! [X0,X1] : apply(apply(w,X0),apply(X1,X1)) = apply(apply(w,apply(b,apply(X0,apply(X1,X1)))),X1)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f58543,plain,
( spl0_158
| ~ spl0_19
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f2108,f1051,f371,f58541]) ).
fof(f58541,plain,
( spl0_158
<=> ! [X0] : apply(apply(X0,X0),apply(X0,X0)) = apply(apply(w,apply(w,apply(w,apply(b,b)))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1051,plain,
( spl0_35
<=> ! [X0,X1] : apply(apply(X0,X0),apply(X1,X1)) = apply(apply(w,apply(apply(w,apply(b,b)),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2108,plain,
( ! [X0] : apply(apply(X0,X0),apply(X0,X0)) = apply(apply(w,apply(w,apply(w,apply(b,b)))),X0)
| ~ spl0_19
| ~ spl0_35 ),
inference(superposition,[],[f1052,f372]) ).
fof(f1052,plain,
( ! [X0,X1] : apply(apply(X0,X0),apply(X1,X1)) = apply(apply(w,apply(apply(w,apply(b,b)),X0)),X1)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f58539,plain,
( spl0_157
| ~ spl0_6
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1767,f1047,f51,f58537]) ).
fof(f58537,plain,
( spl0_157
<=> ! [X2,X0,X1] : apply(apply(apply(b,X0),apply(apply(b,X0),X1)),X2) = apply(X0,apply(X0,apply(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1047,plain,
( spl0_34
<=> ! [X2,X0,X1] : apply(apply(apply(apply(w,b),apply(b,X0)),X1),X2) = apply(X0,apply(X0,apply(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1767,plain,
( ! [X2,X0,X1] : apply(apply(apply(b,X0),apply(apply(b,X0),X1)),X2) = apply(X0,apply(X0,apply(X1,X2)))
| ~ spl0_6
| ~ spl0_34 ),
inference(superposition,[],[f1048,f52]) ).
fof(f1048,plain,
( ! [X2,X0,X1] : apply(apply(apply(apply(w,b),apply(b,X0)),X1),X2) = apply(X0,apply(X0,apply(X1,X2)))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f58535,plain,
( spl0_156
| ~ spl0_30
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1766,f1047,f1016,f58533]) ).
fof(f58533,plain,
( spl0_156
<=> ! [X0,X1] : apply(X0,apply(X0,apply(X0,X1))) = apply(apply(apply(b,X0),apply(apply(w,b),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1016,plain,
( spl0_30
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(X0,X1)),X1) = apply(apply(X0,X1),apply(apply(w,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1766,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X0,X1))) = apply(apply(apply(b,X0),apply(apply(w,b),X0)),X1)
| ~ spl0_30
| ~ spl0_34 ),
inference(superposition,[],[f1048,f1017]) ).
fof(f1017,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(X0,X1)),X1) = apply(apply(X0,X1),apply(apply(w,X0),X1))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f58531,plain,
( spl0_155
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1765,f1047,f1008,f58529]) ).
fof(f58529,plain,
( spl0_155
<=> ! [X0] : apply(b,apply(b,apply(b,X0))) = apply(apply(apply(b,b),apply(apply(w,w),b)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1008,plain,
( spl0_28
<=> ! [X0] : apply(apply(apply(w,b),apply(X0,X0)),X0) = apply(apply(X0,X0),apply(apply(w,w),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1765,plain,
( ! [X0] : apply(b,apply(b,apply(b,X0))) = apply(apply(apply(b,b),apply(apply(w,w),b)),X0)
| ~ spl0_28
| ~ spl0_34 ),
inference(superposition,[],[f1048,f1009]) ).
fof(f1009,plain,
( ! [X0] : apply(apply(apply(w,b),apply(X0,X0)),X0) = apply(apply(X0,X0),apply(apply(w,w),X0))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f58527,plain,
( spl0_154
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1282,f1016,f51,f58525]) ).
fof(f58525,plain,
( spl0_154
<=> ! [X0,X1] : apply(apply(X0,X1),apply(apply(X0,X1),X1)) = apply(apply(X0,X1),apply(apply(w,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1282,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(apply(X0,X1),X1)) = apply(apply(X0,X1),apply(apply(w,X0),X1))
| ~ spl0_6
| ~ spl0_30 ),
inference(superposition,[],[f1017,f52]) ).
fof(f58523,plain,
( spl0_153
| ~ spl0_29
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1281,f1016,f1012,f58521]) ).
fof(f58521,plain,
( spl0_153
<=> ! [X0] : apply(apply(w,X0),apply(apply(X0,X0),X0)) = apply(apply(w,X0),apply(apply(w,w),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1012,plain,
( spl0_29
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(w,X0)),X1) = apply(apply(w,X0),apply(apply(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1281,plain,
( ! [X0] : apply(apply(w,X0),apply(apply(X0,X0),X0)) = apply(apply(w,X0),apply(apply(w,w),X0))
| ~ spl0_29
| ~ spl0_30 ),
inference(superposition,[],[f1017,f1013]) ).
fof(f1013,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(w,X0)),X1) = apply(apply(w,X0),apply(apply(X0,X1),X1))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f58519,plain,
( spl0_152
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1280,f1016,f1008,f58517]) ).
fof(f58517,plain,
( spl0_152
<=> ! [X0] : apply(apply(X0,X0),apply(apply(w,w),X0)) = apply(apply(X0,X0),apply(apply(w,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1280,plain,
( ! [X0] : apply(apply(X0,X0),apply(apply(w,w),X0)) = apply(apply(X0,X0),apply(apply(w,X0),X0))
| ~ spl0_28
| ~ spl0_30 ),
inference(superposition,[],[f1017,f1009]) ).
fof(f58515,plain,
( spl0_151
| ~ spl0_2
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f1208,f1012,f13,f58513]) ).
fof(f58513,plain,
( spl0_151
<=> ! [X0] : apply(apply(apply(w,b),apply(w,w)),X0) = apply(apply(w,w),apply(apply(X0,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1208,plain,
( ! [X0] : apply(apply(apply(w,b),apply(w,w)),X0) = apply(apply(w,w),apply(apply(X0,X0),X0))
| ~ spl0_2
| ~ spl0_29 ),
inference(superposition,[],[f1013,f14]) ).
fof(f58511,plain,
( spl0_150
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f1158,f1012,f51,f58509]) ).
fof(f58509,plain,
( spl0_150
<=> ! [X0,X1] : apply(apply(w,X0),apply(apply(w,X0),X1)) = apply(apply(w,X0),apply(apply(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1158,plain,
( ! [X0,X1] : apply(apply(w,X0),apply(apply(w,X0),X1)) = apply(apply(w,X0),apply(apply(X0,X1),X1))
| ~ spl0_6
| ~ spl0_29 ),
inference(superposition,[],[f1013,f52]) ).
fof(f58507,plain,
( spl0_149
| ~ spl0_6
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f1119,f1008,f51,f58505]) ).
fof(f58505,plain,
( spl0_149
<=> ! [X0] : apply(apply(X0,X0),apply(apply(X0,X0),X0)) = apply(apply(X0,X0),apply(apply(w,w),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1119,plain,
( ! [X0] : apply(apply(X0,X0),apply(apply(X0,X0),X0)) = apply(apply(X0,X0),apply(apply(w,w),X0))
| ~ spl0_6
| ~ spl0_28 ),
inference(superposition,[],[f1009,f52]) ).
fof(f58503,plain,
( spl0_148
| ~ spl0_3
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f880,f669,f21,f58501]) ).
fof(f58501,plain,
( spl0_148
<=> ! [X0,X1] : apply(apply(X0,X0),apply(X0,X1)) = apply(apply(apply(w,apply(w,apply(b,b))),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f669,plain,
( spl0_24
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f880,plain,
( ! [X0,X1] : apply(apply(X0,X0),apply(X0,X1)) = apply(apply(apply(w,apply(w,apply(b,b))),X0),X1)
| ~ spl0_3
| ~ spl0_24 ),
inference(superposition,[],[f22,f670]) ).
fof(f670,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f58499,plain,
( spl0_147
| ~ spl0_3
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f865,f669,f21,f58497]) ).
fof(f58497,plain,
( spl0_147
<=> ! [X0,X1] : apply(X0,apply(apply(X1,X1),X1)) = apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f865,plain,
( ! [X0,X1] : apply(X0,apply(apply(X1,X1),X1)) = apply(apply(w,apply(w,apply(b,apply(b,X0)))),X1)
| ~ spl0_3
| ~ spl0_24 ),
inference(superposition,[],[f670,f22]) ).
fof(f57497,plain,
( spl0_146
| ~ spl0_2
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f825,f665,f21,f13,f57495]) ).
fof(f57495,plain,
( spl0_146
<=> ! [X0,X1] : apply(apply(b,X0),apply(X0,X1)) = apply(apply(apply(w,apply(apply(w,w),b)),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f665,plain,
( spl0_23
<=> ! [X0,X1] : apply(apply(w,apply(apply(w,b),X0)),X1) = apply(apply(X0,apply(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f825,plain,
( ! [X0,X1] : apply(apply(b,X0),apply(X0,X1)) = apply(apply(apply(w,apply(apply(w,w),b)),X0),X1)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_23 ),
inference(forward_demodulation,[],[f785,f14]) ).
