TSTP Solution File: LCL817_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL817_5 : TPTP v8.1.2. Released v6.0.0.
% 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 07:54:00 EDT 2024
% Result : Theorem 20.26s 3.24s
% Output : Refutation 20.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 735
% Syntax : Number of formulae : 2359 ( 297 unt; 81 typ; 0 def)
% Number of atoms : 6462 (1288 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7534 (3350 ~;3342 |; 162 &)
% ( 561 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 92 ( 42 >; 50 *; 0 +; 0 <<)
% Number of predicates : 538 ( 536 usr; 531 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 26 con; 0-6 aty)
% Number of variables : 5273 (5144 !; 88 ?;5273 :)
% ( 41 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
typing: fun(nat,type) > fun(dB,fun(type,bool)) ).
tff(func_def_23,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fTrue: bool ).
tff(func_def_28,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
t: type ).
tff(func_def_32,type,
t2: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t1: type ).
tff(func_def_35,type,
ts: list(type) ).
tff(func_def_36,type,
a: dB ).
tff(func_def_37,type,
as: list(dB) ).
tff(func_def_38,type,
e: fun(nat,type) ).
tff(func_def_39,type,
ea: fun(nat,type) ).
tff(func_def_40,type,
i: nat ).
tff(func_def_41,type,
ia: nat ).
tff(func_def_42,type,
n: nat ).
tff(func_def_43,type,
rs: list(dB) ).
tff(func_def_44,type,
t3: dB ).
tff(func_def_45,type,
u: dB ).
tff(func_def_46,type,
ua: dB ).
tff(func_def_47,type,
sK2: type ).
tff(func_def_48,type,
sK3: list(type) ).
tff(func_def_49,type,
sK4: dB > dB ).
tff(func_def_50,type,
sK5: dB > list(dB) ).
tff(func_def_51,type,
sK6: dB > nat ).
tff(func_def_52,type,
sK7: dB > dB ).
tff(func_def_53,type,
sK8: dB > dB ).
tff(func_def_54,type,
sK9: dB > list(dB) ).
tff(func_def_55,type,
sK10: ( dB * fun(nat,type) ) > type ).
tff(func_def_56,type,
sK11: ( dB * fun(nat,type) ) > type ).
tff(func_def_57,type,
sK12: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_58,type,
sK13: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_59,type,
sK14: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_60,type,
sK15: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_61,type,
sK16: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_62,type,
sK17: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_63,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_64,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_65,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_66,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_67,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_68,type,
sK23: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: dB > $o ).
tff(pred_def_6,type,
sP1: dB > $o ).
tff(f17367,plain,
$false,
inference(avatar_sat_refutation,[],[f525,f530,f535,f539,f543,f548,f553,f558,f562,f566,f576,f580,f585,f590,f597,f602,f606,f610,f614,f618,f628,f637,f641,f645,f659,f663,f668,f673,f679,f685,f691,f697,f702,f707,f711,f715,f720,f730,f734,f739,f744,f749,f754,f758,f762,f766,f785,f789,f794,f802,f806,f811,f817,f831,f837,f843,f848,f854,f861,f865,f869,f873,f877,f882,f890,f895,f903,f907,f911,f915,f920,f927,f931,f939,f944,f951,f955,f959,f964,f968,f973,f981,f1008,f1013,f1021,f1026,f1031,f1036,f1044,f1051,f1058,f1064,f1070,f1075,f1079,f1095,f1101,f1105,f1109,f1113,f1135,f1141,f1145,f1151,f1157,f1162,f1170,f1175,f1179,f1186,f1191,f1198,f1204,f1209,f1217,f1221,f1227,f1233,f1240,f1247,f1254,f1263,f1271,f1282,f1289,f1295,f1312,f1319,f1327,f1332,f1340,f1346,f1351,f1355,f1359,f1363,f1476,f1480,f1484,f1503,f1507,f1513,f1526,f1530,f1559,f1568,f1574,f1578,f1591,f1597,f1610,f1617,f1627,f1634,f1643,f1649,f1653,f1659,f1672,f1678,f1687,f1694,f1703,f1709,f1718,f1722,f1728,f1745,f1752,f1757,f1767,f1772,f1812,f1890,f1899,f1914,f1923,f1931,f1947,f1951,f1955,f1961,f1965,f1993,f1999,f2010,f2033,f2040,f2051,f2060,f2069,f2083,f2097,f2102,f2106,f2114,f2120,f2131,f2140,f2149,f2154,f2162,f2166,f2170,f2178,f2192,f2204,f2208,f2213,f2222,f2227,f2236,f2242,f2249,f2261,f2710,f2737,f2760,f2771,f2776,f2780,f2784,f2788,f2792,f2799,f2804,f2820,f2825,f2829,f2833,f2865,f2870,f2878,f2882,f2886,f2891,f2896,f2900,f2905,f2949,f2988,f2989,f2990,f2991,f2992,f2993,f2994,f2995,f2996,f2997,f2998,f2999,f3000,f3001,f3002,f3003,f3004,f3005,f3006,f3007,f3008,f3009,f3010,f3011,f3012,f3013,f3014,f3015,f3016,f3017,f3018,f3019,f3579,f3656,f3660,f3664,f3672,f3677,f3681,f3685,f3689,f3693,f3697,f3702,f3707,f3758,f3765,f3770,f3775,f3779,f3783,f3825,f3830,f3835,f3840,f3845,f3862,f3866,f3870,f3874,f3878,f3934,f3947,f3951,f3955,f3959,f3963,f4127,f4132,f4136,f4140,f4152,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4213,f4483,f4487,f4491,f4552,f4590,f4594,f4598,f4602,f4667,f4671,f4675,f4680,f4719,f4724,f4728,f4732,f4885,f4890,f4895,f4899,f4903,f4922,f4940,f4945,f4949,f4953,f4957,f4961,f5064,f5068,f5072,f5076,f5090,f5112,f5116,f5120,f5124,f5128,f5132,f5136,f5171,f5245,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5287,f5291,f5296,f5300,f5515,f5563,f5568,f5580,f5584,f5588,f5606,f5610,f5915,f5919,f5923,f5928,f5932,f5936,f5940,f6141,f6147,f6151,f6155,f6159,f6163,f6167,f6171,f6175,f6440,f6478,f6483,f6487,f6491,f6495,f6499,f6503,f6507,f6511,f6516,f6533,f6540,f6714,f6733,f6737,f6741,f6745,f7120,f7125,f7129,f7133,f7137,f7141,f7145,f7149,f7153,f7465,f7469,f7473,f7518,f7534,f7538,f7542,f7546,f7550,f7554,f7977,f8069,f8073,f8161,f8165,f8169,f8174,f8178,f8182,f8186,f8190,f8195,f8213,f8218,f8236,f8240,f8742,f8746,f8750,f8771,f8775,f8779,f8784,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8949,f8953,f8957,f8961,f8967,f8971,f9822,f9826,f9830,f9834,f9838,f9842,f9847,f9851,f9855,f9859,f9864,f10492,f10496,f10500,f10504,f10508,f10512,f10701,f10705,f10709,f10713,f10717,f10723,f10727,f10860,f10864,f10868,f11081,f11085,f11089,f11094,f11114,f11119,f11166,f11194,f11198,f11202,f11206,f11210,f11214,f11328,f12253,f12257,f12261,f12265,f12269,f12275,f12280,f12287,f12734,f12739,f12743,f12747,f12751,f12755,f12759,f12763,f12767,f12771,f12775,f12779,f12784,f12791,f12797,f12802,f12820,f12825,f15405,f15409,f15413,f15417,f15421,f15756,f15760,f15764,f15830,f15834,f16847,f16853,f16858,f16901,f17194,f17196,f17201,f17207,f17211,f17215,f17219,f17366]) ).
tff(f17366,plain,
( ~ spl24_3
| spl24_15
| ~ spl24_168 ),
inference(avatar_split_clause,[],[f17010,f1739,f594,f532]) ).
tff(f532,plain,
( spl24_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).
tff(f594,plain,
( spl24_15
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_15])]) ).
tff(f1739,plain,
( spl24_168
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_168])]) ).
tff(f17010,plain,
( ~ pp(fTrue)
| spl24_15
| ~ spl24_168 ),
inference(superposition,[],[f596,f1740]) ).
tff(f1740,plain,
( ! [X0: bool] : ( fTrue = X0 )
| ~ spl24_168 ),
inference(avatar_component_clause,[],[f1739]) ).
tff(f596,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| spl24_15 ),
inference(avatar_component_clause,[],[f594]) ).
tff(f17219,plain,
( spl24_530
| ~ spl24_82
| ~ spl24_104
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1885,f1810,f1149,f979,f17217]) ).
tff(f17217,plain,
( spl24_530
<=> ! [X3: $tType,X4: fun(nat,fun(dB,X3)),X0: dB,X2: dB,X1: nat] : ( aa(nat,X3,aa(fun(nat,dB),fun(nat,X3),aa(fun(nat,fun(dB,X3)),fun(fun(nat,dB),fun(nat,X3)),combs(nat,dB,X3),X4),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2))),X1) = aa(nat,X3,combc(nat,dB,X3,X4,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_530])]) ).
tff(f979,plain,
( spl24_82
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_82])]) ).
tff(f1149,plain,
( spl24_104
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_104])]) ).
tff(f1810,plain,
( spl24_174
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_174])]) ).
tff(f1885,plain,
( ! [X3: $tType,X2: dB,X0: dB,X1: nat,X4: fun(nat,fun(dB,X3))] : ( aa(nat,X3,aa(fun(nat,dB),fun(nat,X3),aa(fun(nat,fun(dB,X3)),fun(fun(nat,dB),fun(nat,X3)),combs(nat,dB,X3),X4),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2))),X1) = aa(nat,X3,combc(nat,dB,X3,X4,X2),X1) )
| ~ spl24_82
| ~ spl24_104
| ~ spl24_174 ),
inference(forward_demodulation,[],[f1835,f980]) ).
tff(f980,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl24_82 ),
inference(avatar_component_clause,[],[f979]) ).
tff(f1835,plain,
( ! [X3: $tType,X2: dB,X0: dB,X1: nat,X4: fun(nat,fun(dB,X3))] : ( aa(nat,X3,aa(fun(nat,dB),fun(nat,X3),aa(fun(nat,fun(dB,X3)),fun(fun(nat,dB),fun(nat,X3)),combs(nat,dB,X3),X4),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2))),X1) = aa(dB,X3,aa(nat,fun(dB,X3),X4,X1),X2) )
| ~ spl24_104
| ~ spl24_174 ),
inference(superposition,[],[f1811,f1150]) ).
tff(f1150,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl24_104 ),
inference(avatar_component_clause,[],[f1149]) ).
tff(f1811,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl24_174 ),
inference(avatar_component_clause,[],[f1810]) ).
tff(f17215,plain,
( spl24_529
| ~ spl24_142
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1664,f1657,f1511,f17213]) ).
tff(f17213,plain,
( spl24_529
<=> ! [X4: type,X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK12(X1,foldl(dB,dB,app,var(X2),X3),X0))),X4),foldl(dB,dB,app,var(X2),X3)))
| ( sK13(X1,foldl(dB,dB,app,var(X2),X3),X0) = X4 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(foldl(dB,dB,app,var(X2),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_529])]) ).
tff(f1511,plain,
( spl24_142
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_142])]) ).
tff(f1657,plain,
( spl24_158
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_158])]) ).
tff(f1664,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK12(X1,foldl(dB,dB,app,var(X2),X3),X0))),X4),foldl(dB,dB,app,var(X2),X3)))
| ( sK13(X1,foldl(dB,dB,app,var(X2),X3),X0) = X4 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(foldl(dB,dB,app,var(X2),X3)))) )
| ~ spl24_142
| ~ spl24_158 ),
inference(resolution,[],[f1658,f1512]) ).
tff(f1512,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1))) )
| ~ spl24_142 ),
inference(avatar_component_clause,[],[f1511]) ).
tff(f1658,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl24_158 ),
inference(avatar_component_clause,[],[f1657]) ).
tff(f17211,plain,
( spl24_528
| ~ spl24_95
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1305,f1293,f1077,f17209]) ).
tff(f17209,plain,
( spl24_528
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun(list(X0),X1),X3: X0,X2: fun(X0,fun(list(X0),X1))] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK18(X1,list(X0),aa(X0,fun(list(X0),X1),X2,X3),X4)),X3)) != aa(list(X0),X1,X4,sK18(X1,list(X0),aa(X0,fun(list(X0),X1),X2,X3),X4)) )
| ( aa(X0,fun(list(X0),X1),X2,X3) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_528])]) ).
tff(f1077,plain,
( spl24_95
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_95])]) ).
tff(f1293,plain,
( spl24_126
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_126])]) ).
tff(f1305,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: fun(list(X0),X1),X5: X1] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK18(X1,list(X0),aa(X0,fun(list(X0),X1),X2,X3),X4)),X3)) != aa(list(X0),X1,X4,sK18(X1,list(X0),aa(X0,fun(list(X0),X1),X2,X3),X4)) )
| ( aa(X0,fun(list(X0),X1),X2,X3) = X4 ) )
| ~ spl24_95
| ~ spl24_126 ),
inference(superposition,[],[f1078,f1294]) ).
tff(f1294,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_126 ),
inference(avatar_component_clause,[],[f1293]) ).
tff(f1078,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl24_95 ),
inference(avatar_component_clause,[],[f1077]) ).
tff(f17207,plain,
( spl24_527
| ~ spl24_95
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1304,f1293,f1077,f17205]) ).
tff(f17205,plain,
( spl24_527
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun(list(X0),X1),X3: X0,X2: fun(X0,fun(list(X0),X1))] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK18(X1,list(X0),X4,aa(X0,fun(list(X0),X1),X2,X3))),X3)) != aa(list(X0),X1,X4,sK18(X1,list(X0),X4,aa(X0,fun(list(X0),X1),X2,X3))) )
| ( aa(X0,fun(list(X0),X1),X2,X3) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_527])]) ).
tff(f1304,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: fun(list(X0),X1),X5: X1] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK18(X1,list(X0),X4,aa(X0,fun(list(X0),X1),X2,X3))),X3)) != aa(list(X0),X1,X4,sK18(X1,list(X0),X4,aa(X0,fun(list(X0),X1),X2,X3))) )
| ( aa(X0,fun(list(X0),X1),X2,X3) = X4 ) )
| ~ spl24_95
| ~ spl24_126 ),
inference(superposition,[],[f1078,f1294]) ).
tff(f17201,plain,
( spl24_526
| ~ spl24_117
| ~ spl24_162 ),
inference(avatar_split_clause,[],[f1696,f1692,f1225,f17199]) ).
tff(f17199,plain,
( spl24_526
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| ( aa(type,type,combc(type,type,type,fun1,X2),X1) = aa(type,type,combc(type,type,type,fun1,sK13(aa(type,type,combc(type,type,type,fun1,X2),X1),X3,X0)),sK12(aa(type,type,combc(type,type,type,fun1,X2),X1),X3,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_526])]) ).
tff(f1225,plain,
( spl24_117
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_117])]) ).
tff(f1692,plain,
( spl24_162
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_162])]) ).
tff(f1696,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| ( aa(type,type,combc(type,type,type,fun1,X2),X1) = aa(type,type,combc(type,type,type,fun1,sK13(aa(type,type,combc(type,type,type,fun1,X2),X1),X3,X0)),sK12(aa(type,type,combc(type,type,type,fun1,X2),X1),X3,X0)) ) )
| ~ spl24_117
| ~ spl24_162 ),
inference(resolution,[],[f1693,f1226]) ).
tff(f1226,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) )
| ~ spl24_117 ),
inference(avatar_component_clause,[],[f1225]) ).
tff(f1693,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1)) )
| ~ spl24_162 ),
inference(avatar_component_clause,[],[f1692]) ).
tff(f17196,plain,
( ~ spl24_168
| spl24_315 ),
inference(avatar_contradiction_clause,[],[f17195]) ).
tff(f17195,plain,
( $false
| ~ spl24_168
| spl24_315 ),
inference(trivial_inequality_removal,[],[f17009]) ).
tff(f17009,plain,
( ( fTrue != fTrue )
| ~ spl24_168
| spl24_315 ),
inference(superposition,[],[f4921,f1740]) ).
tff(f4921,plain,
( ( fTrue != aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) )
| spl24_315 ),
inference(avatar_component_clause,[],[f4919]) ).
tff(f4919,plain,
( spl24_315
<=> ( fTrue = aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_315])]) ).
tff(f17194,plain,
( ~ spl24_168
| spl24_169 ),
inference(avatar_contradiction_clause,[],[f17193]) ).
tff(f17193,plain,
( $false
| ~ spl24_168
| spl24_169 ),
inference(trivial_inequality_removal,[],[f17071]) ).
tff(f17071,plain,
( ( fTrue != fTrue )
| ~ spl24_168
| spl24_169 ),
inference(superposition,[],[f1744,f1740]) ).
tff(f1744,plain,
( ( fFalse != fTrue )
| spl24_169 ),
inference(avatar_component_clause,[],[f1742]) ).
tff(f1742,plain,
( spl24_169
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_169])]) ).
tff(f16901,plain,
( spl24_168
| ~ spl24_13
| ~ spl24_514 ),
inference(avatar_split_clause,[],[f15826,f15407,f583,f1739]) ).
tff(f583,plain,
( spl24_13
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_13])]) ).
tff(f15407,plain,
( spl24_514
<=> ! [X0: bool] :
( ( fTrue = X0 )
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_514])]) ).
tff(f15826,plain,
( ! [X0: bool] : ( fTrue = X0 )
| ~ spl24_13
| ~ spl24_514 ),
inference(duplicate_literal_removal,[],[f15765]) ).
tff(f15765,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fTrue = X0 ) )
| ~ spl24_13
| ~ spl24_514 ),
inference(resolution,[],[f15408,f584]) ).
tff(f584,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl24_13 ),
inference(avatar_component_clause,[],[f583]) ).
tff(f15408,plain,
( ! [X0: bool] :
( pp(X0)
| ( fTrue = X0 ) )
| ~ spl24_514 ),
inference(avatar_component_clause,[],[f15407]) ).
tff(f16858,plain,
( spl24_525
| ~ spl24_3
| ~ spl24_13
| ~ spl24_514
| ~ spl24_524 ),
inference(avatar_split_clause,[],[f16854,f16851,f15407,f583,f532,f16856]) ).
tff(f16856,plain,
( spl24_525
<=> ! [X2: dB,X0: fun(nat,type),X1: type] : ( sK13(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun1,sK13(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),sK12(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_525])]) ).
tff(f16851,plain,
( spl24_524
<=> ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| ( sK13(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun1,sK13(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),sK12(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_524])]) ).
tff(f16854,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(fTrue)
| ( sK13(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun1,sK13(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),sK12(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))) ) )
| ~ spl24_13
| ~ spl24_514
| ~ spl24_524 ),
inference(forward_demodulation,[],[f16852,f15826]) ).
tff(f16852,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| ( sK13(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun1,sK13(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),sK12(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))) ) )
| ~ spl24_524 ),
inference(avatar_component_clause,[],[f16851]) ).
tff(f16853,plain,
( spl24_524
| ~ spl24_117
| ~ spl24_142 ),
inference(avatar_split_clause,[],[f1515,f1511,f1225,f16851]) ).
tff(f1515,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| ( sK13(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun1,sK13(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),sK12(sK13(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))) ) )
| ~ spl24_117
| ~ spl24_142 ),
inference(resolution,[],[f1512,f1226]) ).
tff(f16847,plain,
( spl24_523
| ~ spl24_132
| ~ spl24_142 ),
inference(avatar_split_clause,[],[f1514,f1511,f1344,f16845]) ).
tff(f16845,plain,
( spl24_523
<=> ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)),zero_zero(nat),sK10(X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0))))),sK11(X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_523])]) ).
tff(f1344,plain,
( spl24_132
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_132])]) ).
tff(f1514,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)),zero_zero(nat),sK10(X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0))))),sK11(X2,shift(type,X0,zero_zero(nat),sK12(X1,abs(X2),X0)))),X2)) )
| ~ spl24_132
| ~ spl24_142 ),
inference(resolution,[],[f1512,f1345]) ).
tff(f1345,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1)) )
| ~ spl24_132 ),
inference(avatar_component_clause,[],[f1344]) ).
tff(f15834,plain,
( spl24_522
| ~ spl24_142
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2027,f2008,f1511,f15832]) ).
tff(f15832,plain,
( spl24_522
<=> ! [X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK12(X1,X2,X0)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_522])]) ).
tff(f2008,plain,
( spl24_187
<=> ! [X2: dB,X3: fun(nat,type),X4: type,X0: nat,X5: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_187])]) ).
tff(f2027,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK12(X1,X2,X0)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) )
| ~ spl24_142
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1512]) ).
tff(f2009,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) )
| ~ spl24_187 ),
inference(avatar_component_clause,[],[f2008]) ).
tff(f15830,plain,
( spl24_521
| ~ spl24_137
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1867,f1810,f1474,f15828]) ).
tff(f15828,plain,
( spl24_521
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: fun(X0,list(X0)),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_521])]) ).
tff(f1474,plain,
( spl24_137
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_137])]) ).
tff(f1867,plain,
( ! [X0: $tType,X2: fun(X0,list(X0)),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) )
| ~ spl24_137
| ~ spl24_174 ),
inference(superposition,[],[f1475,f1811]) ).
tff(f1475,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X2 = X4 ) )
| ~ spl24_137 ),
inference(avatar_component_clause,[],[f1474]) ).
tff(f15764,plain,
( spl24_520
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1820,f1810,f979,f15762]) ).
tff(f15762,plain,
( spl24_520
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X6: X0,X7: fun(X0,X1)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),aa(X3,fun(X0,fun(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_520])]) ).
tff(f1820,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),aa(X3,fun(X0,fun(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl24_82
| ~ spl24_174 ),
inference(superposition,[],[f1811,f980]) ).
tff(f15760,plain,
( spl24_519
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1819,f1810,f979,f15758]) ).
tff(f15758,plain,
( spl24_519
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun(X0,fun(X3,fun(X1,X2))),X6: X0,X7: fun(X0,X1)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_519])]) ).
tff(f1819,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl24_82
| ~ spl24_174 ),
inference(superposition,[],[f1811,f980]) ).
tff(f15756,plain,
( spl24_518
| ~ spl24_82
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1777,f1770,f979,f15754]) ).
tff(f15754,plain,
( spl24_518
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,aa(X2,fun(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun(X0,X1),X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_518])]) ).
tff(f1770,plain,
( spl24_173
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_173])]) ).
tff(f1777,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,aa(X2,fun(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun(X0,X1),X3,X4),X6)) )
| ~ spl24_82
| ~ spl24_173 ),
inference(superposition,[],[f1771,f980]) ).
tff(f1771,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_173 ),
inference(avatar_component_clause,[],[f1770]) ).
tff(f15421,plain,
( spl24_517
| ~ spl24_82
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1776,f1770,f979,f15419]) ).
tff(f15419,plain,
( spl24_517
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_517])]) ).
tff(f1776,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) )
| ~ spl24_82
| ~ spl24_173 ),
inference(superposition,[],[f1771,f980]) ).
tff(f15417,plain,
( spl24_516
| ~ spl24_154
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1734,f1726,f1632,f15415]) ).
tff(f15415,plain,
( spl24_516
<=> ! [X2: type,X3: type,X4: dB,X0: fun(nat,type),X6: list(type),X5: list(dB),X1: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,X6,X3)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_516])]) ).
tff(f1632,plain,
( spl24_154
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_154])]) ).
tff(f1726,plain,
( spl24_167
<=> ! [X4: fun(nat,type),X0: list(dB),X3: dB,X2: list(type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_167])]) ).
tff(f1734,plain,
( ! [X2: type,X3: type,X0: fun(nat,type),X1: nat,X6: list(type),X4: dB,X5: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,X6,X3)),X4)) )
| ~ spl24_154
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1633]) ).
tff(f1633,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3)) )
| ~ spl24_154 ),
inference(avatar_component_clause,[],[f1632]) ).
tff(f1727,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl24_167 ),
inference(avatar_component_clause,[],[f1726]) ).
tff(f15413,plain,
( spl24_515
| ~ spl24_150
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1621,f1615,f1595,f15411]) ).
tff(f15411,plain,
( spl24_515
<=> ! [X2: list(dB),X4: dB,X0: fun(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(foldr(type,type,fun1,sK15(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_515])]) ).
tff(f1595,plain,
( spl24_150
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_150])]) ).
tff(f1615,plain,
( spl24_152
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_152])]) ).
tff(f1621,plain,
( ! [X2: list(dB),X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(foldr(type,type,fun1,sK15(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) )
| ~ spl24_150
| ~ spl24_152 ),
inference(resolution,[],[f1616,f1596]) ).
tff(f1596,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl24_150 ),
inference(avatar_component_clause,[],[f1595]) ).
tff(f1616,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_152 ),
inference(avatar_component_clause,[],[f1615]) ).
tff(f15409,plain,
( ~ spl24_3
| spl24_514
| ~ spl24_13
| ~ spl24_18
| ~ spl24_31
| ~ spl24_383
| ~ spl24_506 ),
inference(avatar_split_clause,[],[f13067,f12777,f6514,f688,f608,f583,f15407,f532]) ).
tff(f608,plain,
( spl24_18
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_18])]) ).
tff(f688,plain,
( spl24_31
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_31])]) ).
tff(f6514,plain,
( spl24_383
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),a)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_383])]) ).
tff(f12777,plain,
( spl24_506
<=> ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_506])]) ).
tff(f13067,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ~ pp(fTrue)
| pp(X0) )
| ~ spl24_13
| ~ spl24_18
| ~ spl24_31
| ~ spl24_383
| ~ spl24_506 ),
inference(forward_demodulation,[],[f13066,f609]) ).
tff(f609,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl24_18 ),
inference(avatar_component_clause,[],[f608]) ).
tff(f13066,plain,
( ! [X0: bool] :
( ~ pp(fTrue)
| pp(X0)
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_13
| ~ spl24_31
| ~ spl24_383
| ~ spl24_506 ),
inference(forward_demodulation,[],[f13028,f1392]) ).
tff(f1392,plain,
( ( fTrue = aa(dB,bool,combc(dB,type,bool,typing(e),t1),u) )
| ~ spl24_13
| ~ spl24_31 ),
inference(resolution,[],[f584,f690]) ).
tff(f690,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ~ spl24_31 ),
inference(avatar_component_clause,[],[f688]) ).
tff(f13028,plain,
( ! [X0: bool] :
( pp(X0)
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_383
| ~ spl24_506 ),
inference(superposition,[],[f6515,f12778]) ).
tff(f12778,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_506 ),
inference(avatar_component_clause,[],[f12777]) ).
tff(f6515,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),a)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_383 ),
inference(avatar_component_clause,[],[f6514]) ).
tff(f15405,plain,
( spl24_513
| ~ spl24_148
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1620,f1615,f1576,f15403]) ).
tff(f15403,plain,
( spl24_513
<=> ! [X2: list(dB),X4: dB,X0: fun(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(foldr(type,type,fun1,sK14(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_513])]) ).
tff(f1576,plain,
( spl24_148
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_148])]) ).
tff(f1620,plain,
( ! [X2: list(dB),X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(foldr(type,type,fun1,sK14(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) )
| ~ spl24_148
| ~ spl24_152 ),
inference(resolution,[],[f1616,f1577]) ).
tff(f1577,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl24_148 ),
inference(avatar_component_clause,[],[f1576]) ).
tff(f12825,plain,
( spl24_512
| ~ spl24_82
| ~ spl24_352
| ~ spl24_511 ),
inference(avatar_split_clause,[],[f12821,f12818,f5578,f979,f12823]) ).
tff(f12823,plain,
( spl24_512
<=> ! [X2: dB,X3: dB,X4: dB,X0: dB,X5: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_512])]) ).
tff(f5578,plain,
( spl24_352
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X0,fun(X3,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_352])]) ).
tff(f12818,plain,
( spl24_511
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_511])]) ).
tff(f12821,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_511 ),
inference(forward_demodulation,[],[f12819,f5642]) ).
tff(f5642,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X2,X7: X0,X4: fun(X3,fun(X2,fun(X0,X1))),X5: X3] : ( aa(X2,X1,combc(X2,X0,X1,aa(X3,fun(X2,fun(X0,X1)),X4,X5),X7),X6) = aa(X3,X1,combc(X3,X0,X1,combc(X3,X2,fun(X0,X1),X4,X6),X7),X5) )
| ~ spl24_82
| ~ spl24_352 ),
inference(superposition,[],[f5579,f980]) ).
tff(f5579,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) )
| ~ spl24_352 ),
inference(avatar_component_clause,[],[f5578]) ).
tff(f12819,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl24_511 ),
inference(avatar_component_clause,[],[f12818]) ).
tff(f12820,plain,
( spl24_511
| ~ spl24_99
| ~ spl24_206 ),
inference(avatar_split_clause,[],[f2182,f2176,f1107,f12818]) ).
tff(f1107,plain,
( spl24_99
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_99])]) ).
tff(f2176,plain,
( spl24_206
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_206])]) ).
tff(f2182,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl24_99
| ~ spl24_206 ),
inference(superposition,[],[f1108,f2177]) ).
tff(f2177,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl24_206 ),
inference(avatar_component_clause,[],[f2176]) ).
tff(f1108,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X1 = X3 ) )
| ~ spl24_99 ),
inference(avatar_component_clause,[],[f1107]) ).
tff(f12802,plain,
( spl24_510
| ~ spl24_82
| ~ spl24_352
| ~ spl24_509 ),
inference(avatar_split_clause,[],[f12798,f12795,f5578,f979,f12800]) ).
tff(f12800,plain,
( spl24_510
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_510])]) ).
tff(f12795,plain,
( spl24_509
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_509])]) ).
tff(f12798,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_509 ),
inference(forward_demodulation,[],[f12796,f5642]) ).
tff(f12796,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl24_509 ),
inference(avatar_component_clause,[],[f12795]) ).
tff(f12797,plain,
( spl24_509
| ~ spl24_100
| ~ spl24_206 ),
inference(avatar_split_clause,[],[f2180,f2176,f1111,f12795]) ).
tff(f1111,plain,
( spl24_100
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_100])]) ).
tff(f2180,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl24_100
| ~ spl24_206 ),
inference(superposition,[],[f1112,f2177]) ).
tff(f1112,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 = X2 ) )
| ~ spl24_100 ),
inference(avatar_component_clause,[],[f1111]) ).
tff(f12791,plain,
( spl24_508
| ~ spl24_82
| ~ spl24_352
| ~ spl24_507 ),
inference(avatar_split_clause,[],[f12786,f12781,f5578,f979,f12788]) ).
tff(f12788,plain,
( spl24_508
<=> sP1(abs(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_508])]) ).
tff(f12781,plain,
( spl24_507
<=> sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_507])]) ).
tff(f12786,plain,
( sP1(abs(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))))
| ~ spl24_82
| ~ spl24_352
| ~ spl24_507 ),
inference(forward_demodulation,[],[f12785,f5642]) ).
tff(f12785,plain,
( sP1(abs(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))))
| ~ spl24_82
| ~ spl24_352
| ~ spl24_507 ),
inference(forward_demodulation,[],[f12783,f5642]) ).
tff(f12783,plain,
( sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_507 ),
inference(avatar_component_clause,[],[f12781]) ).
tff(f12784,plain,
( spl24_507
| ~ spl24_24
| ~ spl24_200 ),
inference(avatar_split_clause,[],[f2141,f2137,f643,f12781]) ).
tff(f643,plain,
( spl24_24
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_24])]) ).
