TSTP Solution File: LCL828_5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL828_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 : n008.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 07:54:06 EDT 2024
% Result : Theorem 1.78s 0.69s
% Output : Refutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 508
% Syntax : Number of formulae : 1380 ( 276 unt; 94 typ; 0 def)
% Number of atoms : 3441 ( 633 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3658 (1503 ~;1492 |; 181 &)
% ( 300 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 28 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 115 ( 51 >; 64 *; 0 +; 0 <<)
% Number of predicates : 290 ( 288 usr; 280 prp; 0-4 aty)
% Number of functors : 81 ( 81 usr; 30 con; 0-5 aty)
% Number of variables : 2878 (2709 !; 133 ?;2878 :)
% ( 36 !>; 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(fun(X0,fun(X1,X2)),fun(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,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_7,type,
abs: dB > dB ).
tff(func_def_8,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_9,type,
var: nat > dB ).
tff(func_def_10,type,
dB_size: dB > nat ).
tff(func_def_11,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_12,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_13,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_14,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_15,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_16,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_17,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_19,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_23,type,
typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fAll:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_27,type,
fFalse: bool ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_31,type,
t1: type ).
tff(func_def_32,type,
t_a: type ).
tff(func_def_33,type,
t: type ).
tff(func_def_34,type,
ts: list(type) ).
tff(func_def_35,type,
ua1: 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,
t2: dB ).
tff(func_def_45,type,
u: dB ).
tff(func_def_46,type,
ua: dB ).
tff(func_def_47,type,
sK4: type ).
tff(func_def_48,type,
sK5: list(type) ).
tff(func_def_49,type,
sK6: type ).
tff(func_def_50,type,
sK7: dB > dB ).
tff(func_def_51,type,
sK8: dB > list(dB) ).
tff(func_def_52,type,
sK9: dB > nat ).
tff(func_def_53,type,
sK10: dB > dB ).
tff(func_def_54,type,
sK11: dB > dB ).
tff(func_def_55,type,
sK12: dB > list(dB) ).
tff(func_def_56,type,
sK13: ( dB * dB ) > dB ).
tff(func_def_57,type,
sK14: ( dB * list(dB) * dB ) > dB ).
tff(func_def_58,type,
sK15: ( dB * list(dB) * dB ) > dB ).
tff(func_def_59,type,
sK16: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_60,type,
sK17: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_61,type,
sK18: ( dB * list(dB) * dB ) > dB ).
tff(func_def_62,type,
sK19: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_63,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_64,type,
sK21: ( dB * dB * dB ) > dB ).
tff(func_def_65,type,
sK22: ( dB * dB * dB ) > dB ).
tff(func_def_66,type,
sK23: ( dB * fun(nat,type) ) > type ).
tff(func_def_67,type,
sK24: ( dB * fun(nat,type) ) > type ).
tff(func_def_68,type,
sK25: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_69,type,
sK26: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_70,type,
sK27: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_71,type,
sK28: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_72,type,
sK29: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_73,type,
sK30: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_74,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_75,type,
sK32:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_76,type,
sK33:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_77,type,
sK34:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_78,type,
sK35: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).
tff(pred_def_5,type,
pp: bool > $o ).
tff(pred_def_6,type,
sP0: dB > $o ).
tff(pred_def_7,type,
sP1: dB > $o ).
tff(pred_def_8,type,
sP2: ( dB * list(dB) * dB ) > $o ).
tff(pred_def_9,type,
sP3: ( dB * dB * dB ) > $o ).
tff(f3771,plain,
$false,
inference(avatar_sat_refutation,[],[f537,f542,f547,f552,f556,f560,f565,f570,f575,f580,f584,f588,f592,f596,f600,f604,f608,f612,f616,f625,f633,f637,f641,f653,f657,f661,f665,f669,f673,f680,f684,f688,f692,f696,f700,f704,f708,f712,f716,f720,f734,f738,f742,f746,f750,f766,f770,f774,f780,f784,f788,f792,f798,f802,f811,f816,f820,f824,f829,f833,f845,f852,f856,f861,f868,f872,f876,f880,f884,f888,f895,f903,f907,f911,f915,f931,f935,f939,f947,f952,f957,f961,f970,f984,f988,f993,f1002,f1006,f1010,f1018,f1022,f1026,f1042,f1046,f1053,f1057,f1061,f1068,f1075,f1079,f1083,f1087,f1102,f1192,f1201,f1206,f1211,f1216,f1223,f1229,f1246,f1256,f1261,f1273,f1277,f1299,f1303,f1307,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1415,f1425,f1429,f1433,f1453,f1457,f1464,f1468,f1486,f1490,f1498,f1502,f1506,f1510,f1546,f1562,f1573,f1587,f1595,f1639,f1650,f1675,f1679,f1684,f1710,f1715,f1719,f1726,f1732,f1739,f1744,f1753,f1757,f1776,f1784,f1808,f1809,f1810,f1811,f1812,f1813,f1814,f1815,f1816,f1817,f1818,f1819,f1820,f1821,f1822,f1827,f1850,f2209,f2231,f2235,f2239,f2245,f2252,f2256,f2261,f2265,f2279,f2283,f2287,f2294,f2299,f2303,f2307,f2311,f2320,f2324,f2339,f2346,f2350,f2354,f2364,f2368,f2383,f2388,f2393,f2397,f2410,f2414,f2418,f2425,f2432,f2440,f2444,f2448,f2484,f2489,f2495,f2499,f2513,f2517,f2522,f2526,f2530,f2534,f2538,f2542,f2578,f2594,f2598,f2602,f2606,f2620,f2624,f2628,f2632,f2636,f2678,f2686,f2690,f2694,f2698,f2702,f2706,f2754,f2761,f2765,f2769,f2784,f2788,f2804,f2808,f2812,f2914,f2918,f2922,f3090,f3103,f3107,f3111,f3115,f3120,f3124,f3128,f3236,f3240,f3244,f3248,f3252,f3289,f3293,f3334,f3338,f3349,f3353,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3621,f3625,f3629,f3634,f3638,f3642,f3646,f3650,f3654,f3770]) ).
tff(f3770,plain,
( ~ spl36_56
| ~ spl36_10
| spl36_7
| ~ spl36_279 ),
inference(avatar_split_clause,[],[f3763,f3652,f562,f577,f813]) ).
tff(f813,plain,
( spl36_56
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_56])]) ).
tff(f577,plain,
( spl36_10
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_10])]) ).
tff(f562,plain,
( spl36_7
<=> pp(aa(dB,bool,it,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,[spl36_7])]) ).
tff(f3652,plain,
( spl36_279
<=> ! [X0: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),X0),t))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),i))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_279])]) ).
tff(f3763,plain,
( ~ pp(aa(dB,bool,it,u))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t))
| spl36_7
| ~ spl36_279 ),
inference(resolution,[],[f3653,f564]) ).
tff(f564,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))
| spl36_7 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f3653,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),i)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),X0),t)) )
| ~ spl36_279 ),
inference(avatar_component_clause,[],[f3652]) ).
tff(f3654,plain,
( spl36_279
| ~ spl36_105
| ~ spl36_147 ),
inference(avatar_split_clause,[],[f1643,f1637,f1198,f3652]) ).
tff(f1198,plain,
( spl36_105
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),ua1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_105])]) ).
tff(f1637,plain,
( spl36_147
<=> ! [X4: nat,X3: dB,X2: type,X1: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_147])]) ).
tff(f1643,plain,
( ! [X0: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),X0),t))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),i))) )
| ~ spl36_105
| ~ spl36_147 ),
inference(resolution,[],[f1638,f1200]) ).
tff(f1200,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),ua1))
| ~ spl36_105 ),
inference(avatar_component_clause,[],[f1198]) ).
tff(f1638,plain,
( ! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4))) )
| ~ spl36_147 ),
inference(avatar_component_clause,[],[f1637]) ).
tff(f3650,plain,
( spl36_278
| ~ spl36_81
| ~ spl36_129 ),
inference(avatar_split_clause,[],[f1441,f1423,f955,f3648]) ).
tff(f3648,plain,
( spl36_278
<=> ! [X0: dB,X3: dB,X2: dB,X1: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),X1)),X0))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_278])]) ).
tff(f955,plain,
( spl36_81
<=> ! [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,[spl36_81])]) ).
tff(f1423,plain,
( spl36_129
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,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)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_129])]) ).
tff(f1441,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),X1)),X0))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) )
| ~ spl36_81
| ~ spl36_129 ),
inference(superposition,[],[f1424,f956]) ).
tff(f956,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 )
| ~ spl36_81 ),
inference(avatar_component_clause,[],[f955]) ).
tff(f1424,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,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)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)) )
| ~ spl36_129 ),
inference(avatar_component_clause,[],[f1423]) ).
tff(f3646,plain,
( spl36_277
| ~ spl36_28
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2468,f2423,f667,f3644]) ).
tff(f3644,plain,
( spl36_277
<=> ! [X0: dB] :
( sP1(abs(abs(abs(abs(X0)))))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_277])]) ).
tff(f667,plain,
( spl36_28
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_28])]) ).
tff(f2423,plain,
( spl36_198
<=> ! [X0: dB] :
( sP1(abs(abs(abs(X0))))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_198])]) ).
tff(f2468,plain,
( ! [X0: dB] :
( sP1(abs(abs(abs(abs(X0)))))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl36_28
| ~ spl36_198 ),
inference(resolution,[],[f2424,f668]) ).
tff(f668,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl36_28 ),
inference(avatar_component_clause,[],[f667]) ).
tff(f2424,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(abs(X0)))) )
| ~ spl36_198 ),
inference(avatar_component_clause,[],[f2423]) ).
tff(f3642,plain,
( spl36_276
| ~ spl36_81
| ~ spl36_129 ),
inference(avatar_split_clause,[],[f1437,f1423,f955,f3640]) ).
tff(f3640,plain,
( spl36_276
<=> ! [X0: dB,X3: dB,X2: dB,X1: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_276])]) ).
tff(f1437,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1)),X3)) )
| ~ spl36_81
| ~ spl36_129 ),
inference(superposition,[],[f1424,f956]) ).
tff(f3638,plain,
( spl36_275
| ~ spl36_38
| ~ spl36_123 ),
inference(avatar_split_clause,[],[f1393,f1342,f710,f3636]) ).
tff(f3636,plain,
( spl36_275
<=> ! [X0: fun(nat,type),X3: type,X2: list(dB),X1: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,X1,X2)),X3))
| pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_275])]) ).
tff(f710,plain,
( spl36_38
<=> ! [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,[spl36_38])]) ).
tff(f1342,plain,
( spl36_123
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_123])]) ).
tff(f1393,plain,
( ! [X2: list(dB),X3: type,X0: fun(nat,type),X1: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,X1,X2)),X3))
| pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X1))) )
| ~ spl36_38
| ~ spl36_123 ),
inference(resolution,[],[f1343,f711]) ).
tff(f711,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl36_38 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f1343,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl36_123 ),
inference(avatar_component_clause,[],[f1342]) ).
tff(f3634,plain,
( spl36_274
| ~ spl36_38
| ~ spl36_105 ),
inference(avatar_split_clause,[],[f1217,f1198,f710,f3631]) ).
tff(f3631,plain,
( spl36_274
<=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_274])]) ).
tff(f1217,plain,
( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a)))
| ~ spl36_38
| ~ spl36_105 ),
inference(resolution,[],[f1200,f711]) ).
tff(f3629,plain,
( spl36_273
| ~ spl36_58
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1186,f1100,f822,f3627]) ).
tff(f3627,plain,
( spl36_273
<=> ! [X0: nat,X1: fun(dB,dB)] : ( aa(dB,dB,X1,var(X0)) = aa(nat,dB,aa(dB,fun(nat,dB),aa(fun(dB,dB),fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(fun(dB,dB),fun(dB,fun(nat,dB))),combs(dB,dB,fun(nat,dB)),subst),X1),var(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_273])]) ).
tff(f822,plain,
( spl36_58
<=> ! [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,[spl36_58])]) ).
tff(f1100,plain,
( spl36_103
<=> ! [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,[spl36_103])]) ).
tff(f1186,plain,
( ! [X0: nat,X1: fun(dB,dB)] : ( aa(dB,dB,X1,var(X0)) = aa(nat,dB,aa(dB,fun(nat,dB),aa(fun(dB,dB),fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(fun(dB,dB),fun(dB,fun(nat,dB))),combs(dB,dB,fun(nat,dB)),subst),X1),var(X0)),X0) )
| ~ spl36_58
| ~ spl36_103 ),
inference(superposition,[],[f823,f1101]) ).
tff(f1101,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)) )
| ~ spl36_103 ),
inference(avatar_component_clause,[],[f1100]) ).
tff(f823,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 )
| ~ spl36_58 ),
inference(avatar_component_clause,[],[f822]) ).
tff(f3625,plain,
( spl36_272
| ~ spl36_63
| ~ spl36_74 ),
inference(avatar_split_clause,[],[f926,f909,f854,f3623]) ).
tff(f3623,plain,
( spl36_272
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,X0),X2: type,X1: fun(type,fun(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),sK31(X0,type,aa(type,fun(type,X0),X1,X2),X3))) != aa(type,X0,X3,sK31(X0,type,aa(type,fun(type,X0),X1,X2),X3)) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_272])]) ).
tff(f854,plain,
( spl36_63
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_63])]) ).
tff(f909,plain,
( spl36_74
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,fun(type,X0)),X2: type,X1: type] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_74])]) ).
tff(f926,plain,
( ! [X0: $tType,X2: type,X3: fun(type,X0),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),sK31(X0,type,aa(type,fun(type,X0),X1,X2),X3))) != aa(type,X0,X3,sK31(X0,type,aa(type,fun(type,X0),X1,X2),X3)) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) )
| ~ spl36_63
| ~ spl36_74 ),
inference(superposition,[],[f855,f910]) ).
tff(f910,plain,
( ! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) )
| ~ spl36_74 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f855,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl36_63 ),
inference(avatar_component_clause,[],[f854]) ).
tff(f3621,plain,
( spl36_271
| ~ spl36_63
| ~ spl36_74 ),
inference(avatar_split_clause,[],[f925,f909,f854,f3619]) ).
tff(f3619,plain,
( spl36_271
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,X0),X2: type,X1: fun(type,fun(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),sK31(X0,type,X3,aa(type,fun(type,X0),X1,X2)))) != aa(type,X0,X3,sK31(X0,type,X3,aa(type,fun(type,X0),X1,X2))) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_271])]) ).
tff(f925,plain,
( ! [X0: $tType,X2: type,X3: fun(type,X0),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),sK31(X0,type,X3,aa(type,fun(type,X0),X1,X2)))) != aa(type,X0,X3,sK31(X0,type,X3,aa(type,fun(type,X0),X1,X2))) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) )
| ~ spl36_63
| ~ spl36_74 ),
inference(superposition,[],[f855,f910]) ).
tff(f3400,plain,
( spl36_270
| ~ spl36_81
| ~ spl36_122 ),
inference(avatar_split_clause,[],[f1386,f1338,f955,f3398]) ).
tff(f3398,plain,
( spl36_270
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X2)))
| ~ 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(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_270])]) ).
tff(f1338,plain,
( spl36_122
<=> ! [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,[spl36_122])]) ).
tff(f1386,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X2)))
| ~ 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(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1),X2))) )
| ~ spl36_81
| ~ spl36_122 ),
inference(superposition,[],[f1339,f956]) ).
tff(f1339,plain,
( ! [X2: dB,X0: list(dB),X1: 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))) )
| ~ spl36_122 ),
inference(avatar_component_clause,[],[f1338]) ).
tff(f3396,plain,
( spl36_269
| ~ spl36_16
| ~ spl36_111 ),
inference(avatar_split_clause,[],[f1248,f1244,f602,f3394]) ).
tff(f3394,plain,
( spl36_269
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),X2))
| ~ sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_269])]) ).
tff(f602,plain,
( spl36_16
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_16])]) ).
tff(f1244,plain,
( spl36_111
<=> ! [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,[spl36_111])]) ).
tff(f1248,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),X2))
| ~ sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)),X2)) )
| ~ spl36_16
| ~ spl36_111 ),
inference(resolution,[],[f1245,f603]) ).
tff(f603,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl36_16 ),
inference(avatar_component_clause,[],[f602]) ).
tff(f1245,plain,
( ! [X2: dB,X3: list(dB),X1: 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,X1),X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,it,X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3)) )
| ~ spl36_111 ),
inference(avatar_component_clause,[],[f1244]) ).
tff(f3392,plain,
( spl36_268
| ~ spl36_74
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1175,f1100,f909,f3390]) ).
tff(f3390,plain,
( spl36_268
<=> ! [X2: $tType,X4: fun(type,fun(type,X2)),X0: type,X3: fun(nat,X2),X1: fun(type,type)] : ( aa(type,X2,aa(type,fun(type,X2),X4,X0),aa(type,type,X1,X0)) = type_case(X2,X3,X4,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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_268])]) ).
tff(f1175,plain,
( ! [X2: $tType,X3: fun(nat,X2),X0: type,X1: fun(type,type),X4: fun(type,fun(type,X2))] : ( aa(type,X2,aa(type,fun(type,X2),X4,X0),aa(type,type,X1,X0)) = type_case(X2,X3,X4,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)) )
| ~ spl36_74
| ~ spl36_103 ),
inference(superposition,[],[f910,f1101]) ).
tff(f3388,plain,
( spl36_267
| ~ spl36_82
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1158,f1100,f959,f3386]) ).
tff(f3386,plain,
( spl36_267
<=> ! [X2: fun(dB,nat),X0: dB,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0)),X2),var(X1))))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_267])]) ).
tff(f959,plain,
( spl36_82
<=> ! [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,[spl36_82])]) ).