fof(f785,plain,
( ! [X0,X1] : apply(apply(b,X0),apply(X0,X1)) = apply(apply(apply(w,apply(apply(w,b),b)),X0),X1)
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f22,f666]) ).
fof(f666,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(w,b),X0)),X1) = apply(apply(X0,apply(X0,X1)),X1)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f57493,plain,
( spl0_145
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f822,f665,f21,f57491]) ).
fof(f57491,plain,
( spl0_145
<=> ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(apply(w,apply(apply(w,b),apply(b,X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f822,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(apply(w,apply(apply(w,b),apply(b,X0))),X1)
| ~ spl0_3
| ~ spl0_23 ),
inference(forward_demodulation,[],[f771,f22]) ).
fof(f771,plain,
( ! [X0,X1] : apply(X0,apply(apply(apply(b,X0),X1),X1)) = apply(apply(w,apply(apply(w,b),apply(b,X0))),X1)
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f666,f22]) ).
fof(f57489,plain,
( spl0_144
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f728,f665,f185,f57487]) ).
fof(f57487,plain,
( spl0_144
<=> ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(w,apply(apply(b,w),apply(w,b))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f728,plain,
( ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(w,apply(apply(b,w),apply(w,b))),X0)
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f666,f186]) ).
fof(f57485,plain,
( spl0_143
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f623,f379,f13,f57483]) ).
fof(f379,plain,
( spl0_21
<=> ! [X0] : apply(X0,apply(X0,X0)) = apply(apply(w,apply(apply(b,w),b)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f623,plain,
( ! [X0] : apply(apply(X0,apply(X0,X0)),X0) = apply(apply(w,apply(w,apply(apply(b,w),b))),X0)
| ~ spl0_2
| ~ spl0_21 ),
inference(superposition,[],[f14,f380]) ).
fof(f380,plain,
( ! [X0] : apply(X0,apply(X0,X0)) = apply(apply(w,apply(apply(b,w),b)),X0)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f57481,plain,
( spl0_142
| ~ spl0_2
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f496,f371,f13,f57479]) ).
fof(f57479,plain,
( spl0_142
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(X0,X1))),X1) = apply(apply(w,apply(apply(w,X0),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f496,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(X0,X1))),X1) = apply(apply(w,apply(apply(w,X0),X1)),X1)
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f372,f14]) ).
fof(f57477,plain,
( spl0_141
| ~ spl0_2
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f492,f371,f13,f57475]) ).
fof(f57475,plain,
( spl0_141
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(w,apply(apply(X0,X1),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f492,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(w,apply(apply(X0,X1),X1)),X1)
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f372,f14]) ).
fof(f57473,plain,
( spl0_140
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f488,f371,f37,f57471]) ).
fof(f57471,plain,
( spl0_140
<=> ! [X0] : apply(apply(w,apply(w,apply(X0,X0))),X0) = apply(apply(w,apply(apply(w,w),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f488,plain,
( ! [X0] : apply(apply(w,apply(w,apply(X0,X0))),X0) = apply(apply(w,apply(apply(w,w),X0)),X0)
| ~ spl0_5
| ~ spl0_19 ),
inference(superposition,[],[f372,f38]) ).
fof(f57469,plain,
( spl0_139
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f485,f371,f37,f57467]) ).
fof(f57467,plain,
( spl0_139
<=> ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(w,apply(apply(X0,X0),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f485,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(w,apply(apply(X0,X0),X0)),X0)
| ~ spl0_5
| ~ spl0_19 ),
inference(superposition,[],[f372,f38]) ).
fof(f57465,plain,
( spl0_138
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f440,f367,f108,f57463]) ).
fof(f57463,plain,
( spl0_138
<=> ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(apply(w,apply(X0,X0)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f367,plain,
( spl0_18
<=> ! [X0] : apply(apply(apply(w,w),X0),X0) = apply(apply(w,apply(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f440,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,w))),X0) = apply(apply(apply(w,apply(X0,X0)),X0),X0)
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f109,f368]) ).
fof(f368,plain,
( ! [X0] : apply(apply(apply(w,w),X0),X0) = apply(apply(w,apply(X0,X0)),X0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f57461,plain,
( spl0_137
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f397,f363,f108,f57459]) ).
fof(f57459,plain,
( spl0_137
<=> ! [X0] : apply(apply(w,apply(w,apply(X0,X0))),X0) = apply(apply(apply(w,apply(w,w)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f363,plain,
( spl0_17
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(X0,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f397,plain,
( ! [X0] : apply(apply(w,apply(w,apply(X0,X0))),X0) = apply(apply(apply(w,apply(w,w)),X0),X0)
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f109,f364]) ).
fof(f364,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(X0,X0),X0),X0)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f57457,plain,
( spl0_136
| ~ spl0_2
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f53722,f31111,f13,f57455]) ).
fof(f57455,plain,
( spl0_136
<=> ! [X0] : apply(X0,apply(X0,apply(X0,X0))) = apply(X0,apply(apply(w,apply(w,b)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f31111,plain,
( spl0_109
<=> ! [X0,X1] : apply(X0,apply(X0,apply(X0,X1))) = apply(X0,apply(apply(apply(w,b),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f53722,plain,
( ! [X0] : apply(X0,apply(X0,apply(X0,X0))) = apply(X0,apply(apply(w,apply(w,b)),X0))
| ~ spl0_2
| ~ spl0_109 ),
inference(superposition,[],[f31112,f14]) ).
fof(f31112,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X0,X1))) = apply(X0,apply(apply(apply(w,b),X0),X1))
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f31111]) ).
fof(f57453,plain,
( spl0_135
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f361,f295,f108,f21,f57450]) ).
fof(f57450,plain,
( spl0_135
<=> apply(apply(w,apply(w,apply(w,apply(w,w)))),b) = apply(apply(b,b),apply(b,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f295,plain,
( spl0_16
<=> apply(b,apply(b,b)) = apply(apply(w,apply(w,w)),b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f361,plain,
( apply(apply(w,apply(w,apply(w,apply(w,w)))),b) = apply(apply(b,b),apply(b,b))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f358,f22]) ).
fof(f358,plain,
( apply(apply(w,apply(w,apply(w,apply(w,w)))),b) = apply(apply(apply(b,apply(b,b)),b),b)
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f109,f297]) ).
fof(f297,plain,
( apply(b,apply(b,b)) = apply(apply(w,apply(w,w)),b)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f57448,plain,
( spl0_134
| ~ spl0_2
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f338,f291,f13,f57446]) ).
fof(f57446,plain,
( spl0_134
<=> ! [X0] : apply(apply(apply(w,apply(w,b)),X0),apply(X0,X0)) = apply(apply(w,X0),apply(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f338,plain,
( ! [X0] : apply(apply(apply(w,apply(w,b)),X0),apply(X0,X0)) = apply(apply(w,X0),apply(X0,X0))
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f14,f292]) ).
fof(f57444,plain,
( spl0_133
| ~ spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f337,f291,f51,f57442]) ).
fof(f57442,plain,
( spl0_133
<=> ! [X0] : apply(apply(apply(w,b),X0),apply(X0,X0)) = apply(X0,apply(apply(w,apply(w,b)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f337,plain,
( ! [X0] : apply(apply(apply(w,b),X0),apply(X0,X0)) = apply(X0,apply(apply(w,apply(w,b)),X0))
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f52,f292]) ).
fof(f57440,plain,
( spl0_132
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f302,f270,f55,f57438]) ).
fof(f57438,plain,
( spl0_132
<=> ! [X0] : apply(b,apply(b,apply(X0,X0))) = apply(apply(w,apply(b,apply(apply(w,w),b))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f302,plain,
( ! [X0] : apply(b,apply(b,apply(X0,X0))) = apply(apply(w,apply(b,apply(apply(w,w),b))),X0)
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f271,f56]) ).
fof(f50126,plain,
( spl0_131
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f287,f274,f185,f50124]) ).
fof(f50124,plain,
( spl0_131
<=> ! [X0] : apply(apply(w,apply(apply(b,X0),apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(apply(b,X0),strong_fixed_point)),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f274,plain,
( spl0_14
<=> apply(apply(w,apply(b,apply(w,w))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f287,plain,
( ! [X0] : apply(apply(w,apply(apply(b,X0),apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(apply(b,X0),strong_fixed_point)),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f280,f186]) ).
fof(f280,plain,
( ! [X0] : apply(apply(w,apply(apply(b,X0),apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(X0,apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f186,f276]) ).
fof(f276,plain,
( apply(apply(w,apply(b,apply(w,w))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f50122,plain,
( spl0_130
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f282,f274,f51,f50119]) ).
fof(f50119,plain,
( spl0_130
<=> apply(apply(apply(w,b),apply(w,apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(b,apply(w,w))),apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f282,plain,
( apply(apply(apply(w,b),apply(w,apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(b,apply(w,w))),apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b))))
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f52,f276]) ).