tff(f2137,plain,
( spl24_200
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_200])]) ).
tff(f2141,plain,
( sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_24
| ~ spl24_200 ),
inference(resolution,[],[f2139,f644]) ).
tff(f644,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl24_24 ),
inference(avatar_component_clause,[],[f643]) ).
tff(f2139,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_200 ),
inference(avatar_component_clause,[],[f2137]) ).
tff(f12779,plain,
( spl24_506
| ~ spl24_82
| ~ spl24_352
| ~ spl24_495 ),
inference(avatar_split_clause,[],[f12735,f12732,f5578,f979,f12777]) ).
tff(f12732,plain,
( spl24_495
<=> ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_495])]) ).
tff(f12735,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_495 ),
inference(forward_demodulation,[],[f12733,f5642]) ).
tff(f12733,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_495 ),
inference(avatar_component_clause,[],[f12732]) ).
tff(f12775,plain,
( spl24_505
| ~ spl24_114
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1906,f1897,f1207,f12773]) ).
tff(f12773,plain,
( spl24_505
<=> ! [X4: list(dB),X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK16(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_505])]) ).
tff(f1207,plain,
( spl24_114
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_114])]) ).
tff(f1897,plain,
( spl24_176
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_176])]) ).
tff(f1906,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK16(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) )
| ~ spl24_114
| ~ spl24_176 ),
inference(resolution,[],[f1898,f1208]) ).
tff(f1208,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl24_114 ),
inference(avatar_component_clause,[],[f1207]) ).
tff(f1898,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) )
| ~ spl24_176 ),
inference(avatar_component_clause,[],[f1897]) ).
tff(f12771,plain,
( spl24_504
| ~ spl24_136
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1852,f1810,f1361,f12769]) ).
tff(f12769,plain,
( spl24_504
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun(X1,X0),X5: list(X0),X2: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_504])]) ).
tff(f1361,plain,
( spl24_136
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X0)),X4: X0,X3: X1,X2: list(X1)] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_136])]) ).
tff(f1852,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X1)),X3: X1,X4: fun(X1,X0),X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) )
| ~ spl24_136
| ~ spl24_174 ),
inference(superposition,[],[f1362,f1811]) ).
tff(f1362,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_136 ),
inference(avatar_component_clause,[],[f1361]) ).
tff(f12767,plain,
( spl24_503
| ~ spl24_126
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1841,f1810,f1293,f12765]) ).
tff(f12765,plain,
( spl24_503
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun(X0,list(X0)),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun(X0,list(X0)),fun(X0,X1),aa(fun(X0,fun(list(X0),X1)),fun(fun(X0,list(X0)),fun(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_503])]) ).
tff(f1841,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: fun(X0,list(X0)),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun(X0,list(X0)),fun(X0,X1),aa(fun(X0,fun(list(X0),X1)),fun(fun(X0,list(X0)),fun(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) )
| ~ spl24_126
| ~ spl24_174 ),
inference(superposition,[],[f1811,f1294]) ).
tff(f12763,plain,
( spl24_502
| ~ spl24_18
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1816,f1810,f608,f12761]) ).
tff(f12761,plain,
( spl24_502
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(X0,X1),X0),X2: fun(X0,X1)] : ( aa(fun(X0,X1),X1,aa(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1),aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1)),combs(fun(X0,X1),X0,X1),combi(fun(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_502])]) ).
tff(f1816,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(fun(X0,X1),X0)] : ( aa(fun(X0,X1),X1,aa(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1),aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1)),combs(fun(X0,X1),X0,X1),combi(fun(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) )
| ~ spl24_18
| ~ spl24_174 ),
inference(superposition,[],[f1811,f609]) ).
tff(f12759,plain,
( spl24_501
| ~ spl24_150
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1661,f1657,f1595,f12757]) ).
tff(f12757,plain,
( spl24_501
<=> ! [X5: list(dB),X4: type,X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK15(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_501])]) ).
tff(f1661,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK15(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) )
| ~ spl24_150
| ~ spl24_158 ),
inference(resolution,[],[f1658,f1596]) ).
tff(f12755,plain,
( spl24_500
| ~ spl24_148
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1660,f1657,f1576,f12753]) ).
tff(f12753,plain,
( spl24_500
<=> ! [X5: list(dB),X4: type,X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK14(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_500])]) ).
tff(f1660,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK14(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) )
| ~ spl24_148
| ~ spl24_158 ),
inference(resolution,[],[f1658,f1577]) ).
tff(f12751,plain,
( spl24_499
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1429,f1361,f12749]) ).
tff(f12749,plain,
( spl24_499
<=> ! [X1: $tType,X0: $tType,X5: list(X1),X3: X0,X4: X1,X2: fun(X0,fun(X1,X0)),X6: X1] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_499])]) ).
tff(f1429,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,X0)),X3: X0,X6: X1,X4: X1,X5: list(X1)] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) )
| ~ spl24_136 ),
inference(superposition,[],[f1362,f1362]) ).
tff(f12747,plain,
( spl24_498
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1422,f1361,f979,f12745]) ).
tff(f12745,plain,
( spl24_498
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun(X2,fun(X0,fun(X1,X0)))] : ( foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),combc(X2,X0,fun(X1,X0),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_498])]) ).
tff(f1422,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),combc(X2,X0,fun(X1,X0),X3,X5),X4),X6),X7) )
| ~ spl24_82
| ~ spl24_136 ),
inference(superposition,[],[f1362,f980]) ).
tff(f12743,plain,
( spl24_497
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1410,f1357,f12741]) ).
tff(f12741,plain,
( spl24_497
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X6: X0,X5: X1,X2: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_497])]) ).
tff(f1357,plain,
( spl24_135
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X1)),X4: X0,X3: list(X0),X2: X1] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_135])]) ).
tff(f1410,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,X1)),X3: list(X0),X6: X0,X4: X0,X5: X1] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) )
| ~ spl24_135 ),
inference(superposition,[],[f1358,f1358]) ).
tff(f1358,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) )
| ~ spl24_135 ),
inference(avatar_component_clause,[],[f1357]) ).
tff(f12739,plain,
( spl24_496
| ~ spl24_82
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1408,f1357,f979,f12737]) ).
tff(f12737,plain,
( spl24_496
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun(X2,fun(X0,fun(X1,X1)))] : ( foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),combc(X2,X0,fun(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_496])]) ).
tff(f1408,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),combc(X2,X0,fun(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),X6,X7)) )
| ~ spl24_82
| ~ spl24_135 ),
inference(superposition,[],[f1358,f980]) ).
tff(f12734,plain,
( spl24_495
| ~ spl24_18
| ~ spl24_303 ),
inference(avatar_split_clause,[],[f4841,f4669,f608,f12732]) ).
tff(f4669,plain,
( spl24_303
<=> ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_303])]) ).
tff(f4841,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_18
| ~ spl24_303 ),
inference(superposition,[],[f609,f4670]) ).
tff(f4670,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = X0 ) )
| ~ spl24_303 ),
inference(avatar_component_clause,[],[f4669]) ).
tff(f12287,plain,
( spl24_494
| ~ spl24_82
| ~ spl24_352
| ~ spl24_493 ),
inference(avatar_split_clause,[],[f12282,f12277,f5578,f979,f12284]) ).
tff(f12284,plain,
( spl24_494
<=> sP1(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_494])]) ).
tff(f12277,plain,
( spl24_493
<=> sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_493])]) ).
tff(f12282,plain,
( sP1(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),a)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))))
| ~ spl24_82
| ~ spl24_352
| ~ spl24_493 ),
inference(forward_demodulation,[],[f12281,f5642]) ).
tff(f12281,plain,
( sP1(aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),zero_zero(nat)),aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))))
| ~ spl24_82
| ~ spl24_352
| ~ spl24_493 ),
inference(forward_demodulation,[],[f12279,f5642]) ).
tff(f12279,plain,
( sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| ~ spl24_493 ),
inference(avatar_component_clause,[],[f12277]) ).
tff(f12280,plain,
( spl24_493
| ~ spl24_16
| ~ spl24_200 ),
inference(avatar_split_clause,[],[f2142,f2137,f600,f12277]) ).
tff(f600,plain,
( spl24_16
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_16])]) ).
tff(f2142,plain,
( sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| ~ spl24_16
| ~ spl24_200 ),
inference(resolution,[],[f2139,f601]) ).
tff(f601,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl24_16 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f12275,plain,
( spl24_492
| ~ spl24_176
| ~ spl24_191 ),
inference(avatar_split_clause,[],[f2063,f2058,f1897,f12273]) ).
tff(f12273,plain,
( spl24_492
<=> ! [X4: dB,X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(X1,X2,X3,X0)),X4))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_492])]) ).
tff(f2058,plain,
( spl24_191
<=> ! [X4: fun(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_191])]) ).
tff(f2063,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK17(X1,X2,X3,X0)),X4))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3))) )
| ~ spl24_176
| ~ spl24_191 ),
inference(resolution,[],[f2059,f1898]) ).
tff(f2059,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl24_191 ),
inference(avatar_component_clause,[],[f2058]) ).
tff(f12269,plain,
( spl24_491
| ~ spl24_158
| ~ spl24_186 ),
inference(avatar_split_clause,[],[f2000,f1996,f1657,f12267]) ).
tff(f12267,plain,
( spl24_491
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),X0),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ( t2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_491])]) ).
tff(f1996,plain,
( spl24_186
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),t2),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_186])]) ).
tff(f2000,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),X0),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ( t2 = X0 ) )
| ~ spl24_158
| ~ spl24_186 ),
inference(resolution,[],[f1998,f1658]) ).
tff(f1998,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),t2),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_186 ),
inference(avatar_component_clause,[],[f1996]) ).
tff(f12265,plain,
( spl24_490
| ~ spl24_112
| ~ spl24_171 ),
inference(avatar_split_clause,[],[f1760,f1755,f1196,f12263]) ).
tff(f12263,plain,
( spl24_490
<=> ! [X4: list(type),X0: fun(nat,type),X3: list(dB),X2: type,X1: nat] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_490])]) ).
tff(f1196,plain,
( spl24_112
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_112])]) ).
tff(f1755,plain,
( spl24_171
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_171])]) ).
tff(f1760,plain,
( ! [X2: type,X3: list(dB),X0: fun(nat,type),X1: nat,X4: list(type)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl24_112
| ~ spl24_171 ),
inference(resolution,[],[f1756,f1197]) ).
tff(f1197,plain,
( ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) )
| ~ spl24_112 ),
inference(avatar_component_clause,[],[f1196]) ).
tff(f1756,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X2,X1),X0))
| listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1) )
| ~ spl24_171 ),
inference(avatar_component_clause,[],[f1755]) ).
tff(f12261,plain,
( spl24_489
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1421,f1361,f979,f12259]) ).
tff(f12259,plain,
( spl24_489
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun(X0,fun(X2,fun(X1,X0)))] : ( foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),aa(X0,fun(X2,fun(X1,X0)),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_489])]) ).
tff(f1421,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),aa(X0,fun(X2,fun(X1,X0)),X3,X5),X4),X6),X7) )
| ~ spl24_82
| ~ spl24_136 ),
inference(superposition,[],[f1362,f980]) ).
tff(f12257,plain,
( spl24_488
| ~ spl24_82
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1407,f1357,f979,f12255]) ).
tff(f12255,plain,
( spl24_488
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun(X0,fun(X2,fun(X1,X1)))] : ( foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),aa(X0,fun(X2,fun(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_488])]) ).
tff(f1407,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),aa(X0,fun(X2,fun(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),X6,X7)) )
| ~ spl24_82
| ~ spl24_135 ),
inference(superposition,[],[f1358,f980]) ).
tff(f12253,plain,
( spl24_487
| ~ spl24_27
| ~ spl24_72 ),
inference(avatar_split_clause,[],[f932,f925,f666,f12251]) ).
tff(f12251,plain,
( spl24_487
<=> ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK4(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK6(foldl(dB,dB,app,var(X0),X1))),sK5(foldl(dB,dB,app,var(X0),X1))) )
| sP0(foldl(dB,dB,app,var(X0),X1))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_487])]) ).
tff(f666,plain,
( spl24_27
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_27])]) ).
tff(f925,plain,
( spl24_72
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_72])]) ).
tff(f932,plain,
( ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK4(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK6(foldl(dB,dB,app,var(X0),X1))),sK5(foldl(dB,dB,app,var(X0),X1))) )
| sP0(foldl(dB,dB,app,var(X0),X1))
| ~ listsp(dB,it,X1) )
| ~ spl24_27
| ~ spl24_72 ),
inference(resolution,[],[f926,f667]) ).
tff(f667,plain,
( ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) )
| ~ spl24_27 ),
inference(avatar_component_clause,[],[f666]) ).
tff(f926,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| sP0(X0) )
| ~ spl24_72 ),
inference(avatar_component_clause,[],[f925]) ).
tff(f11328,plain,
( spl24_486
| ~ spl24_3
| ~ spl24_217
| ~ spl24_425 ),
inference(avatar_split_clause,[],[f11141,f8238,f2708,f532,f11326]) ).
tff(f11326,plain,
( spl24_486
<=> ! [X0: nat] : sP1(abs(abs(abs(var(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_486])]) ).
tff(f2708,plain,
( spl24_217
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_217])]) ).
tff(f8238,plain,
( spl24_425
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_425])]) ).
tff(f11141,plain,
( ! [X0: nat] :
( ~ pp(fTrue)
| sP1(abs(abs(abs(var(X0))))) )
| ~ spl24_217
| ~ spl24_425 ),
inference(superposition,[],[f2709,f8239]) ).
tff(f8239,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl24_425 ),
inference(avatar_component_clause,[],[f8238]) ).
tff(f2709,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl24_217 ),
inference(avatar_component_clause,[],[f2708]) ).
tff(f11214,plain,
( spl24_485
| ~ spl24_109
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1904,f1897,f1177,f11212]) ).
tff(f11212,plain,
( spl24_485
<=> ! [X4: list(dB),X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK14(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_485])]) ).
tff(f1177,plain,
( spl24_109
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_109])]) ).
tff(f1904,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK14(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl24_109
| ~ spl24_176 ),
inference(resolution,[],[f1898,f1178]) ).
tff(f1178,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl24_109 ),
inference(avatar_component_clause,[],[f1177]) ).
tff(f11210,plain,
( spl24_484
| ~ spl24_111
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1903,f1897,f1189,f11208]) ).
tff(f11208,plain,
( spl24_484
<=> ! [X4: list(dB),X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_484])]) ).
tff(f1189,plain,
( spl24_111
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_111])]) ).
tff(f1903,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl24_111
| ~ spl24_176 ),
inference(resolution,[],[f1898,f1190]) ).
tff(f1190,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl24_111 ),
inference(avatar_component_clause,[],[f1189]) ).
tff(f11206,plain,
( spl24_483
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1829,f1810,f979,f11204]) ).
tff(f11204,plain,
( spl24_483
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: X0,X7: fun(X0,fun(X1,X6))] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_483])]) ).
tff(f1829,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X7: fun(X0,fun(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) )
| ~ spl24_82
| ~ spl24_174 ),
inference(superposition,[],[f1811,f980]) ).
tff(f11202,plain,
( spl24_482
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1828,f1810,f979,f11200]) ).
tff(f11200,plain,
( spl24_482
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: X0,X7: fun(X0,fun(X1,X6))] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_482])]) ).
tff(f1828,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X7: fun(X0,fun(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)) )
| ~ spl24_82
| ~ spl24_174 ),
inference(superposition,[],[f1811,f980]) ).
tff(f11198,plain,
( spl24_481
| ~ spl24_82
| ~ spl24_136
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1668,f1657,f1361,f979,f11196]) ).
tff(f11196,plain,
( spl24_481
<=> ! [X3: fun(nat,type),X4: type,X0: nat,X5: type,X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ( X4 = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_481])]) ).
tff(f1668,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ( X4 = X5 ) )
| ~ spl24_82
| ~ spl24_136
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1667,f980]) ).
tff(f1667,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl24_82
| ~ spl24_136
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1665,f980]) ).
tff(f1665,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl24_136
| ~ spl24_158 ),
inference(superposition,[],[f1658,f1362]) ).
tff(f11194,plain,
( spl24_480
| ~ spl24_82
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1551,f1528,f979,f11192]) ).
tff(f11192,plain,
( spl24_480
<=> ! [X1: $tType,X3: $tType,X0: $tType,X2: $tType,X5: fun(X0,X3),X4: fun(X3,fun(X1,X2)),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X3,fun(X1,X2)),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combb(X3,fun(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),X4,aa(X0,X3,X5,X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_480])]) ).
tff(f1528,plain,
( spl24_144
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_144])]) ).
tff(f1551,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X1,X2)),X5: fun(X0,X3)] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X3,fun(X1,X2)),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combb(X3,fun(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),X4,aa(X0,X3,X5,X6)),X7) )
| ~ spl24_82
| ~ spl24_144 ),
inference(superposition,[],[f980,f1529]) ).
tff(f1529,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) )
| ~ spl24_144 ),
inference(avatar_component_clause,[],[f1528]) ).
tff(f11166,plain,
( spl24_479
| ~ spl24_121
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2023,f2008,f1251,f11164]) ).
tff(f11164,plain,
( spl24_479
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_479])]) ).
tff(f1251,plain,
( spl24_121
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_121])]) ).
tff(f2023,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) )
| ~ spl24_121
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1253]) ).
tff(f1253,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl24_121 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f11119,plain,
( spl24_478
| ~ spl24_82
| ~ spl24_352
| ~ spl24_477 ),
inference(avatar_split_clause,[],[f11115,f11112,f5578,f979,f11117]) ).
tff(f11117,plain,
( spl24_478
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_478])]) ).
tff(f11112,plain,
( spl24_477
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_477])]) ).
tff(f11115,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_477 ),
inference(forward_demodulation,[],[f11113,f5642]) ).
tff(f11113,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl24_477 ),
inference(avatar_component_clause,[],[f11112]) ).
tff(f11114,plain,
( spl24_477
| ~ spl24_125
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2013,f2008,f1286,f11112]) ).
tff(f1286,plain,
( spl24_125
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_125])]) ).
tff(f2013,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl24_125
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1288]) ).
tff(f1288,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_125 ),
inference(avatar_component_clause,[],[f1286]) ).
tff(f11094,plain,
( spl24_476
| ~ spl24_82
| ~ spl24_352
| ~ spl24_475 ),
inference(avatar_split_clause,[],[f11090,f11087,f5578,f979,f11092]) ).
tff(f11092,plain,
( spl24_476
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_476])]) ).
tff(f11087,plain,
( spl24_475
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_475])]) ).
tff(f11090,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_475 ),
inference(forward_demodulation,[],[f11088,f5642]) ).
tff(f11088,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl24_475 ),
inference(avatar_component_clause,[],[f11087]) ).
tff(f11089,plain,
( spl24_475
| ~ spl24_119
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2012,f2008,f1237,f11087]) ).
tff(f1237,plain,
( spl24_119
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_119])]) ).
tff(f2012,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl24_119
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1239]) ).
tff(f1239,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_119 ),
inference(avatar_component_clause,[],[f1237]) ).
tff(f11085,plain,
( spl24_474
| ~ spl24_135
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1497,f1482,f1357,f11083]) ).
tff(f11083,plain,
( spl24_474
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK22(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_474])]) ).
tff(f1482,plain,
( spl24_139
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_139])]) ).
tff(f1497,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK22(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) )
| ~ spl24_135
| ~ spl24_139 ),
inference(superposition,[],[f1483,f1358]) ).
tff(f1483,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl24_139 ),
inference(avatar_component_clause,[],[f1482]) ).
tff(f11081,plain,
( spl24_473
| ~ spl24_135
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1493,f1478,f1357,f11079]) ).
tff(f11079,plain,
( spl24_473
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK20(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_473])]) ).
tff(f1478,plain,
( spl24_138
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_138])]) ).
tff(f1493,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK20(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) )
| ~ spl24_135
| ~ spl24_138 ),
inference(superposition,[],[f1479,f1358]) ).
tff(f1479,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl24_138 ),
inference(avatar_component_clause,[],[f1478]) ).
tff(f10868,plain,
( spl24_472
| ~ spl24_112
| ~ spl24_177 ),
inference(avatar_split_clause,[],[f1917,f1912,f1196,f10866]) ).
tff(f10866,plain,
( spl24_472
<=> ! [X5: type,X4: list(type),X0: fun(nat,type),X3: list(dB),X2: nat,X1: dB] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_472])]) ).
tff(f1912,plain,
( spl24_177
<=> ! [X2: nat,X4: dB,X0: list(type),X5: fun(nat,type),X3: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_177])]) ).
tff(f1917,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: dB,X4: list(type),X5: type] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl24_112
| ~ spl24_177 ),
inference(resolution,[],[f1913,f1197]) ).
tff(f1913,plain,
( ! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4)) )
| ~ spl24_177 ),
inference(avatar_component_clause,[],[f1912]) ).
tff(f10864,plain,
( spl24_471
| ~ spl24_79
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1884,f1810,f979,f962,f10862]) ).
tff(f10862,plain,
( spl24_471
<=> ! [X2: $tType,X0: dB,X3: fun(nat,fun(dB,X2)),X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_471])]) ).
tff(f962,plain,
( spl24_79
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_79])]) ).
tff(f1884,plain,
( ! [X2: $tType,X3: fun(nat,fun(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) )
| ~ spl24_79
| ~ spl24_82
| ~ spl24_174 ),
inference(forward_demodulation,[],[f1834,f980]) ).
tff(f1834,plain,
( ! [X2: $tType,X3: fun(nat,fun(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(dB,X2,aa(nat,fun(dB,X2),X3,X1),X0) )
| ~ spl24_79
| ~ spl24_174 ),
inference(superposition,[],[f1811,f963]) ).
tff(f963,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl24_79 ),
inference(avatar_component_clause,[],[f962]) ).
tff(f10860,plain,
( spl24_470
| ~ spl24_59
| ~ spl24_82
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1805,f1770,f979,f858,f10858]) ).
tff(f10858,plain,
( spl24_470
<=> ! [X0: list(type)] : ( map(type,type,aa(type,fun(type,type),fun1,t),aa(type,list(type),combc(type,list(type),list(type),cons(type),X0),foldr(type,type,fun1,ts,t2))) = aa(type,list(type),combc(type,list(type),list(type),cons(type),map(type,type,aa(type,fun(type,type),fun1,t),X0)),t1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_470])]) ).
tff(f858,plain,
( spl24_59
<=> ( t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_59])]) ).
tff(f1805,plain,
( ! [X0: list(type)] : ( map(type,type,aa(type,fun(type,type),fun1,t),aa(type,list(type),combc(type,list(type),list(type),cons(type),X0),foldr(type,type,fun1,ts,t2))) = aa(type,list(type),combc(type,list(type),list(type),cons(type),map(type,type,aa(type,fun(type,type),fun1,t),X0)),t1) )
| ~ spl24_59
| ~ spl24_82
| ~ spl24_173 ),
inference(forward_demodulation,[],[f1784,f980]) ).
tff(f1784,plain,
( ! [X0: list(type)] : ( map(type,type,aa(type,fun(type,type),fun1,t),aa(type,list(type),combc(type,list(type),list(type),cons(type),X0),foldr(type,type,fun1,ts,t2))) = aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),t1),map(type,type,aa(type,fun(type,type),fun1,t),X0)) )
| ~ spl24_59
| ~ spl24_173 ),
inference(superposition,[],[f1771,f860]) ).
tff(f860,plain,
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)) )
| ~ spl24_59 ),
inference(avatar_component_clause,[],[f858]) ).
tff(f10727,plain,
( spl24_469
| ~ spl24_82
| ~ spl24_352
| ~ spl24_467 ),
inference(avatar_split_clause,[],[f10718,f10715,f5578,f979,f10725]) ).
tff(f10725,plain,
( spl24_469
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_469])]) ).
tff(f10715,plain,
( spl24_467
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_467])]) ).
tff(f10718,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_467 ),
inference(forward_demodulation,[],[f10716,f5642]) ).
tff(f10716,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl24_467 ),
inference(avatar_component_clause,[],[f10715]) ).
tff(f10723,plain,
( spl24_468
| ~ spl24_3
| ~ spl24_217
| ~ spl24_416 ),
inference(avatar_split_clause,[],[f10533,f8171,f2708,f532,f10720]) ).
tff(f10720,plain,
( spl24_468
<=> sP1(abs(abs(abs(abs(ua))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_468])]) ).
tff(f8171,plain,
( spl24_416
<=> ( fTrue = aa(dB,bool,it,abs(abs(ua))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_416])]) ).
tff(f10533,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(ua)))))
| ~ spl24_217
| ~ spl24_416 ),
inference(superposition,[],[f2709,f8173]) ).
tff(f8173,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl24_416 ),
inference(avatar_component_clause,[],[f8171]) ).
tff(f10717,plain,
( spl24_467
| ~ spl24_17
| ~ spl24_189 ),
inference(avatar_split_clause,[],[f2042,f2038,f604,f10715]) ).
tff(f604,plain,
( spl24_17
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_17])]) ).
tff(f2038,plain,
( spl24_189
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_189])]) ).
tff(f2042,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl24_17
| ~ spl24_189 ),
inference(resolution,[],[f2039,f605]) ).
tff(f605,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl24_17 ),
inference(avatar_component_clause,[],[f604]) ).
tff(f2039,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_189 ),
inference(avatar_component_clause,[],[f2038]) ).
tff(f10713,plain,
( spl24_466
| ~ spl24_82
| ~ spl24_181 ),
inference(avatar_split_clause,[],[f1984,f1949,f979,f10711]) ).
tff(f10711,plain,
( spl24_466
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK21(X0,X3,X5,X4,X2,X1)),sK22(X0,X3,X5,X4,X2,X1)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_466])]) ).
tff(f1949,plain,
( spl24_181
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_181])]) ).
tff(f1984,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK21(X0,X3,X5,X4,X2,X1)),sK22(X0,X3,X5,X4,X2,X1)) = X5 ) )
| ~ spl24_82
| ~ spl24_181 ),
inference(superposition,[],[f1950,f980]) ).
tff(f1950,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl24_181 ),
inference(avatar_component_clause,[],[f1949]) ).
tff(f10709,plain,
( spl24_465
| ~ spl24_82
| ~ spl24_180 ),
inference(avatar_split_clause,[],[f1976,f1945,f979,f10707]) ).
tff(f10707,plain,
( spl24_465
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK19(X3,X0,X2,X1,X5,X4)),sK20(X3,X0,X2,X1,X5,X4)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_465])]) ).
tff(f1945,plain,
( spl24_180
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_180])]) ).
tff(f1976,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK19(X3,X0,X2,X1,X5,X4)),sK20(X3,X0,X2,X1,X5,X4)) = X5 ) )
| ~ spl24_82
| ~ spl24_180 ),
inference(superposition,[],[f1946,f980]) ).
tff(f1946,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl24_180 ),
inference(avatar_component_clause,[],[f1945]) ).
tff(f10705,plain,
( spl24_464
| ~ spl24_64
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1873,f1810,f880,f10703]) ).
tff(f10703,plain,
( spl24_464
<=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,aa(fun(X0,nat),fun(X0,type),aa(fun(X0,fun(nat,type)),fun(fun(X0,nat),fun(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_464])]) ).
tff(f880,plain,
( spl24_64
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_64])]) ).
tff(f1873,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,aa(fun(X0,nat),fun(X0,type),aa(fun(X0,fun(nat,type)),fun(fun(X0,nat),fun(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2))))
| ~ spl24_64
| ~ spl24_174 ),
inference(superposition,[],[f881,f1811]) ).
tff(f881,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl24_64 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f10701,plain,
( spl24_463
| ~ spl24_96
| ~ spl24_171 ),
inference(avatar_split_clause,[],[f1762,f1755,f1092,f10698]) ).
tff(f10698,plain,
( spl24_463
<=> listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(e)),fEx(type)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_463])]) ).
tff(f1092,plain,
( spl24_96
<=> pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_96])]) ).
tff(f1762,plain,
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(e)),fEx(type)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))
| ~ spl24_96
| ~ spl24_171 ),
inference(resolution,[],[f1756,f1094]) ).
tff(f1094,plain,
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts))
| ~ spl24_96 ),
inference(avatar_component_clause,[],[f1092]) ).
tff(f10512,plain,
( spl24_462
| ~ spl24_162
| ~ spl24_191 ),
inference(avatar_split_clause,[],[f2062,f2058,f1692,f10510]) ).
tff(f10510,plain,
( spl24_462
<=> ! [X4: dB,X0: fun(nat,type),X3: type,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_462])]) ).
tff(f2062,plain,
( ! [X2: dB,X3: type,X0: fun(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) )
| ~ spl24_162
| ~ spl24_191 ),
inference(resolution,[],[f2059,f1693]) ).
tff(f10508,plain,
( spl24_461
| ~ spl24_64
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1886,f1810,f979,f880,f10506]) ).
tff(f10506,plain,
( spl24_461
<=> ! [X0: $tType,X3: nat,X2: fun(nat,X0),X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_461])]) ).
tff(f1886,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3)))
| ~ spl24_64
| ~ spl24_82
| ~ spl24_174 ),
inference(forward_demodulation,[],[f1846,f980]) ).
tff(f1846,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(X0,type,aa(nat,fun(X0,type),X1,X3),aa(nat,X0,X2,X3))),var(X3)))
| ~ spl24_64
| ~ spl24_174 ),
inference(superposition,[],[f881,f1811]) ).
tff(f10504,plain,
( spl24_460
| ~ spl24_139
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1795,f1770,f1482,f10502]) ).
tff(f10502,plain,
( spl24_460
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK22(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_460])]) ).
tff(f1795,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK22(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl24_139
| ~ spl24_173 ),
inference(superposition,[],[f1483,f1771]) ).
tff(f10500,plain,
( spl24_459
| ~ spl24_138
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1794,f1770,f1478,f10498]) ).
tff(f10498,plain,
( spl24_459
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK20(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_459])]) ).
tff(f1794,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK20(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl24_138
| ~ spl24_173 ),
inference(superposition,[],[f1479,f1771]) ).
tff(f10496,plain,
( spl24_458
| ~ spl24_114
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1603,f1595,f1207,f10494]) ).
tff(f10494,plain,
( spl24_458
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_458])]) ).
tff(f1603,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl24_114
| ~ spl24_150 ),
inference(resolution,[],[f1596,f1208]) ).
tff(f10492,plain,
( spl24_457
| ~ spl24_114
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1584,f1576,f1207,f10490]) ).
tff(f10490,plain,
( spl24_457
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_457])]) ).
tff(f1584,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl24_114
| ~ spl24_148 ),
inference(resolution,[],[f1577,f1208]) ).
tff(f9864,plain,
( spl24_456
| ~ spl24_82
| ~ spl24_352
| ~ spl24_455 ),
inference(avatar_split_clause,[],[f9860,f9857,f5578,f979,f9862]) ).
tff(f9862,plain,
( spl24_456
<=> ! [X4: nat,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_456])]) ).
tff(f9857,plain,
( spl24_455
<=> ! [X4: nat,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_455])]) ).
tff(f9860,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_455 ),
inference(forward_demodulation,[],[f9858,f5642]) ).
tff(f9858,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl24_455 ),
inference(avatar_component_clause,[],[f9857]) ).
tff(f9859,plain,
( spl24_455
| ~ spl24_64
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2018,f2008,f880,f9857]) ).
tff(f2018,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl24_64
| ~ spl24_187 ),
inference(resolution,[],[f2009,f881]) ).
tff(f9855,plain,
( spl24_454
| ~ spl24_23
| ~ spl24_82
| ~ spl24_181 ),
inference(avatar_split_clause,[],[f1988,f1949,f979,f639,f9853]) ).