tff(f1158,plain,
( ! [X2: fun(dB,nat),X0: dB,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0)),X2),var(X1))))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl36_82
| ~ spl36_103 ),
inference(superposition,[],[f960,f1101]) ).
tff(f960,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)) )
| ~ spl36_82 ),
inference(avatar_component_clause,[],[f959]) ).
tff(f3384,plain,
( spl36_266
| ~ spl36_38
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1129,f1100,f710,f3382]) ).
tff(f3382,plain,
( spl36_266
<=> ! [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,[spl36_266])]) ).
tff(f1129,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))) )
| ~ spl36_38
| ~ spl36_103 ),
inference(superposition,[],[f711,f1101]) ).
tff(f3380,plain,
( spl36_265
| ~ spl36_74
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1122,f1100,f909,f3378]) ).
tff(f3378,plain,
( spl36_265
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,type),X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),aa(type,type,X3,X2))) = aa(type,X0,aa(fun(type,type),fun(type,X0),aa(fun(type,fun(type,X0)),fun(fun(type,type),fun(type,X0)),combs(type,type,X0),X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_265])]) ).
tff(f1122,plain,
( ! [X0: $tType,X2: type,X3: fun(type,type),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),aa(type,type,X3,X2))) = aa(type,X0,aa(fun(type,type),fun(type,X0),aa(fun(type,fun(type,X0)),fun(fun(type,type),fun(type,X0)),combs(type,type,X0),X1),X3),X2) )
| ~ spl36_74
| ~ spl36_103 ),
inference(superposition,[],[f1101,f910]) ).
tff(f3376,plain,
( spl36_264
| ~ spl36_75
| ~ spl36_86 ),
inference(avatar_split_clause,[],[f998,f991,f913,f3374]) ).
tff(f3374,plain,
( spl36_264
<=> ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X0),X1),X2)),var(X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_264])]) ).
tff(f913,plain,
( spl36_75
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_75])]) ).
tff(f991,plain,
( spl36_86
<=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_86])]) ).
tff(f998,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X0),X1),X2)),var(X1)),X2))
| ~ spl36_75
| ~ spl36_86 ),
inference(superposition,[],[f914,f992]) ).
tff(f992,plain,
( ! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 )
| ~ spl36_86 ),
inference(avatar_component_clause,[],[f991]) ).
tff(f914,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl36_75 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f3372,plain,
( spl36_263
| ~ spl36_21
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2480,f2423,f631,f3370]) ).
tff(f3370,plain,
( spl36_263
<=> ! [X0: dB] :
( sP1(abs(abs(abs(sK11(X0)))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_263])]) ).
tff(f631,plain,
( spl36_21
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_21])]) ).
tff(f2480,plain,
( ! [X0: dB] :
( sP1(abs(abs(abs(sK11(X0)))))
| ~ sP0(X0) )
| ~ spl36_21
| ~ spl36_198 ),
inference(resolution,[],[f2424,f632]) ).
tff(f632,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) )
| ~ spl36_21 ),
inference(avatar_component_clause,[],[f631]) ).
tff(f3353,plain,
( spl36_262
| ~ spl36_68
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1176,f1100,f878,f3351]) ).
tff(f3351,plain,
( spl36_262
<=> ! [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,[spl36_262])]) ).
tff(f878,plain,
( spl36_68
<=> ! [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,[spl36_68])]) ).
tff(f1176,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 ) )
| ~ spl36_68
| ~ spl36_103 ),
inference(superposition,[],[f879,f1101]) ).
tff(f879,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 ) )
| ~ spl36_68 ),
inference(avatar_component_clause,[],[f878]) ).
tff(f3349,plain,
( spl36_261
| ~ spl36_70
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1167,f1100,f886,f3347]) ).
tff(f3347,plain,
( spl36_261
<=> ! [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,[spl36_261])]) ).
tff(f886,plain,
( spl36_70
<=> ! [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,[spl36_70])]) ).
tff(f1167,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 ) )
| ~ spl36_70
| ~ spl36_103 ),
inference(superposition,[],[f887,f1101]) ).
tff(f887,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 ) )
| ~ spl36_70 ),
inference(avatar_component_clause,[],[f886]) ).
tff(f3338,plain,
( spl36_260
| ~ spl36_49
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1145,f1100,f778,f3336]) ).
tff(f3336,plain,
( spl36_260
<=> ! [X0: dB,X1: fun(dB,dB)] :
( ~ pp(aa(dB,bool,aa(fun(dB,dB),fun(dB,bool),aa(fun(dB,fun(dB,bool)),fun(fun(dB,dB),fun(dB,bool)),combs(dB,dB,bool),beta),X1),abs(X0)))
| ( aa(dB,dB,X1,abs(X0)) = abs(sK13(aa(dB,dB,X1,abs(X0)),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_260])]) ).
tff(f778,plain,
( spl36_49
<=> ! [X0: dB,X1: dB] :
( ( abs(sK13(X0,X1)) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_49])]) ).
tff(f1145,plain,
( ! [X0: dB,X1: fun(dB,dB)] :
( ~ pp(aa(dB,bool,aa(fun(dB,dB),fun(dB,bool),aa(fun(dB,fun(dB,bool)),fun(fun(dB,dB),fun(dB,bool)),combs(dB,dB,bool),beta),X1),abs(X0)))
| ( aa(dB,dB,X1,abs(X0)) = abs(sK13(aa(dB,dB,X1,abs(X0)),X0)) ) )
| ~ spl36_49
| ~ spl36_103 ),
inference(superposition,[],[f779,f1101]) ).
tff(f779,plain,
( ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))
| ( abs(sK13(X0,X1)) = X0 ) )
| ~ spl36_49 ),
inference(avatar_component_clause,[],[f778]) ).
tff(f3334,plain,
( spl36_259
| ~ spl36_73
| ~ spl36_94 ),
inference(avatar_split_clause,[],[f1048,f1044,f905,f3332]) ).
tff(f3332,plain,
( spl36_259
<=> ! [X2: list(dB),X0: list(dB),X1: dB] :
( step1(dB,beta,X0,sK17(foldl(dB,dB,app,X1,X2),X0,X1))
| ( foldl(dB,dB,app,X1,X2) = foldl(dB,dB,app,sK18(foldl(dB,dB,app,X1,X2),X0,X1),X0) )
| sP2(foldl(dB,dB,app,X1,X2),X0,X1)
| ~ step1(dB,beta,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_259])]) ).
tff(f905,plain,
( spl36_73
<=> ! [X2: list(dB),X0: dB,X1: list(dB)] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1)))
| ~ step1(dB,beta,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_73])]) ).
tff(f1044,plain,
( spl36_94
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| step1(dB,beta,X1,sK17(X0,X1,X2))
| ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_94])]) ).
tff(f1048,plain,
( ! [X2: list(dB),X0: list(dB),X1: dB] :
( step1(dB,beta,X0,sK17(foldl(dB,dB,app,X1,X2),X0,X1))
| ( foldl(dB,dB,app,X1,X2) = foldl(dB,dB,app,sK18(foldl(dB,dB,app,X1,X2),X0,X1),X0) )
| sP2(foldl(dB,dB,app,X1,X2),X0,X1)
| ~ step1(dB,beta,X0,X2) )
| ~ spl36_73
| ~ spl36_94 ),
inference(resolution,[],[f1045,f906]) ).
tff(f906,plain,
( ! [X2: list(dB),X0: dB,X1: list(dB)] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1)))
| ~ step1(dB,beta,X2,X1) )
| ~ spl36_73 ),
inference(avatar_component_clause,[],[f905]) ).
tff(f1045,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))
| step1(dB,beta,X1,sK17(X0,X1,X2))
| ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
| sP2(X0,X1,X2) )
| ~ spl36_94 ),
inference(avatar_component_clause,[],[f1044]) ).
tff(f3293,plain,
( spl36_258
| ~ spl36_73
| ~ spl36_102 ),
inference(avatar_split_clause,[],[f1096,f1085,f905,f3291]) ).
tff(f3291,plain,
( spl36_258
<=> ! [X2: list(dB),X0: list(dB),X1: dB] :
( step1(dB,beta,X0,sK17(foldl(dB,dB,app,X1,X2),X0,X1))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK18(foldl(dB,dB,app,X1,X2),X0,X1)))
| sP2(foldl(dB,dB,app,X1,X2),X0,X1)
| ~ step1(dB,beta,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_258])]) ).
tff(f1085,plain,
( spl36_102
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| step1(dB,beta,X1,sK17(X0,X1,X2))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_102])]) ).
tff(f1096,plain,
( ! [X2: list(dB),X0: list(dB),X1: dB] :
( step1(dB,beta,X0,sK17(foldl(dB,dB,app,X1,X2),X0,X1))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK18(foldl(dB,dB,app,X1,X2),X0,X1)))
| sP2(foldl(dB,dB,app,X1,X2),X0,X1)
| ~ step1(dB,beta,X0,X2) )
| ~ spl36_73
| ~ spl36_102 ),
inference(resolution,[],[f1086,f906]) ).
tff(f1086,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))
| step1(dB,beta,X1,sK17(X0,X1,X2))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2)))
| sP2(X0,X1,X2) )
| ~ spl36_102 ),
inference(avatar_component_clause,[],[f1085]) ).
tff(f3289,plain,
( spl36_257
| ~ spl36_72
| ~ spl36_77 ),
inference(avatar_split_clause,[],[f940,f933,f901,f3287]) ).
tff(f3287,plain,
( spl36_257
<=> ! [X2: list(dB),X0: nat,X1: dB] :
( ( sK13(X1,foldl(dB,dB,app,var(X0),X2)) = foldl(dB,dB,app,var(X0),sK19(sK13(X1,foldl(dB,dB,app,var(X0),X2)),X2,X0)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(foldl(dB,dB,app,var(X0),X2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_257])]) ).
tff(f901,plain,
( spl36_72
<=> ! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_72])]) ).
tff(f933,plain,
( spl36_77
<=> ! [X2: nat,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X2),sK19(X0,X1,X2)) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_77])]) ).
tff(f940,plain,
( ! [X2: list(dB),X0: nat,X1: dB] :
( ( sK13(X1,foldl(dB,dB,app,var(X0),X2)) = foldl(dB,dB,app,var(X0),sK19(sK13(X1,foldl(dB,dB,app,var(X0),X2)),X2,X0)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(foldl(dB,dB,app,var(X0),X2))),X1)) )
| ~ spl36_72
| ~ spl36_77 ),
inference(resolution,[],[f934,f902]) ).
tff(f902,plain,
( ! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) )
| ~ spl36_72 ),
inference(avatar_component_clause,[],[f901]) ).
tff(f934,plain,
( ! [X2: nat,X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))
| ( foldl(dB,dB,app,var(X2),sK19(X0,X1,X2)) = X0 ) )
| ~ spl36_77 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f3252,plain,
( spl36_256
| ~ spl36_81
| ~ spl36_111 ),
inference(avatar_split_clause,[],[f1251,f1244,f955,f3250]) ).
tff(f3250,plain,
( spl36_256
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X2)))
| ~ pp(aa(dB,bool,it,X1))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_256])]) ).
tff(f1251,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X2)))
| ~ pp(aa(dB,bool,it,X1))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1),X2)) )
| ~ spl36_81
| ~ spl36_111 ),
inference(superposition,[],[f1245,f956]) ).
tff(f3248,plain,
( spl36_255
| ~ spl36_70
| ~ spl36_110 ),
inference(avatar_split_clause,[],[f1236,f1227,f886,f3246]) ).
tff(f3246,plain,
( spl36_255
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) )
| ( aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_255])]) ).
tff(f1227,plain,
( spl36_110
<=> ! [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,[spl36_110])]) ).
tff(f1236,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) )
| ( aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1) = X4 ) )
| ~ spl36_70
| ~ spl36_110 ),
inference(superposition,[],[f887,f1228]) ).
tff(f1228,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)) )
| ~ spl36_110 ),
inference(avatar_component_clause,[],[f1227]) ).
tff(f3244,plain,
( spl36_254
| ~ spl36_69
| ~ spl36_110 ),
inference(avatar_split_clause,[],[f1234,f1227,f882,f3242]) ).
tff(f3242,plain,
( spl36_254
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) )
| ( aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_254])]) ).
tff(f882,plain,
( spl36_69
<=> ! [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,[spl36_69])]) ).
tff(f1234,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) )
| ( aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1) = X3 ) )
| ~ spl36_69
| ~ spl36_110 ),
inference(superposition,[],[f883,f1228]) ).
tff(f883,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 ) )
| ~ spl36_69 ),
inference(avatar_component_clause,[],[f882]) ).
tff(f3240,plain,
( spl36_253
| ~ spl36_38
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1136,f1100,f710,f3238]) ).
tff(f3238,plain,
( spl36_253
<=> ! [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,[spl36_253])]) ).
tff(f1136,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))) )
| ~ spl36_38
| ~ spl36_103 ),
inference(superposition,[],[f711,f1101]) ).
tff(f3236,plain,
( spl36_252
| ~ spl36_16
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2467,f2423,f602,f3234]) ).
tff(f3234,plain,
( spl36_252
<=> ! [X0: dB] :
( sP1(abs(abs(abs(X0))))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_252])]) ).
tff(f2467,plain,
( ! [X0: dB] :
( sP1(abs(abs(abs(X0))))
| ~ sP1(X0) )
| ~ spl36_16
| ~ spl36_198 ),
inference(resolution,[],[f2424,f603]) ).
tff(f3128,plain,
( spl36_251
| ~ spl36_38
| ~ spl36_129 ),
inference(avatar_split_clause,[],[f1434,f1423,f710,f3126]) ).
tff(f3126,plain,
( spl36_251
<=> ! [X0: dB,X3: nat,X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),X2),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_251])]) ).
tff(f1434,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),X2),X3)))) )
| ~ spl36_38
| ~ spl36_129 ),
inference(resolution,[],[f1424,f711]) ).
tff(f3124,plain,
( spl36_250
| ~ spl36_78
| ~ spl36_124 ),
inference(avatar_split_clause,[],[f1395,f1346,f937,f3122]) ).
tff(f3122,plain,
( spl36_250
<=> ! [X0: fun(nat,type),X3: type,X2: list(dB),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK28(X3,X2,var(X1),X0),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_250])]) ).
tff(f937,plain,
( spl36_78
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_78])]) ).
tff(f1346,plain,
( spl36_124
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_124])]) ).
tff(f1395,plain,
( ! [X2: list(dB),X3: type,X0: fun(nat,type),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK28(X3,X2,var(X1),X0),X3) ) )
| ~ spl36_78
| ~ spl36_124 ),
inference(resolution,[],[f1347,f938]) ).
tff(f938,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl36_78 ),
inference(avatar_component_clause,[],[f937]) ).
tff(f1347,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl36_124 ),
inference(avatar_component_clause,[],[f1346]) ).
tff(f3120,plain,
( spl36_249
| ~ spl36_78
| ~ spl36_123 ),
inference(avatar_split_clause,[],[f1387,f1342,f937,f3118]) ).
tff(f3118,plain,
( spl36_249
<=> ! [X0: fun(nat,type),X3: type,X2: list(dB),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK27(X3,X2,var(X1),X0),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_249])]) ).
tff(f1387,plain,
( ! [X2: list(dB),X3: type,X0: fun(nat,type),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK27(X3,X2,var(X1),X0),X3) ) )
| ~ spl36_78
| ~ spl36_123 ),
inference(resolution,[],[f1343,f938]) ).
tff(f3115,plain,
( spl36_248
| ~ spl36_67
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1178,f1100,f874,f3113]) ).
tff(f3113,plain,
( spl36_248
<=> ! [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,[spl36_248])]) ).
tff(f874,plain,
( spl36_67
<=> ! [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,[spl36_67])]) ).
tff(f1178,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 ) )
| ~ spl36_67
| ~ spl36_103 ),
inference(superposition,[],[f875,f1101]) ).
tff(f875,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 ) )
| ~ spl36_67 ),
inference(avatar_component_clause,[],[f874]) ).
tff(f3111,plain,
( spl36_247
| ~ spl36_69
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1165,f1100,f882,f3109]) ).
tff(f3109,plain,
( spl36_247
<=> ! [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,[spl36_247])]) ).
tff(f1165,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 ) )
| ~ spl36_69
| ~ spl36_103 ),
inference(superposition,[],[f883,f1101]) ).
tff(f3107,plain,
( spl36_246
| ~ spl36_58
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1127,f1100,f822,f3105]) ).
tff(f3105,plain,
( spl36_246
<=> ! [X0: fun(dB,nat),X1: dB] : ( aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(aa(dB,nat,X0,X1)))),X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_246])]) ).
tff(f1127,plain,
( ! [X0: fun(dB,nat),X1: dB] : ( aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(aa(dB,nat,X0,X1)))),X0),X1) = X1 )
| ~ spl36_58
| ~ spl36_103 ),
inference(superposition,[],[f1101,f823]) ).
tff(f3103,plain,
( spl36_245
| ~ spl36_74 ),
inference(avatar_split_clause,[],[f923,f909,f3101]) ).
tff(f3101,plain,
( spl36_245
<=> ! [X0: $tType,X5: fun(nat,X0),X3: type,X4: fun(nat,fun(type,X0)),X6: type,X2: type,X1: fun(type,fun(type,fun(type,X0)))] : ( type_case(X0,X5,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,aa(type,fun(type,type),fun1,X3),X6)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_245])]) ).
tff(f923,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,fun(type,X0))),X6: type,X4: fun(nat,fun(type,X0)),X5: fun(nat,X0)] : ( type_case(X0,X5,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,aa(type,fun(type,type),fun1,X3),X6)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)),X6) )
| ~ spl36_74 ),
inference(superposition,[],[f910,f910]) ).
tff(f3090,plain,
( spl36_244
| ~ spl36_78
| ~ spl36_130 ),
inference(avatar_split_clause,[],[f1444,f1427,f937,f3088]) ).