fof(f49764,plain,
( spl0_129
| ~ spl0_19
| ~ spl0_22
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f4804,f1100,f661,f371,f49762]) ).
fof(f49762,plain,
( spl0_129
<=> ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(apply(w,w),apply(b,w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1100,plain,
( spl0_47
<=> ! [X0,X1] : apply(apply(X0,apply(X1,X1)),X1) = apply(apply(w,apply(apply(b,w),apply(b,X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f4804,plain,
( ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(apply(w,w),apply(b,w)),X0)
| ~ spl0_19
| ~ spl0_22
| ~ spl0_47 ),
inference(forward_demodulation,[],[f4636,f662]) ).
fof(f4636,plain,
( ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(w,apply(apply(b,w),apply(b,w))),X0)
| ~ spl0_19
| ~ spl0_47 ),
inference(superposition,[],[f1101,f372]) ).
fof(f1101,plain,
( ! [X0,X1] : apply(apply(X0,apply(X1,X1)),X1) = apply(apply(w,apply(apply(b,w),apply(b,X0))),X1)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f49490,plain,
( spl0_128
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f288,f274,f108,f49487]) ).
fof(f49487,plain,
( spl0_128
<=> apply(apply(w,apply(w,apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(w,strong_fixed_point)),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f288,plain,
( apply(apply(w,apply(w,apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,apply(w,strong_fixed_point)),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f281,f109]) ).
fof(f281,plain,
( apply(apply(w,apply(w,apply(w,apply(b,apply(w,w))))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f109,f276]) ).
fof(f49485,plain,
( spl0_127
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f286,f274,f185,f49482]) ).
fof(f49482,plain,
( spl0_127
<=> apply(apply(w,apply(apply(b,apply(w,apply(b,apply(w,w)))),apply(b,apply(b,w)))),apply(apply(w,w),b)) = apply(apply(w,apply(apply(b,strong_fixed_point),apply(b,apply(b,w)))),apply(apply(w,w),b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f286,plain,
( apply(apply(w,apply(apply(b,apply(w,apply(b,apply(w,w)))),apply(b,apply(b,w)))),apply(apply(w,w),b)) = apply(apply(w,apply(apply(b,strong_fixed_point),apply(b,apply(b,w)))),apply(apply(w,w),b))
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f279,f186]) ).
fof(f279,plain,
( apply(apply(w,apply(apply(b,apply(w,apply(b,apply(w,w)))),apply(b,apply(b,w)))),apply(apply(w,w),b)) = apply(apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b))),apply(apply(w,w),b))
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f186,f276]) ).
fof(f49480,plain,
( spl0_126
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f267,f260,f108,f49478]) ).
fof(f49478,plain,
( spl0_126
<=> ! [X0] : apply(apply(w,apply(w,apply(w,w))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0)))),apply(apply(b,w),apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f267,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,w))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0)))),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f109,f261]) ).
fof(f49226,plain,
( spl0_125
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f209,f185,f29,f49224]) ).
fof(f49224,plain,
( spl0_125
<=> ! [X0] : apply(apply(w,apply(apply(b,X0),apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(X0,strong_fixed_point),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f209,plain,
( ! [X0] : apply(apply(w,apply(apply(b,X0),apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(X0,strong_fixed_point),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f186,f31]) ).
fof(f48735,plain,
( spl0_124
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f264,f260,f112,f48733]) ).
fof(f48733,plain,
( spl0_124
<=> ! [X0] : apply(apply(w,apply(w,apply(apply(b,w),apply(b,apply(b,X0))))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f112,plain,
( spl0_9
<=> ! [X0,X1] : apply(apply(apply(w,X0),X1),X1) = apply(apply(w,apply(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f264,plain,
( ! [X0] : apply(apply(w,apply(w,apply(apply(b,w),apply(b,apply(b,X0))))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_9
| ~ spl0_12 ),
inference(superposition,[],[f113,f261]) ).
fof(f113,plain,
( ! [X0,X1] : apply(apply(apply(w,X0),X1),X1) = apply(apply(w,apply(X0,X1)),X1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f48731,plain,
( spl0_123
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f149,f108,f29,f13,f48728]) ).
fof(f48728,plain,
( spl0_123
<=> apply(apply(w,apply(w,apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,strong_fixed_point),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f149,plain,
( apply(apply(w,apply(w,apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(w,strong_fixed_point),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f123,f14]) ).
fof(f123,plain,
( apply(apply(w,apply(w,apply(b,apply(w,w)))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b))),apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f109,f31]) ).
fof(f48726,plain,
( spl0_122
| ~ spl0_22
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f4658,f1100,f661,f48724]) ).
fof(f48724,plain,
( spl0_122
<=> ! [X0] : apply(apply(w,apply(X0,X0)),X0) = apply(apply(apply(w,w),apply(b,w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f4658,plain,
( ! [X0] : apply(apply(w,apply(X0,X0)),X0) = apply(apply(apply(w,w),apply(b,w)),X0)
| ~ spl0_22
| ~ spl0_47 ),
inference(superposition,[],[f1101,f662]) ).
fof(f48107,plain,
( spl0_121
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f266,f260,f185,f48105]) ).
fof(f48105,plain,
( spl0_121
<=> ! [X0,X1] : apply(apply(w,apply(apply(b,X1),apply(w,w))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(X1,apply(strong_fixed_point,X0)),apply(apply(b,w),apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f266,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(b,X1),apply(w,w))),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(X1,apply(strong_fixed_point,X0)),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f186,f261]) ).
fof(f43689,plain,
( spl0_120
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f268,f260,f13,f43687]) ).
fof(f43687,plain,
( spl0_120
<=> ! [X0] : apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(w,apply(w,w)),apply(apply(b,w),apply(b,apply(b,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f268,plain,
( ! [X0] : apply(apply(strong_fixed_point,X0),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(apply(w,apply(w,w)),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f14,f261]) ).
fof(f43685,plain,
( spl0_119
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f231,f185,f51,f43683]) ).
fof(f43683,plain,
( spl0_119
<=> ! [X2,X0,X1] : apply(apply(apply(w,b),apply(w,apply(apply(b,X0),X1))),X2) = apply(apply(w,apply(apply(b,X0),X1)),apply(apply(X0,apply(X1,X2)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f231,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,b),apply(w,apply(apply(b,X0),X1))),X2) = apply(apply(w,apply(apply(b,X0),X1)),apply(apply(X0,apply(X1,X2)),X2))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f52,f186]) ).
fof(f43178,plain,
( spl0_118
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f221,f185,f43176]) ).
fof(f43176,plain,
( spl0_118
<=> ! [X0,X3,X2,X1] : apply(apply(apply(w,apply(apply(b,X0),X1)),apply(X2,X3)),X3) = apply(apply(w,apply(apply(b,apply(X0,apply(X1,apply(X2,X3)))),X2)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f221,plain,
( ! [X2,X3,X0,X1] : apply(apply(apply(w,apply(apply(b,X0),X1)),apply(X2,X3)),X3) = apply(apply(w,apply(apply(b,apply(X0,apply(X1,apply(X2,X3)))),X2)),X3)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f43174,plain,
( spl0_117
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f220,f185,f43172]) ).
fof(f43172,plain,
( spl0_117
<=> ! [X0,X3,X2,X1] : apply(apply(w,apply(apply(b,apply(w,apply(apply(b,X0),X1))),X2)),X3) = apply(apply(apply(X0,apply(X1,apply(X2,X3))),apply(X2,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f220,plain,
( ! [X2,X3,X0,X1] : apply(apply(w,apply(apply(b,apply(w,apply(apply(b,X0),X1))),X2)),X3) = apply(apply(apply(X0,apply(X1,apply(X2,X3))),apply(X2,X3)),X3)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f43170,plain,
( spl0_116
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f212,f185,f29,f43167]) ).
fof(f43167,plain,
( spl0_116
<=> apply(apply(w,apply(apply(b,apply(b,apply(w,w))),apply(b,apply(b,w)))),apply(apply(w,w),b)) = apply(strong_fixed_point,apply(apply(w,w),b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f212,plain,
( apply(apply(w,apply(apply(b,apply(b,apply(w,w))),apply(b,apply(b,w)))),apply(apply(w,w),b)) = apply(strong_fixed_point,apply(apply(w,w),b))
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f186,f31]) ).
fof(f43165,plain,
( spl0_115
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f63,f51,f29,f43162]) ).
fof(f43162,plain,
( spl0_115
<=> apply(apply(apply(w,b),apply(b,apply(w,w))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(b,apply(w,w)),strong_fixed_point) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f63,plain,
( apply(apply(apply(w,b),apply(b,apply(w,w))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(apply(b,apply(w,w)),strong_fixed_point)
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f52,f31]) ).
fof(f38775,plain,
( spl0_114
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f265,f260,f185,f38773]) ).
fof(f38773,plain,
( spl0_114
<=> ! [X0] : apply(apply(w,apply(apply(b,apply(w,w)),apply(b,w))),apply(b,apply(b,X0))) = apply(apply(strong_fixed_point,X0),apply(b,apply(b,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f265,plain,
( ! [X0] : apply(apply(w,apply(apply(b,apply(w,w)),apply(b,w))),apply(b,apply(b,X0))) = apply(apply(strong_fixed_point,X0),apply(b,apply(b,X0)))
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f186,f261]) ).