tff(f9853,plain,
( spl24_454
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X1,combi(X0),X3,X2)),sK22(X0,X0,X1,combi(X0),X3,X2)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_454])]) ).
tff(f639,plain,
( spl24_23
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_23])]) ).
tff(f1988,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X1,combi(X0),X3,X2)),sK22(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl24_23
| ~ spl24_82
| ~ spl24_181 ),
inference(forward_demodulation,[],[f1986,f980]) ).
tff(f1986,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X1,combi(X0),X3,X2)),sK22(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl24_23
| ~ spl24_181 ),
inference(superposition,[],[f1950,f640]) ).
tff(f640,plain,
( ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 )
| ~ spl24_23 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f9851,plain,
( spl24_453
| ~ spl24_23
| ~ spl24_82
| ~ spl24_180 ),
inference(avatar_split_clause,[],[f1980,f1945,f979,f639,f9849]) ).
tff(f9849,plain,
( spl24_453
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X0,X3,X2,X1,combi(X0))),sK20(X0,X0,X3,X2,X1,combi(X0))) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_453])]) ).
tff(f1980,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X0,X3,X2,X1,combi(X0))),sK20(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl24_23
| ~ spl24_82
| ~ spl24_180 ),
inference(forward_demodulation,[],[f1978,f980]) ).
tff(f1978,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X0,X3,X2,X1,combi(X0))),sK20(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl24_23
| ~ spl24_180 ),
inference(superposition,[],[f1946,f640]) ).
tff(f9847,plain,
( spl24_452
| ~ spl24_3
| ~ spl24_217
| ~ spl24_410 ),
inference(avatar_split_clause,[],[f9428,f7974,f2708,f532,f9844]) ).
tff(f9844,plain,
( spl24_452
<=> sP1(abs(abs(abs(abs(u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_452])]) ).
tff(f7974,plain,
( spl24_410
<=> ( fTrue = aa(dB,bool,it,abs(abs(u))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_410])]) ).
tff(f9428,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(u)))))
| ~ spl24_217
| ~ spl24_410 ),
inference(superposition,[],[f2709,f7976]) ).
tff(f7976,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl24_410 ),
inference(avatar_component_clause,[],[f7974]) ).
tff(f9842,plain,
( spl24_451
| ~ spl24_45
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1845,f1810,f760,f9840]) ).
tff(f9840,plain,
( spl24_451
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X4: X0,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_451])]) ).
tff(f760,plain,
( spl24_45
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_45])]) ).
tff(f1845,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3))) )
| ~ spl24_45
| ~ spl24_174 ),
inference(superposition,[],[f761,f1811]) ).
tff(f761,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl24_45 ),
inference(avatar_component_clause,[],[f760]) ).
tff(f9838,plain,
( spl24_450
| ~ spl24_134
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1791,f1770,f1353,f9836]) ).
tff(f9836,plain,
( spl24_450
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK21(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_450])]) ).
tff(f1353,plain,
( spl24_134
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_134])]) ).
tff(f1791,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK21(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl24_134
| ~ spl24_173 ),
inference(superposition,[],[f1354,f1771]) ).
tff(f1354,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl24_134 ),
inference(avatar_component_clause,[],[f1353]) ).
tff(f9834,plain,
( spl24_449
| ~ spl24_133
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1790,f1770,f1349,f9832]) ).
tff(f9832,plain,
( spl24_449
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK19(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_449])]) ).
tff(f1349,plain,
( spl24_133
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_133])]) ).
tff(f1790,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK19(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl24_133
| ~ spl24_173 ),
inference(superposition,[],[f1350,f1771]) ).
tff(f1350,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl24_133 ),
inference(avatar_component_clause,[],[f1349]) ).
tff(f9830,plain,
( spl24_448
| ~ spl24_135
| ~ spl24_143 ),
inference(avatar_split_clause,[],[f1532,f1524,f1357,f9828]) ).
tff(f9828,plain,
( spl24_448
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_448])]) ).
tff(f1524,plain,
( spl24_143
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_143])]) ).
tff(f1532,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) )
| ~ spl24_135
| ~ spl24_143 ),
inference(superposition,[],[f1525,f1358]) ).
tff(f1525,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 = X3 ) )
| ~ spl24_143 ),
inference(avatar_component_clause,[],[f1524]) ).
tff(f9826,plain,
( spl24_447
| ~ spl24_82
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1298,f1293,f979,f9824]) ).
tff(f9824,plain,
( spl24_447
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun(X2,fun(X0,fun(list(X0),X1)))] : ( list_case(X1,X0,X7,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_447])]) ).
tff(f1298,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X6) )
| ~ spl24_82
| ~ spl24_126 ),
inference(superposition,[],[f1294,f980]) ).
tff(f9822,plain,
( spl24_446
| ~ spl24_82
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1297,f1293,f979,f9820]) ).
tff(f9820,plain,
( spl24_446
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun(X0,fun(X2,fun(list(X0),X1)))] : ( list_case(X1,X0,X7,combc(X0,X2,fun(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_446])]) ).
tff(f1297,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,combc(X0,X2,fun(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X6) )
| ~ spl24_82
| ~ spl24_126 ),
inference(superposition,[],[f1294,f980]) ).
tff(f8971,plain,
( spl24_445
| ~ spl24_98
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1874,f1810,f1103,f8969]) ).
tff(f8969,plain,
( spl24_445
<=> ! [X0: type,X3: type,X2: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_445])]) ).
tff(f1103,plain,
( spl24_98
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_98])]) ).
tff(f1874,plain,
( ! [X2: type,X3: type,X0: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) )
| ~ spl24_98
| ~ spl24_174 ),
inference(superposition,[],[f1104,f1811]) ).
tff(f1104,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_98 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f8967,plain,
( spl24_444
| ~ spl24_100
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1857,f1810,f1111,f8965]) ).
tff(f8965,plain,
( spl24_444
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_444])]) ).
tff(f1857,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) )
| ~ spl24_100
| ~ spl24_174 ),
inference(superposition,[],[f1112,f1811]) ).
tff(f8961,plain,
( spl24_443
| ~ spl24_10
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1842,f1810,f564,f8959]) ).
tff(f8959,plain,
( spl24_443
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: fun(X1,fun(X0,bool))] :
( ( fFalse = aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_443])]) ).
tff(f564,plain,
( spl24_10
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_10])]) ).
tff(f1842,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: fun(X1,X0)] :
( ( fFalse = aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) )
| ~ spl24_10
| ~ spl24_174 ),
inference(superposition,[],[f1811,f565]) ).
tff(f565,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f8957,plain,
( spl24_442
| ~ spl24_10
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1837,f1810,f564,f8955]) ).
tff(f8955,plain,
( spl24_442
<=> ! [X3: $tType,X0: $tType,X4: fun(X0,fun(bool,X3)),X2: X0,X1: fun(X0,bool)] :
( ( aa(X0,X3,aa(fun(X0,bool),fun(X0,X3),aa(fun(X0,fun(bool,X3)),fun(fun(X0,bool),fun(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_442])]) ).
tff(f1837,plain,
( ! [X0: $tType,X3: $tType,X2: X0,X1: fun(X0,bool),X4: fun(X0,fun(bool,X3))] :
( ( aa(X0,X3,aa(fun(X0,bool),fun(X0,X3),aa(fun(X0,fun(bool,X3)),fun(fun(X0,bool),fun(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl24_10
| ~ spl24_174 ),
inference(superposition,[],[f1811,f565]) ).
tff(f8953,plain,
( spl24_441
| ~ spl24_10
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1815,f1810,f564,f8951]) ).
tff(f8951,plain,
( spl24_441
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X4: X0,X3: fun(X0,X1)] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_441])]) ).
tff(f1815,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) )
| ~ spl24_10
| ~ spl24_174 ),
inference(superposition,[],[f1811,f565]) ).
tff(f8949,plain,
( spl24_440
| ~ spl24_164
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1733,f1726,f1707,f8947]) ).
tff(f8947,plain,
( spl24_440
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK16(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_440])]) ).
tff(f1707,plain,
( spl24_164
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_164])]) ).
tff(f1733,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK16(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X4))) )
| ~ spl24_164
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1708]) ).
tff(f1708,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1))) )
| ~ spl24_164 ),
inference(avatar_component_clause,[],[f1707]) ).
tff(f8945,plain,
( spl24_439
| ~ spl24_109
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1602,f1595,f1177,f8943]) ).
tff(f8943,plain,
( spl24_439
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_439])]) ).
tff(f1602,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl24_109
| ~ spl24_150 ),
inference(resolution,[],[f1596,f1178]) ).
tff(f8941,plain,
( spl24_438
| ~ spl24_111
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1601,f1595,f1189,f8939]) ).
tff(f8939,plain,
( spl24_438
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_438])]) ).
tff(f1601,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl24_111
| ~ spl24_150 ),
inference(resolution,[],[f1596,f1190]) ).
tff(f8937,plain,
( spl24_437
| ~ spl24_109
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1583,f1576,f1177,f8935]) ).
tff(f8935,plain,
( spl24_437
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_437])]) ).
tff(f1583,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl24_109
| ~ spl24_148 ),
inference(resolution,[],[f1577,f1178]) ).
tff(f8933,plain,
( spl24_436
| ~ spl24_111
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1582,f1576,f1189,f8931]) ).
tff(f8931,plain,
( spl24_436
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_436])]) ).
tff(f1582,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl24_111
| ~ spl24_148 ),
inference(resolution,[],[f1577,f1190]) ).
tff(f8929,plain,
( spl24_435
| ~ spl24_104
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1427,f1361,f1149,f8927]) ).
tff(f8927,plain,
( spl24_435
<=> ! [X0: dB,X3: list(nat),X2: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_435])]) ).
tff(f1427,plain,
( ! [X2: dB,X3: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X2,X3) )
| ~ spl24_104
| ~ spl24_136 ),
inference(superposition,[],[f1362,f1150]) ).
tff(f8925,plain,
( spl24_434
| ~ spl24_135
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1424,f1361,f1357,f8923]) ).
tff(f8923,plain,
( spl24_434
<=> ! [X0: $tType,X3: list(X0),X4: X0,X5: list(X0),X2: X0,X1: fun(X0,fun(X0,X0))] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_434])]) ).
tff(f1424,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(X0,X0)),X4: X0,X5: list(X0)] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) )
| ~ spl24_135
| ~ spl24_136 ),
inference(superposition,[],[f1362,f1358]) ).
tff(f8921,plain,
( spl24_433
| ~ spl24_3
| ~ spl24_217
| ~ spl24_403 ),
inference(avatar_split_clause,[],[f8755,f7515,f2708,f532,f8918]) ).
tff(f8918,plain,
( spl24_433
<=> sP1(abs(abs(abs(abs(t3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_433])]) ).
tff(f7515,plain,
( spl24_403
<=> ( fTrue = aa(dB,bool,it,abs(abs(t3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_403])]) ).
tff(f8755,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(t3)))))
| ~ spl24_217
| ~ spl24_403 ),
inference(superposition,[],[f2709,f7517]) ).
tff(f7517,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t3))) )
| ~ spl24_403 ),
inference(avatar_component_clause,[],[f7515]) ).
tff(f8784,plain,
( spl24_432
| ~ spl24_82
| ~ spl24_352
| ~ spl24_431 ),
inference(avatar_split_clause,[],[f8780,f8777,f5578,f979,f8782]) ).
tff(f8782,plain,
( spl24_432
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_432])]) ).
tff(f8777,plain,
( spl24_431
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_431])]) ).
tff(f8780,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_431 ),
inference(forward_demodulation,[],[f8778,f5642]) ).
tff(f8778,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl24_431 ),
inference(avatar_component_clause,[],[f8777]) ).
tff(f8779,plain,
( spl24_431
| ~ spl24_17
| ~ spl24_184 ),
inference(avatar_split_clause,[],[f1967,f1963,f604,f8777]) ).
tff(f1963,plain,
( spl24_184
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_184])]) ).
tff(f1967,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl24_17
| ~ spl24_184 ),
inference(resolution,[],[f1964,f605]) ).
tff(f1964,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_184 ),
inference(avatar_component_clause,[],[f1963]) ).
tff(f8775,plain,
( spl24_430
| ~ spl24_82
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1933,f1929,f979,f8773]) ).
tff(f8773,plain,
( spl24_430
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) = aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_430])]) ).
tff(f1929,plain,
( spl24_179
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_179])]) ).
tff(f1933,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) = aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_82
| ~ spl24_179 ),
inference(superposition,[],[f1930,f980]) ).
tff(f1930,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl24_179 ),
inference(avatar_component_clause,[],[f1929]) ).
tff(f8771,plain,
( spl24_429
| ~ spl24_68
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1864,f1810,f905,f8769]) ).
tff(f8769,plain,
( spl24_429
<=> ! [X0: $tType,X2: fun(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_429])]) ).
tff(f905,plain,
( spl24_68
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_68])]) ).
tff(f1864,plain,
( ! [X0: $tType,X2: fun(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ~ spl24_68
| ~ spl24_174 ),
inference(superposition,[],[f906,f1811]) ).
tff(f906,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 )
| ~ spl24_68 ),
inference(avatar_component_clause,[],[f905]) ).
tff(f8750,plain,
( spl24_428
| ~ spl24_26
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1775,f1770,f661,f8748]) ).
tff(f8748,plain,
( spl24_428
<=> ! [X0: $tType,X4: list(nat),X3: X0,X2: nat,X1: fun(nat,X0)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_428])]) ).
tff(f661,plain,
( spl24_26
<=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_26])]) ).
tff(f1775,plain,
( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X4: list(nat)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) )
| ~ spl24_26
| ~ spl24_173 ),
inference(superposition,[],[f1771,f662]) ).
tff(f662,plain,
( ! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 )
| ~ spl24_26 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f8746,plain,
( spl24_427
| ~ spl24_133
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1418,f1357,f1349,f8744]) ).
tff(f8744,plain,
( spl24_427
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK19(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_427])]) ).
tff(f1418,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK19(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) )
| ~ spl24_133
| ~ spl24_135 ),
inference(superposition,[],[f1350,f1358]) ).
tff(f8742,plain,
( spl24_426
| ~ spl24_134
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1417,f1357,f1353,f8740]) ).
tff(f8740,plain,
( spl24_426
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK21(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_426])]) ).
tff(f1417,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK21(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) )
| ~ spl24_134
| ~ spl24_135 ),
inference(superposition,[],[f1354,f1358]) ).
tff(f8240,plain,
( spl24_425
| ~ spl24_108
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5144,f5088,f1173,f8238]) ).
tff(f1173,plain,
( spl24_108
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_108])]) ).
tff(f5088,plain,
( spl24_326
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_326])]) ).
tff(f5144,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl24_108
| ~ spl24_326 ),
inference(resolution,[],[f5089,f1174]) ).
tff(f1174,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl24_108 ),
inference(avatar_component_clause,[],[f1173]) ).
tff(f5089,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( fTrue = aa(dB,bool,it,X0) ) )
| ~ spl24_326 ),
inference(avatar_component_clause,[],[f5088]) ).
tff(f8236,plain,
( spl24_424
| ~ spl24_123
| ~ spl24_191 ),
inference(avatar_split_clause,[],[f2061,f2058,f1268,f8234]) ).
tff(f8234,plain,
( spl24_424
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,dB,dB,app,X0),var(i)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_424])]) ).
tff(f1268,plain,
( spl24_123
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2)),var(i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_123])]) ).
tff(f2061,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,dB,dB,app,X0),var(i)))) )
| ~ spl24_123
| ~ spl24_191 ),
inference(resolution,[],[f2059,f1270]) ).
tff(f1270,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2)),var(i)))
| ~ spl24_123 ),
inference(avatar_component_clause,[],[f1268]) ).
tff(f8218,plain,
( spl24_423
| ~ spl24_82
| ~ spl24_352
| ~ spl24_422 ),
inference(avatar_split_clause,[],[f8214,f8211,f5578,f979,f8216]) ).
tff(f8216,plain,
( spl24_423
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_423])]) ).
tff(f8211,plain,
( spl24_422
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_422])]) ).
tff(f8214,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_422 ),
inference(forward_demodulation,[],[f8212,f5642]) ).
tff(f8212,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl24_422 ),
inference(avatar_component_clause,[],[f8211]) ).
tff(f8213,plain,
( spl24_422
| ~ spl24_90
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2025,f2008,f1048,f8211]) ).
tff(f1048,plain,
( spl24_90
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_90])]) ).
tff(f2025,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl24_90
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1050]) ).
tff(f1050,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_90 ),
inference(avatar_component_clause,[],[f1048]) ).
tff(f8195,plain,
( spl24_421
| ~ spl24_82
| ~ spl24_352
| ~ spl24_420 ),
inference(avatar_split_clause,[],[f8191,f8188,f5578,f979,f8193]) ).
tff(f8193,plain,
( spl24_421
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_421])]) ).
tff(f8188,plain,
( spl24_420
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_420])]) ).
tff(f8191,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_420 ),
inference(forward_demodulation,[],[f8189,f5642]) ).
tff(f8189,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl24_420 ),
inference(avatar_component_clause,[],[f8188]) ).
tff(f8190,plain,
( spl24_420
| ~ spl24_92
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2022,f2008,f1061,f8188]) ).
tff(f1061,plain,
( spl24_92
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_92])]) ).
tff(f2022,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl24_92
| ~ spl24_187 ),
inference(resolution,[],[f2009,f1063]) ).
tff(f1063,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_92 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f8186,plain,
( spl24_419
| ~ spl24_10
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1785,f1770,f564,f8184]) ).
tff(f8184,plain,
( spl24_419
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: fun(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_419])]) ).
tff(f1785,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl24_10
| ~ spl24_173 ),
inference(superposition,[],[f1771,f565]) ).
tff(f8182,plain,
( spl24_418
| ~ spl24_150
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1732,f1726,f1595,f8180]) ).
tff(f8180,plain,
( spl24_418
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_418])]) ).
tff(f1732,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl24_150
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1596]) ).
tff(f8178,plain,
( spl24_417
| ~ spl24_148
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1731,f1726,f1576,f8176]) ).
tff(f8176,plain,
( spl24_417
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK14(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_417])]) ).
tff(f1731,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK14(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl24_148
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1577]) ).
tff(f8174,plain,
( spl24_416
| ~ spl24_234
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5142,f5088,f2867,f8171]) ).
tff(f2867,plain,
( spl24_234
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_234])]) ).
tff(f5142,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl24_234
| ~ spl24_326 ),
inference(resolution,[],[f5089,f2869]) ).
tff(f2869,plain,
( sP1(abs(abs(ua)))
| ~ spl24_234 ),
inference(avatar_component_clause,[],[f2867]) ).
tff(f8169,plain,
( spl24_415
| ~ spl24_82
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1306,f1293,f979,f8167]) ).
tff(f8167,plain,
( spl24_415
<=> ! [X0: $tType,X1: $tType,X2: $tType,X6: fun(X1,X2),X4: X0,X5: list(X0),X3: fun(X0,fun(list(X0),fun(X1,X2))),X7: X1] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_415])]) ).
tff(f1306,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(list(X0),fun(X1,X2))),X6: fun(X1,X2),X7: X1,X4: X0,X5: list(X0)] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) )
| ~ spl24_82
| ~ spl24_126 ),
inference(superposition,[],[f980,f1294]) ).
tff(f8165,plain,
( spl24_414
| ~ spl24_82
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1087,f1077,f979,f8163]) ).
tff(f8163,plain,
( spl24_414
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK18(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK18(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_414])]) ).
tff(f1087,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK18(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK18(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) )
| ~ spl24_82
| ~ spl24_95 ),
inference(superposition,[],[f1078,f980]) ).
tff(f8161,plain,
( spl24_413
| ~ spl24_82
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1082,f1077,f979,f8159]) ).
tff(f8159,plain,
( spl24_413
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X3: fun(X2,fun(X0,X1)),X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK18(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK18(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_413])]) ).
tff(f1082,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK18(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK18(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) )
| ~ spl24_82
| ~ spl24_95 ),
inference(superposition,[],[f1078,f980]) ).
tff(f8073,plain,
( spl24_412
| ~ spl24_45
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1856,f1810,f760,f8071]) ).
tff(f8071,plain,
( spl24_412
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_412])]) ).
tff(f1856,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: fun(X1,X0)] :
( ~ pp(aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) )
| ~ spl24_45
| ~ spl24_174 ),
inference(superposition,[],[f761,f1811]) ).
tff(f8069,plain,
( spl24_411
| ~ spl24_26
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1818,f1810,f661,f8067]) ).
tff(f8067,plain,
( spl24_411
<=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X4: fun(X0,X1),X5: fun(nat,X0),X3: nat] : ( aa(nat,X1,aa(fun(nat,X0),fun(nat,X1),aa(fun(nat,fun(X0,X1)),fun(fun(nat,X0),fun(nat,X1)),combs(nat,X0,X1),shift(fun(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_411])]) ).
tff(f1818,plain,
( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,X0)] : ( aa(nat,X1,aa(fun(nat,X0),fun(nat,X1),aa(fun(nat,fun(X0,X1)),fun(fun(nat,X0),fun(nat,X1)),combs(nat,X0,X1),shift(fun(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) )
| ~ spl24_26
| ~ spl24_174 ),
inference(superposition,[],[f1811,f662]) ).
tff(f7977,plain,
( spl24_410
| ~ spl24_228
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5141,f5088,f2801,f7974]) ).
tff(f2801,plain,
( spl24_228
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_228])]) ).
tff(f5141,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl24_228
| ~ spl24_326 ),
inference(resolution,[],[f5089,f2803]) ).
tff(f2803,plain,
( sP1(abs(abs(u)))
| ~ spl24_228 ),
inference(avatar_component_clause,[],[f2801]) ).
tff(f7554,plain,
( spl24_409
| ~ spl24_26
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1883,f1810,f979,f661,f7552]) ).
tff(f7552,plain,
( spl24_409
<=> ! [X0: $tType,X4: $tType,X3: X0,X5: fun(nat,fun(X0,X4)),X2: nat,X1: fun(nat,X0)] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_409])]) ).
tff(f1883,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X5: fun(nat,fun(X0,X4))] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) )
| ~ spl24_26
| ~ spl24_82
| ~ spl24_174 ),
inference(forward_demodulation,[],[f1827,f980]) ).
tff(f1827,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X5: fun(nat,fun(X0,X4))] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(X0,X4,aa(nat,fun(X0,X4),X5,X2),X3) )
| ~ spl24_26
| ~ spl24_174 ),
inference(superposition,[],[f1811,f662]) ).
tff(f7550,plain,
( spl24_408
| ~ spl24_97
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1876,f1810,f1099,f7548]) ).
tff(f7548,plain,
( spl24_408
<=> ! [X0: type,X3: type,X2: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_408])]) ).
tff(f1099,plain,
( spl24_97
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_97])]) ).
tff(f1876,plain,
( ! [X2: type,X3: type,X0: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_97
| ~ spl24_174 ),
inference(superposition,[],[f1100,f1811]) ).
tff(f1100,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_97 ),
inference(avatar_component_clause,[],[f1099]) ).
tff(f7546,plain,
( spl24_407
| ~ spl24_99
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1859,f1810,f1107,f7544]) ).
tff(f7544,plain,
( spl24_407
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_407])]) ).
tff(f1859,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_99
| ~ spl24_174 ),
inference(superposition,[],[f1108,f1811]) ).
tff(f7542,plain,
( spl24_406
| ~ spl24_82
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1838,f1810,f979,f7540]) ).
tff(f7540,plain,
( spl24_406
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(fun(X2,X0),fun(X2,X1),aa(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_406])]) ).
tff(f1838,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(fun(X2,X0),fun(X2,X1),aa(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) )
| ~ spl24_82
| ~ spl24_174 ),
inference(superposition,[],[f1811,f980]) ).
tff(f7538,plain,
( spl24_405
| ~ spl24_82
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1086,f1077,f979,f7536]) ).
tff(f7536,plain,
( spl24_405
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK18(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK18(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_405])]) ).
tff(f1086,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK18(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK18(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl24_82
| ~ spl24_95 ),
inference(superposition,[],[f1078,f980]) ).
tff(f7534,plain,
( spl24_404
| ~ spl24_82
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1081,f1077,f979,f7532]) ).
tff(f7532,plain,
( spl24_404
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,X1),X4: X2,X3: fun(X0,fun(X2,X1))] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK18(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK18(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_404])]) ).
tff(f1081,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK18(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK18(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl24_82
| ~ spl24_95 ),
inference(superposition,[],[f1078,f980]) ).
tff(f7518,plain,
( spl24_403
| ~ spl24_222
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5140,f5088,f2773,f7515]) ).
tff(f2773,plain,
( spl24_222
<=> sP1(abs(abs(t3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_222])]) ).
tff(f5140,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t3))) )
| ~ spl24_222
| ~ spl24_326 ),
inference(resolution,[],[f5089,f2775]) ).
tff(f2775,plain,
( sP1(abs(abs(t3)))
| ~ spl24_222 ),
inference(avatar_component_clause,[],[f2773]) ).
tff(f7473,plain,
( spl24_402
| ~ spl24_143
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1796,f1770,f1524,f7471]) ).
tff(f7471,plain,
( spl24_402
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_402])]) ).
tff(f1796,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) )
| ~ spl24_143
| ~ spl24_173 ),
inference(superposition,[],[f1525,f1771]) ).
tff(f7469,plain,
( spl24_401
| ~ spl24_125
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1730,f1726,f1286,f7467]) ).
tff(f7467,plain,
( spl24_401
<=> ! [X0: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),X0),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_401])]) ).
tff(f1730,plain,
( ! [X0: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),X0),sK3)) )
| ~ spl24_125
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1288]) ).
tff(f7465,plain,
( spl24_400
| ~ spl24_119
| ~ spl24_167 ),
inference(avatar_split_clause,[],[f1729,f1726,f1237,f7463]) ).
tff(f7463,plain,
( spl24_400
<=> ! [X0: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),X0),ts)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_400])]) ).
tff(f1729,plain,
( ! [X0: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),X0),ts)) )
| ~ spl24_119
| ~ spl24_167 ),
inference(resolution,[],[f1727,f1239]) ).
tff(f7153,plain,
( spl24_399
| ~ spl24_99
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1936,f1929,f1107,f7151]) ).
tff(f7151,plain,
( spl24_399
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_399])]) ).
tff(f1936,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl24_99
| ~ spl24_179 ),
inference(superposition,[],[f1108,f1930]) ).
tff(f7149,plain,
( spl24_398
| ~ spl24_100
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1934,f1929,f1111,f7147]) ).
tff(f7147,plain,
( spl24_398
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_398])]) ).
tff(f1934,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) )
| ~ spl24_100
| ~ spl24_179 ),
inference(superposition,[],[f1112,f1930]) ).
tff(f7145,plain,
( spl24_397
| ~ spl24_75
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1902,f1897,f942,f7143]) ).
tff(f7143,plain,
( spl24_397
<=> ! [X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,var(X3),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_397])]) ).
tff(f942,plain,
( spl24_75
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_75])]) ).
tff(f1902,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun1,X1),sK17(X1,X2,var(X3),X0)) ) )
| ~ spl24_75
| ~ spl24_176 ),
inference(resolution,[],[f1898,f943]) ).
tff(f943,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl24_75 ),
inference(avatar_component_clause,[],[f942]) ).
tff(f7141,plain,
( spl24_396
| ~ spl24_132
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1900,f1897,f1344,f7139]) ).
tff(f7139,plain,
( spl24_396
<=> ! [X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X3,X0))),sK11(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_396])]) ).
tff(f1900,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X3,X0))),sK11(X3,X0)),X3)) )
| ~ spl24_132
| ~ spl24_176 ),
inference(resolution,[],[f1898,f1345]) ).
tff(f7137,plain,
( spl24_395
| ~ spl24_18
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1825,f1810,f608,f7135]) ).
tff(f7135,plain,
( spl24_395
<=> ! [X2: $tType,X0: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun(X0,X0),fun(X0,X2),aa(fun(X0,fun(X0,X2)),fun(fun(X0,X0),fun(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_395])]) ).
tff(f1825,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun(X0,X0),fun(X0,X2),aa(fun(X0,fun(X0,X2)),fun(fun(X0,X0),fun(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) )
| ~ spl24_18
| ~ spl24_174 ),
inference(superposition,[],[f1811,f609]) ).
tff(f7133,plain,
( spl24_394
| ~ spl24_137
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1792,f1770,f1474,f7131]) ).
tff(f7131,plain,
( spl24_394
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_394])]) ).
tff(f1792,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) )
| ~ spl24_137
| ~ spl24_173 ),
inference(superposition,[],[f1475,f1771]) ).
tff(f7129,plain,
( spl24_393
| ~ spl24_53
| ~ spl24_160 ),
inference(avatar_split_clause,[],[f1681,f1676,f815,f7127]) ).
tff(f7127,plain,
( spl24_393
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X1,X2)) != foldl(dB,dB,app,X3,map(dB,dB,combc(dB,nat,dB,lift,X0),X2)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_393])]) ).
tff(f815,plain,
( spl24_53
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_53])]) ).
tff(f1676,plain,
( spl24_160
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_160])]) ).
tff(f1681,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X1,X2)) != foldl(dB,dB,app,X3,map(dB,dB,combc(dB,nat,dB,lift,X0),X2)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl24_53
| ~ spl24_160 ),
inference(superposition,[],[f816,f1677]) ).
tff(f1677,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl24_160 ),
inference(avatar_component_clause,[],[f1676]) ).
tff(f816,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) )
| ( X0 = X2 ) )
| ~ spl24_53 ),
inference(avatar_component_clause,[],[f815]) ).
tff(f7125,plain,
( spl24_392
| ~ spl24_3
| ~ spl24_217
| ~ spl24_349 ),
inference(avatar_split_clause,[],[f6719,f5512,f2708,f532,f7122]) ).
tff(f7122,plain,
( spl24_392
<=> sP1(abs(abs(abs(ua)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_392])]) ).
tff(f5512,plain,
( spl24_349
<=> ( fTrue = aa(dB,bool,it,abs(ua)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_349])]) ).
tff(f6719,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(ua))))
| ~ spl24_217
| ~ spl24_349 ),
inference(superposition,[],[f2709,f5514]) ).
tff(f5514,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl24_349 ),
inference(avatar_component_clause,[],[f5512]) ).
tff(f7120,plain,
( spl24_391
| ~ spl24_64
| ~ spl24_82
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1554,f1528,f979,f880,f7118]) ).
tff(f7118,plain,
( spl24_391
<=> ! [X0: $tType,X3: nat,X2: fun(nat,X0),X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_391])]) ).
tff(f1554,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl24_64
| ~ spl24_82
| ~ spl24_144 ),
inference(forward_demodulation,[],[f1547,f980]) ).
tff(f1547,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(X0,type),fun(fun(nat,X0),fun(nat,type)),combb(X0,type,nat),X1),X2)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl24_64
| ~ spl24_144 ),
inference(superposition,[],[f881,f1529]) ).
tff(f6745,plain,
( spl24_390
| ~ spl24_82
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1788,f1770,f979,f6743]) ).
tff(f6743,plain,
( spl24_390
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_390])]) ).
tff(f1788,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) )
| ~ spl24_82
| ~ spl24_173 ),
inference(superposition,[],[f1771,f980]) ).
tff(f6741,plain,
( spl24_389
| ~ spl24_45
| ~ spl24_164 ),
inference(avatar_split_clause,[],[f1711,f1707,f760,f6739]) ).
tff(f6739,plain,
( spl24_389
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_389])]) ).