tff(f3088,plain,
( spl36_244
<=> ! [X0: fun(nat,type),X3: type,X2: list(dB),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK29(X3,X2,X1,X0),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_244])]) ).
tff(f1427,plain,
( spl36_130
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_130])]) ).
tff(f1444,plain,
( ! [X2: list(dB),X3: type,X0: fun(nat,type),X1: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),foldl(dB,dB,app,var(X1),X2)),X3))
| ( aa(nat,type,X0,X1) = foldr(type,type,fun1,sK29(X3,X2,X1,X0),X3) ) )
| ~ spl36_78
| ~ spl36_130 ),
inference(resolution,[],[f1428,f938]) ).
tff(f1428,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl36_130 ),
inference(avatar_component_clause,[],[f1427]) ).
tff(f2922,plain,
( spl36_243
| ~ spl36_58
| ~ spl36_129 ),
inference(avatar_split_clause,[],[f1440,f1423,f822,f2920]) ).
tff(f2920,plain,
( spl36_243
<=> ! [X2: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),var(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_243])]) ).
tff(f1440,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),var(X0))) )
| ~ spl36_58
| ~ spl36_129 ),
inference(superposition,[],[f1424,f823]) ).
tff(f2918,plain,
( spl36_242
| ~ spl36_17
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1112,f1100,f606,f2916]) ).
tff(f2916,plain,
( spl36_242
<=> ! [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,[spl36_242])]) ).
tff(f606,plain,
( spl36_17
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_17])]) ).
tff(f1112,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) )
| ~ spl36_17
| ~ spl36_103 ),
inference(superposition,[],[f1101,f607]) ).
tff(f607,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl36_17 ),
inference(avatar_component_clause,[],[f606]) ).
tff(f2914,plain,
( spl36_241
| ~ spl36_13
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2469,f2423,f590,f2912]) ).
tff(f2912,plain,
( spl36_241
<=> ! [X0: nat] : sP1(abs(abs(abs(var(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_241])]) ).
tff(f590,plain,
( spl36_13
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_13])]) ).
tff(f2469,plain,
( ! [X0: nat] : sP1(abs(abs(abs(var(X0)))))
| ~ spl36_13
| ~ spl36_198 ),
inference(resolution,[],[f2424,f591]) ).
tff(f591,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl36_13 ),
inference(avatar_component_clause,[],[f590]) ).
tff(f2812,plain,
( spl36_240
| ~ spl36_38
| ~ spl36_92 ),
inference(avatar_split_clause,[],[f1036,f1024,f710,f2810]) ).
tff(f2810,plain,
( spl36_240
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X4: X0,X3: fun(X0,X1)] :
( ~ 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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_240])]) ).
tff(f1024,plain,
( spl36_92
<=> ! [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,[spl36_92])]) ).
tff(f1036,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))) )
| ~ spl36_38
| ~ spl36_92 ),
inference(superposition,[],[f711,f1025]) ).
tff(f1025,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)) )
| ~ spl36_92 ),
inference(avatar_component_clause,[],[f1024]) ).
tff(f2808,plain,
( spl36_239
| ~ spl36_38
| ~ spl36_91 ),
inference(avatar_split_clause,[],[f1031,f1020,f710,f2806]) ).
tff(f2806,plain,
( spl36_239
<=> ! [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),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_239])]) ).
tff(f1020,plain,
( spl36_91
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(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,[spl36_91])]) ).
tff(f1031,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),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))) )
| ~ spl36_38
| ~ spl36_91 ),
inference(superposition,[],[f711,f1021]) ).
tff(f1021,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl36_91 ),
inference(avatar_component_clause,[],[f1020]) ).
tff(f2804,plain,
( spl36_238
| ~ spl36_74
| ~ spl36_91 ),
inference(avatar_split_clause,[],[f1027,f1020,f909,f2802]) ).
tff(f2802,plain,
( spl36_238
<=> ! [X0: $tType,X4: fun(nat,X0),X3: type,X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,aa(fun(type,fun(type,X0)),fun(type,fun(type,X0)),combc(type,type,X0),X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) = aa(type,X0,aa(type,fun(type,X0),X1,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_238])]) ).
tff(f1027,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,aa(fun(type,fun(type,X0)),fun(type,fun(type,X0)),combc(type,type,X0),X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) = aa(type,X0,aa(type,fun(type,X0),X1,X3),X2) )
| ~ spl36_74
| ~ spl36_91 ),
inference(superposition,[],[f1021,f910]) ).
tff(f2788,plain,
( spl36_237
| ~ spl36_58
| ~ spl36_122 ),
inference(avatar_split_clause,[],[f1385,f1338,f822,f2786]) ).
tff(f2786,plain,
( spl36_237
<=> ! [X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X1)))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_237])]) ).
tff(f1385,plain,
( ! [X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X1)))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0),X1))) )
| ~ spl36_58
| ~ spl36_122 ),
inference(superposition,[],[f1339,f823]) ).
tff(f2784,plain,
( spl36_236
| ~ spl36_60
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1162,f1100,f831,f2782]) ).
tff(f2782,plain,
( spl36_236
<=> ! [X0: dB,X1: fun(dB,nat)] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),lift),X1),X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_236])]) ).
tff(f831,plain,
( spl36_60
<=> ! [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,[spl36_60])]) ).
tff(f1162,plain,
( ! [X0: dB,X1: fun(dB,nat)] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(fun(dB,nat),fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(fun(dB,nat),fun(dB,dB)),combs(dB,nat,dB),lift),X1),X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl36_60
| ~ spl36_103 ),
inference(superposition,[],[f832,f1101]) ).
tff(f832,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)) )
| ~ spl36_60 ),
inference(avatar_component_clause,[],[f831]) ).
tff(f2769,plain,
( spl36_235
| ~ spl36_54
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1174,f1100,f800,f2767]) ).
tff(f2767,plain,
( spl36_235
<=> ! [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,[spl36_235])]) ).
tff(f800,plain,
( spl36_54
<=> ! [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,[spl36_54])]) ).
tff(f1174,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)) )
| ~ spl36_54
| ~ spl36_103 ),
inference(superposition,[],[f801,f1101]) ).
tff(f801,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) )
| ~ spl36_54 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f2765,plain,
( spl36_234
| ~ spl36_42
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1140,f1100,f736,f2763]) ).
tff(f2763,plain,
( spl36_234
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0))
| ~ pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_234])]) ).
tff(f736,plain,
( spl36_42
<=> ! [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,[spl36_42])]) ).
tff(f1140,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0))
| ~ pp(X0) )
| ~ spl36_42
| ~ spl36_103 ),
inference(superposition,[],[f737,f1101]) ).
tff(f737,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl36_42 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f2761,plain,
( spl36_233
| ~ spl36_43
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1137,f1100,f740,f2759]) ).
tff(f2759,plain,
( spl36_233
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| ~ pp(X0)
| pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_233])]) ).
tff(f740,plain,
( spl36_43
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_43])]) ).
tff(f1137,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| ~ pp(X0)
| pp(aa(bool,bool,X1,X0)) )
| ~ spl36_43
| ~ spl36_103 ),
inference(superposition,[],[f741,f1101]) ).
tff(f741,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| ~ pp(X1)
| pp(X0) )
| ~ spl36_43 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f2754,plain,
( spl36_232
| ~ spl36_38
| ~ spl36_86 ),
inference(avatar_split_clause,[],[f997,f991,f710,f2752]) ).
tff(f2752,plain,
( spl36_232
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),aa(bool,fun(nat,bool),aa(nat,fun(bool,fun(nat,bool)),aa(fun(nat,bool),fun(nat,fun(bool,fun(nat,bool))),shift(bool),X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_232])]) ).
tff(f997,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),aa(bool,fun(nat,bool),aa(nat,fun(bool,fun(nat,bool)),aa(fun(nat,bool),fun(nat,fun(bool,fun(nat,bool))),shift(bool),X0),X1),X2))) )
| ~ spl36_38
| ~ spl36_86 ),
inference(superposition,[],[f711,f992]) ).
tff(f2706,plain,
( spl36_231
| ~ spl36_58
| ~ spl36_111 ),
inference(avatar_split_clause,[],[f1250,f1244,f822,f2704]) ).
tff(f2704,plain,
( spl36_231
<=> ! [X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X1)))
| ~ pp(aa(dB,bool,it,X0))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_231])]) ).
tff(f1250,plain,
( ! [X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,X0,X1)))
| ~ pp(aa(dB,bool,it,X0))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0),X1)) )
| ~ spl36_58
| ~ spl36_111 ),
inference(superposition,[],[f1245,f823]) ).
tff(f2702,plain,
( spl36_230
| ~ spl36_35
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1141,f1100,f698,f2700]) ).
tff(f2700,plain,
( spl36_230
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_230])]) ).
tff(f698,plain,
( spl36_35
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_35])]) ).
tff(f1141,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) )
| ~ spl36_35
| ~ spl36_103 ),
inference(superposition,[],[f699,f1101]) ).
tff(f699,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X0) )
| ~ spl36_35 ),
inference(avatar_component_clause,[],[f698]) ).
tff(f2698,plain,
( spl36_229
| ~ spl36_32
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1139,f1100,f686,f2696]) ).
tff(f2696,plain,
( spl36_229
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| ~ pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_229])]) ).
tff(f686,plain,
( spl36_32
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_32])]) ).
tff(f1139,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| ~ pp(aa(bool,bool,X1,X0)) )
| ~ spl36_32
| ~ spl36_103 ),
inference(superposition,[],[f687,f1101]) ).
tff(f687,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) )
| ~ spl36_32 ),
inference(avatar_component_clause,[],[f686]) ).
tff(f2694,plain,
( spl36_228
| ~ spl36_38
| ~ spl36_101 ),
inference(avatar_split_clause,[],[f1095,f1081,f710,f2692]) ).
tff(f2692,plain,
( spl36_228
<=> ! [X2: nat,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_228])]) ).
tff(f1081,plain,
( spl36_101
<=> ! [X2: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_101])]) ).
tff(f1095,plain,
( ! [X2: nat,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X2)))) )
| ~ spl36_38
| ~ spl36_101 ),
inference(resolution,[],[f1082,f711]) ).
tff(f1082,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) )
| ~ spl36_101 ),
inference(avatar_component_clause,[],[f1081]) ).
tff(f2690,plain,
( spl36_227
| ~ spl36_38
| ~ spl36_100 ),
inference(avatar_split_clause,[],[f1092,f1077,f710,f2688]) ).
tff(f2688,plain,
( spl36_227
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_227])]) ).
tff(f1077,plain,
( spl36_100
<=> ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_100])]) ).
tff(f1092,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)))) )
| ~ spl36_38
| ~ spl36_100 ),
inference(resolution,[],[f1078,f711]) ).
tff(f1078,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) )
| ~ spl36_100 ),
inference(avatar_component_clause,[],[f1077]) ).
tff(f2686,plain,
( spl36_226
| ~ spl36_38
| ~ spl36_99 ),
inference(avatar_split_clause,[],[f1089,f1073,f710,f2684]) ).
tff(f2684,plain,
( spl36_226
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_226])]) ).
tff(f1073,plain,
( spl36_99
<=> ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_99])]) ).
tff(f1089,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)))) )
| ~ spl36_38
| ~ spl36_99 ),
inference(resolution,[],[f1074,f711]) ).
tff(f1074,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) )
| ~ spl36_99 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f2678,plain,
( spl36_225
| ~ spl36_66
| ~ spl36_72 ),
inference(avatar_split_clause,[],[f918,f901,f870,f2676]) ).
tff(f2676,plain,
( spl36_225
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(foldl(dB,dB,app,var(X0),X1))),X2))
| step1(dB,beta,X1,sK19(sK13(X2,foldl(dB,dB,app,var(X0),X1)),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_225])]) ).
tff(f870,plain,
( spl36_66
<=> ! [X2: nat,X0: dB,X1: list(dB)] :
( step1(dB,beta,X1,sK19(X0,X1,X2))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_66])]) ).
tff(f918,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(foldl(dB,dB,app,var(X0),X1))),X2))
| step1(dB,beta,X1,sK19(sK13(X2,foldl(dB,dB,app,var(X0),X1)),X1,X0)) )
| ~ spl36_66
| ~ spl36_72 ),
inference(resolution,[],[f902,f871]) ).
tff(f871,plain,
( ! [X2: nat,X0: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))
| step1(dB,beta,X1,sK19(X0,X1,X2)) )
| ~ spl36_66 ),
inference(avatar_component_clause,[],[f870]) ).
tff(f2636,plain,
( spl36_224
| ~ spl36_87
| ~ spl36_122 ),
inference(avatar_split_clause,[],[f1382,f1338,f1000,f2634]) ).
tff(f2634,plain,
( spl36_224
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,sK11(X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_224])]) ).
tff(f1000,plain,
( spl36_87
<=> ! [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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_87])]) ).
tff(f1382,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,sK11(X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0))))
| ~ sP0(X0) )
| ~ spl36_87
| ~ spl36_122 ),
inference(resolution,[],[f1339,f1001]) ).
tff(f1001,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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) )
| ~ spl36_87 ),
inference(avatar_component_clause,[],[f1000]) ).
tff(f2632,plain,
( spl36_223
| ~ spl36_56
| ~ spl36_115 ),
inference(avatar_split_clause,[],[f1290,f1275,f813,f2630]) ).
tff(f2630,plain,
( spl36_223
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,u),X0))
| pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),X0),t)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_223])]) ).
tff(f1275,plain,
( spl36_115
<=> ! [X0: dB,X3: fun(nat,type),X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_115])]) ).
tff(f1290,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,u),X0))
| pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),X0),t)) )
| ~ spl36_56
| ~ spl36_115 ),
inference(resolution,[],[f1276,f815]) ).
tff(f815,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t))
| ~ spl36_56 ),
inference(avatar_component_clause,[],[f813]) ).
tff(f1276,plain,
( ! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
| pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1)) )
| ~ spl36_115 ),
inference(avatar_component_clause,[],[f1275]) ).
tff(f2628,plain,
( spl36_222
| ~ spl36_55
| ~ spl36_115 ),
inference(avatar_split_clause,[],[f1289,f1275,f808,f2626]) ).
tff(f2626,plain,
( spl36_222
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,ua),X0))
| pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),X0),t)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_222])]) ).
tff(f808,plain,
( spl36_55
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_55])]) ).
tff(f1289,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,ua),X0))
| pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),X0),t)) )
| ~ spl36_55
| ~ spl36_115 ),
inference(resolution,[],[f1276,f810]) ).
tff(f810,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t))
| ~ spl36_55 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f2624,plain,
( spl36_221
| ~ spl36_81
| ~ spl36_96 ),
inference(avatar_split_clause,[],[f1064,f1055,f955,f2622]) ).
tff(f2622,plain,
( spl36_221
<=> ! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_221])]) ).
tff(f1055,plain,
( spl36_96
<=> ! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_96])]) ).
tff(f1064,plain,
( ! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),zero_zero(nat)))),X1)),X0))
| ~ spl36_81
| ~ spl36_96 ),
inference(superposition,[],[f1056,f956]) ).
tff(f1056,plain,
( ! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))))
| ~ spl36_96 ),
inference(avatar_component_clause,[],[f1055]) ).
tff(f2620,plain,
( spl36_220
| ~ spl36_9
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2477,f2423,f572,f2617]) ).
tff(f2617,plain,
( spl36_220
<=> sP1(abs(abs(abs(ua)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_220])]) ).
tff(f572,plain,
( spl36_9
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_9])]) ).
tff(f2477,plain,
( sP1(abs(abs(abs(ua))))
| ~ spl36_9
| ~ spl36_198 ),
inference(resolution,[],[f2424,f574]) ).
tff(f574,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl36_9 ),
inference(avatar_component_clause,[],[f572]) ).
tff(f2606,plain,
( spl36_219
| ~ spl36_37
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1164,f1100,f706,f2604]) ).
tff(f2604,plain,
( spl36_219
<=> ! [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,[spl36_219])]) ).
tff(f706,plain,
( spl36_37
<=> ! [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,[spl36_37])]) ).
tff(f1164,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) )
| ~ spl36_37
| ~ spl36_103 ),
inference(superposition,[],[f707,f1101]) ).
tff(f707,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl36_37 ),
inference(avatar_component_clause,[],[f706]) ).
tff(f2602,plain,
( spl36_218
| ~ spl36_36
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1163,f1100,f702,f2600]) ).
tff(f2600,plain,
( spl36_218
<=> ! [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,[spl36_218])]) ).
tff(f702,plain,
( spl36_36
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_36])]) ).
tff(f1163,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) )
| ~ spl36_36
| ~ spl36_103 ),
inference(superposition,[],[f703,f1101]) ).
tff(f703,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) )
| ~ spl36_36 ),
inference(avatar_component_clause,[],[f702]) ).
tff(f2598,plain,
( spl36_217
| ~ spl36_34
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1142,f1100,f694,f2596]) ).
tff(f2596,plain,
( spl36_217
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_217])]) ).
tff(f694,plain,
( spl36_34
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_34])]) ).
tff(f1142,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) )
| ~ spl36_34
| ~ spl36_103 ),
inference(superposition,[],[f695,f1101]) ).
tff(f695,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X1) )
| ~ spl36_34 ),
inference(avatar_component_clause,[],[f694]) ).
tff(f2594,plain,
( spl36_216
| ~ spl36_33
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1138,f1100,f690,f2592]) ).
tff(f2592,plain,
( spl36_216
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_216])]) ).
tff(f690,plain,
( spl36_33
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_33])]) ).
tff(f1138,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fimplies),X1),X0))
| pp(X0) )
| ~ spl36_33
| ~ spl36_103 ),
inference(superposition,[],[f691,f1101]) ).
tff(f691,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) )
| ~ spl36_33 ),
inference(avatar_component_clause,[],[f690]) ).
tff(f2578,plain,
( spl36_215
| ~ spl36_10
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2476,f2423,f577,f2575]) ).