fof(f38771,plain,
( spl0_113
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f240,f185,f51,f38769]) ).
fof(f38769,plain,
( spl0_113
<=> ! [X2,X0,X1] : apply(apply(apply(w,b),apply(X0,apply(X1,X2))),X2) = apply(apply(X0,apply(X1,X2)),apply(apply(w,apply(apply(b,X0),X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f240,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,b),apply(X0,apply(X1,X2))),X2) = apply(apply(X0,apply(X1,X2)),apply(apply(w,apply(apply(b,X0),X1)),X2))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f52,f186]) ).
fof(f38767,plain,
( spl0_112
| ~ spl0_6
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f3016,f1067,f51,f38765]) ).
fof(f38765,plain,
( spl0_112
<=> ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(X0,apply(apply(w,apply(b,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f3016,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(X0,apply(apply(w,apply(b,X0)),X1))
| ~ spl0_6
| ~ spl0_39 ),
inference(superposition,[],[f1068,f52]) ).
fof(f38763,plain,
( spl0_111
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f208,f185,f38761]) ).
fof(f38761,plain,
( spl0_111
<=> ! [X0,X3,X2,X1] : apply(apply(X3,apply(apply(w,apply(apply(b,X0),X1)),X2)),X2) = apply(apply(w,apply(apply(b,X3),apply(X0,apply(X1,X2)))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f208,plain,
( ! [X2,X3,X0,X1] : apply(apply(X3,apply(apply(w,apply(apply(b,X0),X1)),X2)),X2) = apply(apply(w,apply(apply(b,X3),apply(X0,apply(X1,X2)))),X2)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f38759,plain,
( spl0_110
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f207,f185,f38757]) ).
fof(f38757,plain,
( spl0_110
<=> ! [X0,X3,X2,X1] : apply(apply(w,apply(apply(b,X3),apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(X3,apply(apply(X0,apply(X1,X2)),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] : apply(apply(w,apply(apply(b,X3),apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(X3,apply(apply(X0,apply(X1,X2)),X2)),X2)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f31113,plain,
( spl0_109
| ~ spl0_6
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1504,f1020,f51,f31111]) ).
fof(f1020,plain,
( spl0_31
<=> ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X0,X1)) = apply(X0,apply(apply(apply(w,b),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1504,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X0,X1))) = apply(X0,apply(apply(apply(w,b),X0),X1))
| ~ spl0_6
| ~ spl0_31 ),
inference(superposition,[],[f1021,f52]) ).
fof(f1021,plain,
( ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X0,X1)) = apply(X0,apply(apply(apply(w,b),X0),X1))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f26662,plain,
( spl0_108
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f253,f185,f112,f108,f13,f26660]) ).
fof(f26660,plain,
( spl0_108
<=> ! [X2,X0,X1] : apply(apply(w,apply(w,apply(X0,apply(X1,X2)))),X2) = apply(apply(apply(w,apply(w,apply(apply(b,X0),X1))),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f253,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(X0,apply(X1,X2)))),X2) = apply(apply(apply(w,apply(w,apply(apply(b,X0),X1))),X2),X2)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f252,f135]) ).
fof(f135,plain,
( ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(X0,X1)),X1)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f109,f14]) ).
fof(f252,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(X0,apply(X1,X2)))),X2) = apply(apply(apply(w,apply(apply(apply(b,X0),X1),X2)),X2),X2)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f239,f113]) ).
fof(f239,plain,
( ! [X2,X0,X1] : apply(apply(apply(apply(w,apply(apply(b,X0),X1)),X2),X2),X2) = apply(apply(w,apply(w,apply(X0,apply(X1,X2)))),X2)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f109,f186]) ).
fof(f26658,plain,
( spl0_107
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f250,f185,f108,f13,f26656]) ).
fof(f26656,plain,
( spl0_107
<=> ! [X2,X0,X1] : apply(apply(w,apply(w,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(apply(w,apply(X0,apply(X1,X2))),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f250,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(apply(w,apply(X0,apply(X1,X2))),X2),X2)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f230,f14]) ).
fof(f230,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(apply(apply(X0,apply(X1,X2)),X2),X2),X2)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f109,f186]) ).
fof(f26654,plain,
( spl0_106
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f228,f185,f55,f26652]) ).
fof(f26652,plain,
( spl0_106
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),apply(X2,X2)) = apply(apply(w,apply(b,apply(X0,apply(X1,apply(X2,X2))))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f228,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),apply(X2,X2)) = apply(apply(w,apply(b,apply(X0,apply(X1,apply(X2,X2))))),X2)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f26650,plain,
( spl0_105
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f214,f185,f55,f26648]) ).
fof(f26648,plain,
( spl0_105
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(w,apply(b,X0))),X1)),X2) = apply(apply(X0,apply(apply(X1,X2),apply(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f214,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(w,apply(b,X0))),X1)),X2) = apply(apply(X0,apply(apply(X1,X2),apply(X1,X2))),X2)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f26398,plain,
( spl0_104
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f213,f185,f37,f26396]) ).
fof(f26396,plain,
( spl0_104
<=> ! [X0,X1] : apply(apply(apply(w,w),apply(X0,X1)),X1) = apply(apply(w,apply(apply(b,apply(apply(X0,X1),apply(X0,X1))),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f213,plain,
( ! [X0,X1] : apply(apply(apply(w,w),apply(X0,X1)),X1) = apply(apply(w,apply(apply(b,apply(apply(X0,X1),apply(X0,X1))),X0)),X1)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f186,f38]) ).
fof(f26394,plain,
( spl0_103
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f211,f185,f55,f26392]) ).
fof(f26392,plain,
( spl0_103
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),X0)),apply(X1,X1)) = apply(apply(X2,apply(apply(w,apply(b,X0)),X1)),apply(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f211,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),X0)),apply(X1,X1)) = apply(apply(X2,apply(apply(w,apply(b,X0)),X1)),apply(X1,X1))
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f26390,plain,
( spl0_102
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f210,f185,f51,f26388]) ).
fof(f26388,plain,
( spl0_102
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),X0)),apply(X0,X1)) = apply(apply(X2,apply(apply(apply(w,b),X0),X1)),apply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f210,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),X0)),apply(X0,X1)) = apply(apply(X2,apply(apply(apply(w,b),X0),X1)),apply(X0,X1))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f186,f52]) ).
fof(f26386,plain,
( spl0_101
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f205,f185,f112,f26384]) ).
fof(f26384,plain,
( spl0_101
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(w,X0),X1))),X1) = apply(apply(X2,apply(apply(w,apply(X0,X1)),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f205,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(w,X0),X1))),X1) = apply(apply(X2,apply(apply(w,apply(X0,X1)),X1)),X1)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f186,f113]) ).
fof(f26382,plain,
( spl0_100
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f204,f185,f108,f26380]) ).
fof(f26380,plain,
( spl0_100
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(X0,X1),X1))),X1) = apply(apply(X2,apply(apply(w,apply(w,X0)),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f204,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(X0,X1),X1))),X1) = apply(apply(X2,apply(apply(w,apply(w,X0)),X1)),X1)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f186,f109]) ).
fof(f26378,plain,
( spl0_99
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f197,f185,f55,f26376]) ).
fof(f197,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(b,apply(w,apply(apply(b,X0),X1)))),X2) = apply(apply(X0,apply(X1,apply(X2,X2))),apply(X2,X2))
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f26374,plain,
( spl0_98
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f175,f112,f51,f26372]) ).
fof(f26372,plain,
( spl0_98
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,X0),X1)),X1) = apply(apply(apply(w,X0),X1),apply(apply(w,apply(X0,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f175,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,X0),X1)),X1) = apply(apply(apply(w,X0),X1),apply(apply(w,apply(X0,X1)),X1))
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f52,f113]) ).
fof(f26370,plain,
( spl0_97
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f141,f108,f51,f26368]) ).
fof(f26368,plain,
( spl0_97
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(apply(X0,X1),X1)),X1) = apply(apply(apply(X0,X1),X1),apply(apply(w,apply(w,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f141,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(apply(X0,X1),X1)),X1) = apply(apply(apply(X0,X1),X1),apply(apply(w,apply(w,X0)),X1))
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f52,f109]) ).
fof(f26366,plain,
( spl0_96
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f77,f51,f37,f26364]) ).
fof(f26364,plain,
( spl0_96
<=> ! [X0] : apply(apply(w,w),apply(apply(w,b),X0)) = apply(apply(X0,apply(X0,apply(apply(w,b),X0))),apply(apply(w,b),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f77,plain,
( ! [X0] : apply(apply(w,w),apply(apply(w,b),X0)) = apply(apply(X0,apply(X0,apply(apply(w,b),X0))),apply(apply(w,b),X0))
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f38,f52]) ).
fof(f26362,plain,
( spl0_95
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f41,f37,f21,f26360]) ).
fof(f41,plain,
( ! [X0,X1] : apply(apply(w,w),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,apply(apply(b,X0),X1))),apply(apply(b,X0),X1))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f38,f22]) ).