tff(f1711,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1)))) )
| ~ spl24_45
| ~ spl24_164 ),
inference(resolution,[],[f1708,f761]) ).
tff(f6737,plain,
( spl24_388
| ~ spl24_135
| ~ spl24_137 ),
inference(avatar_split_clause,[],[f1486,f1474,f1357,f6735]) ).
tff(f6735,plain,
( spl24_388
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_388])]) ).
tff(f1486,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) )
| ~ spl24_135
| ~ spl24_137 ),
inference(superposition,[],[f1475,f1358]) ).
tff(f6733,plain,
( spl24_387
| ~ spl24_26
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1420,f1361,f661,f6731]) ).
tff(f6731,plain,
( spl24_387
<=> ! [X0: $tType,X2: nat,X4: X0,X5: list(X0),X3: fun(X0,nat),X1: fun(nat,fun(X0,nat))] : ( foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_387])]) ).
tff(f1420,plain,
( ! [X0: $tType,X2: nat,X3: fun(X0,nat),X1: fun(nat,fun(X0,nat)),X4: X0,X5: list(X0)] : ( foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) )
| ~ spl24_26
| ~ spl24_136 ),
inference(superposition,[],[f1362,f662]) ).
tff(f6714,plain,
( spl24_386
| ~ spl24_26
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1406,f1357,f661,f6712]) ).
tff(f6712,plain,
( spl24_386
<=> ! [X0: $tType,X3: fun(X0,X0),X4: list(nat),X5: X0,X2: nat,X1: fun(nat,fun(X0,X0))] : ( foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_386])]) ).
tff(f1406,plain,
( ! [X0: $tType,X2: nat,X3: fun(X0,X0),X1: fun(nat,fun(X0,X0)),X4: list(nat),X5: X0] : ( foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5)) )
| ~ spl24_26
| ~ spl24_135 ),
inference(superposition,[],[f1358,f662]) ).
tff(f6540,plain,
( spl24_385
| ~ spl24_82
| ~ spl24_352
| ~ spl24_384 ),
inference(avatar_split_clause,[],[f6534,f6531,f5578,f979,f6538]) ).
tff(f6538,plain,
( spl24_385
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),sK2),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),a)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_385])]) ).
tff(f6531,plain,
( spl24_384
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),sK2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_384])]) ).
tff(f6534,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),sK2),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),a)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_384 ),
inference(forward_demodulation,[],[f6532,f5642]) ).
tff(f6532,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),sK2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) )
| ~ spl24_384 ),
inference(avatar_component_clause,[],[f6531]) ).
tff(f6533,plain,
( spl24_384
| ~ spl24_58
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2026,f2008,f851,f6531]) ).
tff(f851,plain,
( spl24_58
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_58])]) ).
tff(f2026,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),sK2),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) )
| ~ spl24_58
| ~ spl24_187 ),
inference(resolution,[],[f2009,f853]) ).
tff(f853,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),a))
| ~ spl24_58 ),
inference(avatar_component_clause,[],[f851]) ).
tff(f6516,plain,
( spl24_383
| ~ spl24_82
| ~ spl24_352
| ~ spl24_382 ),
inference(avatar_split_clause,[],[f6512,f6509,f5578,f979,f6514]) ).
tff(f6509,plain,
( spl24_382
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_382])]) ).
tff(f6512,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),a)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_82
| ~ spl24_352
| ~ spl24_382 ),
inference(forward_demodulation,[],[f6510,f5642]) ).
tff(f6510,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) )
| ~ spl24_382 ),
inference(avatar_component_clause,[],[f6509]) ).
tff(f6511,plain,
( spl24_382
| ~ spl24_55
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f2021,f2008,f834,f6509]) ).
tff(f834,plain,
( spl24_55
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_55])]) ).
tff(f2021,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X0))) )
| ~ spl24_55
| ~ spl24_187 ),
inference(resolution,[],[f2009,f836]) ).
tff(f836,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),a))
| ~ spl24_55 ),
inference(avatar_component_clause,[],[f834]) ).
tff(f6507,plain,
( spl24_381
| ~ spl24_45
| ~ spl24_162 ),
inference(avatar_split_clause,[],[f1697,f1692,f760,f6505]) ).
tff(f6505,plain,
( spl24_381
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X2),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_381])]) ).
tff(f1697,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X2),X1)))) )
| ~ spl24_45
| ~ spl24_162 ),
inference(resolution,[],[f1693,f761]) ).
tff(f6503,plain,
( spl24_380
| ~ spl24_45
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1604,f1595,f760,f6501]) ).
tff(f6501,plain,
( spl24_380
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_380])]) ).
tff(f1604,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1)))) )
| ~ spl24_45
| ~ spl24_150 ),
inference(resolution,[],[f1596,f761]) ).
tff(f6499,plain,
( spl24_379
| ~ spl24_45
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1585,f1576,f760,f6497]) ).
tff(f6497,plain,
( spl24_379
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK14(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_379])]) ).
tff(f1585,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK14(X1,X3,X2,X0),X1)))) )
| ~ spl24_45
| ~ spl24_148 ),
inference(resolution,[],[f1577,f761]) ).
tff(f6495,plain,
( spl24_378
| ~ spl24_45
| ~ spl24_82
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1553,f1528,f979,f760,f6493]) ).
tff(f6493,plain,
( spl24_378
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,X1),X2: fun(X1,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_378])]) ).
tff(f1553,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) )
| ~ spl24_45
| ~ spl24_82
| ~ spl24_144 ),
inference(forward_demodulation,[],[f1546,f980]) ).
tff(f1546,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))) )
| ~ spl24_45
| ~ spl24_144 ),
inference(superposition,[],[f761,f1529]) ).
tff(f6491,plain,
( spl24_377
| ~ spl24_69
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1464,f1361,f979,f909,f6489]) ).
tff(f6489,plain,
( spl24_377
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_377])]) ).
tff(f909,plain,
( spl24_69
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_69])]) ).
tff(f1464,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl24_69
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1442,f980]) ).
tff(f1442,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl24_69
| ~ spl24_136 ),
inference(superposition,[],[f910,f1362]) ).
tff(f910,plain,
( ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) )
| ( X0 = X2 ) )
| ~ spl24_69 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f6487,plain,
( spl24_376
| ~ spl24_70
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1460,f1361,f979,f913,f6485]) ).
tff(f6485,plain,
( spl24_376
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_376])]) ).
tff(f913,plain,
( spl24_70
<=> ! [X2: list(dB),X0: list(dB),X1: nat,X3: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_70])]) ).
tff(f1460,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl24_70
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1438,f980]) ).
tff(f1438,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl24_70
| ~ spl24_136 ),
inference(superposition,[],[f914,f1362]) ).
tff(f914,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_70 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f6483,plain,
( spl24_375
| ~ spl24_3
| ~ spl24_217
| ~ spl24_347 ),
inference(avatar_split_clause,[],[f6244,f5293,f2708,f532,f6480]) ).
tff(f6480,plain,
( spl24_375
<=> sP1(abs(abs(abs(u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_375])]) ).
tff(f5293,plain,
( spl24_347
<=> ( fTrue = aa(dB,bool,it,abs(u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_347])]) ).
tff(f6244,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(u))))
| ~ spl24_217
| ~ spl24_347 ),
inference(superposition,[],[f2709,f5295]) ).
tff(f5295,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl24_347 ),
inference(avatar_component_clause,[],[f5293]) ).
tff(f6478,plain,
( spl24_374
| ~ spl24_79
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1426,f1361,f962,f6476]) ).
tff(f6476,plain,
( spl24_374
<=> ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_374])]) ).
tff(f1426,plain,
( ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X0,X2) )
| ~ spl24_79
| ~ spl24_136 ),
inference(superposition,[],[f1362,f963]) ).
tff(f6440,plain,
( spl24_373
| ~ spl24_10
| ~ spl24_82
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1552,f1528,f979,f564,f6438]) ).
tff(f6438,plain,
( spl24_373
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,X1),X2: fun(X1,bool)] :
( ( fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_373])]) ).
tff(f1552,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ( fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) )
| ~ spl24_10
| ~ spl24_82
| ~ spl24_144 ),
inference(forward_demodulation,[],[f1541,f980]) ).
tff(f1541,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3),X4) ) )
| ~ spl24_10
| ~ spl24_144 ),
inference(superposition,[],[f1529,f565]) ).
tff(f6175,plain,
( spl24_372
| ~ spl24_67
| ~ spl24_181 ),
inference(avatar_split_clause,[],[f1981,f1949,f900,f6173]) ).
tff(f6173,plain,
( spl24_372
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(dB,X0,X2,X1,as,a)),sK22(dB,X0,X2,X1,as,a)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_372])]) ).
tff(f900,plain,
( spl24_67
<=> ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_67])]) ).
tff(f1981,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(dB,X0,X2,X1,as,a)),sK22(dB,X0,X2,X1,as,a)) = X2 ) )
| ~ spl24_67
| ~ spl24_181 ),
inference(superposition,[],[f1950,f902]) ).
tff(f902,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl24_67 ),
inference(avatar_component_clause,[],[f900]) ).
tff(f6171,plain,
( spl24_371
| ~ spl24_67
| ~ spl24_180 ),
inference(avatar_split_clause,[],[f1973,f1945,f900,f6169]) ).
tff(f6169,plain,
( spl24_371
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,dB,as,a,X2,X1)),sK20(X0,dB,as,a,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_371])]) ).
tff(f1973,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,dB,as,a,X2,X1)),sK20(X0,dB,as,a,X2,X1)) = X2 ) )
| ~ spl24_67
| ~ spl24_180 ),
inference(superposition,[],[f1946,f902]) ).
tff(f6167,plain,
( spl24_370
| ~ spl24_73
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1863,f1810,f929,f6165]) ).
tff(f6165,plain,
( spl24_370
<=> ! [X2: nat,X0: dB,X1: fun(dB,dB),X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_370])]) ).
tff(f929,plain,
( spl24_73
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_73])]) ).
tff(f1863,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: fun(dB,dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) )
| ~ spl24_73
| ~ spl24_174 ),
inference(superposition,[],[f930,f1811]) ).
tff(f930,plain,
( ! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) )
| ~ spl24_73 ),
inference(avatar_component_clause,[],[f929]) ).
tff(f6163,plain,
( spl24_369
| ~ spl24_132
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1579,f1576,f1344,f6161]) ).
tff(f6161,plain,
( spl24_369
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X2,X0))),sK11(X2,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_369])]) ).
tff(f1579,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X2,X0))),sK11(X2,X0)),X2)) )
| ~ spl24_132
| ~ spl24_148 ),
inference(resolution,[],[f1577,f1345]) ).
tff(f6159,plain,
( spl24_368
| ~ spl24_45
| ~ spl24_142 ),
inference(avatar_split_clause,[],[f1520,f1511,f760,f6157]) ).
tff(f6157,plain,
( spl24_368
<=> ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK12(X1,X2,X0))),sK13(X1,X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_368])]) ).
tff(f1520,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK12(X1,X2,X0))),sK13(X1,X2,X0)))) )
| ~ spl24_45
| ~ spl24_142 ),
inference(resolution,[],[f1512,f761]) ).
tff(f6155,plain,
( spl24_367
| ~ spl24_10
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1414,f1357,f564,f6153]) ).
tff(f6153,plain,
( spl24_367
<=> ! [X0: $tType,X4: bool,X3: X0,X2: list(X0),X1: fun(X0,fun(bool,bool))] :
( ( fFalse = aa(bool,bool,aa(X0,fun(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_367])]) ).
tff(f1414,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: fun(X0,fun(bool,bool)),X4: bool] :
( ( fFalse = aa(bool,bool,aa(X0,fun(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) )
| ~ spl24_10
| ~ spl24_135 ),
inference(superposition,[],[f1358,f565]) ).
tff(f6151,plain,
( spl24_366
| ~ spl24_10
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1413,f1357,f564,f6149]) ).
tff(f6149,plain,
( spl24_366
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun(X0,fun(bool,bool))] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_366])]) ).
tff(f1413,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(bool,bool)),X4: bool] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) )
| ~ spl24_10
| ~ spl24_135 ),
inference(superposition,[],[f1358,f565]) ).
tff(f6147,plain,
( spl24_365
| ~ spl24_10
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1411,f1357,f564,f6145]) ).
tff(f6145,plain,
( spl24_365
<=> ! [X0: $tType,X2: list(X0),X4: X0,X3: bool,X1: fun(X0,fun(bool,bool))] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_365])]) ).
tff(f1411,plain,
( ! [X0: $tType,X2: list(X0),X3: bool,X1: fun(X0,fun(bool,bool)),X4: X0] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) )
| ~ spl24_10
| ~ spl24_135 ),
inference(superposition,[],[f1358,f565]) ).
tff(f6141,plain,
( spl24_364
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1300,f1293,f6139]) ).
tff(f6139,plain,
( spl24_364
<=> ! [X1: $tType,X0: $tType,X5: X1,X6: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_364])]) ).
tff(f1300,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ~ spl24_126 ),
inference(superposition,[],[f1294,f1294]) ).
tff(f5940,plain,
( spl24_363
| ~ spl24_132
| ~ spl24_162 ),
inference(avatar_split_clause,[],[f1695,f1692,f1344,f5938]) ).
tff(f5938,plain,
( spl24_363
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X3,X0))),sK11(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_363])]) ).
tff(f1695,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK10(X3,X0))),sK11(X3,X0)),X3)) )
| ~ spl24_132
| ~ spl24_162 ),
inference(resolution,[],[f1693,f1345]) ).
tff(f5936,plain,
( spl24_362
| ~ spl24_53
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1471,f1361,f979,f815,f5934]) ).
tff(f5934,plain,
( spl24_362
<=> ! [X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_362])]) ).
tff(f1471,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) )
| ~ spl24_53
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1449,f980]) ).
tff(f1449,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),X1) != foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ( X0 = X3 ) )
| ~ spl24_53
| ~ spl24_136 ),
inference(superposition,[],[f816,f1362]) ).
tff(f5932,plain,
( spl24_361
| ~ spl24_50
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1457,f1361,f979,f800,f5930]) ).
tff(f5930,plain,
( spl24_361
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_361])]) ).
tff(f800,plain,
( spl24_50
<=> ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_50])]) ).
tff(f1457,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_50
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1435,f980]) ).
tff(f1435,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_50
| ~ spl24_136 ),
inference(superposition,[],[f801,f1362]) ).
tff(f801,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl24_50 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f5928,plain,
( spl24_360
| ~ spl24_3
| ~ spl24_217
| ~ spl24_336 ),
inference(avatar_split_clause,[],[f5593,f5247,f2708,f532,f5925]) ).
tff(f5925,plain,
( spl24_360
<=> sP1(abs(abs(abs(t3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_360])]) ).
tff(f5247,plain,
( spl24_336
<=> ( fTrue = aa(dB,bool,it,abs(t3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_336])]) ).
tff(f5593,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(t3))))
| ~ spl24_217
| ~ spl24_336 ),
inference(superposition,[],[f2709,f5249]) ).
tff(f5249,plain,
( ( fTrue = aa(dB,bool,it,abs(t3)) )
| ~ spl24_336 ),
inference(avatar_component_clause,[],[f5247]) ).
tff(f5923,plain,
( spl24_359
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1454,f1361,f979,f564,f5921]) ).
tff(f5921,plain,
( spl24_359
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_359])]) ).
tff(f1454,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1432,f980]) ).
tff(f1432,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X4),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_10
| ~ spl24_136 ),
inference(superposition,[],[f1362,f565]) ).
tff(f5919,plain,
( spl24_358
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1453,f1361,f979,f564,f5917]) ).
tff(f5917,plain,
( spl24_358
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_358])]) ).
tff(f1453,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) )
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1430,f980]) ).
tff(f1430,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ( fTrue = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3),X4) ) )
| ~ spl24_10
| ~ spl24_136 ),
inference(superposition,[],[f1362,f565]) ).
tff(f5915,plain,
( spl24_357
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1452,f1361,f979,f564,f5913]) ).
tff(f5913,plain,
( spl24_357
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_357])]) ).
tff(f1452,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) )
| ~ spl24_10
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1428,f980]) ).
tff(f1428,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) )
| ( fTrue = aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) ) )
| ~ spl24_10
| ~ spl24_136 ),
inference(superposition,[],[f1362,f565]) ).
tff(f5610,plain,
( spl24_356
| ~ spl24_34
| ~ spl24_177 ),
inference(avatar_split_clause,[],[f1916,f1912,f704,f5608]) ).
tff(f5608,plain,
( spl24_356
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_356])]) ).
tff(f704,plain,
( spl24_34
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_34])]) ).
tff(f1916,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_34
| ~ spl24_177 ),
inference(resolution,[],[f1913,f706]) ).
tff(f706,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3))
| ~ spl24_34 ),
inference(avatar_component_clause,[],[f704]) ).
tff(f5606,plain,
( spl24_355
| ~ spl24_33
| ~ spl24_177 ),
inference(avatar_split_clause,[],[f1915,f1912,f699,f5604]) ).
tff(f5604,plain,
( spl24_355
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_355])]) ).
tff(f699,plain,
( spl24_33
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_33])]) ).
tff(f1915,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0)) )
| ~ spl24_33
| ~ spl24_177 ),
inference(resolution,[],[f1913,f701]) ).
tff(f701,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts))
| ~ spl24_33 ),
inference(avatar_component_clause,[],[f699]) ).
tff(f5588,plain,
( spl24_354
| ~ spl24_82
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1539,f1528,f979,f5586]) ).
tff(f5586,plain,
( spl24_354
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X1),X5: X0,X3: fun(X1,X2)] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_354])]) ).
tff(f1539,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: fun(X0,X1),X5: X0] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) )
| ~ spl24_82
| ~ spl24_144 ),
inference(superposition,[],[f1529,f980]) ).
tff(f5584,plain,
( spl24_353
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f989,f979,f5582]) ).
tff(f5582,plain,
( spl24_353
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_353])]) ).
tff(f989,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) )
| ~ spl24_82 ),
inference(superposition,[],[f980,f980]) ).
tff(f5580,plain,
( spl24_352
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f988,f979,f5578]) ).
tff(f988,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) )
| ~ spl24_82 ),
inference(superposition,[],[f980,f980]) ).
tff(f5568,plain,
( spl24_351
| ~ spl24_24
| ~ spl24_145 ),
inference(avatar_split_clause,[],[f1560,f1556,f643,f5565]) ).
tff(f5565,plain,
( spl24_351
<=> sP1(abs(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_351])]) ).
tff(f1556,plain,
( spl24_145
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_145])]) ).
tff(f1560,plain,
( sP1(abs(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_24
| ~ spl24_145 ),
inference(resolution,[],[f1558,f644]) ).
tff(f1558,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_145 ),
inference(avatar_component_clause,[],[f1556]) ).
tff(f5563,plain,
( spl24_350
| ~ spl24_82
| ~ spl24_143 ),
inference(avatar_split_clause,[],[f1533,f1524,f979,f5561]) ).
tff(f5561,plain,
( spl24_350
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_350])]) ).
tff(f1533,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) )
| ~ spl24_82
| ~ spl24_143 ),
inference(superposition,[],[f1525,f980]) ).
tff(f5515,plain,
( spl24_349
| ~ spl24_76
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5153,f5088,f948,f5512]) ).
tff(f948,plain,
( spl24_76
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_76])]) ).
tff(f5153,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl24_76
| ~ spl24_326 ),
inference(resolution,[],[f5089,f950]) ).
tff(f950,plain,
( sP1(abs(ua))
| ~ spl24_76 ),
inference(avatar_component_clause,[],[f948]) ).
tff(f5300,plain,
( spl24_348
| ~ spl24_75
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1600,f1595,f942,f5298]) ).
tff(f5298,plain,
( spl24_348
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_348])]) ).
tff(f1600,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,var(X2),X0),X1) ) )
| ~ spl24_75
| ~ spl24_150 ),
inference(resolution,[],[f1596,f943]) ).
tff(f5296,plain,
( spl24_347
| ~ spl24_71
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5152,f5088,f917,f5293]) ).
tff(f917,plain,
( spl24_71
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_71])]) ).
tff(f5152,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl24_71
| ~ spl24_326 ),
inference(resolution,[],[f5089,f919]) ).
tff(f919,plain,
( sP1(abs(u))
| ~ spl24_71 ),
inference(avatar_component_clause,[],[f917]) ).
tff(f5291,plain,
( spl24_346
| ~ spl24_75
| ~ spl24_148 ),
inference(avatar_split_clause,[],[f1581,f1576,f942,f5289]) ).
tff(f5289,plain,
( spl24_346
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_346])]) ).
tff(f1581,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) )
| ~ spl24_75
| ~ spl24_148 ),
inference(resolution,[],[f1577,f943]) ).
tff(f5287,plain,
( spl24_345
| ~ spl24_16
| ~ spl24_145 ),
inference(avatar_split_clause,[],[f1561,f1556,f600,f5284]) ).
tff(f5284,plain,
( spl24_345
<=> sP1(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_345])]) ).
tff(f1561,plain,
( sP1(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl24_16
| ~ spl24_145 ),
inference(resolution,[],[f1558,f601]) ).
tff(f5282,plain,
( spl24_344
| ~ spl24_23
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1499,f1482,f639,f5280]) ).
tff(f5280,plain,
( spl24_344
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X1,combi(X0),X3,X2)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_344])]) ).
tff(f1499,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X1,combi(X0),X3,X2)) = X3 ) )
| ~ spl24_23
| ~ spl24_139 ),
inference(superposition,[],[f1483,f640]) ).
tff(f5278,plain,
( spl24_343
| ~ spl24_82
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1498,f1482,f979,f5276]) ).
tff(f5276,plain,
( spl24_343
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X0,X3,X5,X4,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_343])]) ).
tff(f1498,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X0,X3,X5,X4,X2,X1)) = X2 ) )
| ~ spl24_82
| ~ spl24_139 ),
inference(superposition,[],[f1483,f980]) ).
tff(f5274,plain,
( spl24_342
| ~ spl24_23
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1495,f1478,f639,f5272]) ).
tff(f5272,plain,
( spl24_342
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK20(X0,X0,X3,X2,X1,combi(X0))) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_342])]) ).
tff(f1495,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK20(X0,X0,X3,X2,X1,combi(X0))) = X3 ) )
| ~ spl24_23
| ~ spl24_138 ),
inference(superposition,[],[f1479,f640]) ).
tff(f5270,plain,
( spl24_341
| ~ spl24_82
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1494,f1478,f979,f5268]) ).
tff(f5268,plain,
( spl24_341
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK20(X3,X0,X2,X1,X5,X4)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_341])]) ).
tff(f1494,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK20(X3,X0,X2,X1,X5,X4)) = X2 ) )
| ~ spl24_82
| ~ spl24_138 ),
inference(superposition,[],[f1479,f980]) ).
tff(f5266,plain,
( spl24_340
| ~ spl24_82
| ~ spl24_137 ),
inference(avatar_split_clause,[],[f1487,f1474,f979,f5264]) ).
tff(f5264,plain,
( spl24_340
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_340])]) ).
tff(f1487,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) )
| ~ spl24_82
| ~ spl24_137 ),
inference(superposition,[],[f1475,f980]) ).
tff(f5262,plain,
( spl24_339
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1425,f1361,f979,f5260]) ).
tff(f5260,plain,
( spl24_339
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: list(X0),X2: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_339])]) ).
tff(f1425,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X1)),X3: X1,X4: X0,X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) )
| ~ spl24_82
| ~ spl24_136 ),
inference(superposition,[],[f1362,f980]) ).
tff(f5258,plain,
( spl24_338
| ~ spl24_45
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1416,f1357,f760,f5256]) ).
tff(f5256,plain,
( spl24_338
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun(X0,fun(bool,bool))] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_338])]) ).
tff(f1416,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(bool,bool)),X4: bool] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) )
| ~ spl24_45
| ~ spl24_135 ),
inference(superposition,[],[f761,f1358]) ).
tff(f5254,plain,
( spl24_337
| ~ spl24_82
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1412,f1357,f979,f5252]) ).
tff(f5252,plain,
( spl24_337
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X1),X5: X0,X2: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_337])]) ).
tff(f1412,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X0)),X3: X1,X4: list(X1),X5: X0] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) )
| ~ spl24_82
| ~ spl24_135 ),
inference(superposition,[],[f1358,f980]) ).
tff(f5250,plain,
( spl24_336
| ~ spl24_65
| ~ spl24_326 ),
inference(avatar_split_clause,[],[f5151,f5088,f887,f5247]) ).
tff(f887,plain,
( spl24_65
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_65])]) ).
tff(f5151,plain,
( ( fTrue = aa(dB,bool,it,abs(t3)) )
| ~ spl24_65
| ~ spl24_326 ),
inference(resolution,[],[f5089,f889]) ).
tff(f889,plain,
( sP1(abs(t3))
| ~ spl24_65 ),
inference(avatar_component_clause,[],[f887]) ).
tff(f5245,plain,
( spl24_335
| ~ spl24_45
| ~ spl24_112 ),
inference(avatar_split_clause,[],[f1199,f1196,f760,f5243]) ).
tff(f5243,plain,
( spl24_335
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_335])]) ).
tff(f1199,plain,
( ! [X2: list(type),X3: nat,X0: fun(nat,type),X1: list(dB),X4: type] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) )
| ~ spl24_45
| ~ spl24_112 ),
inference(resolution,[],[f1197,f761]) ).
tff(f5171,plain,
( spl24_334
| ~ spl24_75
| ~ spl24_164 ),
inference(avatar_split_clause,[],[f1710,f1707,f942,f5169]) ).
tff(f5169,plain,
( spl24_334
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_334])]) ).
tff(f1710,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1) ) )
| ~ spl24_75
| ~ spl24_164 ),
inference(resolution,[],[f1708,f943]) ).
tff(f5136,plain,
( spl24_333
| ~ spl24_75
| ~ spl24_142 ),
inference(avatar_split_clause,[],[f1516,f1511,f942,f5134]) ).
tff(f5134,plain,
( spl24_333
<=> ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK12(X1,var(X2),X0)),X2) = sK13(X1,var(X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_333])]) ).
tff(f1516,plain,
( ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK12(X1,var(X2),X0)),X2) = sK13(X1,var(X2),X0) ) )
| ~ spl24_75
| ~ spl24_142 ),
inference(resolution,[],[f1512,f943]) ).
tff(f5132,plain,
( spl24_332
| ~ spl24_27
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1455,f1361,f979,f666,f5130]) ).
tff(f5130,plain,
( spl24_332
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_332])]) ).
tff(f1455,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_27
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1433,f980]) ).
tff(f1433,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_27
| ~ spl24_136 ),
inference(superposition,[],[f667,f1362]) ).
tff(f5128,plain,
( spl24_331
| ~ spl24_23
| ~ spl24_134 ),
inference(avatar_split_clause,[],[f1404,f1353,f639,f5126]) ).
tff(f5126,plain,
( spl24_331
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X1,combi(X0),X3,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_331])]) ).
tff(f1404,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X1,combi(X0),X3,X2)) = X2 ) )
| ~ spl24_23
| ~ spl24_134 ),
inference(superposition,[],[f1354,f640]) ).
tff(f5124,plain,
( spl24_330
| ~ spl24_82
| ~ spl24_134 ),
inference(avatar_split_clause,[],[f1403,f1353,f979,f5122]) ).
tff(f5122,plain,
( spl24_330
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X0,X3,X5,X4,X2,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_330])]) ).
tff(f1403,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X0,X3,X5,X4,X2,X1)) = X1 ) )
| ~ spl24_82
| ~ spl24_134 ),
inference(superposition,[],[f1354,f980]) ).
tff(f5120,plain,
( spl24_329
| ~ spl24_23
| ~ spl24_133 ),
inference(avatar_split_clause,[],[f1401,f1349,f639,f5118]) ).
tff(f5118,plain,
( spl24_329
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK19(X0,X0,X3,X2,X1,combi(X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_329])]) ).
tff(f1401,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK19(X0,X0,X3,X2,X1,combi(X0))) = X2 ) )
| ~ spl24_23
| ~ spl24_133 ),
inference(superposition,[],[f1350,f640]) ).
tff(f5116,plain,
( spl24_328
| ~ spl24_82
| ~ spl24_133 ),
inference(avatar_split_clause,[],[f1400,f1349,f979,f5114]) ).
tff(f5114,plain,
( spl24_328
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK19(X3,X0,X2,X1,X5,X4)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_328])]) ).
tff(f1400,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK19(X3,X0,X2,X1,X5,X4)) = X1 ) )
| ~ spl24_82
| ~ spl24_133 ),
inference(superposition,[],[f1350,f980]) ).
tff(f5112,plain,
( spl24_327
| ~ spl24_10
| ~ spl24_82
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1307,f1293,f979,f564,f5110]) ).
tff(f5110,plain,
( spl24_327
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: fun(X0,fun(list(X0),bool)),X1: bool] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_327])]) ).
tff(f1307,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_10
| ~ spl24_82
| ~ spl24_126 ),
inference(forward_demodulation,[],[f1302,f980]) ).
tff(f1302,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X2,X4),X3) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_10
| ~ spl24_126 ),
inference(superposition,[],[f1294,f565]) ).
tff(f5090,plain,
( spl24_326
| ~ spl24_13
| ~ spl24_17 ),
inference(avatar_split_clause,[],[f1368,f604,f583,f5088]) ).
tff(f1368,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) )
| ~ spl24_13
| ~ spl24_17 ),
inference(resolution,[],[f584,f605]) ).
tff(f5076,plain,
( spl24_325
| ~ spl24_130
| ~ spl24_189 ),
inference(avatar_split_clause,[],[f2041,f2038,f1330,f5074]) ).
tff(f5074,plain,
( spl24_325
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0))))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_325])]) ).
tff(f1330,plain,
( spl24_130
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_130])]) ).
tff(f2041,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0))))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_130
| ~ spl24_189 ),
inference(resolution,[],[f2039,f1331]) ).
tff(f1331,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_130 ),
inference(avatar_component_clause,[],[f1330]) ).
tff(f5072,plain,
( spl24_324
| ~ spl24_43
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1862,f1810,f752,f5070]) ).
tff(f5070,plain,
( spl24_324
<=> ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_324])]) ).
tff(f752,plain,
( spl24_43
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_43])]) ).
tff(f1862,plain,
( ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl24_43
| ~ spl24_174 ),
inference(superposition,[],[f753,f1811]) ).
tff(f753,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl24_43 ),
inference(avatar_component_clause,[],[f752]) ).
tff(f5068,plain,
( spl24_323
| ~ spl24_44
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1861,f1810,f756,f5066]) ).
tff(f5066,plain,
( spl24_323
<=> ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_323])]) ).
tff(f756,plain,
( spl24_44
<=> ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_44])]) ).
tff(f1861,plain,
( ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl24_44
| ~ spl24_174 ),
inference(superposition,[],[f757,f1811]) ).
tff(f757,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl24_44 ),
inference(avatar_component_clause,[],[f756]) ).
tff(f5064,plain,
( spl24_322
| ~ spl24_26
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1296,f1293,f661,f5062]) ).
tff(f5062,plain,
( spl24_322
<=> ! [X0: $tType,X5: X0,X4: list(nat),X3: fun(list(nat),X0),X2: nat,X1: fun(nat,fun(list(nat),X0))] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_322])]) ).
tff(f1296,plain,
( ! [X0: $tType,X2: nat,X3: fun(list(nat),X0),X1: fun(nat,fun(list(nat),X0)),X4: list(nat),X5: X0] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) )
| ~ spl24_26
| ~ spl24_126 ),
inference(superposition,[],[f1294,f662]) ).