tff(f2575,plain,
( spl36_215
<=> sP1(abs(abs(abs(u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_215])]) ).
tff(f2476,plain,
( sP1(abs(abs(abs(u))))
| ~ spl36_10
| ~ spl36_198 ),
inference(resolution,[],[f2424,f579]) ).
tff(f579,plain,
( pp(aa(dB,bool,it,u))
| ~ spl36_10 ),
inference(avatar_component_clause,[],[f577]) ).
tff(f2542,plain,
( spl36_214
| ~ spl36_37
| ~ spl36_139 ),
inference(avatar_split_clause,[],[f1524,f1500,f706,f2540]) ).
tff(f2540,plain,
( spl36_214
<=> ! [X4: nat,X0: dB,X3: dB,X2: nat,X1: dB] : ( var(X4) != 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,X0),X3)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_214])]) ).
tff(f1500,plain,
( spl36_139
<=> ! [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,[spl36_139])]) ).
tff(f1524,plain,
( ! [X2: nat,X3: dB,X0: dB,X1: dB,X4: nat] : ( var(X4) != 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,X0),X3)),X1),X2) )
| ~ spl36_37
| ~ spl36_139 ),
inference(superposition,[],[f707,f1501]) ).
tff(f1501,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)) )
| ~ spl36_139 ),
inference(avatar_component_clause,[],[f1500]) ).
tff(f2538,plain,
( spl36_213
| ~ spl36_36
| ~ spl36_139 ),
inference(avatar_split_clause,[],[f1523,f1500,f702,f2536]) ).
tff(f2536,plain,
( spl36_213
<=> ! [X4: dB,X0: dB,X3: dB,X2: nat,X1: dB] : ( abs(X4) != 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,X0),X3)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_213])]) ).
tff(f1523,plain,
( ! [X2: nat,X3: dB,X0: dB,X1: dB,X4: dB] : ( abs(X4) != 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,X0),X3)),X1),X2) )
| ~ spl36_36
| ~ spl36_139 ),
inference(superposition,[],[f703,f1501]) ).
tff(f2534,plain,
( spl36_212
| ~ spl36_29
| ~ spl36_103 ),
inference(avatar_split_clause,[],[f1144,f1100,f671,f2532]) ).
tff(f2532,plain,
( spl36_212
<=> ! [X0: nat,X1: fun(dB,dB)] : ~ pp(aa(dB,bool,aa(fun(dB,dB),fun(dB,bool),aa(fun(dB,fun(dB,bool)),fun(fun(dB,dB),fun(dB,bool)),combs(dB,dB,bool),beta),X1),var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_212])]) ).
tff(f671,plain,
( spl36_29
<=> ! [X0: dB,X1: nat] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_29])]) ).
tff(f1144,plain,
( ! [X0: nat,X1: fun(dB,dB)] : ~ pp(aa(dB,bool,aa(fun(dB,dB),fun(dB,bool),aa(fun(dB,fun(dB,bool)),fun(fun(dB,dB),fun(dB,bool)),combs(dB,dB,bool),beta),X1),var(X0)))
| ~ spl36_29
| ~ spl36_103 ),
inference(superposition,[],[f672,f1101]) ).
tff(f672,plain,
( ! [X0: dB,X1: nat] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))
| ~ spl36_29 ),
inference(avatar_component_clause,[],[f671]) ).
tff(f2530,plain,
( spl36_211
| ~ spl36_23
| ~ spl36_87 ),
inference(avatar_split_clause,[],[f1011,f1000,f639,f2528]) ).
tff(f2528,plain,
( spl36_211
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_211])]) ).
tff(f639,plain,
( spl36_23
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_23])]) ).
tff(f1011,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0)))) )
| ~ spl36_23
| ~ spl36_87 ),
inference(resolution,[],[f1001,f640]) ).
tff(f640,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl36_23 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f2526,plain,
( spl36_210
| ~ spl36_38
| ~ spl36_85 ),
inference(avatar_split_clause,[],[f996,f986,f710,f2524]) ).
tff(f2524,plain,
( spl36_210
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_210])]) ).
tff(f986,plain,
( spl36_85
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_85])]) ).
tff(f996,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)))) )
| ~ spl36_38
| ~ spl36_85 ),
inference(resolution,[],[f987,f711]) ).
tff(f987,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) )
| ~ spl36_85 ),
inference(avatar_component_clause,[],[f986]) ).
tff(f2522,plain,
( spl36_209
| ~ spl36_8
| ~ spl36_198 ),
inference(avatar_split_clause,[],[f2475,f2423,f567,f2519]) ).
tff(f2519,plain,
( spl36_209
<=> sP1(abs(abs(abs(t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_209])]) ).
tff(f567,plain,
( spl36_8
<=> pp(aa(dB,bool,it,t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_8])]) ).
tff(f2475,plain,
( sP1(abs(abs(abs(t2))))
| ~ spl36_8
| ~ spl36_198 ),
inference(resolution,[],[f2424,f569]) ).
tff(f569,plain,
( pp(aa(dB,bool,it,t2))
| ~ spl36_8 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f2517,plain,
( spl36_208
| ~ spl36_69
| ~ spl36_83 ),
inference(avatar_split_clause,[],[f975,f968,f882,f2515]) ).
tff(f2515,plain,
( spl36_208
<=> ! [X3: dB,X4: dB,X0: nat,X5: dB,X2: nat,X1: dB] :
( ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( liftn(X0,X1,X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_208])]) ).
tff(f968,plain,
( spl36_83
<=> ! [X0: nat,X3: nat,X2: dB,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_83])]) ).
tff(f975,plain,
( ! [X2: nat,X3: dB,X0: nat,X1: dB,X4: dB,X5: dB] :
( ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( liftn(X0,X1,X2) = X4 ) )
| ~ spl36_69
| ~ spl36_83 ),
inference(superposition,[],[f883,f969]) ).
tff(f969,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) )
| ~ spl36_83 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f2513,plain,
( spl36_207
| ~ spl36_70
| ~ spl36_83 ),
inference(avatar_split_clause,[],[f973,f968,f886,f2511]) ).
tff(f2511,plain,
( spl36_207
<=> ! [X3: dB,X4: dB,X0: nat,X5: dB,X2: nat,X1: dB] :
( ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( liftn(X0,X3,X2) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_207])]) ).
tff(f973,plain,
( ! [X2: nat,X3: dB,X0: nat,X1: dB,X4: dB,X5: dB] :
( ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( liftn(X0,X3,X2) = X5 ) )
| ~ spl36_70
| ~ spl36_83 ),
inference(superposition,[],[f887,f969]) ).
tff(f2499,plain,
( spl36_206
| ~ spl36_15
| ~ spl36_87 ),
inference(avatar_split_clause,[],[f1012,f1000,f598,f2497]) ).
tff(f2497,plain,
( spl36_206
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_206])]) ).
tff(f598,plain,
( spl36_15
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_15])]) ).
tff(f1012,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))) )
| ~ spl36_15
| ~ spl36_87 ),
inference(resolution,[],[f1001,f599]) ).
tff(f599,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl36_15 ),
inference(avatar_component_clause,[],[f598]) ).
tff(f2495,plain,
( spl36_205
| ~ spl36_74 ),
inference(avatar_split_clause,[],[f924,f909,f2493]) ).
tff(f2493,plain,
( spl36_205
<=> ! [X0: $tType,X3: type,X4: fun(nat,X0),X5: fun(nat,X0),X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) = type_case(X0,X5,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_205])]) ).
tff(f924,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,X0)),X4: fun(nat,X0),X5: fun(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) = type_case(X0,X5,X1,aa(type,type,aa(type,fun(type,type),fun1,X2),X3)) )
| ~ spl36_74 ),
inference(superposition,[],[f910,f910]) ).
tff(f2489,plain,
( spl36_204
| ~ spl36_87
| ~ spl36_111 ),
inference(avatar_split_clause,[],[f1247,f1244,f1000,f2487]) ).
tff(f2487,plain,
( spl36_204
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,sK11(X0)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_204])]) ).
tff(f1247,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,sK11(X0)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)))
| ~ sP0(X0) )
| ~ spl36_87
| ~ spl36_111 ),
inference(resolution,[],[f1245,f1001]) ).
tff(f2484,plain,
( spl36_203
| ~ spl36_73
| ~ spl36_77 ),
inference(avatar_split_clause,[],[f941,f933,f905,f2482]) ).
tff(f2482,plain,
( spl36_203
<=> ! [X2: list(dB),X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X0),sK19(foldl(dB,dB,app,var(X0),X1),X2,X0)) )
| ~ step1(dB,beta,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_203])]) ).
tff(f941,plain,
( ! [X2: list(dB),X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X0),sK19(foldl(dB,dB,app,var(X0),X1),X2,X0)) )
| ~ step1(dB,beta,X2,X1) )
| ~ spl36_73
| ~ spl36_77 ),
inference(resolution,[],[f934,f906]) ).
tff(f2448,plain,
( spl36_202
| ~ spl36_23
| ~ spl36_82 ),
inference(avatar_split_clause,[],[f962,f959,f639,f2446]) ).
tff(f2446,plain,
( spl36_202
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),var(X1)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_202])]) ).
tff(f962,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),var(X1)),X2))) )
| ~ spl36_23
| ~ spl36_82 ),
inference(resolution,[],[f960,f640]) ).
tff(f2444,plain,
( spl36_201
| ~ spl36_38
| ~ spl36_72 ),
inference(avatar_split_clause,[],[f919,f901,f710,f2442]) ).
tff(f2442,plain,
( spl36_201
<=> ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X0)),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_201])]) ).
tff(f919,plain,
( ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X0)),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,X0))) )
| ~ spl36_38
| ~ spl36_72 ),
inference(resolution,[],[f902,f711]) ).
tff(f2440,plain,
( spl36_200
| ~ spl36_38
| ~ spl36_65 ),
inference(avatar_split_clause,[],[f890,f866,f710,f2438]) ).
tff(f2438,plain,
( spl36_200
<=> ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,abs(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_200])]) ).
tff(f866,plain,
( spl36_65
<=> ! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_65])]) ).
tff(f890,plain,
( ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,abs(X0)))) )
| ~ spl36_38
| ~ spl36_65 ),
inference(resolution,[],[f867,f711]) ).
tff(f867,plain,
( ! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)) )
| ~ spl36_65 ),
inference(avatar_component_clause,[],[f866]) ).
tff(f2432,plain,
( spl36_199
| ~ spl36_15
| ~ spl36_82 ),
inference(avatar_split_clause,[],[f963,f959,f598,f2430]) ).
tff(f2430,plain,
( spl36_199
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),var(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_199])]) ).
tff(f963,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X0),var(X1)),X2)) )
| ~ spl36_15
| ~ spl36_82 ),
inference(resolution,[],[f960,f599]) ).
tff(f2425,plain,
( spl36_198
| ~ spl36_28
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1759,f1755,f667,f2423]) ).
tff(f1755,plain,
( spl36_160
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_160])]) ).
tff(f1759,plain,
( ! [X0: dB] :
( sP1(abs(abs(abs(X0))))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl36_28
| ~ spl36_160 ),
inference(resolution,[],[f1756,f668]) ).
tff(f1756,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl36_160 ),
inference(avatar_component_clause,[],[f1755]) ).
tff(f2418,plain,
( spl36_197
| ~ spl36_38
| ~ spl36_96 ),
inference(avatar_split_clause,[],[f1062,f1055,f710,f2416]) ).
tff(f2416,plain,
( spl36_197
<=> ! [X0: dB,X1: dB] : pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_197])]) ).
tff(f1062,plain,
( ! [X0: dB,X1: dB] : pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X1))))
| ~ spl36_38
| ~ spl36_96 ),
inference(resolution,[],[f1056,f711]) ).
tff(f2414,plain,
( spl36_196
| ~ spl36_38
| ~ spl36_75 ),
inference(avatar_split_clause,[],[f927,f913,f710,f2412]) ).
tff(f2412,plain,
( spl36_196
<=> ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),var(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_196])]) ).
tff(f927,plain,
( ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),var(X1))))
| ~ spl36_38
| ~ spl36_75 ),
inference(resolution,[],[f914,f711]) ).
tff(f2410,plain,
( spl36_195
| ~ spl36_49
| ~ spl36_72 ),
inference(avatar_split_clause,[],[f917,f901,f778,f2408]) ).
tff(f2408,plain,
( spl36_195
<=> ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(abs(X0))),X1))
| ( sK13(X1,abs(X0)) = abs(sK13(sK13(X1,abs(X0)),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_195])]) ).
tff(f917,plain,
( ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(abs(X0))),X1))
| ( sK13(X1,abs(X0)) = abs(sK13(sK13(X1,abs(X0)),X0)) ) )
| ~ spl36_49
| ~ spl36_72 ),
inference(resolution,[],[f902,f779]) ).
tff(f2397,plain,
( spl36_194
| ~ spl36_58
| ~ spl36_96 ),
inference(avatar_split_clause,[],[f1063,f1055,f822,f2395]) ).
tff(f2395,plain,
( spl36_194
<=> ! [X0: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_194])]) ).
tff(f1063,plain,
( ! [X0: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(var(zero_zero(nat)))),X0)),X0))
| ~ spl36_58
| ~ spl36_96 ),
inference(superposition,[],[f1056,f823]) ).
tff(f2393,plain,
( spl36_193
| ~ spl36_38
| ~ spl36_73 ),
inference(avatar_split_clause,[],[f921,f905,f710,f2391]) ).
tff(f2391,plain,
( spl36_193
<=> ! [X2: dB,X0: list(dB),X1: list(dB)] :
( ~ step1(dB,beta,X0,X1)
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_193])]) ).
tff(f921,plain,
( ! [X2: dB,X0: list(dB),X1: list(dB)] :
( ~ step1(dB,beta,X0,X1)
| pp(aa(fun(dB,bool),bool,fEx(dB),aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)))) )
| ~ spl36_38
| ~ spl36_73 ),
inference(resolution,[],[f906,f711]) ).
tff(f2388,plain,
( spl36_192
| ~ spl36_38
| ~ spl36_56 ),
inference(avatar_split_clause,[],[f835,f813,f710,f2385]) ).
tff(f2385,plain,
( spl36_192
<=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_192])]) ).
tff(f835,plain,
( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u)))
| ~ spl36_38
| ~ spl36_56 ),
inference(resolution,[],[f815,f711]) ).
tff(f2383,plain,
( spl36_191
| ~ spl36_38
| ~ spl36_55 ),
inference(avatar_split_clause,[],[f834,f808,f710,f2380]) ).
tff(f2380,plain,
( spl36_191
<=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_191])]) ).
tff(f834,plain,
( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua)))
| ~ spl36_38
| ~ spl36_55 ),
inference(resolution,[],[f810,f711]) ).
tff(f2368,plain,
( spl36_190
| ~ spl36_37
| ~ spl36_110 ),
inference(avatar_split_clause,[],[f1233,f1227,f706,f2366]) ).
tff(f2366,plain,
( spl36_190
<=> ! [X2: dB,X0: dB,X1: nat,X3: nat] : ( var(X3) != aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_190])]) ).
tff(f1233,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: nat] : ( var(X3) != aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) )
| ~ spl36_37
| ~ spl36_110 ),
inference(superposition,[],[f707,f1228]) ).
tff(f2364,plain,
( spl36_189
| ~ spl36_36
| ~ spl36_110 ),
inference(avatar_split_clause,[],[f1232,f1227,f702,f2362]) ).
tff(f2362,plain,
( spl36_189
<=> ! [X2: dB,X0: dB,X1: nat,X3: dB] : ( abs(X3) != aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_189])]) ).
tff(f1232,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat] : ( abs(X3) != aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),X1) )
| ~ spl36_36
| ~ spl36_110 ),
inference(superposition,[],[f703,f1228]) ).
tff(f2354,plain,
( spl36_188
| ~ spl36_17
| ~ spl36_63 ),
inference(avatar_split_clause,[],[f863,f854,f606,f2352]) ).
tff(f2352,plain,
( spl36_188
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK31(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK31(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_188])]) ).
tff(f863,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK31(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK31(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl36_17
| ~ spl36_63 ),
inference(superposition,[],[f855,f607]) ).
tff(f2350,plain,
( spl36_187
| ~ spl36_17
| ~ spl36_63 ),
inference(avatar_split_clause,[],[f862,f854,f606,f2348]) ).
tff(f2348,plain,
( spl36_187
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK31(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK31(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_187])]) ).
tff(f862,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK31(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK31(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl36_17
| ~ spl36_63 ),
inference(superposition,[],[f855,f607]) ).
tff(f2346,plain,
( spl36_186
| ~ spl36_21
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1771,f1755,f631,f2344]) ).
tff(f2344,plain,
( spl36_186
<=> ! [X0: dB] :
( sP1(abs(abs(sK11(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_186])]) ).
tff(f1771,plain,
( ! [X0: dB] :
( sP1(abs(abs(sK11(X0))))
| ~ sP0(X0) )
| ~ spl36_21
| ~ spl36_160 ),
inference(resolution,[],[f1756,f632]) ).
tff(f2339,plain,
( spl36_185
| ~ spl36_81
| ~ spl36_82 ),
inference(avatar_split_clause,[],[f966,f959,f955,f2337]) ).
tff(f2337,plain,
( spl36_185
<=> ! [X0: dB,X1: nat] :
( pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_185])]) ).
tff(f966,plain,
( ! [X0: dB,X1: nat] :
( pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) )
| ~ spl36_81
| ~ spl36_82 ),
inference(superposition,[],[f960,f956]) ).
tff(f2324,plain,
( spl36_184
| ~ spl36_49
| ~ spl36_65 ),
inference(avatar_split_clause,[],[f889,f866,f778,f2322]) ).
tff(f2322,plain,
( spl36_184
<=> ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| ( abs(X1) = abs(sK13(abs(X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_184])]) ).