fof(f18572,plain,
( spl0_94
| ~ spl0_19
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f862,f669,f371,f18570]) ).
fof(f18570,plain,
( spl0_94
<=> ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(w,apply(w,apply(b,w))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f862,plain,
( ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(w,apply(w,apply(b,w))),X0)
| ~ spl0_19
| ~ spl0_24 ),
inference(superposition,[],[f670,f372]) ).
fof(f13354,plain,
( spl0_93
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f263,f260,f55,f13352]) ).
fof(f13352,plain,
( spl0_93
<=> ! [X0] : apply(strong_fixed_point,apply(X0,X0)) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(apply(w,apply(b,b)),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f263,plain,
( ! [X0] : apply(strong_fixed_point,apply(X0,X0)) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(apply(w,apply(b,b)),X0))))
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f261,f56]) ).
fof(f13350,plain,
( spl0_92
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f860,f669,f375,f13348]) ).
fof(f13348,plain,
( spl0_92
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(w,apply(b,w))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f375,plain,
( spl0_20
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f860,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(w,apply(b,w))),X0)
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f670,f376]) ).
fof(f376,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(X0,X0)),X0)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f13346,plain,
( spl0_91
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f245,f185,f51,f21,f13344]) ).
fof(f13344,plain,
( spl0_91
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(apply(w,b),apply(b,X0)),X1)),X2) = apply(apply(X0,apply(X0,apply(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f245,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(apply(w,b),apply(b,X0)),X1)),X2) = apply(apply(X0,apply(X0,apply(X1,X2))),X2)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f193,f22]) ).
fof(f193,plain,
( ! [X2,X0,X1] : apply(apply(X0,apply(apply(apply(b,X0),X1),X2)),X2) = apply(apply(w,apply(apply(apply(w,b),apply(b,X0)),X1)),X2)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f186,f52]) ).
fof(f13342,plain,
( spl0_90
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f219,f185,f21,f13340]) ).
fof(f13340,plain,
( spl0_90
<=> ! [X0,X3,X2,X1] : apply(apply(w,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3) = apply(apply(X0,apply(X1,apply(X2,X3))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f219,plain,
( ! [X2,X3,X0,X1] : apply(apply(w,apply(apply(b,apply(apply(b,X0),X1)),X2)),X3) = apply(apply(X0,apply(X1,apply(X2,X3))),X3)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f186,f22]) ).
fof(f13338,plain,
( spl0_89
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f216,f185,f51,f13336]) ).
fof(f13336,plain,
( spl0_89
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(apply(w,b),X0)),X1)),X2) = apply(apply(X0,apply(X0,apply(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f216,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(apply(w,b),X0)),X1)),X2) = apply(apply(X0,apply(X0,apply(X1,X2))),X2)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f186,f52]) ).
fof(f13334,plain,
( spl0_88
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f215,f185,f13,f13332]) ).
fof(f13332,plain,
( spl0_88
<=> ! [X2,X0,X1] : apply(apply(apply(w,X0),apply(X1,X2)),X2) = apply(apply(w,apply(apply(b,apply(X0,apply(X1,X2))),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f215,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,X0),apply(X1,X2)),X2) = apply(apply(w,apply(apply(b,apply(X0,apply(X1,X2))),X1)),X2)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f186,f14]) ).
fof(f13330,plain,
( spl0_87
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f206,f185,f21,f13328]) ).
fof(f13328,plain,
( spl0_87
<=> ! [X0,X3,X2,X1] : apply(apply(w,apply(apply(b,X3),apply(apply(b,X0),X1))),X2) = apply(apply(X3,apply(X0,apply(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f206,plain,
( ! [X2,X3,X0,X1] : apply(apply(w,apply(apply(b,X3),apply(apply(b,X0),X1))),X2) = apply(apply(X3,apply(X0,apply(X1,X2))),X2)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f186,f22]) ).
fof(f13326,plain,
( spl0_86
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f203,f185,f51,f13324]) ).
fof(f13324,plain,
( spl0_86
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(w,b),X0))),X1) = apply(apply(X2,apply(X0,apply(X0,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f203,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(apply(w,b),X0))),X1) = apply(apply(X2,apply(X0,apply(X0,X1))),X1)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f186,f52]) ).
fof(f13322,plain,
( spl0_85
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f201,f185,f55,f13320]) ).
fof(f13320,plain,
( spl0_85
<=> ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(w,apply(b,X0)))),X1) = apply(apply(X2,apply(X0,apply(X1,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f201,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(w,apply(b,X0)))),X1) = apply(apply(X2,apply(X0,apply(X1,X1))),X1)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f13318,plain,
( spl0_84
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f194,f185,f55,f13316]) ).
fof(f13316,plain,
( spl0_84
<=> ! [X2,X0,X1] : apply(apply(X0,apply(apply(X1,X1),X2)),X2) = apply(apply(w,apply(apply(w,apply(b,apply(b,X0))),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f194,plain,
( ! [X2,X0,X1] : apply(apply(X0,apply(apply(X1,X1),X2)),X2) = apply(apply(w,apply(apply(w,apply(b,apply(b,X0))),X1)),X2)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f13314,plain,
( spl0_83
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f191,f185,f13312]) ).
fof(f13312,plain,
( spl0_83
<=> ! [X2,X0,X1] : apply(apply(apply(X0,X1),apply(X1,X2)),X2) = apply(apply(w,apply(apply(w,apply(apply(b,b),X0)),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f191,plain,
( ! [X2,X0,X1] : apply(apply(apply(X0,X1),apply(X1,X2)),X2) = apply(apply(w,apply(apply(w,apply(apply(b,b),X0)),X1)),X2)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f13310,plain,
( spl0_82
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f188,f185,f55,f13308]) ).
fof(f13308,plain,
( spl0_82
<=> ! [X2,X0,X1] : apply(apply(apply(X0,X0),apply(X1,X2)),X2) = apply(apply(w,apply(apply(apply(w,apply(b,b)),X0),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f188,plain,
( ! [X2,X0,X1] : apply(apply(apply(X0,X0),apply(X1,X2)),X2) = apply(apply(w,apply(apply(apply(w,apply(b,b)),X0),X1)),X2)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f13306,plain,
( spl0_81
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f770,f665,f371,f13304]) ).
fof(f13304,plain,
( spl0_81
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(apply(w,b),w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f770,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(apply(w,b),w)),X0)
| ~ spl0_19
| ~ spl0_23 ),
inference(superposition,[],[f666,f372]) ).
fof(f13302,plain,
( spl0_80
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f181,f112,f108,f13300]) ).
fof(f13300,plain,
( spl0_80
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,X0),X1))),X1) = apply(apply(w,apply(w,apply(w,apply(X0,X1)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f181,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,X0),X1))),X1) = apply(apply(w,apply(w,apply(w,apply(X0,X1)))),X1)
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f174,f109]) ).
fof(f174,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,X0),X1))),X1) = apply(apply(apply(apply(w,apply(X0,X1)),X1),X1),X1)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f109,f113]) ).
fof(f13298,plain,
( spl0_79
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f148,f108,f13296]) ).
fof(f13296,plain,
( spl0_79
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(apply(X0,X1),X1))),X1) = apply(apply(w,apply(w,apply(w,apply(w,X0)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f148,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(X0,X1),X1))),X1) = apply(apply(w,apply(w,apply(w,apply(w,X0)))),X1)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f121,f109]) ).
fof(f121,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(X0,X1),X1))),X1) = apply(apply(apply(apply(w,apply(w,X0)),X1),X1),X1)
| ~ spl0_8 ),
inference(superposition,[],[f109,f109]) ).
fof(f13294,plain,
( spl0_78
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f94,f55,f51,f13292]) ).
fof(f13292,plain,
( spl0_78
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(w,apply(b,X0))),X1) = apply(apply(w,apply(b,X0)),apply(X0,apply(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f94,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(w,apply(b,X0))),X1) = apply(apply(w,apply(b,X0)),apply(X0,apply(X1,X1)))
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f52,f56]) ).
fof(f13290,plain,
( spl0_77
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f85,f55,f21,f13288]) ).
fof(f13288,plain,
( spl0_77
<=> ! [X2,X0,X1] : apply(apply(w,apply(b,X2)),apply(apply(b,X0),X1)) = apply(X2,apply(X0,apply(X1,apply(apply(b,X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f85,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(b,X2)),apply(apply(b,X0),X1)) = apply(X2,apply(X0,apply(X1,apply(apply(b,X0),X1))))
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f56,f22]) ).
fof(f13286,plain,
( spl0_76
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f84,f55,f51,f13284]) ).
fof(f13284,plain,
( spl0_76
<=> ! [X0,X1] : apply(apply(w,apply(b,X1)),apply(apply(w,b),X0)) = apply(X1,apply(X0,apply(X0,apply(apply(w,b),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f84,plain,
( ! [X0,X1] : apply(apply(w,apply(b,X1)),apply(apply(w,b),X0)) = apply(X1,apply(X0,apply(X0,apply(apply(w,b),X0))))
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f56,f52]) ).
fof(f13282,plain,
( spl0_75
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f65,f51,f13280]) ).