tff(f4961,plain,
( spl24_321
| ~ spl24_45
| ~ spl24_154 ),
inference(avatar_split_clause,[],[f1636,f1632,f760,f4959]) ).
tff(f4959,plain,
( spl24_321
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_321])]) ).
tff(f1636,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) )
| ~ spl24_45
| ~ spl24_154 ),
inference(resolution,[],[f1633,f761]) ).
tff(f4957,plain,
( spl24_320
| ~ spl24_68
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1419,f1357,f905,f4955]) ).
tff(f4955,plain,
( spl24_320
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_320])]) ).
tff(f1419,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ~ spl24_68
| ~ spl24_135 ),
inference(superposition,[],[f906,f1358]) ).
tff(f4953,plain,
( spl24_319
| ~ spl24_24
| ~ spl24_130 ),
inference(avatar_split_clause,[],[f1333,f1330,f643,f4951]) ).
tff(f4951,plain,
( spl24_319
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_319])]) ).
tff(f1333,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0)))) )
| ~ spl24_24
| ~ spl24_130 ),
inference(resolution,[],[f1331,f644]) ).
tff(f4949,plain,
( spl24_318
| ~ spl24_82
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1301,f1293,f979,f4947]) ).
tff(f4947,plain,
( spl24_318
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_318])]) ).
tff(f1301,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) )
| ~ spl24_82
| ~ spl24_126 ),
inference(superposition,[],[f1294,f980]) ).
tff(f4945,plain,
( spl24_317
| ~ spl24_109
| ~ spl24_121 ),
inference(avatar_split_clause,[],[f1256,f1251,f1177,f4942]) ).
tff(f4942,plain,
( spl24_317
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK14(t2,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_317])]) ).
tff(f1256,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK14(t2,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t1))))
| ~ spl24_109
| ~ spl24_121 ),
inference(resolution,[],[f1253,f1178]) ).
tff(f4940,plain,
( spl24_316
| ~ spl24_111
| ~ spl24_121 ),
inference(avatar_split_clause,[],[f1255,f1251,f1189,f4937]) ).
tff(f4937,plain,
( spl24_316
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK15(t2,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_316])]) ).
tff(f1255,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK15(t2,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t1))))
| ~ spl24_111
| ~ spl24_121 ),
inference(resolution,[],[f1253,f1190]) ).
tff(f4922,plain,
( spl24_168
| ~ spl24_315
| ~ spl24_303 ),
inference(avatar_split_clause,[],[f4866,f4669,f4919,f1739]) ).
tff(f4866,plain,
( ! [X0: bool] :
( ( fTrue != aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) )
| ( fTrue = X0 ) )
| ~ spl24_303 ),
inference(equality_factoring,[],[f4670]) ).
tff(f4903,plain,
( spl24_314
| ~ spl24_43
| ~ spl24_206 ),
inference(avatar_split_clause,[],[f2185,f2176,f752,f4901]) ).
tff(f4901,plain,
( spl24_314
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_314])]) ).
tff(f2185,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl24_43
| ~ spl24_206 ),
inference(superposition,[],[f753,f2177]) ).
tff(f4899,plain,
( spl24_313
| ~ spl24_44
| ~ spl24_206 ),
inference(avatar_split_clause,[],[f2184,f2176,f756,f4897]) ).
tff(f4897,plain,
( spl24_313
<=> ! [X4: nat,X0: dB,X3: dB,X2: dB,X1: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_313])]) ).
tff(f2184,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl24_44
| ~ spl24_206 ),
inference(superposition,[],[f757,f2177]) ).
tff(f4895,plain,
( spl24_312
| ~ spl24_125
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1619,f1615,f1286,f4892]) ).
tff(f4892,plain,
( spl24_312
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK17(foldr(type,type,fun1,sK3,t2),a,var(i),shift(type,e,i,t1))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_312])]) ).
tff(f1619,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK17(foldr(type,type,fun1,sK3,t2),a,var(i),shift(type,e,i,t1))),a))
| ~ spl24_125
| ~ spl24_152 ),
inference(resolution,[],[f1616,f1288]) ).
tff(f4890,plain,
( spl24_311
| ~ spl24_119
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1618,f1615,f1237,f4887]) ).
tff(f4887,plain,
( spl24_311
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK17(foldr(type,type,fun1,ts,t2),a,var(i),shift(type,e,i,t1))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_311])]) ).
tff(f1618,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK17(foldr(type,type,fun1,ts,t2),a,var(i),shift(type,e,i,t1))),a))
| ~ spl24_119
| ~ spl24_152 ),
inference(resolution,[],[f1616,f1239]) ).
tff(f4885,plain,
( spl24_310
| ~ spl24_16
| ~ spl24_130 ),
inference(avatar_split_clause,[],[f1334,f1330,f600,f4883]) ).
tff(f4883,plain,
( spl24_310
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_310])]) ).
tff(f1334,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))) )
| ~ spl24_16
| ~ spl24_130 ),
inference(resolution,[],[f1331,f601]) ).
tff(f4732,plain,
( spl24_309
| ~ spl24_130
| ~ spl24_184 ),
inference(avatar_split_clause,[],[f1966,f1963,f1330,f4730]) ).
tff(f4730,plain,
( spl24_309
<=> ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_309])]) ).
tff(f1966,plain,
( ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_130
| ~ spl24_184 ),
inference(resolution,[],[f1964,f1331]) ).
tff(f4728,plain,
( spl24_308
| ~ spl24_73
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1462,f1361,f979,f929,f4726]) ).
tff(f4726,plain,
( spl24_308
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_308])]) ).
tff(f1462,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl24_73
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1440,f980]) ).
tff(f1440,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) )
| ~ spl24_73
| ~ spl24_136 ),
inference(superposition,[],[f930,f1362]) ).
tff(f4724,plain,
( spl24_307
| ~ spl24_24
| ~ spl24_128 ),
inference(avatar_split_clause,[],[f1320,f1316,f643,f4721]) ).
tff(f4721,plain,
( spl24_307
<=> sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_307])]) ).
tff(f1316,plain,
( spl24_128
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_128])]) ).
tff(f1320,plain,
( sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_24
| ~ spl24_128 ),
inference(resolution,[],[f1318,f644]) ).
tff(f1318,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_128 ),
inference(avatar_component_clause,[],[f1316]) ).
tff(f4719,plain,
( spl24_306
| ~ spl24_45
| ~ spl24_96 ),
inference(avatar_split_clause,[],[f1096,f1092,f760,f4716]) ).
tff(f4716,plain,
( spl24_306
<=> pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_306])]) ).
tff(f1096,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl24_45
| ~ spl24_96 ),
inference(resolution,[],[f1094,f761]) ).
tff(f4680,plain,
( spl24_305
| ~ spl24_16
| ~ spl24_128 ),
inference(avatar_split_clause,[],[f1321,f1316,f600,f4677]) ).
tff(f4677,plain,
( spl24_305
<=> sP1(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_305])]) ).
tff(f1321,plain,
( sP1(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))
| ~ spl24_16
| ~ spl24_128 ),
inference(resolution,[],[f1318,f601]) ).
tff(f4675,plain,
( spl24_304
| ~ spl24_82
| ~ spl24_104 ),
inference(avatar_split_clause,[],[f1152,f1149,f979,f4673]) ).
tff(f4673,plain,
( spl24_304
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_304])]) ).
tff(f1152,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 )
| ~ spl24_82
| ~ spl24_104 ),
inference(superposition,[],[f1150,f980]) ).
tff(f4671,plain,
( spl24_303
| spl24_15
| ~ spl24_290 ),
inference(avatar_split_clause,[],[f4577,f4198,f594,f4669]) ).
tff(f4198,plain,
( spl24_290
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_290])]) ).
tff(f4577,plain,
( ! [X0: bool] :
( ( aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) = X0 )
| ( fTrue = X0 ) )
| spl24_15
| ~ spl24_290 ),
inference(resolution,[],[f4199,f596]) ).
tff(f4199,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl24_290 ),
inference(avatar_component_clause,[],[f4198]) ).
tff(f4667,plain,
( spl24_302
| ~ spl24_64
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f1002,f979,f880,f4665]) ).
tff(f4665,plain,
( spl24_302
<=> ! [X0: $tType,X3: nat,X2: X0,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_302])]) ).
tff(f1002,plain,
( ! [X0: $tType,X2: X0,X3: nat,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3)))
| ~ spl24_64
| ~ spl24_82 ),
inference(superposition,[],[f881,f980]) ).
tff(f4602,plain,
( spl24_301
| ~ spl24_61
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1466,f1361,f979,f867,f4600]) ).
tff(f4600,plain,
( spl24_301
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_301])]) ).
tff(f867,plain,
( spl24_61
<=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_61])]) ).
tff(f1466,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl24_61
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1444,f980]) ).
tff(f1444,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl24_61
| ~ spl24_136 ),
inference(superposition,[],[f868,f1362]) ).
tff(f868,plain,
( ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) )
| ( X1 = X3 ) )
| ~ spl24_61 ),
inference(avatar_component_clause,[],[f867]) ).
tff(f4598,plain,
( spl24_300
| ~ spl24_62
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1458,f1361,f979,f871,f4596]) ).
tff(f4596,plain,
( spl24_300
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_300])]) ).
tff(f871,plain,
( spl24_62
<=> ! [X0: list(dB),X3: nat,X2: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_62])]) ).
tff(f1458,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl24_62
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1436,f980]) ).
tff(f1436,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl24_62
| ~ spl24_136 ),
inference(superposition,[],[f872,f1362]) ).
tff(f872,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_62 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f4594,plain,
( spl24_299
| ~ spl24_24
| ~ spl24_106 ),
inference(avatar_split_clause,[],[f1163,f1160,f643,f4592]) ).
tff(f4592,plain,
( spl24_299
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_299])]) ).
tff(f1160,plain,
( spl24_106
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_106])]) ).
tff(f1163,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) )
| ~ spl24_24
| ~ spl24_106 ),
inference(resolution,[],[f1161,f644]) ).
tff(f1161,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_106 ),
inference(avatar_component_clause,[],[f1160]) ).
tff(f4590,plain,
( spl24_298
| ~ spl24_10
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1088,f1077,f564,f4588]) ).
tff(f4588,plain,
( spl24_298
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_298])]) ).
tff(f1088,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X1,X2)) ) )
| ~ spl24_10
| ~ spl24_95 ),
inference(superposition,[],[f1078,f565]) ).
tff(f4552,plain,
( spl24_297
| ~ spl24_10
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1083,f1077,f564,f4550]) ).
tff(f4550,plain,
( spl24_297
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_297])]) ).
tff(f1083,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X2,X1)) ) )
| ~ spl24_10
| ~ spl24_95 ),
inference(superposition,[],[f1078,f565]) ).
tff(f4491,plain,
( spl24_296
| ~ spl24_16
| ~ spl24_106 ),
inference(avatar_split_clause,[],[f1164,f1160,f600,f4489]) ).
tff(f4489,plain,
( spl24_296
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_296])]) ).
tff(f1164,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) )
| ~ spl24_16
| ~ spl24_106 ),
inference(resolution,[],[f1161,f601]) ).
tff(f4487,plain,
( spl24_295
| ~ spl24_45
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f995,f979,f760,f4485]) ).
tff(f4485,plain,
( spl24_295
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_295])]) ).
tff(f995,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) )
| ~ spl24_45
| ~ spl24_82 ),
inference(superposition,[],[f761,f980]) ).
tff(f4483,plain,
( spl24_294
| ~ spl24_45
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f994,f979,f760,f4481]) ).
tff(f4481,plain,
( spl24_294
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_294])]) ).
tff(f994,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) )
| ~ spl24_45
| ~ spl24_82 ),
inference(superposition,[],[f761,f980]) ).
tff(f4213,plain,
( spl24_293
| ~ spl24_45
| ~ spl24_186 ),
inference(avatar_split_clause,[],[f2004,f1996,f760,f4210]) ).
tff(f4210,plain,
( spl24_293
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_293])]) ).
tff(f2004,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),t2)))
| ~ spl24_45
| ~ spl24_186 ),
inference(resolution,[],[f1998,f761]) ).
tff(f4208,plain,
( spl24_292
| ~ spl24_68
| ~ spl24_173 ),
inference(avatar_split_clause,[],[f1789,f1770,f905,f4206]) ).
tff(f4206,plain,
( spl24_292
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_292])]) ).
tff(f1789,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ~ spl24_68
| ~ spl24_173 ),
inference(superposition,[],[f906,f1771]) ).
tff(f4204,plain,
( spl24_291
| ~ spl24_90
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1663,f1657,f1048,f4202]) ).
tff(f4202,plain,
( spl24_291
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_291])]) ).
tff(f1663,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) )
| ~ spl24_90
| ~ spl24_158 ),
inference(resolution,[],[f1658,f1050]) ).
tff(f4200,plain,
( spl24_290
| ~ spl24_3
| ~ spl24_215 ),
inference(avatar_split_clause,[],[f2466,f2247,f532,f4198]) ).
tff(f2247,plain,
( spl24_215
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_215])]) ).
tff(f2466,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl24_3
| ~ spl24_215 ),
inference(superposition,[],[f534,f2248]) ).
tff(f2248,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl24_215 ),
inference(avatar_component_clause,[],[f2247]) ).
tff(f534,plain,
( pp(fTrue)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f532]) ).
tff(f4196,plain,
( spl24_289
| ~ spl24_92
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1662,f1657,f1061,f4194]) ).
tff(f4194,plain,
( spl24_289
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_289])]) ).
tff(f1662,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t2 = X0 ) )
| ~ spl24_92
| ~ spl24_158 ),
inference(resolution,[],[f1658,f1063]) ).
tff(f4192,plain,
( spl24_288
| ~ spl24_82
| ~ spl24_100 ),
inference(avatar_split_clause,[],[f1127,f1111,f979,f4190]) ).
tff(f4190,plain,
( spl24_288
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_288])]) ).
tff(f1127,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_82
| ~ spl24_100 ),
inference(superposition,[],[f1112,f980]) ).
tff(f4188,plain,
( spl24_287
| ~ spl24_82
| ~ spl24_99 ),
inference(avatar_split_clause,[],[f1124,f1107,f979,f4186]) ).
tff(f4186,plain,
( spl24_287
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_287])]) ).
tff(f1124,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_82
| ~ spl24_99 ),
inference(superposition,[],[f1108,f980]) ).
tff(f4184,plain,
( spl24_286
| ~ spl24_82
| ~ spl24_98 ),
inference(avatar_split_clause,[],[f1120,f1103,f979,f4182]) ).
tff(f4182,plain,
( spl24_286
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_286])]) ).
tff(f1120,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_82
| ~ spl24_98 ),
inference(superposition,[],[f1104,f980]) ).
tff(f4180,plain,
( spl24_285
| ~ spl24_82
| ~ spl24_97 ),
inference(avatar_split_clause,[],[f1115,f1099,f979,f4178]) ).
tff(f4178,plain,
( spl24_285
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_285])]) ).
tff(f1115,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_82
| ~ spl24_97 ),
inference(superposition,[],[f1100,f980]) ).
tff(f4176,plain,
( spl24_284
| ~ spl24_10
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f993,f979,f564,f4174]) ).
tff(f4174,plain,
( spl24_284
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_284])]) ).
tff(f993,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) )
| ~ spl24_10
| ~ spl24_82 ),
inference(superposition,[],[f980,f565]) ).
tff(f4172,plain,
( spl24_283
| ~ spl24_10
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f986,f979,f564,f4170]) ).
tff(f4170,plain,
( spl24_283
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_283])]) ).
tff(f986,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) )
| ~ spl24_10
| ~ spl24_82 ),
inference(superposition,[],[f980,f565]) ).
tff(f4152,plain,
( spl24_282
| ~ spl24_11
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f1370,f583,f574,f4150]) ).
tff(f4150,plain,
( spl24_282
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_282])]) ).
tff(f574,plain,
( spl24_11
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_11])]) ).
tff(f1370,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) )
| ~ spl24_11
| ~ spl24_13 ),
inference(resolution,[],[f584,f575]) ).
tff(f575,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f574]) ).
tff(f4140,plain,
( spl24_281
| ~ spl24_46
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1468,f1361,f979,f764,f4138]) ).
tff(f4138,plain,
( spl24_281
<=> ! [X4: list(dB),X0: dB,X3: nat,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_281])]) ).
tff(f764,plain,
( spl24_46
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_46])]) ).
tff(f1468,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ~ spl24_46
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1446,f980]) ).
tff(f1446,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ~ spl24_46
| ~ spl24_136 ),
inference(superposition,[],[f765,f1362]) ).
tff(f765,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) )
| ~ spl24_46 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f4136,plain,
( spl24_280
| ~ spl24_46
| ~ spl24_82
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1456,f1361,f979,f764,f4134]) ).
tff(f4134,plain,
( spl24_280
<=> ! [X4: list(dB),X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_280])]) ).
tff(f1456,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl24_46
| ~ spl24_82
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1434,f980]) ).
tff(f1434,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != foldl(dB,dB,app,abs(X3),X4) )
| ~ spl24_46
| ~ spl24_136 ),
inference(superposition,[],[f765,f1362]) ).
tff(f4132,plain,
( spl24_279
| ~ spl24_45
| ~ spl24_125 ),
inference(avatar_split_clause,[],[f1290,f1286,f760,f4129]) ).
tff(f4129,plain,
( spl24_279
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_279])]) ).
tff(f1290,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2))))
| ~ spl24_45
| ~ spl24_125 ),
inference(resolution,[],[f1288,f761]) ).
tff(f4127,plain,
( spl24_278
| ~ spl24_45
| ~ spl24_119 ),
inference(avatar_split_clause,[],[f1241,f1237,f760,f4124]) ).
tff(f4124,plain,
( spl24_278
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_278])]) ).
tff(f1241,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2))))
| ~ spl24_45
| ~ spl24_119 ),
inference(resolution,[],[f1239,f761]) ).
tff(f3963,plain,
( spl24_277
| ~ spl24_67
| ~ spl24_143 ),
inference(avatar_split_clause,[],[f1531,f1524,f900,f3961]) ).
tff(f3961,plain,
( spl24_277
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_277])]) ).
tff(f1531,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) )
| ~ spl24_67
| ~ spl24_143 ),
inference(superposition,[],[f1525,f902]) ).
tff(f3959,plain,
( spl24_276
| ~ spl24_18
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1085,f1077,f608,f3957]) ).
tff(f3957,plain,
( spl24_276
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK18(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_276])]) ).
tff(f1085,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK18(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl24_18
| ~ spl24_95 ),
inference(superposition,[],[f1078,f609]) ).
tff(f3955,plain,
( spl24_275
| ~ spl24_10
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1084,f1077,f564,f3953]) ).
tff(f3953,plain,
( spl24_275
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK18(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_275])]) ).
tff(f1084,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK18(X0,bool,X1,X2) ) )
| ~ spl24_10
| ~ spl24_95 ),
inference(superposition,[],[f1078,f565]) ).
tff(f3951,plain,
( spl24_274
| ~ spl24_18
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1080,f1077,f608,f3949]) ).
tff(f3949,plain,
( spl24_274
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK18(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_274])]) ).
tff(f1080,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK18(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl24_18
| ~ spl24_95 ),
inference(superposition,[],[f1078,f609]) ).
tff(f3947,plain,
( spl24_273
| ~ spl24_45
| ~ spl24_88 ),
inference(avatar_split_clause,[],[f1038,f1034,f760,f3945]) ).
tff(f3945,plain,
( spl24_273
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_273])]) ).
tff(f1034,plain,
( spl24_88
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_88])]) ).
tff(f1038,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) )
| ~ spl24_45
| ~ spl24_88 ),
inference(resolution,[],[f1035,f761]) ).
tff(f1035,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_88 ),
inference(avatar_component_clause,[],[f1034]) ).
tff(f3934,plain,
( spl24_272
| ~ spl24_22
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2727,f2708,f635,f3932]) ).
tff(f3932,plain,
( spl24_272
<=> ! [X0: dB] :
( sP1(abs(abs(sK8(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_272])]) ).
tff(f635,plain,
( spl24_22
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_22])]) ).
tff(f2727,plain,
( ! [X0: dB] :
( sP1(abs(abs(sK8(X0))))
| ~ sP0(X0) )
| ~ spl24_22
| ~ spl24_217 ),
inference(resolution,[],[f2709,f636]) ).
tff(f636,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_22 ),
inference(avatar_component_clause,[],[f635]) ).
tff(f3878,plain,
( spl24_271
| ~ spl24_43
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1939,f1929,f752,f3876]) ).
tff(f3876,plain,
( spl24_271
<=> ! [X2: dB,X0: nat,X1: dB,X3: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_271])]) ).
tff(f1939,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl24_43
| ~ spl24_179 ),
inference(superposition,[],[f753,f1930]) ).
tff(f3874,plain,
( spl24_270
| ~ spl24_44
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1938,f1929,f756,f3872]) ).
tff(f3872,plain,
( spl24_270
<=> ! [X2: dB,X0: nat,X1: dB,X3: nat] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_270])]) ).
tff(f1938,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl24_44
| ~ spl24_179 ),
inference(superposition,[],[f757,f1930]) ).
tff(f3870,plain,
( spl24_269
| ~ spl24_67
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1496,f1482,f900,f3868]) ).
tff(f3868,plain,
( spl24_269
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_269])]) ).
tff(f1496,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(dB,X0,X2,X1,as,a)) ) )
| ~ spl24_67
| ~ spl24_139 ),
inference(superposition,[],[f1483,f902]) ).
tff(f3866,plain,
( spl24_268
| ~ spl24_67
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1492,f1478,f900,f3864]) ).
tff(f3864,plain,
( spl24_268
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK20(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_268])]) ).
tff(f1492,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK20(X0,dB,as,a,X2,X1)) ) )
| ~ spl24_67
| ~ spl24_138 ),
inference(superposition,[],[f1479,f902]) ).
tff(f3862,plain,
( spl24_267
| ~ spl24_67
| ~ spl24_137 ),
inference(avatar_split_clause,[],[f1485,f1474,f900,f3860]) ).
tff(f3860,plain,
( spl24_267
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_267])]) ).
tff(f1485,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) )
| ~ spl24_67
| ~ spl24_137 ),
inference(superposition,[],[f1475,f902]) ).
tff(f3845,plain,
( spl24_266
| ~ spl24_90
| ~ spl24_111 ),
inference(avatar_split_clause,[],[f1193,f1189,f1048,f3842]) ).
tff(f3842,plain,
( spl24_266
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_266])]) ).
tff(f1193,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t1))))
| ~ spl24_90
| ~ spl24_111 ),
inference(resolution,[],[f1190,f1050]) ).
tff(f3840,plain,
( spl24_265
| ~ spl24_92
| ~ spl24_111 ),
inference(avatar_split_clause,[],[f1192,f1189,f1061,f3837]) ).
tff(f3837,plain,
( spl24_265
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK15(t2,rs,var(i),shift(type,e,i,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_265])]) ).
tff(f1192,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK15(t2,rs,var(i),shift(type,e,i,t1))))
| ~ spl24_92
| ~ spl24_111 ),
inference(resolution,[],[f1190,f1063]) ).
tff(f3835,plain,
( spl24_264
| ~ spl24_90
| ~ spl24_109 ),
inference(avatar_split_clause,[],[f1181,f1177,f1048,f3832]) ).
tff(f3832,plain,
( spl24_264
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_264])]) ).
tff(f1181,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t1))))
| ~ spl24_90
| ~ spl24_109 ),
inference(resolution,[],[f1178,f1050]) ).
tff(f3830,plain,
( spl24_263
| ~ spl24_92
| ~ spl24_109 ),
inference(avatar_split_clause,[],[f1180,f1177,f1061,f3827]) ).
tff(f3827,plain,
( spl24_263
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK14(t2,rs,var(i),shift(type,e,i,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_263])]) ).
tff(f1180,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK14(t2,rs,var(i),shift(type,e,i,t1))))
| ~ spl24_92
| ~ spl24_109 ),
inference(resolution,[],[f1178,f1063]) ).
tff(f3825,plain,
( spl24_262
| ~ spl24_26
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f987,f979,f661,f3823]) ).
tff(f3823,plain,
( spl24_262
<=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_262])]) ).
tff(f987,plain,
( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) )
| ~ spl24_26
| ~ spl24_82 ),
inference(superposition,[],[f980,f662]) ).
tff(f3783,plain,
( spl24_261
| ~ spl24_67
| ~ spl24_134 ),
inference(avatar_split_clause,[],[f1402,f1353,f900,f3781]) ).
tff(f3781,plain,
( spl24_261
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_261])]) ).
tff(f1402,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(dB,X0,X2,X1,as,a)) ) )
| ~ spl24_67
| ~ spl24_134 ),
inference(superposition,[],[f1354,f902]) ).
tff(f3779,plain,
( spl24_260
| ~ spl24_67
| ~ spl24_133 ),
inference(avatar_split_clause,[],[f1399,f1349,f900,f3777]) ).
tff(f3777,plain,
( spl24_260
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK19(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_260])]) ).
tff(f1399,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK19(X0,dB,as,a,X2,X1)) ) )
| ~ spl24_67
| ~ spl24_133 ),
inference(superposition,[],[f1350,f902]) ).
tff(f3775,plain,
( spl24_259
| ~ spl24_90
| ~ spl24_114 ),
inference(avatar_split_clause,[],[f1211,f1207,f1048,f3772]) ).
tff(f3772,plain,
( spl24_259
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK16(t_a,rs,i,shift(type,ea,ia,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_259])]) ).
tff(f1211,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t1),rs),sK16(t_a,rs,i,shift(type,ea,ia,t1))))
| ~ spl24_90
| ~ spl24_114 ),
inference(resolution,[],[f1208,f1050]) ).
tff(f3770,plain,
( spl24_258
| ~ spl24_92
| ~ spl24_114 ),
inference(avatar_split_clause,[],[f1210,f1207,f1061,f3767]) ).
tff(f3767,plain,
( spl24_258
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK16(t2,rs,i,shift(type,e,i,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_258])]) ).
tff(f1210,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),rs),sK16(t2,rs,i,shift(type,e,i,t1))))
| ~ spl24_92
| ~ spl24_114 ),
inference(resolution,[],[f1208,f1063]) ).
tff(f3765,plain,
( spl24_257
| ~ spl24_59
| ~ spl24_98 ),
inference(avatar_split_clause,[],[f1119,f1103,f858,f3763]) ).
tff(f3763,plain,
( spl24_257
<=> ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( foldr(type,type,fun1,ts,t2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_257])]) ).
tff(f1119,plain,
( ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( foldr(type,type,fun1,ts,t2) = X1 ) )
| ~ spl24_59
| ~ spl24_98 ),
inference(superposition,[],[f1104,f860]) ).
tff(f3758,plain,
( spl24_256
| ~ spl24_79
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f990,f979,f962,f3756]) ).
tff(f3756,plain,
( spl24_256
<=> ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_256])]) ).
tff(f990,plain,
( ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 )
| ~ spl24_79
| ~ spl24_82 ),
inference(superposition,[],[f980,f963]) ).
tff(f3707,plain,
( spl24_255
| ~ spl24_45
| ~ spl24_92 ),
inference(avatar_split_clause,[],[f1065,f1061,f760,f3704]) ).
tff(f3704,plain,
( spl24_255
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_255])]) ).
tff(f1065,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),t2)))
| ~ spl24_45
| ~ spl24_92 ),
inference(resolution,[],[f1063,f761]) ).
tff(f3702,plain,
( spl24_254
| ~ spl24_45
| ~ spl24_90 ),
inference(avatar_split_clause,[],[f1052,f1048,f760,f3699]) ).
tff(f3699,plain,
( spl24_254
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_254])]) ).
tff(f1052,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a)))
| ~ spl24_45
| ~ spl24_90 ),
inference(resolution,[],[f1050,f761]) ).
tff(f3697,plain,
( spl24_253
| ~ spl24_24
| ~ spl24_84 ),
inference(avatar_split_clause,[],[f1014,f1011,f643,f3695]) ).
tff(f3695,plain,
( spl24_253
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_253])]) ).
tff(f1011,plain,
( spl24_84
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_84])]) ).
tff(f1014,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) )
| ~ spl24_24
| ~ spl24_84 ),
inference(resolution,[],[f1012,f644]) ).
tff(f1012,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_84 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f3693,plain,
( spl24_252
| ~ spl24_73
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f998,f979,f929,f3691]) ).
tff(f3691,plain,
( spl24_252
<=> ! [X2: nat,X0: dB,X1: dB,X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_252])]) ).
tff(f998,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: dB] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) )
| ~ spl24_73
| ~ spl24_82 ),
inference(superposition,[],[f930,f980]) ).
tff(f3689,plain,
( spl24_251
| ~ spl24_24
| ~ spl24_77 ),
inference(avatar_split_clause,[],[f982,f953,f643,f3687]) ).
tff(f3687,plain,
( spl24_251
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK4(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_251])]) ).
tff(f953,plain,
( spl24_77
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_77])]) ).
tff(f982,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK4(X0))) )
| ~ spl24_24
| ~ spl24_77 ),
inference(resolution,[],[f954,f644]) ).
tff(f954,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK4(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl24_77 ),
inference(avatar_component_clause,[],[f953]) ).
tff(f3685,plain,
( spl24_250
| ~ spl24_17
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2711,f2708,f604,f3683]) ).
tff(f3683,plain,
( spl24_250
<=> ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_250])]) ).
tff(f2711,plain,
( ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) )
| ~ spl24_17
| ~ spl24_217 ),
inference(resolution,[],[f2709,f605]) ).
tff(f3681,plain,
( spl24_249
| ~ spl24_45
| ~ spl24_64 ),
inference(avatar_split_clause,[],[f883,f880,f760,f3679]) ).
tff(f3679,plain,
( spl24_249
<=> ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_249])]) ).
tff(f883,plain,
( ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1))))
| ~ spl24_45
| ~ spl24_64 ),
inference(resolution,[],[f881,f761]) ).
tff(f3677,plain,
( spl24_248
| ~ spl24_45
| ~ spl24_58 ),
inference(avatar_split_clause,[],[f855,f851,f760,f3674]) ).
tff(f3674,plain,
( spl24_248
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_248])]) ).
tff(f855,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2)))
| ~ spl24_45
| ~ spl24_58 ),
inference(resolution,[],[f853,f761]) ).
tff(f3672,plain,
( spl24_247
| ~ spl24_45
| ~ spl24_55 ),
inference(avatar_split_clause,[],[f838,f834,f760,f3669]) ).
tff(f3669,plain,
( spl24_247
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_247])]) ).
tff(f838,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t1)),t)))
| ~ spl24_45
| ~ spl24_55 ),
inference(resolution,[],[f836,f761]) ).
tff(f3664,plain,
( spl24_246
| ~ spl24_16
| ~ spl24_84 ),
inference(avatar_split_clause,[],[f1015,f1011,f600,f3662]) ).
tff(f3662,plain,
( spl24_246
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_246])]) ).
tff(f1015,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) )
| ~ spl24_16
| ~ spl24_84 ),
inference(resolution,[],[f1012,f601]) ).
tff(f3660,plain,
( spl24_245
| ~ spl24_16
| ~ spl24_77 ),
inference(avatar_split_clause,[],[f983,f953,f600,f3658]) ).
tff(f3658,plain,
( spl24_245
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_245])]) ).
tff(f983,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK4(X0)) )
| ~ spl24_16
| ~ spl24_77 ),
inference(resolution,[],[f954,f601]) ).
tff(f3656,plain,
( spl24_244
| ~ spl24_24
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f974,f971,f643,f3654]) ).
tff(f3654,plain,
( spl24_244
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_244])]) ).