tff(f889,plain,
( ! [X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X0),X1))
| ( abs(X1) = abs(sK13(abs(X1),X0)) ) )
| ~ spl36_49
| ~ spl36_65 ),
inference(resolution,[],[f867,f779]) ).
tff(f2320,plain,
( spl36_183
| ~ spl36_23
| ~ spl36_61 ),
inference(avatar_split_clause,[],[f846,f843,f639,f2318]) ).
tff(f2318,plain,
( spl36_183
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),var(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_183])]) ).
tff(f843,plain,
( spl36_61
<=> ! [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,[spl36_61])]) ).
tff(f846,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),var(X1)))) )
| ~ spl36_23
| ~ spl36_61 ),
inference(resolution,[],[f844,f640]) ).
tff(f844,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)) )
| ~ spl36_61 ),
inference(avatar_component_clause,[],[f843]) ).
tff(f2311,plain,
( spl36_182
| ~ spl36_66
| ~ spl36_73 ),
inference(avatar_split_clause,[],[f920,f905,f870,f2309]) ).
tff(f2309,plain,
( spl36_182
<=> ! [X2: nat,X0: list(dB),X1: list(dB)] :
( ~ step1(dB,beta,X0,X1)
| step1(dB,beta,X0,sK19(foldl(dB,dB,app,var(X2),X1),X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_182])]) ).
tff(f920,plain,
( ! [X2: nat,X0: list(dB),X1: list(dB)] :
( ~ step1(dB,beta,X0,X1)
| step1(dB,beta,X0,sK19(foldl(dB,dB,app,var(X2),X1),X0,X2)) )
| ~ spl36_66
| ~ spl36_73 ),
inference(resolution,[],[f906,f871]) ).
tff(f2307,plain,
( spl36_181
| ~ spl36_15
| ~ spl36_61 ),
inference(avatar_split_clause,[],[f847,f843,f598,f2305]) ).
tff(f2305,plain,
( spl36_181
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),var(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_181])]) ).
tff(f847,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),var(X1))) )
| ~ spl36_15
| ~ spl36_61 ),
inference(resolution,[],[f844,f599]) ).
tff(f2303,plain,
( spl36_180
| ~ spl36_23
| ~ spl36_60 ),
inference(avatar_split_clause,[],[f839,f831,f639,f2301]) ).
tff(f2301,plain,
( spl36_180
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_180])]) ).
tff(f839,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1))) )
| ~ spl36_23
| ~ spl36_60 ),
inference(resolution,[],[f832,f640]) ).
tff(f2299,plain,
( spl36_179
| ~ spl36_23
| ~ spl36_57 ),
inference(avatar_split_clause,[],[f836,f818,f639,f2297]) ).
tff(f2297,plain,
( spl36_179
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK7(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_179])]) ).
tff(f818,plain,
( spl36_57
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_57])]) ).
tff(f836,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK7(X0))) )
| ~ spl36_23
| ~ spl36_57 ),
inference(resolution,[],[f819,f640]) ).
tff(f819,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl36_57 ),
inference(avatar_component_clause,[],[f818]) ).
tff(f2294,plain,
( spl36_178
| spl36_163
| ~ spl36_38
| ~ spl36_42 ),
inference(avatar_split_clause,[],[f756,f736,f710,f1782,f2292]) ).
tff(f2292,plain,
( spl36_178
<=> ! [X1: bool] :
( ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_178])]) ).
tff(f1782,plain,
( spl36_163
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_163])]) ).
tff(f756,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) )
| ~ spl36_38
| ~ spl36_42 ),
inference(resolution,[],[f737,f711]) ).
tff(f2287,plain,
( spl36_177
| ~ spl36_15
| ~ spl36_60 ),
inference(avatar_split_clause,[],[f840,f831,f598,f2285]) ).
tff(f2285,plain,
( spl36_177
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_177])]) ).
tff(f840,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(nat,dB,aa(dB,fun(nat,dB),lift,X0),X1)) )
| ~ spl36_15
| ~ spl36_60 ),
inference(resolution,[],[f832,f599]) ).
tff(f2283,plain,
( spl36_176
| ~ spl36_15
| ~ spl36_57 ),
inference(avatar_split_clause,[],[f837,f818,f598,f2281]) ).
tff(f2281,plain,
( spl36_176
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_176])]) ).
tff(f837,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK7(X0)) )
| ~ spl36_15
| ~ spl36_57 ),
inference(resolution,[],[f819,f599]) ).
tff(f2279,plain,
( spl36_175
| ~ spl36_16
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1758,f1755,f602,f2277]) ).
tff(f2277,plain,
( spl36_175
<=> ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_175])]) ).
tff(f1758,plain,
( ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) )
| ~ spl36_16
| ~ spl36_160 ),
inference(resolution,[],[f1756,f603]) ).
tff(f2265,plain,
( spl36_174
| ~ spl36_36
| ~ spl36_83 ),
inference(avatar_split_clause,[],[f978,f968,f702,f2263]) ).
tff(f2263,plain,
( spl36_174
<=> ! [X4: dB,X0: nat,X3: dB,X2: nat,X1: dB] : ( abs(X4) != liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_174])]) ).
tff(f978,plain,
( ! [X2: nat,X3: dB,X0: nat,X1: dB,X4: dB] : ( abs(X4) != liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) )
| ~ spl36_36
| ~ spl36_83 ),
inference(superposition,[],[f703,f969]) ).
tff(f2261,plain,
( spl36_173
| ~ spl36_37
| ~ spl36_83 ),
inference(avatar_split_clause,[],[f977,f968,f706,f2259]) ).
tff(f2259,plain,
( spl36_173
<=> ! [X4: nat,X0: nat,X3: dB,X2: nat,X1: dB] : ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != var(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_173])]) ).
tff(f977,plain,
( ! [X2: nat,X3: dB,X0: nat,X1: dB,X4: nat] : ( liftn(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X3),X2) != var(X4) )
| ~ spl36_37
| ~ spl36_83 ),
inference(superposition,[],[f707,f969]) ).
tff(f2256,plain,
( spl36_163
| spl36_172
| ~ spl36_32
| ~ spl36_38 ),
inference(avatar_split_clause,[],[f729,f710,f686,f2254,f1782]) ).
tff(f2254,plain,
( spl36_172
<=> ! [X0: bool] : pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fimplies,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_172])]) ).
tff(f729,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fimplies,X0)))
| ~ pp(X1) )
| ~ spl36_32
| ~ spl36_38 ),
inference(resolution,[],[f711,f687]) ).
tff(f2252,plain,
( spl36_171
| ~ spl36_33
| ~ spl36_38 ),
inference(avatar_split_clause,[],[f728,f710,f690,f2250]) ).
tff(f2250,plain,
( spl36_171
<=> ! [X0: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fimplies,X0)))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_171])]) ).
tff(f728,plain,
( ! [X0: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fimplies,X0)))
| pp(X0) )
| ~ spl36_33
| ~ spl36_38 ),
inference(resolution,[],[f711,f691]) ).
tff(f2245,plain,
( spl36_170
| ~ spl36_29
| ~ spl36_72 ),
inference(avatar_split_clause,[],[f916,f901,f671,f2243]) ).
tff(f2243,plain,
( spl36_170
<=> ! [X0: nat,X1: dB] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(var(X0))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_170])]) ).
tff(f916,plain,
( ! [X0: nat,X1: dB] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(var(X0))),X1))
| ~ spl36_29
| ~ spl36_72 ),
inference(resolution,[],[f902,f672]) ).
tff(f2239,plain,
( spl36_169
| ~ spl36_23
| ~ spl36_44 ),
inference(avatar_split_clause,[],[f759,f744,f639,f2237]) ).
tff(f2237,plain,
( spl36_169
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_169])]) ).
tff(f744,plain,
( spl36_44
<=> ! [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,[spl36_44])]) ).
tff(f759,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl36_23
| ~ spl36_44 ),
inference(resolution,[],[f745,f640]) ).
tff(f745,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl36_44 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f2235,plain,
( spl36_168
| ~ spl36_23
| ~ spl36_41 ),
inference(avatar_split_clause,[],[f751,f732,f639,f2233]) ).
tff(f2233,plain,
( spl36_168
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(abs(sK7(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_168])]) ).
tff(f732,plain,
( spl36_41
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_41])]) ).
tff(f751,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(abs(sK7(X0))) )
| ~ spl36_23
| ~ spl36_41 ),
inference(resolution,[],[f733,f640]) ).
tff(f733,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) )
| ~ spl36_41 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f2231,plain,
( spl36_167
| ~ spl36_15
| ~ spl36_41 ),
inference(avatar_split_clause,[],[f752,f732,f598,f2229]) ).
tff(f2229,plain,
( spl36_167
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_167])]) ).
tff(f752,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(sK7(X0)) )
| ~ spl36_15
| ~ spl36_41 ),
inference(resolution,[],[f733,f599]) ).
tff(f2209,plain,
( spl36_166
| ~ spl36_13
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1760,f1755,f590,f2207]) ).
tff(f2207,plain,
( spl36_166
<=> ! [X0: nat] : sP1(abs(abs(var(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_166])]) ).
tff(f1760,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl36_13
| ~ spl36_160 ),
inference(resolution,[],[f1756,f591]) ).
tff(f1850,plain,
( spl36_165
| ~ spl36_9
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1768,f1755,f572,f1847]) ).
tff(f1847,plain,
( spl36_165
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_165])]) ).
tff(f1768,plain,
( sP1(abs(abs(ua)))
| ~ spl36_9
| ~ spl36_160 ),
inference(resolution,[],[f1756,f574]) ).
tff(f1827,plain,
( spl36_164
| ~ spl36_10
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1767,f1755,f577,f1824]) ).
tff(f1824,plain,
( spl36_164
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_164])]) ).
tff(f1767,plain,
( sP1(abs(abs(u)))
| ~ spl36_10
| ~ spl36_160 ),
inference(resolution,[],[f1756,f579]) ).
tff(f1822,plain,
( ~ spl36_3
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1785]) ).
tff(f1785,plain,
( $false
| ~ spl36_3
| ~ spl36_163 ),
inference(resolution,[],[f1783,f546]) ).
tff(f546,plain,
( pp(fTrue)
| ~ spl36_3 ),
inference(avatar_component_clause,[],[f544]) ).
tff(f544,plain,
( spl36_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_3])]) ).
tff(f1783,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl36_163 ),
inference(avatar_component_clause,[],[f1782]) ).
tff(f1821,plain,
( ~ spl36_13
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1788]) ).
tff(f1788,plain,
( $false
| ~ spl36_13
| ~ spl36_163 ),
inference(resolution,[],[f1783,f591]) ).
tff(f1820,plain,
( ~ spl36_8
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1791]) ).
tff(f1791,plain,
( $false
| ~ spl36_8
| ~ spl36_163 ),
inference(resolution,[],[f1783,f569]) ).
tff(f1819,plain,
( ~ spl36_10
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1792]) ).
tff(f1792,plain,
( $false
| ~ spl36_10
| ~ spl36_163 ),
inference(resolution,[],[f1783,f579]) ).
tff(f1818,plain,
( ~ spl36_9
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1793]) ).
tff(f1793,plain,
( $false
| ~ spl36_9
| ~ spl36_163 ),
inference(resolution,[],[f1783,f574]) ).
tff(f1817,plain,
( ~ spl36_96
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1798]) ).
tff(f1798,plain,
( $false
| ~ spl36_96
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1056]) ).
tff(f1816,plain,
( ~ spl36_75
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1799]) ).
tff(f1799,plain,
( $false
| ~ spl36_75
| ~ spl36_163 ),
inference(resolution,[],[f1783,f914]) ).
tff(f1815,plain,
( ~ spl36_113
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1800]) ).
tff(f1800,plain,
( $false
| ~ spl36_113
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1260]) ).
tff(f1260,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1))
| ~ spl36_113 ),
inference(avatar_component_clause,[],[f1258]) ).
tff(f1258,plain,
( spl36_113
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_113])]) ).
tff(f1814,plain,
( ~ spl36_112
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1801]) ).
tff(f1801,plain,
( $false
| ~ spl36_112
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1255]) ).
tff(f1255,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a))
| ~ spl36_112 ),
inference(avatar_component_clause,[],[f1253]) ).
tff(f1253,plain,
( spl36_112
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_112])]) ).
tff(f1813,plain,
( ~ spl36_55
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1802]) ).
tff(f1802,plain,
( $false
| ~ spl36_55
| ~ spl36_163 ),
inference(resolution,[],[f1783,f810]) ).
tff(f1812,plain,
( ~ spl36_56
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1803]) ).
tff(f1803,plain,
( $false
| ~ spl36_56
| ~ spl36_163 ),
inference(resolution,[],[f1783,f815]) ).
tff(f1811,plain,
( ~ spl36_105
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1804]) ).
tff(f1804,plain,
( $false
| ~ spl36_105
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1200]) ).
tff(f1810,plain,
( ~ spl36_106
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1805]) ).
tff(f1805,plain,
( $false
| ~ spl36_106
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1205]) ).
tff(f1205,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK4))
| ~ spl36_106 ),
inference(avatar_component_clause,[],[f1203]) ).
tff(f1203,plain,
( spl36_106
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_106])]) ).
tff(f1809,plain,
( ~ spl36_108
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1806]) ).
tff(f1806,plain,
( $false
| ~ spl36_108
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1215]) ).
tff(f1215,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK6))
| ~ spl36_108 ),
inference(avatar_component_clause,[],[f1213]) ).
tff(f1213,plain,
( spl36_108
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_108])]) ).
tff(f1808,plain,
( ~ spl36_151
| ~ spl36_163 ),
inference(avatar_contradiction_clause,[],[f1807]) ).
tff(f1807,plain,
( $false
| ~ spl36_151
| ~ spl36_163 ),
inference(resolution,[],[f1783,f1683]) ).
tff(f1683,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl36_151 ),
inference(avatar_component_clause,[],[f1681]) ).
tff(f1681,plain,
( spl36_151
<=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_151])]) ).
tff(f1784,plain,
( spl36_162
| spl36_163
| ~ spl36_17
| ~ spl36_38 ),
inference(avatar_split_clause,[],[f730,f710,f606,f1782,f1778]) ).
tff(f1778,plain,
( spl36_162
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_162])]) ).
tff(f730,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl36_17
| ~ spl36_38 ),
inference(superposition,[],[f711,f607]) ).
tff(f1776,plain,
( spl36_161
| ~ spl36_8
| ~ spl36_160 ),
inference(avatar_split_clause,[],[f1766,f1755,f567,f1773]) ).
tff(f1773,plain,
( spl36_161
<=> sP1(abs(abs(t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_161])]) ).
tff(f1766,plain,
( sP1(abs(abs(t2)))
| ~ spl36_8
| ~ spl36_160 ),
inference(resolution,[],[f1756,f569]) ).
tff(f1757,plain,
( spl36_160
| ~ spl36_23
| ~ spl36_28 ),
inference(avatar_split_clause,[],[f674,f667,f639,f1755]) ).
tff(f674,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl36_23
| ~ spl36_28 ),
inference(resolution,[],[f668,f640]) ).
tff(f1753,plain,
( spl36_159
| ~ spl36_132
| ~ spl36_156 ),
inference(avatar_split_clause,[],[f1734,f1729,f1451,f1750]) ).
tff(f1750,plain,
( spl36_159
<=> listsp(dB,it,rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_159])]) ).
tff(f1451,plain,
( spl36_132
<=> ! [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,[spl36_132])]) ).
tff(f1729,plain,
( spl36_156
<=> listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst))))))))),rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_156])]) ).
tff(f1734,plain,
( listsp(dB,it,rs)
| ~ spl36_132
| ~ spl36_156 ),
inference(resolution,[],[f1731,f1452]) ).
tff(f1452,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,X2,X3) )
| ~ spl36_132 ),
inference(avatar_component_clause,[],[f1451]) ).
tff(f1731,plain,
( listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst))))))))),rs)
| ~ spl36_156 ),
inference(avatar_component_clause,[],[f1729]) ).
tff(f1744,plain,
spl36_158,
inference(avatar_split_clause,[],[f370,f1741]) ).
tff(f1741,plain,
( spl36_158
<=> listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_158])]) ).
tff(f370,plain,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),rs),
inference(cnf_transformation,[],[f76]) ).
tff(f76,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),rs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__096listsp_A_I_Ft_O_A_IALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_A_G_A_IEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_J_Ars_096) ).
tff(f1739,plain,
spl36_157,
inference(avatar_split_clause,[],[f369,f1736]) ).
tff(f1736,plain,
( spl36_157
<=> listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_157])]) ).
tff(f369,plain,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),as),
inference(cnf_transformation,[],[f72]) ).
tff(f72,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Cons_I2_J) ).
tff(f1732,plain,
spl36_156,
inference(avatar_split_clause,[],[f368,f1729]) ).
tff(f368,plain,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst))))))))),rs),
inference(cnf_transformation,[],[f73]) ).
tff(f73,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst))))))))),rs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Var_Ohyps) ).
tff(f1726,plain,
spl36_155,
inference(avatar_split_clause,[],[f367,f1723]) ).
tff(f1723,plain,
( spl36_155
<=> listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))),rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_155])]) ).
tff(f367,plain,
listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))),rs),
inference(cnf_transformation,[],[f74]) ).
tff(f74,axiom,
listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))),rs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73__096listsp_A_I_Ft_O_AALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_Ars_096) ).
tff(f1719,plain,
spl36_154,
inference(avatar_split_clause,[],[f508,f1717]) ).
tff(f1717,plain,
( spl36_154
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X0: dB,X6: type,X2: nat,X1: 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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_154])]) ).
tff(f508,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f268]) ).
tff(f268,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = 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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[],[f10]) ).