fof(f13280,plain,
( spl0_75
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,b),X0)),X1) = apply(X0,apply(X0,apply(apply(apply(w,b),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f65,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,b),X0)),X1) = apply(X0,apply(X0,apply(apply(apply(w,b),X0),X1)))
| ~ spl0_6 ),
inference(superposition,[],[f52,f52]) ).
fof(f13278,plain,
( spl0_74
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f62,f51,f21,f13276]) ).
fof(f13276,plain,
( spl0_74
<=> ! [X2,X0,X1] : apply(apply(apply(w,b),apply(apply(b,X0),X1)),X2) = apply(apply(apply(b,X0),X1),apply(X0,apply(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f62,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,b),apply(apply(b,X0),X1)),X2) = apply(apply(apply(b,X0),X1),apply(X0,apply(X1,X2)))
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f52,f22]) ).
fof(f13274,plain,
( spl0_73
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f61,f51,f13272]) ).
fof(f13272,plain,
( spl0_73
<=> ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,b),X0)),X1) = apply(apply(apply(w,b),X0),apply(X0,apply(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f61,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(apply(w,b),X0)),X1) = apply(apply(apply(w,b),X0),apply(X0,apply(X0,X1)))
| ~ spl0_6 ),
inference(superposition,[],[f52,f52]) ).
fof(f12492,plain,
( spl0_72
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f723,f661,f375,f185,f12490]) ).
fof(f12490,plain,
( spl0_72
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(w,w),apply(b,w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f723,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(w,w),apply(b,w)),X0)
| ~ spl0_10
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f708,f559]) ).
fof(f559,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(apply(b,w),X0)),X0)
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f376,f186]) ).
fof(f708,plain,
( ! [X0] : apply(apply(w,apply(apply(b,w),X0)),X0) = apply(apply(apply(w,w),apply(b,w)),X0)
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f186,f662]) ).
fof(f8257,plain,
( spl0_71
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f559,f375,f185,f8255]) ).
fof(f8255,plain,
( spl0_71
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(apply(b,w),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f6073,plain,
( spl0_70
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f241,f185,f13,f6071]) ).
fof(f6071,plain,
( spl0_70
<=> ! [X2,X0,X1] : apply(apply(w,apply(X0,apply(X1,X2))),X2) = apply(apply(apply(w,apply(apply(b,X0),X1)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f241,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(X0,apply(X1,X2))),X2) = apply(apply(apply(w,apply(apply(b,X0),X1)),X2),X2)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f14,f186]) ).
fof(f6069,plain,
( spl0_69
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f225,f185,f51,f6067]) ).
fof(f6067,plain,
( spl0_69
<=> ! [X0,X1] : apply(apply(X0,X1),apply(apply(X0,X1),X1)) = apply(apply(w,apply(apply(b,apply(w,b)),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f225,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(apply(X0,X1),X1)) = apply(apply(w,apply(apply(b,apply(w,b)),X0)),X1)
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f186,f52]) ).
fof(f6065,plain,
( spl0_68
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f202,f185,f13,f6063]) ).
fof(f6063,plain,
( spl0_68
<=> ! [X2,X0,X1] : apply(apply(X2,apply(apply(w,X0),X1)),X1) = apply(apply(w,apply(apply(b,X2),apply(X0,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f202,plain,
( ! [X2,X0,X1] : apply(apply(X2,apply(apply(w,X0),X1)),X1) = apply(apply(w,apply(apply(b,X2),apply(X0,X1))),X1)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f186,f14]) ).
fof(f6061,plain,
( spl0_67
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f200,f185,f13,f6059]) ).
fof(f200,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X2),apply(w,X0))),X1) = apply(apply(X2,apply(apply(X0,X1),X1)),X1)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f186,f14]) ).
fof(f6057,plain,
( spl0_66
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f199,f185,f37,f6055]) ).
fof(f6055,plain,
( spl0_66
<=> ! [X0,X1] : apply(apply(X1,apply(apply(w,w),X0)),X0) = apply(apply(w,apply(apply(b,X1),apply(X0,X0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f199,plain,
( ! [X0,X1] : apply(apply(X1,apply(apply(w,w),X0)),X0) = apply(apply(w,apply(apply(b,X1),apply(X0,X0))),X0)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f186,f38]) ).
fof(f6053,plain,
( spl0_65
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f554,f375,f55,f6051]) ).
fof(f6051,plain,
( spl0_65
<=> ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(w,apply(b,w)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f554,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(w,apply(b,w)),X0),X0)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f376,f56]) ).
fof(f6049,plain,
( spl0_64
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f198,f185,f37,f6047]) ).
fof(f198,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(b,X1),apply(w,w))),X0) = apply(apply(X1,apply(apply(X0,X0),X0)),X0)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f186,f38]) ).
fof(f6045,plain,
( spl0_63
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f195,f185,f55,f6043]) ).
fof(f6043,plain,
( spl0_63
<=> ! [X0,X1] : apply(apply(X0,apply(apply(b,X0),X1)),X1) = apply(apply(apply(w,apply(b,w)),apply(b,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f195,plain,
( ! [X0,X1] : apply(apply(X0,apply(apply(b,X0),X1)),X1) = apply(apply(apply(w,apply(b,w)),apply(b,X0)),X1)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f6041,plain,
( spl0_62
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f157,f112,f55,f6039]) ).
fof(f6039,plain,
( spl0_62
<=> ! [X0,X1] : apply(apply(w,apply(apply(X0,X0),X1)),X1) = apply(apply(apply(apply(w,apply(b,w)),X0),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f157,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(X0,X0),X1)),X1) = apply(apply(apply(apply(w,apply(b,w)),X0),X1),X1)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f113,f56]) ).
fof(f6037,plain,
( spl0_61
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f122,f108,f21,f6035]) ).
fof(f122,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(w,apply(apply(b,X0),X1))),X2) = apply(apply(apply(X0,apply(X1,X2)),X2),X2)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f109,f22]) ).
fof(f6033,plain,
( spl0_60
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f120,f108,f51,f6031]) ).
fof(f120,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(apply(w,b),X0))),X1) = apply(apply(apply(X0,apply(X0,X1)),X1),X1)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f109,f52]) ).
fof(f6029,plain,
( spl0_59
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f118,f108,f55,f6027]) ).
fof(f6027,plain,
( spl0_59
<=> ! [X0,X1] : apply(apply(w,apply(w,apply(w,apply(b,X0)))),X1) = apply(apply(apply(X0,apply(X1,X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f118,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(w,apply(b,X0)))),X1) = apply(apply(apply(X0,apply(X1,X1)),X1),X1)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f109,f56]) ).
fof(f6025,plain,
( spl0_58
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f101,f55,f51,f6023]) ).
fof(f6023,plain,
( spl0_58
<=> ! [X0,X1] : apply(apply(X0,X0),apply(apply(X0,X0),X1)) = apply(apply(apply(w,apply(b,apply(w,b))),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f101,plain,
( ! [X0,X1] : apply(apply(X0,X0),apply(apply(X0,X0),X1)) = apply(apply(apply(w,apply(b,apply(w,b))),X0),X1)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f52,f56]) ).
fof(f6021,plain,
( spl0_57
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f99,f55,f37,f6019]) ).
fof(f6019,plain,
( spl0_57
<=> ! [X0] : apply(apply(w,w),apply(X0,X0)) = apply(apply(apply(w,apply(b,apply(X0,X0))),X0),apply(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f99,plain,
( ! [X0] : apply(apply(w,w),apply(X0,X0)) = apply(apply(apply(w,apply(b,apply(X0,X0))),X0),apply(X0,X0))
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f38,f56]) ).
fof(f6017,plain,
( spl0_56
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f87,f55,f37,f6015]) ).
fof(f6015,plain,
( spl0_56
<=> ! [X0] : apply(apply(w,w),apply(X0,X0)) = apply(apply(w,apply(b,apply(apply(X0,X0),apply(X0,X0)))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f87,plain,
( ! [X0] : apply(apply(w,w),apply(X0,X0)) = apply(apply(w,apply(b,apply(apply(X0,X0),apply(X0,X0)))),X0)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f56,f38]) ).
fof(f6013,plain,
( spl0_55
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f86,f55,f6011]) ).
fof(f6011,plain,
( spl0_55
<=> ! [X0,X1] : apply(apply(w,apply(b,X1)),apply(X0,X0)) = apply(X1,apply(apply(w,apply(b,apply(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f86,plain,
( ! [X0,X1] : apply(apply(w,apply(b,X1)),apply(X0,X0)) = apply(X1,apply(apply(w,apply(b,apply(X0,X0))),X0))
| ~ spl0_7 ),
inference(superposition,[],[f56,f56]) ).
fof(f6009,plain,
( spl0_54
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f536,f371,f185,f13,f6007]) ).
fof(f6007,plain,
( spl0_54
<=> ! [X0] : apply(apply(w,apply(X0,X0)),X0) = apply(apply(w,apply(apply(w,b),w)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f536,plain,
( ! [X0] : apply(apply(w,apply(X0,X0)),X0) = apply(apply(w,apply(apply(w,b),w)),X0)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_demodulation,[],[f484,f14]) ).