tff(f971,plain,
( spl24_81
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_81])]) ).
tff(f974,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) )
| ~ spl24_24
| ~ spl24_81 ),
inference(resolution,[],[f972,f644]) ).
tff(f972,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_81 ),
inference(avatar_component_clause,[],[f971]) ).
tff(f3579,plain,
( spl24_243
| ~ spl24_11
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2713,f2708,f574,f3577]) ).
tff(f3577,plain,
( spl24_243
<=> ! [X0: nat] : sP1(abs(abs(var(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_243])]) ).
tff(f2713,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl24_11
| ~ spl24_217 ),
inference(resolution,[],[f2709,f575]) ).
tff(f3019,plain,
( ~ spl24_3
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2950]) ).
tff(f2950,plain,
( $false
| ~ spl24_3
| ~ spl24_220 ),
inference(resolution,[],[f2759,f534]) ).
tff(f2759,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl24_220 ),
inference(avatar_component_clause,[],[f2758]) ).
tff(f2758,plain,
( spl24_220
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_220])]) ).
tff(f3018,plain,
( ~ spl24_37
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2951]) ).
tff(f2951,plain,
( $false
| ~ spl24_37
| ~ spl24_220 ),
inference(resolution,[],[f2759,f719]) ).
tff(f719,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl24_37 ),
inference(avatar_component_clause,[],[f718]) ).
tff(f718,plain,
( spl24_37
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_37])]) ).
tff(f3017,plain,
( ~ spl24_11
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2953]) ).
tff(f2953,plain,
( $false
| ~ spl24_11
| ~ spl24_220 ),
inference(resolution,[],[f2759,f575]) ).
tff(f3016,plain,
( ~ spl24_145
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2955]) ).
tff(f2955,plain,
( $false
| ~ spl24_145
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1558]) ).
tff(f3015,plain,
( ~ spl24_200
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2957]) ).
tff(f2957,plain,
( $false
| ~ spl24_200
| ~ spl24_220 ),
inference(resolution,[],[f2759,f2139]) ).
tff(f3014,plain,
( ~ spl24_128
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2958]) ).
tff(f2958,plain,
( $false
| ~ spl24_128
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1318]) ).
tff(f3013,plain,
( ~ spl24_6
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2959]) ).
tff(f2959,plain,
( $false
| ~ spl24_6
| ~ spl24_220 ),
inference(resolution,[],[f2759,f547]) ).
tff(f547,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl24_6 ),
inference(avatar_component_clause,[],[f545]) ).
tff(f545,plain,
( spl24_6
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_6])]) ).
tff(f3012,plain,
( ~ spl24_8
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2960]) ).
tff(f2960,plain,
( $false
| ~ spl24_8
| ~ spl24_220 ),
inference(resolution,[],[f2759,f557]) ).
tff(f557,plain,
( pp(aa(dB,bool,it,u))
| ~ spl24_8 ),
inference(avatar_component_clause,[],[f555]) ).
tff(f555,plain,
( spl24_8
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_8])]) ).
tff(f3011,plain,
( ~ spl24_7
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2961]) ).
tff(f2961,plain,
( $false
| ~ spl24_7
| ~ spl24_220 ),
inference(resolution,[],[f2759,f552]) ).
tff(f552,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl24_7 ),
inference(avatar_component_clause,[],[f550]) ).
tff(f550,plain,
( spl24_7
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_7])]) ).
tff(f3010,plain,
( ~ spl24_220
| ~ spl24_236 ),
inference(avatar_contradiction_clause,[],[f2965]) ).
tff(f2965,plain,
( $false
| ~ spl24_220
| ~ spl24_236 ),
inference(resolution,[],[f2759,f2881]) ).
tff(f2881,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl24_236 ),
inference(avatar_component_clause,[],[f2880]) ).
tff(f2880,plain,
( spl24_236
<=> ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_236])]) ).
tff(f3009,plain,
( ~ spl24_119
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2966]) ).
tff(f2966,plain,
( $false
| ~ spl24_119
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1239]) ).
tff(f3008,plain,
( ~ spl24_125
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2967]) ).
tff(f2967,plain,
( $false
| ~ spl24_125
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1288]) ).
tff(f3007,plain,
( ~ spl24_64
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2968]) ).
tff(f2968,plain,
( $false
| ~ spl24_64
| ~ spl24_220 ),
inference(resolution,[],[f2759,f881]) ).
tff(f3006,plain,
( ~ spl24_123
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2969]) ).
tff(f2969,plain,
( $false
| ~ spl24_123
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1270]) ).
tff(f3005,plain,
( ~ spl24_55
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2970]) ).
tff(f2970,plain,
( $false
| ~ spl24_55
| ~ spl24_220 ),
inference(resolution,[],[f2759,f836]) ).
tff(f3004,plain,
( ~ spl24_92
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2971]) ).
tff(f2971,plain,
( $false
| ~ spl24_92
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1063]) ).
tff(f3003,plain,
( ~ spl24_121
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2972]) ).
tff(f2972,plain,
( $false
| ~ spl24_121
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1253]) ).
tff(f3002,plain,
( ~ spl24_186
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2973]) ).
tff(f2973,plain,
( $false
| ~ spl24_186
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1998]) ).
tff(f3001,plain,
( ~ spl24_90
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2974]) ).
tff(f2974,plain,
( $false
| ~ spl24_90
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1050]) ).
tff(f3000,plain,
( ~ spl24_29
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2975]) ).
tff(f2975,plain,
( $false
| ~ spl24_29
| ~ spl24_220 ),
inference(resolution,[],[f2759,f678]) ).
tff(f678,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua))
| ~ spl24_29 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f676,plain,
( spl24_29
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_29])]) ).
tff(f2999,plain,
( ~ spl24_31
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2976]) ).
tff(f2976,plain,
( $false
| ~ spl24_31
| ~ spl24_220 ),
inference(resolution,[],[f2759,f690]) ).
tff(f2998,plain,
( ~ spl24_58
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2977]) ).
tff(f2977,plain,
( $false
| ~ spl24_58
| ~ spl24_220 ),
inference(resolution,[],[f2759,f853]) ).
tff(f2997,plain,
( ~ spl24_33
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2978]) ).
tff(f2978,plain,
( $false
| ~ spl24_33
| ~ spl24_220 ),
inference(resolution,[],[f2759,f701]) ).
tff(f2996,plain,
( ~ spl24_34
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2979]) ).
tff(f2979,plain,
( $false
| ~ spl24_34
| ~ spl24_220 ),
inference(resolution,[],[f2759,f706]) ).
tff(f2995,plain,
( ~ spl24_165
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2980]) ).
tff(f2980,plain,
( $false
| ~ spl24_165
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1717]) ).
tff(f1717,plain,
( pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),ts))
| ~ spl24_165 ),
inference(avatar_component_clause,[],[f1715]) ).
tff(f1715,plain,
( spl24_165
<=> pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_165])]) ).
tff(f2994,plain,
( ~ spl24_96
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2981]) ).
tff(f2981,plain,
( $false
| ~ spl24_96
| ~ spl24_220 ),
inference(resolution,[],[f2759,f1094]) ).
tff(f2993,plain,
( ~ spl24_220
| ~ spl24_229 ),
inference(avatar_contradiction_clause,[],[f2982]) ).
tff(f2982,plain,
( $false
| ~ spl24_220
| ~ spl24_229 ),
inference(resolution,[],[f2759,f2819]) ).
tff(f2819,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t1)))
| ~ spl24_229 ),
inference(avatar_component_clause,[],[f2817]) ).
tff(f2817,plain,
( spl24_229
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_229])]) ).
tff(f2992,plain,
( ~ spl24_220
| ~ spl24_230 ),
inference(avatar_contradiction_clause,[],[f2983]) ).
tff(f2983,plain,
( $false
| ~ spl24_220
| ~ spl24_230 ),
inference(resolution,[],[f2759,f2824]) ).
tff(f2824,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t1)))
| ~ spl24_230 ),
inference(avatar_component_clause,[],[f2822]) ).
tff(f2822,plain,
( spl24_230
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_230])]) ).
tff(f2991,plain,
( ~ spl24_220
| ~ spl24_231 ),
inference(avatar_contradiction_clause,[],[f2984]) ).
tff(f2984,plain,
( $false
| ~ spl24_220
| ~ spl24_231 ),
inference(resolution,[],[f2759,f2828]) ).
tff(f2828,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl24_231 ),
inference(avatar_component_clause,[],[f2827]) ).
tff(f2827,plain,
( spl24_231
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_231])]) ).
tff(f2990,plain,
( ~ spl24_219
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2985]) ).
tff(f2985,plain,
( $false
| ~ spl24_219
| ~ spl24_220 ),
inference(resolution,[],[f2759,f2756]) ).
tff(f2756,plain,
( pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool)))
| ~ spl24_219 ),
inference(avatar_component_clause,[],[f2754]) ).
tff(f2754,plain,
( spl24_219
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_219])]) ).
tff(f2989,plain,
( ~ spl24_216
| ~ spl24_220 ),
inference(avatar_contradiction_clause,[],[f2986]) ).
tff(f2986,plain,
( $false
| ~ spl24_216
| ~ spl24_220 ),
inference(resolution,[],[f2759,f2260]) ).
tff(f2260,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl24_216 ),
inference(avatar_component_clause,[],[f2258]) ).
tff(f2258,plain,
( spl24_216
<=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_216])]) ).
tff(f2988,plain,
( ~ spl24_220
| ~ spl24_235 ),
inference(avatar_contradiction_clause,[],[f2987]) ).
tff(f2987,plain,
( $false
| ~ spl24_220
| ~ spl24_235 ),
inference(resolution,[],[f2759,f2877]) ).
tff(f2877,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t1),as)))
| ~ spl24_235 ),
inference(avatar_component_clause,[],[f2875]) ).
tff(f2875,plain,
( spl24_235
<=> pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t1),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_235])]) ).
tff(f2949,plain,
( spl24_220
| spl24_242
| ~ spl24_45
| ~ spl24_49 ),
inference(avatar_split_clause,[],[f797,f792,f760,f2947,f2758]) ).
tff(f2947,plain,
( spl24_242
<=> ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_242])]) ).
tff(f792,plain,
( spl24_49
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_49])]) ).
tff(f797,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) )
| ~ spl24_45
| ~ spl24_49 ),
inference(resolution,[],[f793,f761]) ).
tff(f793,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_49 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f2905,plain,
( spl24_241
| ~ spl24_26
| ~ spl24_75
| ~ spl24_123 ),
inference(avatar_split_clause,[],[f1275,f1268,f942,f661,f2902]) ).
tff(f2902,plain,
( spl24_241
<=> ( t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_241])]) ).
tff(f1275,plain,
( ( t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2) )
| ~ spl24_26
| ~ spl24_75
| ~ spl24_123 ),
inference(forward_demodulation,[],[f1272,f662]) ).
tff(f1272,plain,
( ( aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2) = aa(nat,type,shift(type,e,i,t1),i) )
| ~ spl24_75
| ~ spl24_123 ),
inference(resolution,[],[f1270,f943]) ).
tff(f2900,plain,
( spl24_240
| ~ spl24_68
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f1001,f979,f905,f2898]) ).
tff(f2898,plain,
( spl24_240
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_240])]) ).
tff(f1001,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 )
| ~ spl24_68
| ~ spl24_82 ),
inference(superposition,[],[f906,f980]) ).
tff(f2896,plain,
( spl24_239
| ~ spl24_59
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f992,f979,f858,f2893]) ).
tff(f2893,plain,
( spl24_239
<=> ( t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_239])]) ).
tff(f992,plain,
( ( t1 = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),t) )
| ~ spl24_59
| ~ spl24_82 ),
inference(superposition,[],[f980,f860]) ).
tff(f2891,plain,
( spl24_238
| ~ spl24_67
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f991,f979,f900,f2888]) ).
tff(f2888,plain,
( spl24_238
<=> ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_238])]) ).
tff(f991,plain,
( ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) )
| ~ spl24_67
| ~ spl24_82 ),
inference(superposition,[],[f980,f902]) ).
tff(f2886,plain,
( spl24_237
| ~ spl24_16
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f975,f971,f600,f2884]) ).
tff(f2884,plain,
( spl24_237
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_237])]) ).
tff(f975,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl24_16
| ~ spl24_81 ),
inference(resolution,[],[f972,f601]) ).
tff(f2882,plain,
( spl24_236
| ~ spl24_26
| ~ spl24_64 ),
inference(avatar_split_clause,[],[f884,f880,f661,f2880]) ).
tff(f884,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl24_26
| ~ spl24_64 ),
inference(superposition,[],[f881,f662]) ).
tff(f2878,plain,
( spl24_235
| ~ spl24_33
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f777,f760,f699,f2875]) ).
tff(f777,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t1),as)))
| ~ spl24_33
| ~ spl24_45 ),
inference(resolution,[],[f761,f701]) ).
tff(f2870,plain,
( spl24_234
| ~ spl24_7
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2724,f2708,f550,f2867]) ).
tff(f2724,plain,
( sP1(abs(abs(ua)))
| ~ spl24_7
| ~ spl24_217 ),
inference(resolution,[],[f2709,f552]) ).
tff(f2865,plain,
( spl24_233
| ~ spl24_59
| ~ spl24_97 ),
inference(avatar_split_clause,[],[f1114,f1099,f858,f2863]) ).
tff(f2863,plain,
( spl24_233
<=> ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( t = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_233])]) ).
tff(f1114,plain,
( ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( t = X0 ) )
| ~ spl24_59
| ~ spl24_97 ),
inference(superposition,[],[f1100,f860]) ).
tff(f2833,plain,
( spl24_232
| ~ spl24_26
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f780,f760,f661,f2831]) ).
tff(f2831,plain,
( spl24_232
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_232])]) ).
tff(f780,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) )
| ~ spl24_26
| ~ spl24_45 ),
inference(superposition,[],[f761,f662]) ).
tff(f2829,plain,
( spl24_231
| ~ spl24_37
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f776,f760,f718,f2827]) ).
tff(f776,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl24_37
| ~ spl24_45 ),
inference(resolution,[],[f761,f719]) ).
tff(f2825,plain,
( spl24_230
| ~ spl24_31
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f775,f760,f688,f2822]) ).
tff(f775,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t1)))
| ~ spl24_31
| ~ spl24_45 ),
inference(resolution,[],[f761,f690]) ).
tff(f2820,plain,
( spl24_229
| ~ spl24_29
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f774,f760,f676,f2817]) ).
tff(f774,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t1)))
| ~ spl24_29
| ~ spl24_45 ),
inference(resolution,[],[f761,f678]) ).
tff(f2804,plain,
( spl24_228
| ~ spl24_8
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2723,f2708,f555,f2801]) ).
tff(f2723,plain,
( sP1(abs(abs(u)))
| ~ spl24_8
| ~ spl24_217 ),
inference(resolution,[],[f2709,f557]) ).
tff(f2799,plain,
( spl24_227
| ~ spl24_10
| ~ spl24_26 ),
inference(avatar_split_clause,[],[f664,f661,f564,f2797]) ).
tff(f2797,plain,
( spl24_227
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_227])]) ).
tff(f664,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) )
| ~ spl24_10
| ~ spl24_26 ),
inference(superposition,[],[f662,f565]) ).
tff(f2792,plain,
( spl24_226
| ~ spl24_43
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f997,f979,f752,f2790]) ).
tff(f2790,plain,
( spl24_226
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_226])]) ).
tff(f997,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl24_43
| ~ spl24_82 ),
inference(superposition,[],[f753,f980]) ).
tff(f2788,plain,
( spl24_225
| ~ spl24_44
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f996,f979,f756,f2786]) ).
tff(f2786,plain,
( spl24_225
<=> ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_225])]) ).
tff(f996,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl24_44
| ~ spl24_82 ),
inference(superposition,[],[f757,f980]) ).
tff(f2784,plain,
( spl24_224
| ~ spl24_24
| ~ spl24_50 ),
inference(avatar_split_clause,[],[f822,f800,f643,f2782]) ).
tff(f2782,plain,
( spl24_224
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_224])]) ).
tff(f822,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl24_24
| ~ spl24_50 ),
inference(resolution,[],[f801,f644]) ).
tff(f2780,plain,
( spl24_223
| ~ spl24_24
| ~ spl24_47 ),
inference(avatar_split_clause,[],[f818,f783,f643,f2778]) ).
tff(f2778,plain,
( spl24_223
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(abs(sK4(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_223])]) ).
tff(f783,plain,
( spl24_47
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_47])]) ).
tff(f818,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(abs(sK4(X0))) )
| ~ spl24_24
| ~ spl24_47 ),
inference(resolution,[],[f784,f644]) ).
tff(f784,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK4(X0)))
| sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) )
| ~ spl24_47 ),
inference(avatar_component_clause,[],[f783]) ).
tff(f2776,plain,
( spl24_222
| ~ spl24_6
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2722,f2708,f545,f2773]) ).
tff(f2722,plain,
( sP1(abs(abs(t3)))
| ~ spl24_6
| ~ spl24_217 ),
inference(resolution,[],[f2709,f547]) ).
tff(f2771,plain,
( spl24_221
| ~ spl24_16
| ~ spl24_47 ),
inference(avatar_split_clause,[],[f819,f783,f600,f2769]) ).
tff(f2769,plain,
( spl24_221
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_221])]) ).
tff(f819,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(sK4(X0)) )
| ~ spl24_16
| ~ spl24_47 ),
inference(resolution,[],[f784,f601]) ).
tff(f2760,plain,
( spl24_219
| spl24_220
| ~ spl24_18
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f779,f760,f608,f2758,f2754]) ).
tff(f779,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl24_18
| ~ spl24_45 ),
inference(superposition,[],[f761,f609]) ).
tff(f2737,plain,
( spl24_218
| ~ spl24_10
| ~ spl24_18 ),
inference(avatar_split_clause,[],[f631,f608,f564,f2735]) ).
tff(f2735,plain,
( spl24_218
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_218])]) ).
tff(f631,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_10
| ~ spl24_18 ),
inference(superposition,[],[f609,f565]) ).
tff(f2710,plain,
( spl24_217
| ~ spl24_24
| ~ spl24_35 ),
inference(avatar_split_clause,[],[f724,f709,f643,f2708]) ).
tff(f709,plain,
( spl24_35
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_35])]) ).
tff(f724,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl24_24
| ~ spl24_35 ),
inference(resolution,[],[f710,f644]) ).
tff(f710,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl24_35 ),
inference(avatar_component_clause,[],[f709]) ).
tff(f2261,plain,
( spl24_216
| ~ spl24_11
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f769,f760,f574,f2258]) ).
tff(f769,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl24_11
| ~ spl24_45 ),
inference(resolution,[],[f761,f575]) ).
tff(f2249,plain,
( spl24_215
| ~ spl24_10 ),
inference(avatar_split_clause,[],[f567,f564,f2247]) ).
tff(f567,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl24_10 ),
inference(superposition,[],[f565,f565]) ).
tff(f2242,plain,
( spl24_214
| ~ spl24_82
| ~ spl24_213 ),
inference(avatar_split_clause,[],[f2238,f2234,f979,f2240]) ).
tff(f2240,plain,
( spl24_214
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_214])]) ).
tff(f2234,plain,
( spl24_213
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_213])]) ).
tff(f2238,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) )
| ~ spl24_82
| ~ spl24_213 ),
inference(forward_demodulation,[],[f2237,f980]) ).
tff(f2237,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) )
| ~ spl24_82
| ~ spl24_213 ),
inference(forward_demodulation,[],[f2235,f980]) ).
tff(f2235,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) )
| ~ spl24_213 ),
inference(avatar_component_clause,[],[f2234]) ).
tff(f2236,plain,
spl24_213,
inference(avatar_split_clause,[],[f470,f2234]) ).
tff(f470,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ),
inference(definition_unfolding,[],[f382,f385]) ).
tff(f385,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: fun(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType,X82: fun(list(X0),bool),X53: fun(X0,bool)] : ( set_Cons(X0,X53,X82) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X53))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X82)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_set__Cons__def) ).
tff(f382,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: list(fun(X0,bool)),X2: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType,X83: list(fun(X0,bool)),X53: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X53),X83)) = set_Cons(X0,X53,listset(X0,X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_listset_Osimps_I2_J) ).
tff(f2227,plain,
( spl24_212
| ~ spl24_82
| ~ spl24_211 ),
inference(avatar_split_clause,[],[f2223,f2220,f979,f2225]) ).
tff(f2225,plain,
( spl24_212
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_212])]) ).
tff(f2220,plain,
( spl24_211
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_211])]) ).
tff(f2223,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_82
| ~ spl24_211 ),
inference(forward_demodulation,[],[f2221,f980]) ).
tff(f2221,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_211 ),
inference(avatar_component_clause,[],[f2220]) ).
tff(f2222,plain,
spl24_211,
inference(avatar_split_clause,[],[f428,f2220]) ).
tff(f428,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X26: list(type),X27: list(dB),X9: dB,X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X9),X27)),X26))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X10),X9))),typings(X10,X27)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_typings_Osimps_I2_J) ).
tff(f2213,plain,
( spl24_210
| ~ spl24_82
| ~ spl24_209 ),
inference(avatar_split_clause,[],[f2209,f2206,f979,f2211]) ).
tff(f2211,plain,
( spl24_210
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_210])]) ).
tff(f2206,plain,
( spl24_209
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_209])]) ).
tff(f2209,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_82
| ~ spl24_209 ),
inference(forward_demodulation,[],[f2207,f980]) ).
tff(f2207,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) )
| ~ spl24_209 ),
inference(avatar_component_clause,[],[f2206]) ).
tff(f2208,plain,
spl24_209,
inference(avatar_split_clause,[],[f427,f2206]) ).
tff(f427,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
inference(cnf_transformation,[],[f290]) ).
tff(f2204,plain,
( spl24_208
| ~ spl24_7
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f1379,f583,f550,f2201]) ).
tff(f2201,plain,
( spl24_208
<=> ( aa(dB,bool,it,ua) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_208])]) ).
tff(f1379,plain,
( ( aa(dB,bool,it,ua) = fTrue )
| ~ spl24_7
| ~ spl24_13 ),
inference(resolution,[],[f584,f552]) ).
tff(f2192,plain,
spl24_207,
inference(avatar_split_clause,[],[f457,f2190]) ).
tff(f2190,plain,
( spl24_207
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_207])]) ).
tff(f457,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X50: list(X2),X51: fun(X2,X1),X58: X0,X63: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X63,X58,map(X2,X1,X51,X50)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X63),X51),X58,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_foldl__map) ).
tff(f2178,plain,
( spl24_206
| ~ spl24_82
| ~ spl24_205 ),
inference(avatar_split_clause,[],[f2174,f2168,f979,f2176]) ).
tff(f2168,plain,
( spl24_205
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_205])]) ).
tff(f2174,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl24_82
| ~ spl24_205 ),
inference(forward_demodulation,[],[f2173,f980]) ).
tff(f2173,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl24_82
| ~ spl24_205 ),
inference(forward_demodulation,[],[f2172,f980]) ).
tff(f2172,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl24_82
| ~ spl24_205 ),
inference(forward_demodulation,[],[f2171,f980]) ).
tff(f2171,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl24_82
| ~ spl24_205 ),
inference(forward_demodulation,[],[f2169,f980]) ).
tff(f2169,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) )
| ~ spl24_205 ),
inference(avatar_component_clause,[],[f2168]) ).
tff(f2170,plain,
spl24_205,
inference(avatar_split_clause,[],[f404,f2168]) ).
tff(f404,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X31: nat,X32: dB,X33: dB,X21: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X21),X33)),X32),X31) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X21),X32),X31)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X33),X32),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_subst__App) ).
tff(f2166,plain,
spl24_204,
inference(avatar_split_clause,[],[f512,f2164]) ).
tff(f2164,plain,
( spl24_204
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_204])]) ).
tff(f512,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f511,f442]) ).
tff(f442,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X85: X0,X86: X1,X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X84,X86),X85) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X85),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f511,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f510,f442]) ).
tff(f510,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f509,f442]) ).
tff(f509,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f459,f442]) ).
tff(f459,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X6: dB,X8: type,X4: nat,X10: fun(nat,type),X9: dB,X11: type,X12: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X12),X11) )
=> ( pp(aa(dB,bool,it,X9))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X4,X12)),X9),X8))
=> ( pp(aa(dB,bool,it,X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X6),X12))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X9),X6),X4))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_MI1) ).
tff(f2162,plain,
spl24_203,
inference(avatar_split_clause,[],[f508,f2160]) ).
tff(f2160,plain,
( spl24_203
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_203])]) ).
tff(f508,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f507,f442]) ).
tff(f507,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f506,f442]) ).
tff(f506,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f505,f442]) ).
tff(f505,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f458,f442]) ).
tff(f458,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f237]) ).
tff(f237,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X6: dB,X8: type,X4: nat,X10: fun(nat,type),X9: dB,X11: type,X12: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X12),X11) )
=> ( pp(aa(dB,bool,it,X9))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X4,X11)),X9),X8))
=> ( pp(aa(dB,bool,it,X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X6),X11))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X9),X6),X4))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_MI2) ).
tff(f2154,plain,
( spl24_202
| ~ spl24_8
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f1378,f583,f555,f2151]) ).
tff(f2151,plain,
( spl24_202
<=> ( aa(dB,bool,it,u) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_202])]) ).
tff(f1378,plain,
( ( aa(dB,bool,it,u) = fTrue )
| ~ spl24_8
| ~ spl24_13 ),
inference(resolution,[],[f584,f557]) ).
tff(f2149,plain,
spl24_201,
inference(avatar_split_clause,[],[f431,f2147]) ).
tff(f2147,plain,
( spl24_201
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_201])]) ).
tff(f431,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X52: fun(X0,bool),X53: fun(X0,bool),X54: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X53)),X52),X54)
<=> ( listsp(X0,X52,X54)
& listsp(X0,X53,X54) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_listsp__conj__eq) ).
tff(f2140,plain,
( spl24_200
| ~ spl24_82
| ~ spl24_199 ),
inference(avatar_split_clause,[],[f2135,f2128,f979,f2137]) ).
tff(f2128,plain,
( spl24_199
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_199])]) ).
tff(f2135,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_82
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2134,f980]) ).
tff(f2134,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_82
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2133,f980]) ).
tff(f2133,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_82
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2132,f980]) ).
tff(f2132,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))))
| ~ spl24_82
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2130,f980]) ).
tff(f2130,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat))))
| ~ spl24_199 ),
inference(avatar_component_clause,[],[f2128]) ).
tff(f2131,plain,
spl24_199,
inference(avatar_split_clause,[],[f334,f2128]) ).
tff(f334,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f2120,plain,
( spl24_198
| ~ spl24_82
| ~ spl24_197 ),
inference(avatar_split_clause,[],[f2116,f2112,f979,f2118]) ).
tff(f2118,plain,
( spl24_198
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_198])]) ).
tff(f2112,plain,
( spl24_197
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_197])]) ).
tff(f2116,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl24_82
| ~ spl24_197 ),
inference(forward_demodulation,[],[f2115,f980]) ).
tff(f2115,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl24_82
| ~ spl24_197 ),
inference(forward_demodulation,[],[f2113,f980]) ).
tff(f2113,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl24_197 ),
inference(avatar_component_clause,[],[f2112]) ).
tff(f2114,plain,
spl24_197,
inference(avatar_split_clause,[],[f403,f2112]) ).
tff(f403,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X4: nat,X6: dB,X27: list(dB),X9: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X9,X27)),X6),X4) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X9),X6),X4),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X6),X4),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_subst__map) ).
tff(f2106,plain,
spl24_196,
inference(avatar_split_clause,[],[f430,f2104]) ).
tff(f2104,plain,
( spl24_196
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_196])]) ).
tff(f430,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f292]) ).
tff(f2102,plain,
( spl24_195
| ~ spl24_6
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f1377,f583,f545,f2099]) ).
tff(f2099,plain,
( spl24_195
<=> ( aa(dB,bool,it,t3) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_195])]) ).
tff(f1377,plain,
( ( aa(dB,bool,it,t3) = fTrue )
| ~ spl24_6
| ~ spl24_13 ),
inference(resolution,[],[f584,f547]) ).
tff(f2097,plain,
spl24_194,
inference(avatar_split_clause,[],[f429,f2095]) ).
tff(f2095,plain,
( spl24_194
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_194])]) ).
tff(f429,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f292]) ).
tff(f2083,plain,
spl24_193,
inference(avatar_split_clause,[],[f518,f2081]) ).
tff(f2081,plain,
( spl24_193
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_193])]) ).
tff(f518,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f517,f442]) ).
tff(f517,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f462,f442]) ).
tff(f462,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f244,f303]) ).
tff(f303,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
=> ( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f244,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( pp(aa(list(type),bool,typings(X6,X4),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X5: type,X26: list(type),X8: type,X48: list(dB),X27: list(dB),X4: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,foldl(dB,dB,app,var(X4),X27),X48)),X8))
=> ( pp(aa(list(type),bool,typings(X10,X27),X26))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X4),X27)),X5))
=> ? [X49: list(type)] :
( pp(aa(list(type),bool,typings(X10,X48),X49))
& ( foldr(type,type,fun1,X49,X8) = X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_var__app__types) ).
tff(f2069,plain,
spl24_192,
inference(avatar_split_clause,[],[f520,f2067]) ).
tff(f2067,plain,
( spl24_192
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_192])]) ).
tff(f520,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f519,f442]) ).
tff(f519,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f461,f442]) ).
tff(f461,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f304]) ).
tff(f2060,plain,
( spl24_191
| ~ spl24_82
| ~ spl24_190 ),
inference(avatar_split_clause,[],[f2056,f2049,f979,f2058]) ).
tff(f2049,plain,
( spl24_190
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_190])]) ).
tff(f2056,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl24_82
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2055,f980]) ).
tff(f2055,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl24_82
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2054,f980]) ).
tff(f2054,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_82
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2053,f980]) ).
tff(f2053,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_82
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2052,f980]) ).
tff(f2052,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_82
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2050,f980]) ).
tff(f2050,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_190 ),
inference(avatar_component_clause,[],[f2049]) ).
tff(f2051,plain,
spl24_190,
inference(avatar_split_clause,[],[f438,f2049]) ).
tff(f438,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X9: dB,X5: type,X8: type,X22: dB,X19: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X19),X22),aa(type,type,aa(type,fun(type,type),fun1,X8),X5)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X19),X9),X8))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X19),aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X9)),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_App) ).
tff(f2040,plain,
( spl24_189
| ~ spl24_82
| ~ spl24_188 ),
inference(avatar_split_clause,[],[f2035,f2031,f979,f2038]) ).
tff(f2031,plain,
( spl24_188
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_188])]) ).
tff(f2035,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_82
| ~ spl24_188 ),
inference(forward_demodulation,[],[f2034,f980]) ).
tff(f2034,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl24_82
| ~ spl24_188 ),
inference(forward_demodulation,[],[f2032,f980]) ).
tff(f2032,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl24_188 ),
inference(avatar_component_clause,[],[f2031]) ).
tff(f2033,plain,
spl24_188,
inference(avatar_split_clause,[],[f396,f2031]) ).
tff(f396,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f218]) ).
tff(f218,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0)))
=> ( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X46: list(dB),X22: dB,X45: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X45),X22),zero_zero(nat)),X46)))
=> ( pp(aa(dB,bool,it,X22))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X45)),X22),X46))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Beta) ).
tff(f2010,plain,
spl24_187,
inference(avatar_split_clause,[],[f516,f2008]) ).
tff(f516,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ),
inference(forward_demodulation,[],[f515,f442]) ).
tff(f515,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f514,f442]) ).