tff(f10,axiom,
! [X10: dB,X11: type,X12: nat,X13: fun(nat,type),X14: dB,X15: type,X16: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X16),X15) )
=> ( pp(aa(dB,bool,it,X14))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),X12),X16)),X14),X11))
=> ( pp(aa(dB,bool,it,X10))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X10),X16))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X14),X10),X12))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_MI1) ).
tff(f1715,plain,
spl36_153,
inference(avatar_split_clause,[],[f507,f1713]) ).
tff(f1713,plain,
( spl36_153
<=> ! [X3: fun(nat,type),X4: dB,X0: dB,X6: type,X5: type,X2: nat,X1: 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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_153])]) ).
tff(f507,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f266]) ).
tff(f266,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = 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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[],[f11]) ).
tff(f11,axiom,
! [X10: dB,X11: type,X12: nat,X13: fun(nat,type),X14: dB,X15: type,X16: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X16),X15) )
=> ( pp(aa(dB,bool,it,X14))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),X12),X15)),X14),X11))
=> ( pp(aa(dB,bool,it,X10))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X10),X15))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X14),X10),X12))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_MI2) ).
tff(f1710,plain,
spl36_152,
inference(avatar_split_clause,[],[f506,f1708]) ).
tff(f1708,plain,
( spl36_152
<=> ! [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,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),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,[spl36_152])]) ).
tff(f506,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,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),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,[],[f208]) ).
tff(f208,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,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),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,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X57: list(X2),X58: fun(X2,X1),X59: X0,X60: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X60,X59,map(X2,X1,X58,X57)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),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)),X60)),X58),X59,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_foldl__map) ).
tff(f1684,plain,
( spl36_151
| ~ spl36_13
| ~ spl36_38 ),
inference(avatar_split_clause,[],[f723,f710,f590,f1681]) ).
tff(f723,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl36_13
| ~ spl36_38 ),
inference(resolution,[],[f711,f591]) ).
tff(f1679,plain,
spl36_150,
inference(avatar_split_clause,[],[f532,f1677]) ).
tff(f1677,plain,
( spl36_150
<=> ! [X3: fun(nat,type),X4: type,X0: nat,X5: dB,X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1)),X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_150])]) ).
tff(f532,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1)),X5),X4)) ),
inference(equality_resolution,[],[f509]) ).
tff(f509,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),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,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),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(flattening,[],[f270]) ).
tff(f270,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),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
=> ( ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[],[f17]) ).
tff(f17,axiom,
! [X12: nat,X22: type,X10: dB,X23: fun(nat,type),X11: type,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),X11))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X23),X10),X22))
=> ( ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X23),X12),X22) = X13 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X23),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X14),X10),X12)),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subst__lemma) ).
tff(f1675,plain,
spl36_149,
inference(avatar_split_clause,[],[f504,f1673]) ).
tff(f1673,plain,
( spl36_149
<=> ! [X3: type,X4: dB,X0: list(type),X5: fun(nat,type),X2: nat,X1: list(dB)] :
( typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1),X0)
| ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_149])]) ).
tff(f504,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1),X0)
| ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1),X0)
| ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(flattening,[],[f263]) ).
tff(f263,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1),X0)
| ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3))
=> ( typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1,X0)
=> typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1),X0) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X32: list(type),X33: list(dB),X12: nat,X11: type,X10: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X10),X11))
=> ( typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),X12),X11),X33,X32)
=> typings(X13,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X10)),X12),X33),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_substs__lemma) ).
tff(f1650,plain,
spl36_148,
inference(avatar_split_clause,[],[f465,f1648]) ).
tff(f1648,plain,
( spl36_148
<=> ! [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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_148])]) ).
tff(f465,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X12: nat,X10: dB,X33: list(dB),X14: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X14,X33)),X10),X12) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X14),X10),X12),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X10)),X12),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_subst__map) ).
tff(f1639,plain,
spl36_147,
inference(avatar_split_clause,[],[f371,f1637]) ).
tff(f371,plain,
! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK4))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f214,f281]) ).
tff(f281,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK4)) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(flattening,[],[f213]) ).
tff(f213,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2))
=> ( pp(aa(dB,bool,it,X3))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4))) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
( ? [X8: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X8))
& ! [X4: fun(nat,type),X5: type,X6: dB,X7: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X7),t)),a),X5))
=> ( pp(aa(dB,bool,it,X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X6),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X6),X7))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Cons_I1_J) ).
tff(f1595,plain,
spl36_146,
inference(avatar_split_clause,[],[f505,f1593]) ).
tff(f1593,plain,
( spl36_146
<=> ! [X1: $tType,X0: $tType,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0)),X2: X1] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK32(X0,X1,X5))),sK33(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK33(X0,X1,X5))),sK32(X0,X1,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_146])]) ).
tff(f505,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK32(X0,X1,X5))),sK33(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK33(X0,X1,X5))),sK32(X0,X1,X5)) ) ),
inference(cnf_transformation,[],[f348]) ).
tff(f348,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK32(X0,X1,X5))),sK33(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK33(X0,X1,X5))),sK32(X0,X1,X5)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34])],[f265,f347]) ).
tff(f347,plain,
! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X0))] :
( ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK32(X0,X1,X5))),sK33(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK34(X0,X1,X5)),sK33(X0,X1,X5))),sK32(X0,X1,X5)) ) ),
introduced(choice_axiom,[]) ).
tff(f265,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) ) ),
inference(ennf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ! [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) = aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X1: $tType,X0: $tType,X29: X0,X57: list(X0),X50: X1,X58: fun(X1,fun(X0,X1))] :
( ! [X73: X0,X79: X0,X76: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),X58,aa(X0,X1,aa(X1,fun(X0,X1),X58,X76),X73)),X79) = aa(X0,X1,aa(X1,fun(X0,X1),X58,aa(X0,X1,aa(X1,fun(X0,X1),X58,X76),X79)),X73) )
=> ( aa(X0,X1,aa(X1,fun(X0,X1),X58,foldl(X1,X0,X58,X50,X57)),X29) = foldl(X1,X0,X58,aa(X0,X1,aa(X1,fun(X0,X1),X58,X50),X29),X57) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_foldl__fun__comm) ).
tff(f1587,plain,
spl36_145,
inference(avatar_split_clause,[],[f500,f1585]) ).
tff(f1585,plain,
( spl36_145
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_145])]) ).
tff(f500,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X14: dB,X22: type,X11: type,X50: dB,X30: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X30),X50),aa(type,type,aa(type,fun(type,type),fun1,X11),X22)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X30),X14),X11))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X30),aa(dB,dB,aa(dB,fun(dB,dB),app,X50),X14)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_App) ).
tff(f1573,plain,
spl36_144,
inference(avatar_split_clause,[],[f477,f1571]) ).
tff(f1571,plain,
( spl36_144
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_144])]) ).
tff(f477,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X22: type,X14: dB,X11: type,X30: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X30),zero_zero(nat)),X11)),X14),X22))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X30),abs(X14)),aa(type,type,aa(type,fun(type,type),fun1,X11),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Abs) ).
tff(f1562,plain,
spl36_143,
inference(avatar_split_clause,[],[f497,f1560]) ).
tff(f1560,plain,
( spl36_143
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_143])]) ).
tff(f497,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X22: type,X12: nat,X11: type,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),X11))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),X12),X22)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X14),X12)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lift__type) ).
tff(f1546,plain,
spl36_142,
inference(avatar_split_clause,[],[f455,f1544]) ).
tff(f1544,plain,
( spl36_142
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK25(X0,X1,X2))),X1),sK26(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_142])]) ).
tff(f455,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK25(X0,X1,X2))),X1),sK26(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK25(X0,X1,X2))),X1),sK26(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f239,f324]) ).
tff(f324,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK25(X0,X1,X2))),X1),sK26(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f239,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4)) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X11: type,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),abs(X14)),X11))
=> ~ ! [X61: type,X9: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X61),X9) = X11 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),zero_zero(nat)),X61)),X14),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_typing__elims_I3_J) ).
tff(f1510,plain,
spl36_141,
inference(avatar_split_clause,[],[f510,f1508]) ).
tff(f1508,plain,
( spl36_141
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( ( foldr(type,type,fun1,sK35(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_141])]) ).
tff(f510,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK35(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f350]) ).
tff(f350,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ( typings(X6,X3,sK35(X0,X2,X3,X6))
& ( foldr(type,type,fun1,sK35(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[sK35])],[f273,f349]) ).
tff(f349,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
=> ( typings(X6,X3,sK35(X0,X2,X3,X6))
& ( foldr(type,type,fun1,sK35(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f273,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f272]) ).
tff(f272,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f212]) ).
tff(f212,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( typings(X6,X4,X1)
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X22: type,X32: list(type),X11: type,X65: list(dB),X33: list(dB),X12: nat,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,foldl(dB,dB,app,var(X12),X33),X65)),X11))
=> ( typings(X13,X33,X32)
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,var(X12),X33)),X22))
=> ? [X66: list(type)] :
( typings(X13,X65,X66)
& ( foldr(type,type,fun1,X66,X11) = X22 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_var__app__types) ).
tff(f1506,plain,
( spl36_140
| ~ spl36_21
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f648,f639,f631,f1504]) ).
tff(f1504,plain,
( spl36_140
<=> ! [X0: dB] :
( sP1(abs(sK11(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_140])]) ).
tff(f648,plain,
( ! [X0: dB] :
( sP1(abs(sK11(X0)))
| ~ sP0(X0) )
| ~ spl36_21
| ~ spl36_23 ),
inference(resolution,[],[f640,f632]) ).
tff(f1502,plain,
spl36_139,
inference(avatar_split_clause,[],[f464,f1500]) ).
tff(f464,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,[],[f180]) ).
tff(f180,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,[],[f37]) ).
tff(f37,axiom,
! [X42: nat,X41: dB,X49: dB,X20: 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,X20),X49)),X41),X42) = 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,X20),X41),X42)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X49),X41),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_subst__App) ).
tff(f1498,plain,
spl36_138,
inference(avatar_split_clause,[],[f453,f1496]) ).
tff(f1496,plain,
( spl36_138
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK23(X1,X2))),X1),sK24(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_138])]) ).
tff(f453,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK23(X1,X2))),X1),sK24(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK23(X1,X2))),X1),sK24(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f238,f322]) ).
tff(f322,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK23(X1,X2))),X1),sK24(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f238,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4)) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X11: type,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),abs(X14)),X11))
=> ~ ! [X9: type,X67: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),zero_zero(nat)),X9)),X14),X67)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_abs__typeE) ).
tff(f1490,plain,
spl36_137,
inference(avatar_split_clause,[],[f511,f1488]) ).
tff(f1488,plain,
( spl36_137
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( typings(X6,X3,sK35(X0,X2,X3,X6))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_137])]) ).
tff(f511,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( typings(X6,X3,sK35(X0,X2,X3,X6))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ typings(X6,X4,X1)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f350]) ).
tff(f1486,plain,
spl36_136,
inference(avatar_split_clause,[],[f366,f1483]) ).
tff(f1483,plain,
( spl36_136
<=> 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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_136])]) ).
tff(f366,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),rs),
inference(cnf_transformation,[],[f28]) ).
tff(f28,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),rs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Ars_096) ).
tff(f1468,plain,
spl36_135,
inference(avatar_split_clause,[],[f493,f1466]) ).
tff(f1466,plain,
( spl36_135
<=> ! [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,[spl36_135])]) ).
tff(f493,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,[],[f346]) ).
tff(f346,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,[],[f345]) ).
tff(f345,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,[],[f195]) ).
tff(f195,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,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X34: fun(X0,bool),X35: fun(X0,bool),X36: 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),X35)),X34),X36)
<=> ( listsp(X0,X34,X36)
& listsp(X0,X35,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_listsp__conj__eq) ).
tff(f1464,plain,
spl36_134,
inference(avatar_split_clause,[],[f474,f1462]) ).
tff(f1462,plain,
( spl36_134
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_134])]) ).
tff(f474,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK30(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[sK30])],[f249,f333]) ).
tff(f333,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK30(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK30(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f249,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4)) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X11: type,X10: dB,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),aa(dB,dB,aa(dB,fun(dB,dB),app,X14),X10)),X11))
=> ~ ! [X61: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),aa(type,type,aa(type,fun(type,type),fun1,X61),X11)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X10),X61)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_typing__elims_I2_J) ).
tff(f1457,plain,
spl36_133,
inference(avatar_split_clause,[],[f492,f1455]) ).
tff(f1455,plain,
( spl36_133
<=> ! [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,[spl36_133])]) ).
tff(f492,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,[],[f346]) ).
tff(f1453,plain,
spl36_132,
inference(avatar_split_clause,[],[f491,f1451]) ).
tff(f491,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,[],[f346]) ).
tff(f1433,plain,
spl36_131,
inference(avatar_split_clause,[],[f496,f1431]) ).
tff(f1431,plain,
( spl36_131
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3),X2)
| ~ typings(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_131])]) ).
tff(f496,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3),X2)
| ~ typings(X4,X3,X2) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3),X2)
| ~ typings(X4,X3,X2) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( typings(X4,X3,X2)
=> typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3),X2) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X22: type,X12: nat,X32: list(type),X33: list(dB),X13: fun(nat,type)] :
( typings(X13,X33,X32)
=> typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X13),X12),X22),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X12),X33),X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lift__types) ).
tff(f1429,plain,
spl36_130,
inference(avatar_split_clause,[],[f472,f1427]) ).
tff(f472,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( typings(X3,X1,sK29(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f248,f331]) ).
tff(f331,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
=> ( typings(X3,X1,sK29(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK29(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f248,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0)))
=> ~ typings(X3,X1,X4) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X11: type,X33: list(dB),X12: nat,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,var(X12),X33)),X11))
=> ~ ! [X24: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),var(X12)),foldr(type,type,fun1,X24,X11)))
=> ~ typings(X13,X33,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_var__app__typesE) ).
tff(f1425,plain,
spl36_129,
inference(avatar_split_clause,[],[f466,f1423]) ).
tff(f466,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,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)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,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)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2)) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X3),X2))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,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,[],[f85]) ).
tff(f85,axiom,
! [X18: nat,X20: dB,X41: dB,X19: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X19),X41))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X19),X20),X18)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X41),X20),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_subst__preserves__beta) ).
tff(f1415,plain,
spl36_128,
inference(avatar_split_clause,[],[f499,f1413]) ).
tff(f1413,plain,
( spl36_128
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_128])]) ).
tff(f499,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f259]) ).
tff(f259,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X22: type,X11: type,X33: list(dB),X12: nat,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,var(X12),X33)),X11))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,var(X12),X33)),X22))
=> ( X11 = X22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_var__app__type__eq) ).
tff(f1360,plain,
( spl36_127
| ~ spl36_16
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f643,f639,f602,f1358]) ).
tff(f1358,plain,
( spl36_127
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_127])]) ).
tff(f643,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl36_16
| ~ spl36_23 ),
inference(resolution,[],[f640,f603]) ).
tff(f1356,plain,
spl36_126,
inference(avatar_split_clause,[],[f498,f1354]) ).
tff(f1354,plain,
( spl36_126
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ typings(X4,X0,X2)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_126])]) ).
tff(f498,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ typings(X4,X0,X2)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ typings(X4,X0,X2)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ typings(X4,X0,X2)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1)))
=> ( typings(X4,X0,X2)
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X33: list(dB),X11: type,X32: list(type),X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),foldr(type,type,fun1,X32,X11)))
=> ( typings(X13,X33,X32)
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,X14,X33)),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_list__app__typeI) ).
tff(f1352,plain,
spl36_125,
inference(avatar_split_clause,[],[f475,f1350]) ).
tff(f1350,plain,
( spl36_125
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK30(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_125])]) ).
tff(f475,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK30(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f334]) ).
tff(f1348,plain,
spl36_124,
inference(avatar_split_clause,[],[f470,f1346]) ).
tff(f470,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( typings(X3,X1,sK28(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f247,f329]) ).
tff(f329,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( typings(X3,X1,sK28(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK28(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f247,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X11: type,X33: list(dB),X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,X14,X33)),X11))
=> ? [X24: list(type)] :
( typings(X13,X33,X24)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),foldr(type,type,fun1,X24,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_list__app__typeD) ).
tff(f1344,plain,
spl36_123,
inference(avatar_split_clause,[],[f468,f1342]) ).
tff(f468,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( typings(X3,X1,sK27(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f246,f327]) ).
tff(f327,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( typings(X3,X1,sK27(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK27(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f246,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0)))
=> ~ typings(X3,X1,X4) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X11: type,X33: list(dB),X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),foldl(dB,dB,app,X14,X33)),X11))
=> ~ ! [X24: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),foldr(type,type,fun1,X24,X11)))
=> ~ typings(X13,X33,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_list__app__typeE) ).
tff(f1340,plain,
spl36_122,
inference(avatar_split_clause,[],[f457,f1338]) ).
tff(f457,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,[],[f242]) ).
tff(f242,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,[],[f241]) ).
tff(f241,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,[],[f174]) ).
tff(f174,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,[],[f61]) ).
tff(f61,axiom,
! [X62: list(dB),X50: dB,X63: 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,X63),X50),zero_zero(nat)),X62)))
=> ( pp(aa(dB,bool,it,X50))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X63)),X50),X62))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Beta) ).
tff(f1336,plain,
spl36_121,
inference(avatar_split_clause,[],[f449,f1334]) ).
tff(f1334,plain,
( spl36_121
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_121])]) ).
tff(f449,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 ) )
| ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 ) )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f318,f320,f319]) ).
tff(f319,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X3))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0 ) )
=> ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f320,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
=> ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f318,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X3))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(rectify,[],[f280]) ).
tff(f280,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(definition_folding,[],[f237,f279]) ).
tff(f279,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP3(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f237,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(flattening,[],[f236]) ).