fof(f484,plain,
( ! [X0] : apply(apply(w,apply(X0,X0)),X0) = apply(apply(w,apply(apply(b,w),w)),X0)
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f372,f186]) ).
fof(f6005,plain,
( spl0_53
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f83,f55,f6003]) ).
fof(f6003,plain,
( spl0_53
<=> ! [X0,X1] : apply(apply(w,apply(b,apply(w,apply(b,X0)))),X1) = apply(X0,apply(apply(X1,X1),apply(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f83,plain,
( ! [X0,X1] : apply(apply(w,apply(b,apply(w,apply(b,X0)))),X1) = apply(X0,apply(apply(X1,X1),apply(X1,X1)))
| ~ spl0_7 ),
inference(superposition,[],[f56,f56]) ).
fof(f6001,plain,
( spl0_52
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f78,f51,f21,f5999]) ).
fof(f5999,plain,
( spl0_52
<=> ! [X2,X0,X1] : apply(apply(apply(w,b),apply(apply(b,X0),X1)),X2) = apply(X0,apply(X1,apply(X0,apply(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f78,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,b),apply(apply(b,X0),X1)),X2) = apply(X0,apply(X1,apply(X0,apply(X1,X2))))
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f66,f22]) ).
fof(f66,plain,
( ! [X2,X0,X1] : apply(apply(apply(w,b),apply(apply(b,X0),X1)),X2) = apply(X0,apply(X1,apply(apply(apply(b,X0),X1),X2)))
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f52,f22]) ).
fof(f3362,plain,
( spl0_51
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f516,f371,f185,f3360]) ).
fof(f3360,plain,
( spl0_51
<=> ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(apply(b,w),X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f516,plain,
( ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(w,apply(apply(b,w),X0)),X1)
| ~ spl0_10
| ~ spl0_19 ),
inference(superposition,[],[f372,f186]) ).
fof(f1452,plain,
( spl0_50
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f464,f367,f112,f55,f1450]) ).
fof(f1450,plain,
( spl0_50
<=> ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(apply(w,apply(b,w)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f464,plain,
( ! [X0] : apply(apply(w,apply(w,X0)),X0) = apply(apply(apply(w,apply(b,w)),X0),X0)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_demodulation,[],[f434,f113]) ).
fof(f434,plain,
( ! [X0] : apply(apply(apply(w,w),X0),X0) = apply(apply(apply(w,apply(b,w)),X0),X0)
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f368,f56]) ).
fof(f1110,plain,
( spl0_49
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f234,f185,f21,f1108]) ).
fof(f234,plain,
( ! [X2,X0,X1] : apply(apply(X0,X1),apply(X1,X2)) = apply(apply(apply(w,apply(apply(b,b),X0)),X1),X2)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f22,f186]) ).
fof(f1106,plain,
( spl0_48
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f226,f185,f21,f1104]) ).
fof(f226,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X2) = apply(X0,apply(apply(X1,X2),X2))
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f186,f22]) ).
fof(f1102,plain,
( spl0_47
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f196,f185,f1100]) ).
fof(f196,plain,
( ! [X0,X1] : apply(apply(X0,apply(X1,X1)),X1) = apply(apply(w,apply(apply(b,w),apply(b,X0))),X1)
| ~ spl0_10 ),
inference(superposition,[],[f186,f186]) ).
fof(f1098,plain,
( spl0_46
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f172,f112,f108,f1096]) ).
fof(f172,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(w,X0))),X1) = apply(apply(apply(w,apply(X0,X1)),X1),X1)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f109,f113]) ).
fof(f1094,plain,
( spl0_45
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f164,f112,f37,f1092]) ).
fof(f164,plain,
( ! [X0] : apply(apply(w,w),apply(w,X0)) = apply(apply(w,apply(X0,apply(w,X0))),apply(w,X0))
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f113,f38]) ).
fof(f1090,plain,
( spl0_44
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f131,f108,f1088]) ).
fof(f131,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(X0,X1))),X1) = apply(apply(apply(w,apply(w,X0)),X1),X1)
| ~ spl0_8 ),
inference(superposition,[],[f109,f109]) ).
fof(f1086,plain,
( spl0_43
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f104,f55,f21,f1084]) ).
fof(f104,plain,
( ! [X2,X0,X1] : apply(X0,apply(apply(X1,X1),X2)) = apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f22,f56]) ).
fof(f1082,plain,
( spl0_42
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f304,f270,f108,f1079]) ).
fof(f1079,plain,
( spl0_42
<=> apply(apply(w,apply(w,apply(w,w))),b) = apply(apply(b,apply(b,b)),b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f304,plain,
( apply(apply(w,apply(w,apply(w,w))),b) = apply(apply(b,apply(b,b)),b)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f109,f271]) ).
fof(f1077,plain,
( spl0_41
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f100,f55,f21,f1075]) ).
fof(f1075,plain,
( spl0_41
<=> ! [X2,X0,X1] : apply(apply(X0,X0),apply(X1,X2)) = apply(apply(apply(apply(w,apply(b,b)),X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f100,plain,
( ! [X2,X0,X1] : apply(apply(X0,X0),apply(X1,X2)) = apply(apply(apply(apply(w,apply(b,b)),X0),X1),X2)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f22,f56]) ).
fof(f1073,plain,
( spl0_40
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f98,f55,f13,f1071]) ).
fof(f1071,plain,
( spl0_40
<=> ! [X0,X1] : apply(apply(w,X0),apply(X1,X1)) = apply(apply(apply(w,apply(b,X0)),X1),apply(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f98,plain,
( ! [X0,X1] : apply(apply(w,X0),apply(X1,X1)) = apply(apply(apply(w,apply(b,X0)),X1),apply(X1,X1))
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f14,f56]) ).
fof(f1069,plain,
( spl0_39
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f97,f55,f51,f1067]) ).
fof(f97,plain,
( ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X1,X1)) = apply(X0,apply(apply(w,apply(b,X0)),X1))
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f52,f56]) ).
fof(f1065,plain,
( spl0_38
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f91,f55,f21,f1063]) ).
fof(f1063,plain,
( spl0_38
<=> ! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,X2))) = apply(apply(w,apply(b,apply(apply(b,X0),X1))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f91,plain,
( ! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,X2))) = apply(apply(w,apply(b,apply(apply(b,X0),X1))),X2)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f56,f22]) ).
fof(f1061,plain,
( spl0_37
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f90,f55,f51,f1059]) ).
fof(f1059,plain,
( spl0_37
<=> ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(apply(w,apply(b,apply(apply(w,b),X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f90,plain,
( ! [X0,X1] : apply(X0,apply(X0,apply(X1,X1))) = apply(apply(w,apply(b,apply(apply(w,b),X0))),X1)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f56,f52]) ).
fof(f1057,plain,
( spl0_36
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f89,f55,f13,f1055]) ).
fof(f89,plain,
( ! [X0,X1] : apply(apply(w,X0),apply(X1,X1)) = apply(apply(w,apply(b,apply(X0,apply(X1,X1)))),X1)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f56,f14]) ).
fof(f1053,plain,
( spl0_35
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f81,f55,f1051]) ).
fof(f81,plain,
( ! [X0,X1] : apply(apply(X0,X0),apply(X1,X1)) = apply(apply(w,apply(apply(w,apply(b,b)),X0)),X1)
| ~ spl0_7 ),
inference(superposition,[],[f56,f56]) ).
fof(f1049,plain,
( spl0_34
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f79,f51,f21,f1047]) ).
fof(f79,plain,
( ! [X2,X0,X1] : apply(apply(apply(apply(w,b),apply(b,X0)),X1),X2) = apply(X0,apply(X0,apply(X1,X2)))
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f72,f22]) ).
fof(f72,plain,
( ! [X2,X0,X1] : apply(X0,apply(apply(apply(b,X0),X1),X2)) = apply(apply(apply(apply(w,b),apply(b,X0)),X1),X2)
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f22,f52]) ).
fof(f1045,plain,
( spl0_33
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f71,f51,f13,f1043]) ).
fof(f1043,plain,
( spl0_33
<=> ! [X0,X1] : apply(apply(w,X0),apply(X0,X1)) = apply(apply(apply(apply(w,b),X0),X1),apply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f71,plain,
( ! [X0,X1] : apply(apply(w,X0),apply(X0,X1)) = apply(apply(apply(apply(w,b),X0),X1),apply(X0,X1))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f14,f52]) ).
fof(f1041,plain,
( spl0_32
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f68,f51,f37,f1038]) ).
fof(f1038,plain,
( spl0_32
<=> apply(apply(w,w),apply(w,b)) = apply(apply(w,b),apply(apply(w,b),apply(w,b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f68,plain,
( apply(apply(w,w),apply(w,b)) = apply(apply(w,b),apply(apply(w,b),apply(w,b)))
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f52,f38]) ).
fof(f1022,plain,
( spl0_31
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f64,f51,f1020]) ).
fof(f64,plain,
( ! [X0,X1] : apply(apply(apply(w,b),X0),apply(X0,X1)) = apply(X0,apply(apply(apply(w,b),X0),X1))
| ~ spl0_6 ),
inference(superposition,[],[f52,f52]) ).