tff(f514,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f513,f442]) ).
tff(f513,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f498,f442]) ).
tff(f498,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f460]) ).
tff(f460,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
=> ( ( shift(type,X3,X0,X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X4: nat,X5: type,X6: dB,X7: fun(nat,type),X8: type,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X8))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X7),X6),X5))
=> ( ( shift(type,X7,X4,X5) = X10 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X7),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X9),X6),X4)),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subst__lemma) ).
tff(f1999,plain,
( spl24_186
| ~ spl24_82
| ~ spl24_185 ),
inference(avatar_split_clause,[],[f1994,f1990,f979,f1996]) ).
tff(f1990,plain,
( spl24_185
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_185])]) ).
tff(f1994,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),t2),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_82
| ~ spl24_185 ),
inference(forward_demodulation,[],[f1992,f980]) ).
tff(f1992,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),t2))
| ~ spl24_185 ),
inference(avatar_component_clause,[],[f1990]) ).
tff(f1993,plain,
spl24_185,
inference(avatar_split_clause,[],[f333,f1990]) ).
tff(f333,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),t2)),
inference(cnf_transformation,[],[f38]) ).
tff(f38,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__096e_0600_058Ts_A_061_062_062_AT_H_062_A_092_060turnstile_062_AVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_A_058_AT_H_096) ).
tff(f1965,plain,
( spl24_184
| ~ spl24_82
| ~ spl24_182 ),
inference(avatar_split_clause,[],[f1957,f1953,f979,f1963]) ).
tff(f1953,plain,
( spl24_182
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_182])]) ).
tff(f1957,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_82
| ~ spl24_182 ),
inference(forward_demodulation,[],[f1956,f980]) ).
tff(f1956,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl24_82
| ~ spl24_182 ),
inference(forward_demodulation,[],[f1954,f980]) ).
tff(f1954,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl24_182 ),
inference(avatar_component_clause,[],[f1953]) ).
tff(f1961,plain,
( spl24_183
| ~ spl24_22
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f653,f643,f635,f1959]) ).
tff(f1959,plain,
( spl24_183
<=> ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_183])]) ).
tff(f653,plain,
( ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_22
| ~ spl24_24 ),
inference(resolution,[],[f644,f636]) ).
tff(f1955,plain,
spl24_182,
inference(avatar_split_clause,[],[f475,f1953]) ).
tff(f475,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f356]) ).
tff(f356,plain,
! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f260,f261]) ).
tff(f261,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f260,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f259]) ).
tff(f259,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1951,plain,
spl24_181,
inference(avatar_split_clause,[],[f453,f1949]) ).
tff(f453,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f300,f301]) ).
tff(f301,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
=> ( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f300,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(rectify,[],[f299]) ).
tff(f299,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
<=> ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType,X1: $tType,X66: list(X1),X51: fun(X1,X0),X50: list(X0),X18: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X18),X50) = map(X1,X0,X51,X66) )
<=> ? [X67: X1,X68: list(X1)] :
( ( map(X1,X0,X51,X68) = X50 )
& ( aa(X1,X0,X51,X67) = X18 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X67),X68) = X66 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Cons__eq__map__conv) ).
tff(f1947,plain,
spl24_180,
inference(avatar_split_clause,[],[f449,f1945]) ).
tff(f449,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f296,f297]) ).
tff(f297,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
=> ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f296,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(rectify,[],[f295]) ).
tff(f295,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(nnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X1: $tType,X0: $tType,X66: list(X0),X69: X0,X50: list(X1),X51: fun(X1,X0)] :
( ( map(X1,X0,X51,X50) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X69),X66) )
<=> ? [X67: X1,X68: list(X1)] :
( ( map(X1,X0,X51,X68) = X66 )
& ( aa(X1,X0,X51,X67) = X69 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X67),X68) = X50 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_map__eq__Cons__conv) ).
tff(f1931,plain,
( spl24_179
| ~ spl24_82
| ~ spl24_178 ),
inference(avatar_split_clause,[],[f1927,f1921,f979,f1929]) ).
tff(f1921,plain,
( spl24_178
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_178])]) ).
tff(f1927,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl24_82
| ~ spl24_178 ),
inference(forward_demodulation,[],[f1926,f980]) ).
tff(f1926,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )
| ~ spl24_82
| ~ spl24_178 ),
inference(forward_demodulation,[],[f1925,f980]) ).
tff(f1925,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_82
| ~ spl24_178 ),
inference(forward_demodulation,[],[f1924,f980]) ).
tff(f1924,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_82
| ~ spl24_178 ),
inference(forward_demodulation,[],[f1922,f980]) ).
tff(f1922,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) )
| ~ spl24_178 ),
inference(avatar_component_clause,[],[f1921]) ).
tff(f1923,plain,
spl24_178,
inference(avatar_split_clause,[],[f384,f1921]) ).
tff(f384,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X31: nat,X21: dB,X32: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X32),X21)),X31) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X32),X31)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X21),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lift_Osimps_I2_J) ).
tff(f1914,plain,
spl24_177,
inference(avatar_split_clause,[],[f504,f1912]) ).
tff(f504,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ),
inference(forward_demodulation,[],[f448,f442]) ).
tff(f448,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(flattening,[],[f235]) ).
tff(f235,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0)) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X26: list(type),X27: list(dB),X4: nat,X8: type,X6: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X6),X8))
=> ( pp(aa(list(type),bool,typings(shift(type,X10,X4,X8),X27),X26))
=> pp(aa(list(type),bool,typings(X10,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X6),X4),X27)),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_substs__lemma) ).
tff(f1899,plain,
( spl24_176
| ~ spl24_82
| ~ spl24_175 ),
inference(avatar_split_clause,[],[f1894,f1888,f979,f1897]) ).
tff(f1888,plain,
( spl24_175
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_175])]) ).
tff(f1894,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) )
| ~ spl24_82
| ~ spl24_175 ),
inference(forward_demodulation,[],[f1893,f980]) ).
tff(f1893,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) )
| ~ spl24_82
| ~ spl24_175 ),
inference(forward_demodulation,[],[f1892,f980]) ).
tff(f1892,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_82
| ~ spl24_175 ),
inference(forward_demodulation,[],[f1891,f980]) ).
tff(f1891,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_82
| ~ spl24_175 ),
inference(forward_demodulation,[],[f1889,f980]) ).
tff(f1889,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_175 ),
inference(avatar_component_clause,[],[f1888]) ).
tff(f1890,plain,
spl24_175,
inference(avatar_split_clause,[],[f412,f1888]) ).
tff(f412,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f224,f278]) ).
tff(f278,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))
=> ~ ! [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4)) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X8: type,X6: dB,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),aa(dB,dB,aa(dB,fun(dB,dB),app,X9),X6)),X8))
=> ~ ! [X30: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),aa(type,type,aa(type,fun(type,type),fun1,X30),X8)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X6),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_typing__elims_I2_J) ).
tff(f1812,plain,
spl24_174,
inference(avatar_split_clause,[],[f447,f1810]) ).
tff(f447,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X85: X0,X86: fun(X0,X1),X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X84),X86),X85) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X85),aa(X0,X1,X86,X85)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1772,plain,
( spl24_173
| ~ spl24_82
| ~ spl24_172 ),
inference(avatar_split_clause,[],[f1768,f1765,f979,f1770]) ).
tff(f1765,plain,
( spl24_172
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_172])]) ).
tff(f1768,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_82
| ~ spl24_172 ),
inference(forward_demodulation,[],[f1766,f980]) ).
tff(f1766,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) )
| ~ spl24_172 ),
inference(avatar_component_clause,[],[f1765]) ).
tff(f1767,plain,
spl24_172,
inference(avatar_split_clause,[],[f432,f1765]) ).
tff(f432,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType,X1: $tType,X50: list(X1),X18: X1,X51: fun(X1,X0)] : ( map(X1,X0,X51,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X18),X50)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X51,X18)),map(X1,X0,X51,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_map_Osimps_I2_J) ).
tff(f1757,plain,
( spl24_171
| ~ spl24_82
| ~ spl24_170 ),
inference(avatar_split_clause,[],[f1753,f1750,f979,f1755]) ).
tff(f1750,plain,
( spl24_170
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_170])]) ).
tff(f1753,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl24_82
| ~ spl24_170 ),
inference(forward_demodulation,[],[f1751,f980]) ).
tff(f1751,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl24_170 ),
inference(avatar_component_clause,[],[f1750]) ).
tff(f1752,plain,
spl24_170,
inference(avatar_split_clause,[],[f391,f1750]) ).
tff(f391,plain,
! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X2,X1),X0))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X26: list(type),X27: list(dB),X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,X27),X26))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X10)),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_lists__typings) ).
tff(f1745,plain,
( spl24_168
| ~ spl24_169
| ~ spl24_10 ),
inference(avatar_split_clause,[],[f572,f564,f1742,f1739]) ).
tff(f572,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl24_10 ),
inference(equality_factoring,[],[f565]) ).
tff(f1728,plain,
( spl24_167
| ~ spl24_82
| ~ spl24_166 ),
inference(avatar_split_clause,[],[f1724,f1720,f979,f1726]) ).
tff(f1720,plain,
( spl24_166
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_166])]) ).
tff(f1724,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl24_82
| ~ spl24_166 ),
inference(forward_demodulation,[],[f1723,f980]) ).
tff(f1723,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl24_82
| ~ spl24_166 ),
inference(forward_demodulation,[],[f1721,f980]) ).
tff(f1721,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl24_166 ),
inference(avatar_component_clause,[],[f1720]) ).
tff(f1722,plain,
spl24_166,
inference(avatar_split_clause,[],[f436,f1720]) ).
tff(f436,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(flattening,[],[f229]) ).
tff(f229,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1)))
=> ( pp(aa(list(type),bool,typings(X4,X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X27: list(dB),X8: type,X26: list(type),X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),foldr(type,type,fun1,X26,X8)))
=> ( pp(aa(list(type),bool,typings(X10,X27),X26))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X9,X27)),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_list__app__typeI) ).
tff(f1718,plain,
spl24_165,
inference(avatar_split_clause,[],[f332,f1715]) ).
tff(f332,plain,
pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),ts)),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__096e_0600_058Ts_A_061_062_062_AT_H_062_A_124_124_N_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_A_058_ATs_096) ).
tff(f1709,plain,
( spl24_164
| ~ spl24_82
| ~ spl24_163 ),
inference(avatar_split_clause,[],[f1705,f1701,f979,f1707]) ).
tff(f1701,plain,
( spl24_163
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_163])]) ).
tff(f1705,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2))) )
| ~ spl24_82
| ~ spl24_163 ),
inference(forward_demodulation,[],[f1704,f980]) ).
tff(f1704,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_82
| ~ spl24_163 ),
inference(forward_demodulation,[],[f1702,f980]) ).
tff(f1702,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_163 ),
inference(avatar_component_clause,[],[f1701]) ).
tff(f1703,plain,
spl24_163,
inference(avatar_split_clause,[],[f410,f1701]) ).
tff(f410,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f223,f276]) ).
tff(f276,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f223,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X8: type,X27: list(dB),X4: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X4),X27)),X8))
=> ~ ! [X23: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),var(X4)),foldr(type,type,fun1,X23,X8)))
=> ~ pp(aa(list(type),bool,typings(X10,X27),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_var__app__typesE) ).
tff(f1694,plain,
( spl24_162
| ~ spl24_82
| ~ spl24_161 ),
inference(avatar_split_clause,[],[f1690,f1685,f979,f1692]) ).
tff(f1685,plain,
( spl24_161
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_161])]) ).
tff(f1690,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) )
| ~ spl24_82
| ~ spl24_161 ),
inference(forward_demodulation,[],[f1689,f980]) ).
tff(f1689,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_82
| ~ spl24_161 ),
inference(forward_demodulation,[],[f1688,f980]) ).
tff(f1688,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_82
| ~ spl24_161 ),
inference(forward_demodulation,[],[f1686,f980]) ).
tff(f1686,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_161 ),
inference(avatar_component_clause,[],[f1685]) ).
tff(f1687,plain,
spl24_161,
inference(avatar_split_clause,[],[f409,f1685]) ).
tff(f409,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X5: type,X9: dB,X8: type,X19: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X19,zero_zero(nat),X8)),X9),X5))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X19),abs(X9)),aa(type,type,aa(type,fun(type,type),fun1,X8),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Abs) ).
tff(f1678,plain,
( spl24_160
| ~ spl24_82
| ~ spl24_159 ),
inference(avatar_split_clause,[],[f1674,f1670,f979,f1676]) ).
tff(f1670,plain,
( spl24_159
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_159])]) ).
tff(f1674,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl24_82
| ~ spl24_159 ),
inference(forward_demodulation,[],[f1673,f980]) ).
tff(f1673,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_82
| ~ spl24_159 ),
inference(forward_demodulation,[],[f1671,f980]) ).
tff(f1671,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_159 ),
inference(avatar_component_clause,[],[f1670]) ).
tff(f1672,plain,
spl24_159,
inference(avatar_split_clause,[],[f383,f1670]) ).
tff(f383,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X4: nat,X27: list(dB),X9: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X9,X27)),X4) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X9),X4),map(dB,dB,combc(dB,nat,dB,lift,X4),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_lift__map) ).
tff(f1659,plain,
( spl24_158
| ~ spl24_82
| ~ spl24_157 ),
inference(avatar_split_clause,[],[f1655,f1651,f979,f1657]) ).
tff(f1651,plain,
( spl24_157
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_157])]) ).
tff(f1655,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl24_82
| ~ spl24_157 ),
inference(forward_demodulation,[],[f1654,f980]) ).
tff(f1654,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl24_82
| ~ spl24_157 ),
inference(forward_demodulation,[],[f1652,f980]) ).
tff(f1652,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl24_157 ),
inference(avatar_component_clause,[],[f1651]) ).
tff(f1653,plain,
spl24_157,
inference(avatar_split_clause,[],[f437,f1651]) ).
tff(f437,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f231]) ).
tff(f231,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X5: type,X8: type,X27: list(dB),X4: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X4),X27)),X8))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X4),X27)),X5))
=> ( X5 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_var__app__type__eq) ).
tff(f1649,plain,
( spl24_156
| ~ spl24_82
| ~ spl24_155 ),
inference(avatar_split_clause,[],[f1644,f1640,f979,f1646]) ).
tff(f1646,plain,
( spl24_156
<=> listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t1))),fEx(type)),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_156])]) ).
tff(f1640,plain,
( spl24_155
<=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_155])]) ).
tff(f1644,plain,
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t1))),fEx(type)),as)
| ~ spl24_82
| ~ spl24_155 ),
inference(forward_demodulation,[],[f1642,f980]) ).
tff(f1642,plain,
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as)
| ~ spl24_155 ),
inference(avatar_component_clause,[],[f1640]) ).
tff(f1643,plain,
spl24_155,
inference(avatar_split_clause,[],[f331,f1640]) ).
tff(f331,plain,
listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as),
inference(cnf_transformation,[],[f58]) ).
tff(f58,axiom,
listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096) ).
tff(f1634,plain,
( spl24_154
| ~ spl24_82
| ~ spl24_153 ),
inference(avatar_split_clause,[],[f1630,f1625,f979,f1632]) ).
tff(f1625,plain,
( spl24_153
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_153])]) ).
tff(f1630,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) )
| ~ spl24_82
| ~ spl24_153 ),
inference(forward_demodulation,[],[f1629,f980]) ).
tff(f1629,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_82
| ~ spl24_153 ),
inference(forward_demodulation,[],[f1628,f980]) ).
tff(f1628,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_82
| ~ spl24_153 ),
inference(forward_demodulation,[],[f1626,f980]) ).
tff(f1626,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_153 ),
inference(avatar_component_clause,[],[f1625]) ).
tff(f1627,plain,
spl24_153,
inference(avatar_split_clause,[],[f435,f1625]) ).
tff(f435,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X5: type,X4: nat,X8: type,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X8))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X4,X5)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X9),X4)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_lift__type) ).
tff(f1617,plain,
( spl24_152
| ~ spl24_82
| ~ spl24_151 ),
inference(avatar_split_clause,[],[f1613,f1608,f979,f1615]) ).
tff(f1608,plain,
( spl24_151
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_151])]) ).
tff(f1613,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_82
| ~ spl24_151 ),
inference(forward_demodulation,[],[f1612,f980]) ).
tff(f1612,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_82
| ~ spl24_151 ),
inference(forward_demodulation,[],[f1611,f980]) ).
tff(f1611,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_82
| ~ spl24_151 ),
inference(forward_demodulation,[],[f1609,f980]) ).
tff(f1609,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_151 ),
inference(avatar_component_clause,[],[f1608]) ).
tff(f1610,plain,
spl24_151,
inference(avatar_split_clause,[],[f413,f1608]) ).
tff(f413,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f1597,plain,
( spl24_150
| ~ spl24_82
| ~ spl24_149 ),
inference(avatar_split_clause,[],[f1593,f1589,f979,f1595]) ).
tff(f1589,plain,
( spl24_149
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_149])]) ).
tff(f1593,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2)) )
| ~ spl24_82
| ~ spl24_149 ),
inference(forward_demodulation,[],[f1592,f980]) ).
tff(f1592,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_82
| ~ spl24_149 ),
inference(forward_demodulation,[],[f1590,f980]) ).
tff(f1590,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_149 ),
inference(avatar_component_clause,[],[f1589]) ).
tff(f1591,plain,
spl24_149,
inference(avatar_split_clause,[],[f407,f1589]) ).
tff(f407,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f221,f274]) ).
tff(f274,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f221,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X8: type,X27: list(dB),X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X9,X27)),X8))
=> ? [X23: list(type)] :
( pp(aa(list(type),bool,typings(X10,X27),X23))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),foldr(type,type,fun1,X23,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_list__app__typeD) ).
tff(f1578,plain,
( spl24_148
| ~ spl24_82
| ~ spl24_146 ),
inference(avatar_split_clause,[],[f1570,f1566,f979,f1576]) ).
tff(f1566,plain,
( spl24_146
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_146])]) ).
tff(f1570,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) )
| ~ spl24_82
| ~ spl24_146 ),
inference(forward_demodulation,[],[f1569,f980]) ).
tff(f1569,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_82
| ~ spl24_146 ),
inference(forward_demodulation,[],[f1567,f980]) ).
tff(f1567,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_146 ),
inference(avatar_component_clause,[],[f1566]) ).
tff(f1574,plain,
( spl24_147
| ~ spl24_17
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f648,f643,f604,f1572]) ).
tff(f1572,plain,
( spl24_147
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_147])]) ).
tff(f648,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl24_17
| ~ spl24_24 ),
inference(resolution,[],[f644,f605]) ).
tff(f1568,plain,
spl24_146,
inference(avatar_split_clause,[],[f405,f1566]) ).
tff(f405,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f220,f272]) ).
tff(f272,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X8: type,X27: list(dB),X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X9,X27)),X8))
=> ~ ! [X23: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),foldr(type,type,fun1,X23,X8)))
=> ~ pp(aa(list(type),bool,typings(X10,X27),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_list__app__typeE) ).
tff(f1559,plain,
spl24_145,
inference(avatar_split_clause,[],[f330,f1556]) ).
tff(f330,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))),
inference(cnf_transformation,[],[f41]) ).
tff(f41,axiom,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__096IT_A_IVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1530,plain,
spl24_144,
inference(avatar_split_clause,[],[f446,f1528]) ).
tff(f446,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X85: X0,X86: fun(X0,X1),X84: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X84),X86),X85) = aa(X1,X2,X84,aa(X0,X1,X86,X85)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1526,plain,
spl24_143,
inference(avatar_split_clause,[],[f440,f1524]) ).
tff(f440,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(flattening,[],[f293]) ).
tff(f293,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(nnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X55: list(X0),X56: X0,X57: list(X0),X58: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X58),X57) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X56),X55) )
<=> ( ( X55 = X57 )
& ( X56 = X58 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_list_Oinject) ).
tff(f1513,plain,
( spl24_142
| ~ spl24_82
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1509,f1505,f979,f1511]) ).
tff(f1505,plain,
( spl24_141
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_141])]) ).
tff(f1509,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1)) )
| ~ spl24_82
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1508,f980]) ).
tff(f1508,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_82
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1506,f980]) ).
tff(f1506,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_141 ),
inference(avatar_component_clause,[],[f1505]) ).
tff(f1507,plain,
spl24_141,
inference(avatar_split_clause,[],[f394,f1505]) ).
tff(f394,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f216,f268]) ).
tff(f268,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f216,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X8: type,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),abs(X9)),X8))
=> ~ ! [X30: type,X75: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X30),X75) = X8 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,zero_zero(nat),X30)),X9),X75)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_typing__elims_I3_J) ).
tff(f1503,plain,
( spl24_140
| ~ spl24_16
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f646,f635,f600,f1501]) ).
tff(f1501,plain,
( spl24_140
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_140])]) ).
tff(f646,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) )
| ~ spl24_16
| ~ spl24_22 ),
inference(resolution,[],[f636,f601]) ).
tff(f1484,plain,
spl24_139,
inference(avatar_split_clause,[],[f455,f1482]) ).
tff(f455,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f1480,plain,
spl24_138,
inference(avatar_split_clause,[],[f451,f1478]) ).
tff(f451,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1476,plain,
spl24_137,
inference(avatar_split_clause,[],[f439,f1474]) ).
tff(f439,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f1363,plain,
spl24_136,
inference(avatar_split_clause,[],[f503,f1361]) ).
tff(f503,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f445,f442]) ).
tff(f445,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X1: $tType,X50: list(X1),X18: X1,X58: X0,X51: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X51,X58,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X18),X50)) = foldl(X0,X1,X51,aa(X1,X0,aa(X0,fun(X1,X0),X51,X58),X18),X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_foldl__Cons) ).
tff(f1359,plain,
spl24_135,
inference(avatar_split_clause,[],[f502,f1357]) ).
tff(f502,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ),
inference(forward_demodulation,[],[f444,f442]) ).
tff(f444,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X0: $tType,X58: X0,X50: list(X1),X18: X1,X51: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X51,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X18),X50),X58) = aa(X0,X0,aa(X1,fun(X0,X0),X51,X18),foldr(X1,X0,X51,X50,X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_foldr_Osimps_I2_J) ).
tff(f1355,plain,
spl24_134,
inference(avatar_split_clause,[],[f454,f1353]) ).
tff(f454,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f1351,plain,
spl24_133,
inference(avatar_split_clause,[],[f450,f1349]) ).
tff(f450,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1346,plain,
( spl24_132
| ~ spl24_82
| ~ spl24_131 ),
inference(avatar_split_clause,[],[f1342,f1338,f979,f1344]) ).
tff(f1338,plain,
( spl24_131
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_131])]) ).
tff(f1342,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1)) )
| ~ spl24_82
| ~ spl24_131 ),
inference(forward_demodulation,[],[f1341,f980]) ).
tff(f1341,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_82
| ~ spl24_131 ),
inference(forward_demodulation,[],[f1339,f980]) ).
tff(f1339,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_131 ),
inference(avatar_component_clause,[],[f1338]) ).
tff(f1340,plain,
spl24_131,
inference(avatar_split_clause,[],[f392,f1338]) ).
tff(f392,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f215,f266]) ).
tff(f266,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X8: type,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),abs(X9)),X8))
=> ~ ! [X75: type,X76: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,zero_zero(nat),X75)),X9),X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_abs__typeE) ).
tff(f1332,plain,
( spl24_130
| ~ spl24_82
| ~ spl24_129 ),
inference(avatar_split_clause,[],[f1328,f1325,f979,f1330]) ).
tff(f1325,plain,
( spl24_129
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_129])]) ).
tff(f1328,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_82
| ~ spl24_129 ),
inference(forward_demodulation,[],[f1326,f980]) ).
tff(f1326,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_129 ),
inference(avatar_component_clause,[],[f1325]) ).
tff(f1327,plain,
spl24_129,
inference(avatar_split_clause,[],[f354,f1325]) ).
tff(f354,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f1319,plain,
( spl24_128
| ~ spl24_82
| ~ spl24_127 ),
inference(avatar_split_clause,[],[f1314,f1309,f979,f1316]) ).
tff(f1309,plain,
( spl24_127
<=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_127])]) ).
tff(f1314,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_82
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1313,f980]) ).
tff(f1313,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),u)))
| ~ spl24_82
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1311,f980]) ).
tff(f1311,plain,
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))))
| ~ spl24_127 ),
inference(avatar_component_clause,[],[f1309]) ).
tff(f1312,plain,
spl24_127,
inference(avatar_split_clause,[],[f329,f1309]) ).
tff(f329,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f1295,plain,
spl24_126,
inference(avatar_split_clause,[],[f501,f1293]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f443,f442]) ).
tff(f443,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X1: $tType,X57: list(X1),X58: X1,X61: fun(X1,fun(list(X1),X0)),X62: X0] : ( list_case(X0,X1,X62,X61,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X58),X57)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X61,X58),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_list_Osimps_I5_J) ).
tff(f1289,plain,
( spl24_125
| ~ spl24_82
| ~ spl24_124 ),
inference(avatar_split_clause,[],[f1284,f1279,f979,f1286]) ).
tff(f1279,plain,
( spl24_124
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_124])]) ).
tff(f1284,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_82
| ~ spl24_124 ),
inference(forward_demodulation,[],[f1283,f980]) ).
tff(f1283,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t2)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_82
| ~ spl24_124 ),
inference(forward_demodulation,[],[f1281,f980]) ).
tff(f1281,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t2)))
| ~ spl24_124 ),
inference(avatar_component_clause,[],[f1279]) ).
tff(f1282,plain,
spl24_124,
inference(avatar_split_clause,[],[f469,f1279]) ).
tff(f469,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t2))),
inference(definition_unfolding,[],[f337,f310]) ).
tff(f310,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_True) ).
tff(f337,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t2))),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f205,f250]) ).
tff(f250,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2))) )
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t2))) ) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t2)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
~ ! [X23: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X23,t2)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1271,plain,
( spl24_123
| ~ spl24_82
| ~ spl24_122 ),
inference(avatar_split_clause,[],[f1265,f1260,f979,f1268]) ).
tff(f1260,plain,
( spl24_122
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_122])]) ).
tff(f1265,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t2)),sK2)),var(i)))
| ~ spl24_82
| ~ spl24_122 ),
inference(forward_demodulation,[],[f1264,f980]) ).
tff(f1264,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2))),var(i)))
| ~ spl24_82
| ~ spl24_122 ),
inference(forward_demodulation,[],[f1262,f980]) ).
tff(f1262,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2))))
| ~ spl24_122 ),
inference(avatar_component_clause,[],[f1260]) ).
tff(f1263,plain,
spl24_122,
inference(avatar_split_clause,[],[f468,f1260]) ).
tff(f468,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2)))),
inference(definition_unfolding,[],[f335,f310]) ).
tff(f335,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2)))),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f204,f248]) ).
tff(f248,plain,
( ? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2)))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t2)))) ) ),
introduced(choice_axiom,[]) ).
tff(f204,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2)))) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t2))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0)) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
~ ! [X13: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X13),foldr(type,type,fun1,ts,t2))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1254,plain,
( spl24_121
| ~ spl24_82
| ~ spl24_120 ),
inference(avatar_split_clause,[],[f1249,f1244,f979,f1251]) ).
tff(f1244,plain,
( spl24_120
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_120])]) ).
tff(f1249,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl24_82
| ~ spl24_120 ),
inference(forward_demodulation,[],[f1248,f980]) ).
tff(f1248,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)))
| ~ spl24_82
| ~ spl24_120 ),
inference(forward_demodulation,[],[f1246,f980]) ).
tff(f1246,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t2))
| ~ spl24_120 ),
inference(avatar_component_clause,[],[f1244]) ).
tff(f1247,plain,
spl24_120,
inference(avatar_split_clause,[],[f467,f1244]) ).
tff(f467,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t2)),
inference(definition_unfolding,[],[f328,f310]) ).
tff(f328,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t2)),
inference(cnf_transformation,[],[f39]) ).
tff(f39,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f1240,plain,
( spl24_119
| ~ spl24_82
| ~ spl24_118 ),
inference(avatar_split_clause,[],[f1235,f1230,f979,f1237]) ).
tff(f1230,plain,
( spl24_118
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_118])]) ).
tff(f1235,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_82
| ~ spl24_118 ),
inference(forward_demodulation,[],[f1234,f980]) ).
tff(f1234,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t2)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_82
| ~ spl24_118 ),
inference(forward_demodulation,[],[f1232,f980]) ).
tff(f1232,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2)))
| ~ spl24_118 ),
inference(avatar_component_clause,[],[f1230]) ).
tff(f1233,plain,
spl24_118,
inference(avatar_split_clause,[],[f466,f1230]) ).
tff(f466,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t2))),
inference(definition_unfolding,[],[f327,f310]) ).
tff(f327,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t2))),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_headT) ).
tff(f1227,plain,
( spl24_117
| ~ spl24_82
| ~ spl24_116 ),
inference(avatar_split_clause,[],[f1223,f1219,f979,f1225]) ).
tff(f1219,plain,
( spl24_116
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_116])]) ).
tff(f1223,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) )
| ~ spl24_82
| ~ spl24_116 ),
inference(forward_demodulation,[],[f1222,f980]) ).
tff(f1222,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_82
| ~ spl24_116 ),
inference(forward_demodulation,[],[f1220,f980]) ).
tff(f1220,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_116 ),
inference(avatar_component_clause,[],[f1219]) ).
tff(f1221,plain,
spl24_116,
inference(avatar_split_clause,[],[f393,f1219]) ).
tff(f393,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f269]) ).
tff(f1217,plain,
( ~ spl24_115
| ~ spl24_67
| ~ spl24_68 ),
inference(avatar_split_clause,[],[f921,f905,f900,f1214]) ).
tff(f1214,plain,
( spl24_115
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_115])]) ).
tff(f921,plain,
( ( as != rs )
| ~ spl24_67
| ~ spl24_68 ),
inference(superposition,[],[f906,f902]) ).
tff(f1209,plain,
( spl24_114
| ~ spl24_82
| ~ spl24_113 ),
inference(avatar_split_clause,[],[f1205,f1202,f979,f1207]) ).
tff(f1202,plain,
( spl24_113
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_113])]) ).
tff(f1205,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl24_82
| ~ spl24_113 ),
inference(forward_demodulation,[],[f1203,f980]) ).
tff(f1203,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_113 ),
inference(avatar_component_clause,[],[f1202]) ).
tff(f1204,plain,
spl24_113,
inference(avatar_split_clause,[],[f411,f1202]) ).
tff(f411,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f277]) ).
tff(f1198,plain,
spl24_112,
inference(avatar_split_clause,[],[f434,f1196]) ).
tff(f434,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X4,X3),X2))
=> pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X5: type,X4: nat,X26: list(type),X27: list(dB),X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,X27),X26))
=> pp(aa(list(type),bool,typings(shift(type,X10,X4,X5),map(dB,dB,combc(dB,nat,dB,lift,X4),X27)),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_lift__types) ).
tff(f1191,plain,
( spl24_111
| ~ spl24_82
| ~ spl24_110 ),
inference(avatar_split_clause,[],[f1187,f1184,f979,f1189]) ).
tff(f1184,plain,
( spl24_110
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_110])]) ).
tff(f1187,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl24_82
| ~ spl24_110 ),
inference(forward_demodulation,[],[f1185,f980]) ).
tff(f1185,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_110 ),
inference(avatar_component_clause,[],[f1184]) ).
tff(f1186,plain,
spl24_110,
inference(avatar_split_clause,[],[f408,f1184]) ).