tff(f236,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: dB,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))
=> ( ! [X3: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 )
=> ( abs(X3) != X2 ) )
=> ( ! [X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) )
=> ~ ! [X5: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X5)) ) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X49: dB,X20: dB,X41: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X20)),X49))
=> ( ! [X76: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X76),X20),zero_zero(nat)) = X49 )
=> ( abs(X76) != X41 ) )
=> ( ! [X75: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X75),X20) = X49 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X41),X75)) )
=> ~ ! [X75: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X75) = X49 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X20),X75)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_beta__cases_I3_J) ).
tff(f1332,plain,
spl36_120,
inference(avatar_split_clause,[],[f427,f1330]) ).
tff(f1330,plain,
( spl36_120
<=> ! [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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_120])]) ).
tff(f427,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X12: nat,X33: list(dB),X14: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X14,X33)),X12) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X14),X12),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X12),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_lift__map) ).
tff(f1328,plain,
spl36_119,
inference(avatar_split_clause,[],[f365,f1325]) ).
tff(f1325,plain,
( spl36_119
<=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_119])]) ).
tff(f365,plain,
listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),as)),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Cons_I3_J) ).
tff(f1307,plain,
( spl36_118
| ~ spl36_15
| ~ spl36_21 ),
inference(avatar_split_clause,[],[f642,f631,f598,f1305]) ).
tff(f1305,plain,
( spl36_118
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_118])]) ).
tff(f642,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK11(X0)) )
| ~ spl36_15
| ~ spl36_21 ),
inference(resolution,[],[f632,f599]) ).
tff(f1303,plain,
spl36_117,
inference(avatar_split_clause,[],[f451,f1301]) ).
tff(f1301,plain,
( spl36_117
<=> ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_117])]) ).
tff(f451,plain,
! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f1299,plain,
spl36_116,
inference(avatar_split_clause,[],[f450,f1297]) ).
tff(f1297,plain,
( spl36_116
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_116])]) ).
tff(f450,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f1277,plain,
spl36_115,
inference(avatar_split_clause,[],[f467,f1275]) ).
tff(f467,plain,
! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1)) ),
inference(flattening,[],[f244]) ).
tff(f244,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1)) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
=> ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X1)) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X74: dB,X11: type,X14: dB,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X14),X11))
=> ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X14),X74))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),X74),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subject__reduction) ).
tff(f1273,plain,
spl36_114,
inference(avatar_split_clause,[],[f452,f1271]) ).
tff(f1271,plain,
( spl36_114
<=> ! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_114])]) ).
tff(f452,plain,
! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK21(X0,X1,X2)))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK22(X0,X1,X2)))
| sP3(X2,X0,X1)
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f1261,plain,
spl36_113,
inference(avatar_split_clause,[],[f364,f1258]) ).
tff(f364,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_nT) ).
tff(f1256,plain,
spl36_112,
inference(avatar_split_clause,[],[f363,f1253]) ).
tff(f363,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Var_I2_J) ).
tff(f1246,plain,
spl36_111,
inference(avatar_split_clause,[],[f518,f1244]) ).
tff(f518,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,[],[f392]) ).
tff(f392,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,[],[f297]) ).
tff(f297,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,sK11(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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f295,f296]) ).
tff(f296,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,sK11(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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f295,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,[],[f294]) ).
tff(f294,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,[],[f274]) ).
tff(f274,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(f1229,plain,
spl36_110,
inference(avatar_split_clause,[],[f426,f1227]) ).
tff(f426,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,[],[f156]) ).
tff(f156,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,[],[f38]) ).
tff(f38,axiom,
! [X42: nat,X20: dB,X41: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X20)),X42) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X41),X42)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X20),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_lift_Osimps_I2_J) ).
tff(f1223,plain,
spl36_109,
inference(avatar_split_clause,[],[f430,f1221]) ).
tff(f1221,plain,
( spl36_109
<=> ! [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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ typings(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_109])]) ).
tff(f430,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ typings(X2,X1,X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ typings(X2,X1,X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( 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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X32: list(type),X33: list(dB),X13: fun(nat,type)] :
( typings(X13,X33,X32)
=> 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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lists__typings) ).
tff(f1216,plain,
spl36_108,
inference(avatar_split_clause,[],[f374,f1213]) ).
tff(f374,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK6)),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK6)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f216,f285]) ).
tff(f285,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK6)) ),
introduced(choice_axiom,[]) ).
tff(f216,plain,
? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)),
inference(ennf_transformation,[],[f120]) ).
tff(f120,plain,
~ ! [X0: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
~ ! [X9: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1211,plain,
( ~ spl36_107
| spl36_7
| ~ spl36_16 ),
inference(avatar_split_clause,[],[f626,f602,f562,f1208]) ).
tff(f1208,plain,
( spl36_107
<=> sP1(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,[spl36_107])]) ).
tff(f626,plain,
( ~ sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))
| spl36_7
| ~ spl36_16 ),
inference(resolution,[],[f603,f564]) ).
tff(f1206,plain,
spl36_106,
inference(avatar_split_clause,[],[f372,f1203]) ).
tff(f372,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK4)),
inference(cnf_transformation,[],[f282]) ).
tff(f1201,plain,
spl36_105,
inference(avatar_split_clause,[],[f362,f1198]) ).
tff(f362,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),ua1)),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),ua1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AU_096) ).
tff(f1192,plain,
spl36_104,
inference(avatar_split_clause,[],[f443,f1190]) ).
tff(f1190,plain,
( spl36_104
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_104])]) ).
tff(f443,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( sP2(X0,X1,X2)
| ( ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
& step1(dB,beta,X1,sK17(X0,X1,X2)) )
| ( ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2))) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f308,f310,f309]) ).
tff(f309,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X3: list(dB)] :
( ( foldl(dB,dB,app,X2,X3) = X0 )
& step1(dB,beta,X1,X3) )
=> ( ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
& step1(dB,beta,X1,sK17(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f310,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X4: dB] :
( ( foldl(dB,dB,app,X4,X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) )
=> ( ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f308,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( sP2(X0,X1,X2)
| ? [X3: list(dB)] :
( ( foldl(dB,dB,app,X2,X3) = X0 )
& step1(dB,beta,X1,X3) )
| ? [X4: dB] :
( ( foldl(dB,dB,app,X4,X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X4)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(rectify,[],[f278]) ).
tff(f278,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( sP2(X0,X1,X2)
| ? [X4: list(dB)] :
( ( foldl(dB,dB,app,X2,X4) = X0 )
& step1(dB,beta,X1,X4) )
| ? [X3: dB] :
( ( foldl(dB,dB,app,X3,X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(definition_folding,[],[f234,f277]) ).
tff(f277,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X5: dB] :
( ? [X6: dB,X7: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),zero_zero(nat)),X7) = X0 )
& ( cons(dB,X6,X7) = X1 ) )
& ( abs(X5) = X2 ) )
| ~ sP2(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f234,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X5: dB] :
( ? [X6: dB,X7: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),zero_zero(nat)),X7) = X0 )
& ( cons(dB,X6,X7) = X1 ) )
& ( abs(X5) = X2 ) )
| ? [X4: list(dB)] :
( ( foldl(dB,dB,app,X2,X4) = X0 )
& step1(dB,beta,X1,X4) )
| ? [X3: dB] :
( ( foldl(dB,dB,app,X3,X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X5: dB] :
( ? [X6: dB,X7: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),zero_zero(nat)),X7) = X0 )
& ( cons(dB,X6,X7) = X1 ) )
& ( abs(X5) = X2 ) )
| ? [X4: list(dB)] :
( ( foldl(dB,dB,app,X2,X4) = X0 )
& step1(dB,beta,X1,X4) )
| ? [X3: dB] :
( ( foldl(dB,dB,app,X3,X1) = X0 )
& pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))
=> ( ! [X3: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X3))
=> ( foldl(dB,dB,app,X3,X1) != X0 ) )
=> ( ! [X4: list(dB)] :
( step1(dB,beta,X1,X4)
=> ( foldl(dB,dB,app,X2,X4) != X0 ) )
=> ~ ! [X5: dB] :
( ( abs(X5) = X2 )
=> ! [X6: dB,X7: list(dB)] :
( ( cons(dB,X6,X7) = X1 )
=> ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),zero_zero(nat)),X7) != X0 ) ) ) ) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X50: dB,X52: list(dB),X63: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X63,X52)),X50))
=> ( ! [X82: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X63),X82))
=> ( foldl(dB,dB,app,X82,X52) != X50 ) )
=> ( ! [X83: list(dB)] :
( step1(dB,beta,X52,X83)
=> ( foldl(dB,dB,app,X63,X83) != X50 ) )
=> ~ ! [X75: dB] :
( ( abs(X75) = X63 )
=> ! [X84: dB,X85: list(dB)] :
( ( cons(dB,X84,X85) = X52 )
=> ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X75),X84),zero_zero(nat)),X85) != X50 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_apps__betasE) ).
tff(f1102,plain,
spl36_103,
inference(avatar_split_clause,[],[f503,f1100]) ).
tff(f503,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,[],[f205]) ).
tff(f205,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,[],[f108]) ).
tff(f108,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X88: X0,X89: fun(X0,X1),X87: 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),X87),X89),X88) = aa(X1,X2,aa(X0,fun(X1,X2),X87,X88),aa(X0,X1,X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1087,plain,
spl36_102,
inference(avatar_split_clause,[],[f441,f1085]) ).
tff(f441,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| step1(dB,beta,X1,sK17(X0,X1,X2))
| pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK18(X0,X1,X2)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f1083,plain,
spl36_101,
inference(avatar_split_clause,[],[f437,f1081]) ).
tff(f437,plain,
! [X2: dB,X0: nat,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: nat,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X18: nat,X41: dB,X19: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X19),X41))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(nat,dB,aa(dB,fun(nat,dB),lift,X19),X18)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X41),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_lift__preserves__beta) ).
tff(f1079,plain,
spl36_100,
inference(avatar_split_clause,[],[f436,f1077]) ).
tff(f436,plain,
! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: dB,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: dB,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0)),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X49: dB,X20: dB,X41: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X41),X20))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X49)),aa(dB,dB,aa(dB,fun(dB,dB),app,X20),X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_appL) ).
tff(f1075,plain,
spl36_99,
inference(avatar_split_clause,[],[f435,f1073]) ).
tff(f435,plain,
! [X2: dB,X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: dB,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: dB,X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2)),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X49: dB,X20: dB,X41: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X41),X20))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X49),X41)),aa(dB,dB,aa(dB,fun(dB,dB),app,X49),X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_appR) ).
tff(f1068,plain,
spl36_98,
inference(avatar_split_clause,[],[f444,f1066]) ).
tff(f1066,plain,
( spl36_98
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
| ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_98])]) ).
tff(f444,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| ( foldl(dB,dB,app,X2,sK17(X0,X1,X2)) = X0 )
| ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f1061,plain,
spl36_97,
inference(avatar_split_clause,[],[f454,f1059]) ).
tff(f1059,plain,
( spl36_97
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_97])]) ).
tff(f454,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1057,plain,
spl36_96,
inference(avatar_split_clause,[],[f403,f1055]) ).
tff(f403,plain,
! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X20: dB,X41: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X41)),X20)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X41),X20),zero_zero(nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_beta) ).
tff(f1053,plain,
( spl36_95
| ~ spl36_13
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f644,f639,f590,f1051]) ).
tff(f1051,plain,
( spl36_95
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_95])]) ).
tff(f644,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl36_13
| ~ spl36_23 ),
inference(resolution,[],[f640,f591]) ).
tff(f1046,plain,
spl36_94,
inference(avatar_split_clause,[],[f442,f1044]) ).
tff(f442,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( sP2(X0,X1,X2)
| step1(dB,beta,X1,sK17(X0,X1,X2))
| ( foldl(dB,dB,app,sK18(X0,X1,X2),X1) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f1042,plain,
spl36_93,
inference(avatar_split_clause,[],[f440,f1040]) ).
tff(f1040,plain,
( spl36_93
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),sK15(X0,X1,X2)),zero_zero(nat)),sK16(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_93])]) ).
tff(f440,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),sK15(X0,X1,X2)),zero_zero(nat)),sK16(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),sK15(X0,X1,X2)),zero_zero(nat)),sK16(X0,X1,X2)) = X0 )
& ( cons(dB,sK15(X0,X1,X2),sK16(X0,X1,X2)) = X1 )
& ( abs(sK14(X0,X1,X2)) = X2 ) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f304,f306,f305]) ).
tff(f305,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X3: dB] :
( ? [X4: dB,X5: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X4),zero_zero(nat)),X5) = X0 )
& ( cons(dB,X4,X5) = X1 ) )
& ( abs(X3) = X2 ) )
=> ( ? [X5: list(dB),X4: dB] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),X4),zero_zero(nat)),X5) = X0 )
& ( cons(dB,X4,X5) = X1 ) )
& ( abs(sK14(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f306,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X5: list(dB),X4: dB] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),X4),zero_zero(nat)),X5) = X0 )
& ( cons(dB,X4,X5) = X1 ) )
=> ( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK14(X0,X1,X2)),sK15(X0,X1,X2)),zero_zero(nat)),sK16(X0,X1,X2)) = X0 )
& ( cons(dB,sK15(X0,X1,X2),sK16(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f304,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X3: dB] :
( ? [X4: dB,X5: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X4),zero_zero(nat)),X5) = X0 )
& ( cons(dB,X4,X5) = X1 ) )
& ( abs(X3) = X2 ) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f303]) ).
tff(f303,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ? [X5: dB] :
( ? [X6: dB,X7: list(dB)] :
( ( foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),zero_zero(nat)),X7) = X0 )
& ( cons(dB,X6,X7) = X1 ) )
& ( abs(X5) = X2 ) )
| ~ sP2(X0,X1,X2) ),
inference(nnf_transformation,[],[f277]) ).
tff(f1026,plain,
spl36_92,
inference(avatar_split_clause,[],[f502,f1024]) ).
tff(f502,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,[],[f204]) ).
tff(f204,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,[],[f105]) ).
tff(f105,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X88: X0,X89: fun(X0,X1),X87: 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),X87),X89),X88) = aa(X1,X2,X87,aa(X0,X1,X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1022,plain,
spl36_91,
inference(avatar_split_clause,[],[f501,f1020]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X88: X0,X89: X1,X87: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X87),X89),X88) = aa(X1,X2,aa(X0,fun(X1,X2),X87,X88),X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1018,plain,
spl36_90,
inference(avatar_split_clause,[],[f473,f1016]) ).
tff(f1016,plain,
( spl36_90
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( typings(X3,X1,sK29(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_90])]) ).
tff(f473,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typings(X3,X1,sK29(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f332]) ).
tff(f1010,plain,
spl36_89,
inference(avatar_split_clause,[],[f471,f1008]) ).
tff(f1008,plain,
( spl36_89
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( typings(X3,X1,sK28(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_89])]) ).
tff(f471,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typings(X3,X1,sK28(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f330]) ).
tff(f1006,plain,
spl36_88,
inference(avatar_split_clause,[],[f469,f1004]) ).
tff(f1004,plain,
( spl36_88
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( typings(X3,X1,sK27(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_88])]) ).
tff(f469,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typings(X3,X1,sK27(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f328]) ).
tff(f1002,plain,
spl36_87,
inference(avatar_split_clause,[],[f390,f1000]) ).
tff(f390,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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f993,plain,
spl36_86,
inference(avatar_split_clause,[],[f531,f991]) ).
tff(f531,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ),
inference(equality_resolution,[],[f495]) ).
tff(f495,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X11: X0,X13: fun(nat,X0),X31: nat,X12: nat] :
( ( X12 = X31 )
=> ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X13),X12),X11),X31) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_shift__eq) ).
tff(f988,plain,
spl36_85,
inference(avatar_split_clause,[],[f434,f986]) ).
tff(f434,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X62: list(dB),X50: dB,X63: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X63),X50))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X63,X62)),foldl(dB,dB,app,X50,X62))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_apps__preserves__beta) ).
tff(f984,plain,
spl36_84,
inference(avatar_split_clause,[],[f380,f982]) ).
tff(f982,plain,
( spl36_84
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_84])]) ).
tff(f380,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0)) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X33: list(dB)] :
( listsp(dB,it,X33)
=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_lifts__IT) ).
tff(f970,plain,
spl36_83,
inference(avatar_split_clause,[],[f462,f968]) ).
tff(f462,plain,
! [X2: dB,X3: nat,X0: nat,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: nat,X1: dB,X2: dB,X3: nat] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X42: nat,X20: dB,X41: dB,X21: nat] : ( liftn(X21,aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X20),X42) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X21,X41,X42)),liftn(X21,X20,X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_liftn_Osimps_I2_J) ).
tff(f961,plain,
spl36_82,
inference(avatar_split_clause,[],[f432,f959]) ).
tff(f432,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,[],[f227]) ).
tff(f227,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,[],[f162]) ).
tff(f162,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,[],[f12]) ).
tff(f12,axiom,
! [X17: nat,X18: nat,X19: dB] :
( pp(aa(dB,bool,it,X19))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X19),var(X18)),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subst__Var__IT) ).
tff(f957,plain,
spl36_81,
inference(avatar_split_clause,[],[f425,f955]) ).
tff(f425,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,[],[f155]) ).
tff(f155,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,[],[f34]) ).
tff(f34,axiom,
! [X41: dB,X42: nat,X20: 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,X20),X42)),X41),X42) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subst__lift) ).
tff(f952,plain,
spl36_80,
inference(avatar_split_clause,[],[f373,f949]) ).
tff(f949,plain,
( spl36_80
<=> typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_80])]) ).
tff(f373,plain,
typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,sK5),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f215,f283]) ).
tff(f283,plain,
( ? [X0: list(type)] : typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,X0)
=> typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,sK5) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
? [X0: list(type)] : typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,X0),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
~ ! [X0: list(type)] : ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,X0),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
~ ! [X24: list(type)] : ~ typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096_B_Bthesis_O_A_I_B_BTs_O_Ae_060i_058T_062_A_124_124_N_Ars_A_058_ATs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f947,plain,
spl36_79,
inference(avatar_split_clause,[],[f361,f944]) ).