fof(f1018,plain,
( spl0_30
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f60,f51,f13,f1016]) ).
fof(f60,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(X0,X1)),X1) = apply(apply(X0,X1),apply(apply(w,X0),X1))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f52,f14]) ).
fof(f1014,plain,
( spl0_29
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f59,f51,f13,f1012]) ).
fof(f59,plain,
( ! [X0,X1] : apply(apply(apply(w,b),apply(w,X0)),X1) = apply(apply(w,X0),apply(apply(X0,X1),X1))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f52,f14]) ).
fof(f1010,plain,
( spl0_28
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f58,f51,f37,f1008]) ).
fof(f58,plain,
( ! [X0] : apply(apply(apply(w,b),apply(X0,X0)),X0) = apply(apply(X0,X0),apply(apply(w,w),X0))
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f52,f38]) ).
fof(f684,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f189,f185,f37,f682]) ).
fof(f682,plain,
( spl0_27
<=> ! [X0] : apply(apply(b,apply(b,X0)),X0) = apply(apply(w,apply(apply(w,w),b)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f189,plain,
( ! [X0] : apply(apply(b,apply(b,X0)),X0) = apply(apply(w,apply(apply(w,w),b)),X0)
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f186,f38]) ).
fof(f680,plain,
( spl0_26
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f598,f379,f371,f677]) ).
fof(f677,plain,
( spl0_26
<=> apply(b,apply(b,b)) = apply(apply(w,apply(w,apply(b,w))),b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f598,plain,
( apply(b,apply(b,b)) = apply(apply(w,apply(w,apply(b,w))),b)
| ~ spl0_19
| ~ spl0_21 ),
inference(superposition,[],[f380,f372]) ).
fof(f675,plain,
( spl0_25
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f130,f108,f51,f673]) ).
fof(f673,plain,
( spl0_25
<=> ! [X0] : apply(apply(w,apply(w,apply(w,b))),X0) = apply(apply(X0,apply(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f130,plain,
( ! [X0] : apply(apply(w,apply(w,apply(w,b))),X0) = apply(apply(X0,apply(X0,X0)),X0)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f109,f52]) ).
fof(f671,plain,
( spl0_24
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f95,f55,f13,f669]) ).
fof(f95,plain,
( ! [X0,X1] : apply(apply(w,apply(w,apply(b,X0))),X1) = apply(apply(X0,apply(X1,X1)),X1)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f14,f56]) ).
fof(f667,plain,
( spl0_23
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f76,f51,f13,f665]) ).
fof(f76,plain,
( ! [X0,X1] : apply(apply(w,apply(apply(w,b),X0)),X1) = apply(apply(X0,apply(X0,X1)),X1)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f14,f52]) ).
fof(f663,plain,
( spl0_22
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f43,f37,f21,f661]) ).
fof(f43,plain,
( ! [X0] : apply(X0,apply(apply(b,X0),apply(b,X0))) = apply(apply(w,w),apply(b,X0))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f38,f22]) ).
fof(f381,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f224,f185,f55,f379]) ).
fof(f224,plain,
( ! [X0] : apply(X0,apply(X0,X0)) = apply(apply(w,apply(apply(b,w),b)),X0)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f186,f56]) ).
fof(f377,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f166,f112,f108,f375]) ).
fof(f166,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(w,apply(X0,X0)),X0)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f113,f109]) ).
fof(f373,plain,
( spl0_19
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f135,f108,f13,f371]) ).
fof(f369,plain,
( spl0_18
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f49,f37,f13,f367]) ).
fof(f49,plain,
( ! [X0] : apply(apply(apply(w,w),X0),X0) = apply(apply(w,apply(X0,X0)),X0)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f14,f38]) ).
fof(f365,plain,
( spl0_17
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f45,f37,f13,f363]) ).
fof(f45,plain,
( ! [X0] : apply(apply(w,apply(w,w)),X0) = apply(apply(apply(X0,X0),X0),X0)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f14,f38]) ).
fof(f298,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f134,f108,f51,f295]) ).
fof(f134,plain,
( apply(b,apply(b,b)) = apply(apply(w,apply(w,w)),b)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f109,f52]) ).
fof(f293,plain,
( spl0_15
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f69,f51,f13,f291]) ).
fof(f69,plain,
( ! [X0] : apply(apply(w,apply(w,b)),X0) = apply(X0,apply(X0,X0))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f52,f14]) ).
fof(f277,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f34,f29,f13,f274]) ).
fof(f34,plain,
( apply(apply(w,apply(b,apply(w,w))),apply(apply(b,apply(b,w)),apply(apply(w,w),b))) = apply(strong_fixed_point,apply(apply(b,apply(b,w)),apply(apply(w,w),b)))
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f14,f31]) ).
fof(f272,plain,
( spl0_13
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f47,f37,f21,f270]) ).
fof(f47,plain,
( ! [X0] : apply(apply(apply(w,w),b),X0) = apply(b,apply(b,X0))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f22,f38]) ).
fof(f262,plain,
( spl0_12
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f258,f255,f37,f21,f260]) ).
fof(f255,plain,
( spl0_11
<=> ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f258,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f256,f47]) ).
fof(f256,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( spl0_11
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f29,f21,f255]) ).
fof(f35,plain,
( ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(w,w),b),X0)))
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f33,f22]) ).
fof(f33,plain,
( ! [X0] : apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(w,w),b)),X0)) = apply(strong_fixed_point,X0)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f22,f31]) ).
fof(f187,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f27,f21,f13,f185]) ).
fof(f27,plain,
( ! [X2,X0,X1] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f14,f22]) ).
fof(f114,plain,
( spl0_9
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f18,f13,f112]) ).
fof(f18,plain,
( ! [X0,X1] : apply(apply(apply(w,X0),X1),X1) = apply(apply(w,apply(X0,X1)),X1)
| ~ spl0_2 ),
inference(superposition,[],[f14,f14]) ).
fof(f110,plain,
( spl0_8
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f17,f13,f108]) ).
fof(f17,plain,
( ! [X0,X1] : apply(apply(w,apply(w,X0)),X1) = apply(apply(apply(X0,X1),X1),X1)
| ~ spl0_2 ),
inference(superposition,[],[f14,f14]) ).
fof(f57,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f25,f21,f13,f55]) ).
fof(f25,plain,
( ! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f22,f14]) ).
fof(f53,plain,
( spl0_6
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f24,f21,f13,f51]) ).
fof(f24,plain,
( ! [X0,X1] : apply(X0,apply(X0,X1)) = apply(apply(apply(w,b),X0),X1)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f22,f14]) ).
fof(f39,plain,
( spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f16,f13,f37]) ).
fof(f16,plain,
( ! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0)
| ~ spl0_2 ),
inference(superposition,[],[f14,f14]) ).
fof(f32,plain,
spl0_4,
inference(avatar_split_clause,[],[f6,f29]) ).
fof(f6,plain,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,w),b))),
inference(forward_demodulation,[],[f5,f2]) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f5,plain,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(w,b),b))),
inference(forward_demodulation,[],[f3,f2]) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f23,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f21]) ).
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f15,plain,
spl0_2,
inference(avatar_split_clause,[],[f2,f13]) ).
fof(f11,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f4,f8]) ).
fof(f4,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COL003-20 : TPTP v8.1.2. Released v2.1.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n016.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 18:27:22 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (30210)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (30213)WARNING: value z3 for option sas not known
% 0.15/0.32 % (30212)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32 % (30213)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.32 % (30217)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)
% 0.15/0.32 % (30214)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32 % (30211)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.32 % (30216)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.32 % (30215)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [3]
% 0.15/0.33 TRYING [3]
% 0.15/0.33 TRYING [4]
% 0.15/0.33 TRYING [4]
% 0.15/0.36 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.46 TRYING [6]
% 0.15/0.48 TRYING [6]
% 3.97/0.87 TRYING [7]
% 5.38/1.08 TRYING [7]
% 7.57/1.42 TRYING [1]
% 7.57/1.42 TRYING [2]
% 7.57/1.42 TRYING [3]
% 7.57/1.43 TRYING [4]
% 8.06/1.46 TRYING [5]
% 8.69/1.59 TRYING [6]
% 17.03/2.76 TRYING [7]
% 26.76/4.14 TRYING [8]
% 53.15/7.97 TRYING [8]
% 67.54/9.99 TRYING [8]
% 102.65/15.01 % (30215)First to succeed.
% 103.36/15.03 % (30215)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30210"
% 103.36/15.05 % (30215)Refutation found. Thanks to Tanya!
% 103.36/15.05 % SZS status Unsatisfiable for theBenchmark
% 103.36/15.05 % SZS output start Proof for theBenchmark
% See solution above
% 103.36/15.05 % (30215)------------------------------
% 103.36/15.05 % (30215)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 103.36/15.05 % (30215)Termination reason: Refutation
% 103.36/15.05
% 103.36/15.05 % (30215)Memory used [KB]: 137475
% 103.36/15.05 % (30215)Time elapsed: 14.711 s
% 103.36/15.05 % (30215)Instructions burned: 29899 (million)
% 103.36/15.05 % (30210)Success in time 14.696 s
%------------------------------------------------------------------------------