tff(f408,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1179,plain,
( spl24_109
| ~ spl24_82
| ~ spl24_107 ),
inference(avatar_split_clause,[],[f1171,f1168,f979,f1177]) ).
tff(f1168,plain,
( spl24_107
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_107])]) ).
tff(f1171,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl24_82
| ~ spl24_107 ),
inference(forward_demodulation,[],[f1169,f980]) ).
tff(f1169,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_107 ),
inference(avatar_component_clause,[],[f1168]) ).
tff(f1175,plain,
( spl24_108
| ~ spl24_11
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f649,f643,f574,f1173]) ).
tff(f649,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl24_11
| ~ spl24_24 ),
inference(resolution,[],[f644,f575]) ).
tff(f1170,plain,
spl24_107,
inference(avatar_split_clause,[],[f406,f1168]) ).
tff(f406,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f1162,plain,
( spl24_106
| ~ spl24_82
| ~ spl24_105 ),
inference(avatar_split_clause,[],[f1158,f1155,f979,f1160]) ).
tff(f1155,plain,
( spl24_105
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_105])]) ).
tff(f1158,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_82
| ~ spl24_105 ),
inference(forward_demodulation,[],[f1156,f980]) ).
tff(f1156,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_105 ),
inference(avatar_component_clause,[],[f1155]) ).
tff(f1157,plain,
spl24_105,
inference(avatar_split_clause,[],[f389,f1155]) ).
tff(f389,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X28: nat,X20: nat,X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X29),var(X20)),X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_subst__Var__IT) ).
tff(f1151,plain,
( spl24_104
| ~ spl24_82
| ~ spl24_103 ),
inference(avatar_split_clause,[],[f1147,f1143,f979,f1149]) ).
tff(f1143,plain,
( spl24_103
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_103])]) ).
tff(f1147,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl24_82
| ~ spl24_103 ),
inference(forward_demodulation,[],[f1146,f980]) ).
tff(f1146,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl24_82
| ~ spl24_103 ),
inference(forward_demodulation,[],[f1144,f980]) ).
tff(f1144,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl24_103 ),
inference(avatar_component_clause,[],[f1143]) ).
tff(f1145,plain,
spl24_103,
inference(avatar_split_clause,[],[f381,f1143]) ).
tff(f381,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X32: dB,X31: nat,X21: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X21),X31)),X32),X31) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_subst__lift) ).
tff(f1141,plain,
spl24_102,
inference(avatar_split_clause,[],[f325,f1138]) ).
tff(f1138,plain,
( spl24_102
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_102])]) ).
tff(f325,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),
inference(cnf_transformation,[],[f37]) ).
tff(f37,axiom,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__096listsp_AIT_A_Imap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1135,plain,
spl24_101,
inference(avatar_split_clause,[],[f324,f1132]) ).
tff(f1132,plain,
( spl24_101
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_101])]) ).
tff(f324,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t2))),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t2))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__096e_0600_058Ts_A_061_062_062_AT_H_062_A_092_060turnstile_062_AVar_A0_A_058_ATs_A_061_062_062_AT_H_096) ).
tff(f1113,plain,
spl24_100,
inference(avatar_split_clause,[],[f425,f1111]) ).
tff(f425,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f288]) ).
tff(f288,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X34: dB,X35: dB,X36: dB,X37: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X37),X36) = aa(dB,dB,aa(dB,fun(dB,dB),app,X35),X34) )
<=> ( ( X34 = X36 )
& ( X35 = X37 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_dB_Osimps_I2_J) ).
tff(f1109,plain,
spl24_99,
inference(avatar_split_clause,[],[f424,f1107]) ).
tff(f424,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1105,plain,
spl24_98,
inference(avatar_split_clause,[],[f422,f1103]) ).
tff(f422,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(flattening,[],[f286]) ).
tff(f286,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X14: type,X15: type,X16: type,X17: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X17),X16) = aa(type,type,aa(type,fun(type,type),fun1,X15),X14) )
<=> ( ( X14 = X16 )
& ( X15 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type_Osimps_I2_J) ).
tff(f1101,plain,
spl24_97,
inference(avatar_split_clause,[],[f421,f1099]) ).
tff(f421,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1095,plain,
spl24_96,
inference(avatar_split_clause,[],[f322,f1092]) ).
tff(f322,plain,
pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096e_A_124_124_N_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_A_058_ATs_096) ).
tff(f1079,plain,
spl24_95,
inference(avatar_split_clause,[],[f414,f1077]) ).
tff(f414,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f225,f280]) ).
tff(f280,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f225,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X0: $tType,X63: fun(X0,X1),X51: fun(X0,X1)] :
( ! [X64: X0] : ( aa(X0,X1,X51,X64) = aa(X0,X1,X63,X64) )
=> ( X51 = X63 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f1075,plain,
( spl24_94
| ~ spl24_82
| ~ spl24_93 ),
inference(avatar_split_clause,[],[f1071,f1068,f979,f1073]) ).
tff(f1073,plain,
( spl24_94
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_94])]) ).
tff(f1068,plain,
( spl24_93
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_93])]) ).
tff(f1071,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl24_82
| ~ spl24_93 ),
inference(forward_demodulation,[],[f1069,f980]) ).
tff(f1069,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl24_93 ),
inference(avatar_component_clause,[],[f1068]) ).
tff(f1070,plain,
spl24_93,
inference(avatar_split_clause,[],[f353,f1068]) ).
tff(f353,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f1064,plain,
( spl24_92
| ~ spl24_82
| ~ spl24_91 ),
inference(avatar_split_clause,[],[f1059,f1055,f979,f1061]) ).
tff(f1055,plain,
( spl24_91
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_91])]) ).
tff(f1059,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_82
| ~ spl24_91 ),
inference(forward_demodulation,[],[f1057,f980]) ).
tff(f1057,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t2))
| ~ spl24_91 ),
inference(avatar_component_clause,[],[f1055]) ).
tff(f1058,plain,
spl24_91,
inference(avatar_split_clause,[],[f464,f1055]) ).
tff(f464,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t2)),
inference(definition_unfolding,[],[f321,f310]) ).
tff(f321,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t2)),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nT) ).
tff(f1051,plain,
( spl24_90
| ~ spl24_82
| ~ spl24_89 ),
inference(avatar_split_clause,[],[f1045,f1041,f979,f1048]) ).
tff(f1041,plain,
( spl24_89
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_89])]) ).
tff(f1045,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_82
| ~ spl24_89 ),
inference(forward_demodulation,[],[f1043,f980]) ).
tff(f1043,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a))
| ~ spl24_89 ),
inference(avatar_component_clause,[],[f1041]) ).
tff(f1044,plain,
spl24_89,
inference(avatar_split_clause,[],[f463,f1041]) ).
tff(f463,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f320,f310]) ).
tff(f320,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f47]) ).
tff(f47,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Var_I2_J) ).
tff(f1036,plain,
( spl24_88
| ~ spl24_82
| ~ spl24_87 ),
inference(avatar_split_clause,[],[f1032,f1029,f979,f1034]) ).
tff(f1029,plain,
( spl24_87
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_87])]) ).
tff(f1032,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_82
| ~ spl24_87 ),
inference(forward_demodulation,[],[f1030,f980]) ).
tff(f1030,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_87 ),
inference(avatar_component_clause,[],[f1029]) ).
tff(f1031,plain,
spl24_87,
inference(avatar_split_clause,[],[f400,f1029]) ).
tff(f400,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X53: fun(X0,bool),X18: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X18),X53))
<=> pp(aa(X0,bool,X53,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f1026,plain,
( spl24_86
| ~ spl24_82
| ~ spl24_85 ),
inference(avatar_split_clause,[],[f1022,f1019,f979,f1024]) ).
tff(f1024,plain,
( spl24_86
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_86])]) ).
tff(f1019,plain,
( spl24_85
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_85])]) ).
tff(f1022,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl24_82
| ~ spl24_85 ),
inference(forward_demodulation,[],[f1020,f980]) ).
tff(f1020,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl24_85 ),
inference(avatar_component_clause,[],[f1019]) ).
tff(f1021,plain,
spl24_85,
inference(avatar_split_clause,[],[f399,f1019]) ).
tff(f399,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f1013,plain,
( spl24_84
| ~ spl24_82
| ~ spl24_83 ),
inference(avatar_split_clause,[],[f1009,f1006,f979,f1011]) ).
tff(f1006,plain,
( spl24_83
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_83])]) ).
tff(f1009,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_82
| ~ spl24_83 ),
inference(forward_demodulation,[],[f1007,f980]) ).
tff(f1007,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_83 ),
inference(avatar_component_clause,[],[f1006]) ).
tff(f1008,plain,
spl24_83,
inference(avatar_split_clause,[],[f370,f1006]) ).
tff(f370,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X20: nat,X21: dB] :
( pp(aa(dB,bool,it,X21))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X21),var(X20)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_app__Var__IT) ).
tff(f981,plain,
spl24_82,
inference(avatar_split_clause,[],[f442,f979]) ).
tff(f973,plain,
( spl24_81
| ~ spl24_80 ),
inference(avatar_split_clause,[],[f969,f966,f971]) ).
tff(f966,plain,
( spl24_80
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_80])]) ).
tff(f969,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_80 ),
inference(forward_demodulation,[],[f967,f442]) ).
tff(f967,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_80 ),
inference(avatar_component_clause,[],[f966]) ).
tff(f968,plain,
spl24_80,
inference(avatar_split_clause,[],[f369,f966]) ).
tff(f369,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X20: nat,X21: dB] :
( pp(aa(dB,bool,it,X21))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X21),X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_lift__IT) ).
tff(f964,plain,
( spl24_79
| ~ spl24_78 ),
inference(avatar_split_clause,[],[f960,f957,f962]) ).
tff(f957,plain,
( spl24_78
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_78])]) ).
tff(f960,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl24_78 ),
inference(forward_demodulation,[],[f958,f442]) ).
tff(f958,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl24_78 ),
inference(avatar_component_clause,[],[f957]) ).
tff(f959,plain,
spl24_78,
inference(avatar_split_clause,[],[f364,f957]) ).
tff(f364,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X33: dB,X31: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X31)),X33),X31) = X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subst__eq) ).
tff(f955,plain,
spl24_77,
inference(avatar_split_clause,[],[f348,f953]) ).
tff(f348,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) )
| ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f255,f257,f256]) ).
tff(f256,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f257,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f255,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f254]) ).
tff(f254,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f951,plain,
( spl24_76
| ~ spl24_7
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f652,f643,f550,f948]) ).
tff(f652,plain,
( sP1(abs(ua))
| ~ spl24_7
| ~ spl24_24 ),
inference(resolution,[],[f644,f552]) ).
tff(f944,plain,
( spl24_75
| ~ spl24_74 ),
inference(avatar_split_clause,[],[f940,f937,f942]) ).
tff(f937,plain,
( spl24_74
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_74])]) ).
tff(f940,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl24_74 ),
inference(forward_demodulation,[],[f938,f442]) ).
tff(f938,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) )
| ~ spl24_74 ),
inference(avatar_component_clause,[],[f937]) ).
tff(f939,plain,
spl24_74,
inference(avatar_split_clause,[],[f395,f937]) ).
tff(f395,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X8: type,X4: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),var(X4)),X8))
=> ( aa(nat,type,X10,X4) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_typing__elims_I1_J) ).
tff(f931,plain,
spl24_73,
inference(avatar_split_clause,[],[f402,f929]) ).
tff(f402,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X46: list(dB),X43: nat,X9: dB,X22: dB] : ( foldl(dB,dB,app,var(X43),X46) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X22)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Abs__App__neq__Var__apps) ).
tff(f927,plain,
spl24_72,
inference(avatar_split_clause,[],[f346,f925]) ).
tff(f346,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f920,plain,
( spl24_71
| ~ spl24_8
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f651,f643,f555,f917]) ).
tff(f651,plain,
( sP1(abs(u))
| ~ spl24_8
| ~ spl24_24 ),
inference(resolution,[],[f644,f557]) ).
tff(f915,plain,
spl24_70,
inference(avatar_split_clause,[],[f419,f913]) ).
tff(f419,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(flattening,[],[f284]) ).
tff(f284,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X46: list(dB),X43: nat,X44: list(dB),X47: nat] :
( ( foldl(dB,dB,app,var(X47),X44) = foldl(dB,dB,app,var(X43),X46) )
<=> ( ( X44 = X46 )
& ( X43 = X47 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Var__apps__eq__Var__apps__conv) ).
tff(f911,plain,
spl24_69,
inference(avatar_split_clause,[],[f416,f909]) ).
tff(f416,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(flattening,[],[f282]) ).
tff(f282,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X46: list(dB),X22: dB,X44: list(dB),X45: dB] :
( ( foldl(dB,dB,app,abs(X45),X44) = foldl(dB,dB,app,abs(X22),X46) )
<=> ( ( X44 = X46 )
& ( X22 = X45 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Abs__apps__eq__Abs__apps__conv) ).
tff(f907,plain,
spl24_68,
inference(avatar_split_clause,[],[f379,f905]) ).
tff(f379,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType,X60: list(X0),X59: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X59),X60) != X60 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_not__Cons__self2) ).
tff(f903,plain,
spl24_67,
inference(avatar_split_clause,[],[f319,f900]) ).
tff(f319,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f11]) ).
tff(f11,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Cons) ).
tff(f895,plain,
spl24_66,
inference(avatar_split_clause,[],[f500,f892]) ).
tff(f892,plain,
( spl24_66
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_66])]) ).
tff(f500,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),t1)),
inference(forward_demodulation,[],[f465,f318]) ).
tff(f318,plain,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_T) ).
tff(f465,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)))),
inference(definition_unfolding,[],[f326,f310]) ).
tff(f326,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)))),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t),foldr(type,type,fun1,ts,t2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_varT) ).
tff(f890,plain,
( spl24_65
| ~ spl24_6
| ~ spl24_24 ),
inference(avatar_split_clause,[],[f650,f643,f545,f887]) ).
tff(f650,plain,
( sP1(abs(t3))
| ~ spl24_6
| ~ spl24_24 ),
inference(resolution,[],[f644,f547]) ).
tff(f882,plain,
( spl24_64
| ~ spl24_63 ),
inference(avatar_split_clause,[],[f878,f875,f880]) ).
tff(f875,plain,
( spl24_63
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_63])]) ).
tff(f878,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl24_63 ),
inference(forward_demodulation,[],[f876,f442]) ).
tff(f876,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl24_63 ),
inference(avatar_component_clause,[],[f875]) ).
tff(f877,plain,
spl24_63,
inference(avatar_split_clause,[],[f479,f875]) ).
tff(f479,plain,
! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f390]) ).
tff(f390,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X8: type,X18: nat,X19: fun(nat,type)] :
( ( aa(nat,type,X19,X18) = X8 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X19),var(X18)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_typing_OVar) ).
tff(f873,plain,
spl24_62,
inference(avatar_split_clause,[],[f418,f871]) ).
tff(f418,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f869,plain,
spl24_61,
inference(avatar_split_clause,[],[f415,f867]) ).
tff(f415,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f865,plain,
spl24_60,
inference(avatar_split_clause,[],[f344,f863]) ).
tff(f863,plain,
( spl24_60
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_60])]) ).
tff(f344,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X27: list(dB)] :
( listsp(dB,it,X27)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_lifts__IT) ).
tff(f861,plain,
spl24_59,
inference(avatar_split_clause,[],[f318,f858]) ).
tff(f854,plain,
( spl24_58
| ~ spl24_57 ),
inference(avatar_split_clause,[],[f849,f845,f851]) ).
tff(f845,plain,
( spl24_57
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_57])]) ).
tff(f849,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),a))
| ~ spl24_57 ),
inference(forward_demodulation,[],[f847,f442]) ).
tff(f847,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
| ~ spl24_57 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f848,plain,
spl24_57,
inference(avatar_split_clause,[],[f336,f845]) ).
tff(f336,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2)),
inference(cnf_transformation,[],[f249]) ).
tff(f843,plain,
( spl24_56
| ~ spl24_11
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f619,f600,f574,f841]) ).
tff(f841,plain,
( spl24_56
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_56])]) ).
tff(f619,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl24_11
| ~ spl24_16 ),
inference(resolution,[],[f601,f575]) ).
tff(f837,plain,
( spl24_55
| ~ spl24_54 ),
inference(avatar_split_clause,[],[f832,f828,f834]) ).
tff(f828,plain,
( spl24_54
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_54])]) ).
tff(f832,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),a))
| ~ spl24_54 ),
inference(forward_demodulation,[],[f830,f442]) ).
tff(f830,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t))
| ~ spl24_54 ),
inference(avatar_component_clause,[],[f828]) ).
tff(f831,plain,
spl24_54,
inference(avatar_split_clause,[],[f317,f828]) ).
tff(f317,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_argT) ).
tff(f817,plain,
spl24_53,
inference(avatar_split_clause,[],[f397,f815]) ).
tff(f397,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
inference(nnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X22: dB,X27: list(dB),X45: dB] :
( ( foldl(dB,dB,app,X45,X27) = foldl(dB,dB,app,X22,X27) )
<=> ( X22 = X45 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_apps__eq__tail__conv) ).
tff(f811,plain,
( spl24_52
| ~ spl24_51 ),
inference(avatar_split_clause,[],[f807,f804,f809]) ).
tff(f809,plain,
( spl24_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_52])]) ).
tff(f804,plain,
( spl24_51
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_51])]) ).
tff(f807,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl24_51 ),
inference(forward_demodulation,[],[f805,f442]) ).
tff(f805,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) )
| ~ spl24_51 ),
inference(avatar_component_clause,[],[f804]) ).
tff(f806,plain,
spl24_51,
inference(avatar_split_clause,[],[f388,f804]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X0: $tType,X87: X0,X59: X0] :
( ( X59 = X87 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X59),X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f802,plain,
spl24_50,
inference(avatar_split_clause,[],[f368,f800]) ).
tff(f368,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X43: nat,X44: list(dB)] :
( listsp(dB,it,X44)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X43),X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_IT_OVar) ).
tff(f794,plain,
( spl24_49
| ~ spl24_48 ),
inference(avatar_split_clause,[],[f790,f787,f792]) ).
tff(f787,plain,
( spl24_48
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_48])]) ).
tff(f790,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_48 ),
inference(forward_demodulation,[],[f788,f442]) ).
tff(f788,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_48 ),
inference(avatar_component_clause,[],[f787]) ).
tff(f789,plain,
spl24_48,
inference(avatar_split_clause,[],[f365,f787]) ).
tff(f365,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X86: bool,X84: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86))
| ~ pp(X86)
| ~ pp(X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f785,plain,
spl24_47,
inference(avatar_split_clause,[],[f349,f783]) ).
tff(f349,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f766,plain,
spl24_46,
inference(avatar_split_clause,[],[f401,f764]) ).
tff(f401,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X46: list(dB),X45: dB,X27: list(dB),X43: nat] : ( foldl(dB,dB,app,var(X43),X27) != foldl(dB,dB,app,abs(X45),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Var__apps__neq__Abs__apps) ).
tff(f762,plain,
spl24_45,
inference(avatar_split_clause,[],[f387,f760]) ).
tff(f387,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X59: X0,X84: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X84))
| ~ pp(aa(X0,bool,X84,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f758,plain,
spl24_44,
inference(avatar_split_clause,[],[f377,f756]) ).
tff(f377,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X40: nat,X41: dB,X42: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X41) != var(X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_dB_Osimps_I5_J) ).
tff(f754,plain,
spl24_43,
inference(avatar_split_clause,[],[f375,f752]) ).
tff(f375,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X72: dB,X73: dB,X74: dB] : ( abs(X72) != aa(dB,dB,aa(dB,fun(dB,dB),app,X74),X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osimps_I8_J) ).
tff(f749,plain,
( spl24_42
| ~ spl24_41 ),
inference(avatar_split_clause,[],[f745,f742,f747]) ).
tff(f747,plain,
( spl24_42
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_42])]) ).
tff(f742,plain,
( spl24_41
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_41])]) ).
tff(f745,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl24_41 ),
inference(forward_demodulation,[],[f743,f442]) ).
tff(f743,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_41 ),
inference(avatar_component_clause,[],[f742]) ).
tff(f744,plain,
spl24_41,
inference(avatar_split_clause,[],[f367,f742]) ).
tff(f367,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X86: bool,X84: bool] :
( pp(X84)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f739,plain,
( spl24_40
| ~ spl24_39 ),
inference(avatar_split_clause,[],[f735,f732,f737]) ).
tff(f737,plain,
( spl24_40
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_40])]) ).
tff(f732,plain,
( spl24_39
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_39])]) ).
tff(f735,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl24_39 ),
inference(forward_demodulation,[],[f733,f442]) ).
tff(f733,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_39 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f734,plain,
spl24_39,
inference(avatar_split_clause,[],[f366,f732]) ).
tff(f366,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X86: bool,X84: bool] :
( pp(X86)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f730,plain,
spl24_38,
inference(avatar_split_clause,[],[f347,f728]) ).
tff(f728,plain,
( spl24_38
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_38])]) ).
tff(f347,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f720,plain,
( spl24_37
| ~ spl24_36 ),
inference(avatar_split_clause,[],[f716,f713,f718]) ).
tff(f713,plain,
( spl24_36
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_36])]) ).
tff(f716,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl24_36 ),
inference(forward_demodulation,[],[f714,f442]) ).
tff(f714,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl24_36 ),
inference(avatar_component_clause,[],[f713]) ).
tff(f715,plain,
spl24_36,
inference(avatar_split_clause,[],[f478,f713]) ).
tff(f478,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f386]) ).
tff(f386,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X87: X0,X59: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X59),X87))
| ( X59 != X87 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f711,plain,
spl24_35,
inference(avatar_split_clause,[],[f345,f709]) ).
tff(f345,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,abs(X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Lambda) ).
tff(f707,plain,
spl24_34,
inference(avatar_split_clause,[],[f338,f704]) ).
tff(f338,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3)),
inference(cnf_transformation,[],[f251]) ).
tff(f702,plain,
spl24_33,
inference(avatar_split_clause,[],[f316,f699]) ).
tff(f316,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_argsT) ).
tff(f697,plain,
( spl24_32
| ~ spl24_7
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f622,f600,f550,f694]) ).
tff(f694,plain,
( spl24_32
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_32])]) ).
tff(f622,plain,
( sP1(ua)
| ~ spl24_7
| ~ spl24_16 ),
inference(resolution,[],[f601,f552]) ).
tff(f691,plain,
( spl24_31
| ~ spl24_30 ),
inference(avatar_split_clause,[],[f686,f682,f688]) ).
tff(f682,plain,
( spl24_30
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_30])]) ).
tff(f686,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ~ spl24_30 ),
inference(forward_demodulation,[],[f684,f442]) ).
tff(f684,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1))
| ~ spl24_30 ),
inference(avatar_component_clause,[],[f682]) ).
tff(f685,plain,
spl24_30,
inference(avatar_split_clause,[],[f315,f682]) ).
tff(f315,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uT) ).
tff(f679,plain,
( spl24_29
| ~ spl24_28 ),
inference(avatar_split_clause,[],[f674,f670,f676]) ).
tff(f670,plain,
( spl24_28
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_28])]) ).
tff(f674,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua))
| ~ spl24_28 ),
inference(forward_demodulation,[],[f672,f442]) ).
tff(f672,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1))
| ~ spl24_28 ),
inference(avatar_component_clause,[],[f670]) ).
tff(f673,plain,
spl24_28,
inference(avatar_split_clause,[],[f314,f670]) ).
tff(f314,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Var_I4_J) ).
tff(f668,plain,
spl24_27,
inference(avatar_split_clause,[],[f474,f666]) ).
tff(f474,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f350]) ).
tff(f350,plain,
! [X2: list(dB),X3: nat,X0: dB] :
( sP1(X0)
| ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ),
inference(cnf_transformation,[],[f258]) ).
tff(f663,plain,
spl24_26,
inference(avatar_split_clause,[],[f489,f661]) ).
tff(f489,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f433]) ).
tff(f433,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X8: X0,X10: fun(nat,X0),X25: nat,X4: nat] :
( ( X4 = X25 )
=> ( aa(nat,X0,shift(X0,X10,X4,X8),X25) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_shift__eq) ).
tff(f659,plain,
( spl24_25
| ~ spl24_8
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f621,f600,f555,f656]) ).
tff(f656,plain,
( spl24_25
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).
tff(f621,plain,
( sP1(u)
| ~ spl24_8
| ~ spl24_16 ),
inference(resolution,[],[f601,f557]) ).
tff(f645,plain,
spl24_24,
inference(avatar_split_clause,[],[f473,f643]) ).
tff(f473,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f351]) ).
tff(f351,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f258]) ).
tff(f641,plain,
spl24_23,
inference(avatar_split_clause,[],[f363,f639]) ).
tff(f363,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X54: list(X0)] : ( map(X0,X0,combi(X0),X54) = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_map__ident) ).
tff(f637,plain,
spl24_22,
inference(avatar_split_clause,[],[f355,f635]) ).
tff(f355,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f628,plain,
( spl24_21
| ~ spl24_6
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f620,f600,f545,f625]) ).
tff(f625,plain,
( spl24_21
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_21])]) ).
tff(f620,plain,
( sP1(t3)
| ~ spl24_6
| ~ spl24_16 ),
inference(resolution,[],[f601,f547]) ).
tff(f618,plain,
spl24_20,
inference(avatar_split_clause,[],[f373,f616]) ).
tff(f616,plain,
( spl24_20
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_20])]) ).
tff(f373,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X38: nat,X39: nat] :
( ( var(X39) = var(X38) )
<=> ( X38 = X39 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_dB_Osimps_I1_J) ).
tff(f614,plain,
spl24_19,
inference(avatar_split_clause,[],[f371,f612]) ).
tff(f612,plain,
( spl24_19
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_19])]) ).
tff(f371,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X70: dB,X71: dB] :
( ( abs(X71) = abs(X70) )
<=> ( X70 = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dB_Osimps_I3_J) ).
tff(f610,plain,
spl24_18,
inference(avatar_split_clause,[],[f362,f608]) ).
tff(f362,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X84: X0] : ( aa(X0,X0,combi(X0),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f606,plain,
spl24_17,
inference(avatar_split_clause,[],[f358,f604]) ).
tff(f358,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f126,f246,f245]) ).
tff(f126,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X58: dB] :
( pp(aa(dB,bool,it,X58))
<=> ( ? [X79: dB,X80: dB,X81: list(dB)] :
( pp(aa(dB,bool,it,X80))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X79),X80),zero_zero(nat)),X81)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X79)),X80),X81) = X58 ) )
| ? [X79: dB] :
( pp(aa(dB,bool,it,X79))
& ( abs(X79) = X58 ) )
| ? [X77: list(dB),X78: nat] :
( listsp(dB,it,X77)
& ( foldl(dB,dB,app,var(X78),X77) = X58 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_IT_Osimps) ).
tff(f602,plain,
spl24_16,
inference(avatar_split_clause,[],[f357,f600]) ).
tff(f357,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f597,plain,
( ~ spl24_15
| spl24_14 ),
inference(avatar_split_clause,[],[f592,f587,f594]) ).
tff(f587,plain,
( spl24_14
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_14])]) ).
tff(f592,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| spl24_14 ),
inference(forward_demodulation,[],[f591,f442]) ).
tff(f591,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))
| spl24_14 ),
inference(forward_demodulation,[],[f589,f442]) ).
tff(f589,plain,
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t))
| spl24_14 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f590,plain,
~ spl24_14,
inference(avatar_split_clause,[],[f305,f587]) ).
tff(f305,plain,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f585,plain,
( spl24_13
| spl24_1
| ~ spl24_10 ),
inference(avatar_split_clause,[],[f568,f564,f522,f583]) ).
tff(f522,plain,
( spl24_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_1])]) ).
tff(f568,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl24_1
| ~ spl24_10 ),
inference(superposition,[],[f524,f565]) ).
tff(f524,plain,
( ~ pp(fFalse)
| spl24_1 ),
inference(avatar_component_clause,[],[f522]) ).
tff(f580,plain,
spl24_12,
inference(avatar_split_clause,[],[f361,f578]) ).
tff(f578,plain,
( spl24_12
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_12])]) ).
tff(f361,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X65: fun(X0,bool)] : ( collect(X0,X65) = X65 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
tff(f576,plain,
spl24_11,
inference(avatar_split_clause,[],[f340,f574]) ).
tff(f340,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X24: nat] : pp(aa(dB,bool,it,var(X24))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Var__IT) ).
tff(f566,plain,
spl24_10,
inference(avatar_split_clause,[],[f341,f564]) ).
tff(f341,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X84: bool] :
( ( fFalse = X84 )
| ( fTrue = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f562,plain,
spl24_9,
inference(avatar_split_clause,[],[f339,f560]) ).
tff(f560,plain,
( spl24_9
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_9])]) ).
tff(f339,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X40: nat] : ( zero_zero(nat) = dB_size(var(X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dB_Osize_I1_J) ).
tff(f558,plain,
spl24_8,
inference(avatar_split_clause,[],[f313,f555]) ).
tff(f313,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT) ).
tff(f553,plain,
spl24_7,
inference(avatar_split_clause,[],[f312,f550]) ).
tff(f312,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Var_I3_J) ).
tff(f548,plain,
spl24_6,
inference(avatar_split_clause,[],[f311,f545]) ).
tff(f311,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096IT_At_096) ).
tff(f543,plain,
spl24_5,
inference(avatar_split_clause,[],[f359,f541]) ).
tff(f541,plain,
( spl24_5
<=> ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_5])]) ).
tff(f359,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X40: nat,X72: dB] : ( var(X40) != abs(X72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dB_Osimps_I7_J) ).
tff(f539,plain,
spl24_4,
inference(avatar_split_clause,[],[f352,f537]) ).
tff(f537,plain,
( spl24_4
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_4])]) ).
tff(f352,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f535,plain,
spl24_3,
inference(avatar_split_clause,[],[f309,f532]) ).
tff(f309,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f530,plain,
spl24_2,
inference(avatar_split_clause,[],[f308,f527]) ).
tff(f527,plain,
( spl24_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).
tff(f308,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f525,plain,
~ spl24_1,
inference(avatar_split_clause,[],[f306,f522]) ).
tff(f306,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL817_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.11 % 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
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 14:33:00 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % (24271)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.34 % (24274)WARNING: value z3 for option sas not known
% 0.15/0.34 % (24277)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)
% 0.15/0.34 % (24275)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.34 % (24273)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.34 % (24272)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.34 % (24278)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)
% 0.15/0.34 % (24276)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)
% 0.15/0.34 % (24274)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)
% 0.15/0.34 % (24278)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.34 % Exception at run slice level
% 0.15/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % Exception at run slice level
% 0.15/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % Exception at run slice level
% 0.15/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.36 % (24281)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.36 % (24280)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.36 % (24279)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.37 % (24280)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37 % (24279)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % (24282)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 19.61/3.16 % (24276)First to succeed.
% 20.26/3.23 % (24276)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24271"
% 20.26/3.24 % (24276)Refutation found. Thanks to Tanya!
% 20.26/3.24 % SZS status Theorem for theBenchmark
% 20.26/3.24 % SZS output start Proof for theBenchmark
% See solution above
% 20.26/3.26 % (24276)------------------------------
% 20.26/3.26 % (24276)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 20.26/3.26 % (24276)Termination reason: Refutation
% 20.26/3.26
% 20.26/3.26 % (24276)Memory used [KB]: 24746
% 20.26/3.26 % (24276)Time elapsed: 2.893 s
% 20.26/3.26 % (24276)Instructions burned: 5584 (million)
% 20.26/3.26 % (24271)Success in time 2.927 s
%------------------------------------------------------------------------------