tff(f944,plain,
( spl36_79
<=> typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,ts) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_79])]) ).
tff(f361,plain,
typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,ts),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),rs,ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14__096e_060i_058T_062_A_124_124_N_Ars_A_058_ATs_096) ).
tff(f939,plain,
spl36_78,
inference(avatar_split_clause,[],[f456,f937]) ).
tff(f456,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X11: type,X12: nat,X13: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X13),var(X12)),X11))
=> ( aa(nat,type,X13,X12) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_typing__elims_I1_J) ).
tff(f935,plain,
spl36_77,
inference(avatar_split_clause,[],[f446,f933]) ).
tff(f446,plain,
! [X2: nat,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X2),sK19(X0,X1,X2)) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: dB,X1: list(dB),X2: nat] :
( ( ( foldl(dB,dB,app,var(X2),sK19(X0,X1,X2)) = X0 )
& step1(dB,beta,X1,sK19(X0,X1,X2)) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f235,f312]) ).
tff(f312,plain,
! [X0: dB,X1: list(dB),X2: nat] :
( ? [X3: list(dB)] :
( ( foldl(dB,dB,app,var(X2),X3) = X0 )
& step1(dB,beta,X1,X3) )
=> ( ( foldl(dB,dB,app,var(X2),sK19(X0,X1,X2)) = X0 )
& step1(dB,beta,X1,sK19(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f235,plain,
! [X0: dB,X1: list(dB),X2: nat] :
( ? [X3: list(dB)] :
( ( foldl(dB,dB,app,var(X2),X3) = X0 )
& step1(dB,beta,X1,X3) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: dB,X1: list(dB),X2: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))
=> ? [X3: list(dB)] :
( ( foldl(dB,dB,app,var(X2),X3) = X0 )
& step1(dB,beta,X1,X3) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X80: dB,X52: list(dB),X51: nat] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X51),X52)),X80))
=> ? [X81: list(dB)] :
( ( foldl(dB,dB,app,var(X51),X81) = X80 )
& step1(dB,beta,X52,X81) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_head__Var__reduction) ).
tff(f931,plain,
spl36_76,
inference(avatar_split_clause,[],[f447,f929]) ).
tff(f929,plain,
( spl36_76
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_76])]) ).
tff(f447,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( ( abs(sK20(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) )
| ~ sP3(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f315,f316]) ).
tff(f316,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
=> ( ( abs(sK20(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f315,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f314]) ).
tff(f314,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP3(X2,X0,X1) ),
inference(nnf_transformation,[],[f279]) ).
tff(f915,plain,
spl36_75,
inference(avatar_split_clause,[],[f521,f913]) ).
tff(f521,plain,
! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f433]) ).
tff(f433,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X11: type,X29: nat,X30: fun(nat,type)] :
( ( aa(nat,type,X30,X29) = X11 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X30),var(X29)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_typing_OVar) ).
tff(f911,plain,
spl36_74,
inference(avatar_split_clause,[],[f494,f909]) ).
tff(f494,plain,
! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: type,X2: type,X3: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType,X27: type,X28: type,X77: fun(type,fun(type,X0)),X78: fun(nat,X0)] : ( type_case(X0,X78,X77,aa(type,type,aa(type,fun(type,type),fun1,X28),X27)) = aa(type,X0,aa(type,fun(type,X0),X77,X28),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_type_Osimps_I6_J) ).
tff(f907,plain,
spl36_73,
inference(avatar_split_clause,[],[f431,f905]) ).
tff(f431,plain,
! [X2: list(dB),X0: dB,X1: list(dB)] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1)))
| ~ step1(dB,beta,X2,X1) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: dB,X1: list(dB),X2: list(dB)] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1)))
| ~ step1(dB,beta,X2,X1) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: dB,X1: list(dB),X2: list(dB)] :
( step1(dB,beta,X2,X1)
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X0,X2)),foldl(dB,dB,app,X0,X1))) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X63: dB,X62: list(dB),X52: list(dB)] :
( step1(dB,beta,X52,X62)
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X63,X52)),foldl(dB,dB,app,X63,X62))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_apps__preserves__betas) ).
tff(f903,plain,
spl36_72,
inference(avatar_split_clause,[],[f415,f901]) ).
tff(f415,plain,
! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: dB,X1: dB] :
( ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1)))
& ( abs(sK13(X0,X1)) = X0 ) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f224,f299]) ).
tff(f299,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2))
& ( abs(X2) = X0 ) )
=> ( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK13(X0,X1)))
& ( abs(sK13(X0,X1)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2))
& ( abs(X2) = X0 ) )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))
=> ~ ! [X2: dB] :
( ( abs(X2) = X0 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X2)) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X41: dB,X19: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X19)),X41))
=> ~ ! [X75: dB] :
( ( abs(X75) = X41 )
=> ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X19),X75)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_beta__cases_I2_J) ).
tff(f895,plain,
( spl36_71
| ~ spl36_9
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f647,f639,f572,f892]) ).
tff(f892,plain,
( spl36_71
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_71])]) ).
tff(f647,plain,
( sP1(abs(ua))
| ~ spl36_9
| ~ spl36_23 ),
inference(resolution,[],[f640,f574]) ).
tff(f888,plain,
spl36_70,
inference(avatar_split_clause,[],[f489,f886]) ).
tff(f489,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,[],[f344]) ).
tff(f344,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,[],[f343]) ).
tff(f343,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,[],[f194]) ).
tff(f194,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,[],[f36]) ).
tff(f36,axiom,
! [X45: dB,X46: dB,X47: dB,X48: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X48),X47) = aa(dB,dB,aa(dB,fun(dB,dB),app,X46),X45) )
<=> ( ( X45 = X47 )
& ( X46 = X48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dB_Osimps_I2_J) ).
tff(f884,plain,
spl36_69,
inference(avatar_split_clause,[],[f488,f882]) ).
tff(f488,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,[],[f344]) ).
tff(f880,plain,
spl36_68,
inference(avatar_split_clause,[],[f486,f878]) ).
tff(f486,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,[],[f342]) ).
tff(f342,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,[],[f341]) ).
tff(f341,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,[],[f193]) ).
tff(f193,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,[],[f21]) ).
tff(f21,axiom,
! [X25: type,X26: type,X27: type,X28: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X28),X27) = aa(type,type,aa(type,fun(type,type),fun1,X26),X25) )
<=> ( ( X25 = X27 )
& ( X26 = X28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_type_Osimps_I2_J) ).
tff(f876,plain,
spl36_67,
inference(avatar_split_clause,[],[f485,f874]) ).
tff(f485,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,[],[f342]) ).
tff(f872,plain,
spl36_66,
inference(avatar_split_clause,[],[f445,f870]) ).
tff(f445,plain,
! [X2: nat,X0: dB,X1: list(dB)] :
( step1(dB,beta,X1,sK19(X0,X1,X2))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f868,plain,
spl36_65,
inference(avatar_split_clause,[],[f413,f866]) ).
tff(f413,plain,
! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0)) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: dB,X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),X0))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),abs(X0))) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X20: dB,X41: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X41),X20))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X41)),abs(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_abs) ).
tff(f861,plain,
( spl36_64
| ~ spl36_10
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f646,f639,f577,f858]) ).
tff(f858,plain,
( spl36_64
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_64])]) ).
tff(f646,plain,
( sP1(abs(u))
| ~ spl36_10
| ~ spl36_23 ),
inference(resolution,[],[f640,f579]) ).
tff(f856,plain,
spl36_63,
inference(avatar_split_clause,[],[f478,f854]) ).
tff(f478,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f336]) ).
tff(f336,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f253,f335]) ).
tff(f335,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,sK31(X0,X1,X2,X3)) != aa(X1,X0,X2,sK31(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f253,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,[],[f190]) ).
tff(f190,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,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X60: fun(X0,X1),X58: fun(X0,X1)] :
( ! [X73: X0] : ( aa(X0,X1,X58,X73) = aa(X0,X1,X60,X73) )
=> ( X58 = X60 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f852,plain,
spl36_62,
inference(avatar_split_clause,[],[f389,f850]) ).
tff(f850,plain,
( spl36_62
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_62])]) ).
tff(f389,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f845,plain,
spl36_61,
inference(avatar_split_clause,[],[f412,f843]) ).
tff(f412,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,[],[f222]) ).
tff(f222,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,[],[f145]) ).
tff(f145,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,[],[f48]) ).
tff(f48,axiom,
! [X18: nat,X20: dB] :
( pp(aa(dB,bool,it,X20))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X20),var(X18)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_app__Var__IT) ).
tff(f833,plain,
spl36_60,
inference(avatar_split_clause,[],[f411,f831]) ).
tff(f411,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,[],[f221]) ).
tff(f221,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,[],[f144]) ).
tff(f144,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,[],[f13]) ).
tff(f13,axiom,
! [X18: nat,X20: dB] :
( pp(aa(dB,bool,it,X20))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X20),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_lift__IT) ).
tff(f829,plain,
( spl36_59
| ~ spl36_8
| ~ spl36_23 ),
inference(avatar_split_clause,[],[f645,f639,f567,f826]) ).
tff(f826,plain,
( spl36_59
<=> sP1(abs(t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_59])]) ).
tff(f645,plain,
( sP1(abs(t2))
| ~ spl36_8
| ~ spl36_23 ),
inference(resolution,[],[f640,f569]) ).
tff(f824,plain,
spl36_58,
inference(avatar_split_clause,[],[f401,f822]) ).
tff(f401,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,[],[f134]) ).
tff(f134,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,[],[f50]) ).
tff(f50,axiom,
! [X49: dB,X42: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X42)),X49),X42) = X49 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_subst__eq) ).
tff(f820,plain,
spl36_57,
inference(avatar_split_clause,[],[f384,f818]) ).
tff(f384,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,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,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) )
| ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f290,f292,f291]) ).
tff(f291,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f292,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f290,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,[],[f289]) ).
tff(f289,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,[],[f288]) ).
tff(f288,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,[],[f275]) ).
tff(f275,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(f816,plain,
spl36_56,
inference(avatar_split_clause,[],[f360,f813]) ).
tff(f360,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_uT) ).
tff(f811,plain,
spl36_55,
inference(avatar_split_clause,[],[f359,f808]) ).
tff(f359,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Var_I4_J) ).
tff(f802,plain,
spl36_54,
inference(avatar_split_clause,[],[f461,f800]) ).
tff(f461,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,[],[f177]) ).
tff(f177,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,[],[f59]) ).
tff(f59,axiom,
! [X62: list(dB),X51: nat,X14: dB,X50: dB] : ( foldl(dB,dB,app,var(X51),X62) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X50)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Abs__App__neq__Var__apps) ).
tff(f798,plain,
spl36_53,
inference(avatar_split_clause,[],[f382,f796]) ).
tff(f796,plain,
( spl36_53
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_53])]) ).
tff(f382,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f792,plain,
( spl36_52
| ~ spl36_13
| ~ spl36_15 ),
inference(avatar_split_clause,[],[f617,f598,f590,f790]) ).
tff(f790,plain,
( spl36_52
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_52])]) ).
tff(f617,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl36_13
| ~ spl36_15 ),
inference(resolution,[],[f599,f591]) ).
tff(f788,plain,
spl36_51,
inference(avatar_split_clause,[],[f483,f786]) ).
tff(f786,plain,
( spl36_51
<=> ! [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,[spl36_51])]) ).
tff(f483,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,[],[f340]) ).
tff(f340,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,[],[f339]) ).
tff(f339,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,[],[f192]) ).
tff(f192,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,[],[f56]) ).
tff(f56,axiom,
! [X62: list(dB),X51: nat,X52: list(dB),X64: nat] :
( ( foldl(dB,dB,app,var(X64),X52) = foldl(dB,dB,app,var(X51),X62) )
<=> ( ( X52 = X62 )
& ( X51 = X64 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Var__apps__eq__Var__apps__conv) ).
tff(f784,plain,
spl36_50,
inference(avatar_split_clause,[],[f480,f782]) ).
tff(f782,plain,
( spl36_50
<=> ! [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,[spl36_50])]) ).
tff(f480,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,[],[f338]) ).
tff(f338,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,[],[f337]) ).
tff(f337,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,[],[f191]) ).
tff(f191,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,[],[f55]) ).
tff(f55,axiom,
! [X62: list(dB),X50: dB,X52: list(dB),X63: dB] :
( ( foldl(dB,dB,app,abs(X63),X52) = foldl(dB,dB,app,abs(X50),X62) )
<=> ( ( X52 = X62 )
& ( X50 = X63 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Abs__apps__eq__Abs__apps__conv) ).
tff(f780,plain,
spl36_49,
inference(avatar_split_clause,[],[f414,f778]) ).
tff(f414,plain,
! [X0: dB,X1: dB] :
( ( abs(sK13(X0,X1)) = X0 )
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f774,plain,
spl36_48,
inference(avatar_split_clause,[],[f482,f772]) ).
tff(f772,plain,
( spl36_48
<=> ! [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,[spl36_48])]) ).
tff(f482,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,[],[f340]) ).
tff(f770,plain,
spl36_47,
inference(avatar_split_clause,[],[f479,f768]) ).
tff(f768,plain,
( spl36_47
<=> ! [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,[spl36_47])]) ).
tff(f479,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,[],[f338]) ).
tff(f766,plain,
spl36_46,
inference(avatar_split_clause,[],[f439,f764]) ).
tff(f764,plain,
( spl36_46
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( cons(dB,sK15(X0,X1,X2),sK16(X0,X1,X2)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_46])]) ).
tff(f439,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( cons(dB,sK15(X0,X1,X2),sK16(X0,X1,X2)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f307]) ).
tff(f750,plain,
spl36_45,
inference(avatar_split_clause,[],[f458,f748]) ).
tff(f748,plain,
( spl36_45
<=> ! [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,[spl36_45])]) ).
tff(f458,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,[],[f326]) ).
tff(f326,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,[],[f175]) ).
tff(f175,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X50: dB,X33: list(dB),X63: dB] :
( ( foldl(dB,dB,app,X63,X33) = foldl(dB,dB,app,X50,X33) )
<=> ( X50 = X63 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_apps__eq__tail__conv) ).
tff(f746,plain,
spl36_44,
inference(avatar_split_clause,[],[f410,f744]) ).
tff(f410,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,[],[f220]) ).
tff(f220,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,[],[f143]) ).
tff(f143,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X51: nat,X52: list(dB)] :
( listsp(dB,it,X52)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X51),X52))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_IT_OVar) ).
tff(f742,plain,
spl36_43,
inference(avatar_split_clause,[],[f409,f740]) ).
tff(f409,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X89: bool,X87: bool] :
( pp(X89)
| ~ pp(X87)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X87),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
tff(f738,plain,
spl36_42,
inference(avatar_split_clause,[],[f404,f736]) ).
tff(f404,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X89: bool,X87: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X87),X89))
| ~ pp(X89)
| ~ pp(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f734,plain,
spl36_41,
inference(avatar_split_clause,[],[f385,f732]) ).
tff(f385,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f720,plain,
spl36_40,
inference(avatar_split_clause,[],[f460,f718]) ).
tff(f718,plain,
( spl36_40
<=> ! [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,[spl36_40])]) ).
tff(f460,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,[],[f176]) ).
tff(f176,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,[],[f58]) ).
tff(f58,axiom,
! [X62: list(dB),X63: dB,X33: list(dB),X51: nat] : ( foldl(dB,dB,app,var(X51),X33) != foldl(dB,dB,app,abs(X63),X62) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Var__apps__neq__Abs__apps) ).
tff(f716,plain,
spl36_39,
inference(avatar_split_clause,[],[f429,f714]) ).
tff(f714,plain,
( spl36_39
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_39])]) ).
tff(f429,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X0: $tType,X86: X0,X87: fun(X0,bool)] :
( pp(aa(X0,bool,X87,X86))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fAll_1_1_U) ).
tff(f712,plain,
spl36_38,
inference(avatar_split_clause,[],[f428,f710]) ).
tff(f428,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,[],[f158]) ).
tff(f158,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,X86: X0,X87: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X87))
| ~ pp(aa(X0,bool,X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f708,plain,
spl36_37,
inference(avatar_split_clause,[],[f422,f706]) ).
tff(f422,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X43: nat,X55: dB,X56: dB] : ( var(X43) != aa(dB,dB,aa(dB,fun(dB,dB),app,X56),X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_dB_Osimps_I5_J) ).
tff(f704,plain,
spl36_36,
inference(avatar_split_clause,[],[f420,f702]) ).
tff(f420,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X53: dB,X54: dB,X44: dB] : ( abs(X44) != aa(dB,dB,aa(dB,fun(dB,dB),app,X54),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_dB_Osimps_I9_J) ).
tff(f700,plain,
spl36_35,
inference(avatar_split_clause,[],[f408,f698]) ).
tff(f408,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X89: bool,X87: bool] :
( pp(X89)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X87),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f696,plain,
spl36_34,
inference(avatar_split_clause,[],[f407,f694]) ).
tff(f407,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X89: bool,X87: bool] :
( pp(X87)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X87),X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f692,plain,
spl36_33,
inference(avatar_split_clause,[],[f406,f690]) ).
tff(f406,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X89: bool,X87: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X87),X89))
| pp(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
tff(f688,plain,
spl36_32,
inference(avatar_split_clause,[],[f405,f686]) ).
tff(f405,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X87: bool,X89: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X87),X89))
| ~ pp(X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
tff(f684,plain,
spl36_31,
inference(avatar_split_clause,[],[f383,f682]) ).
tff(f682,plain,
( spl36_31
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_31])]) ).
tff(f383,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f680,plain,
( spl36_30
| ~ spl36_9
| ~ spl36_15 ),
inference(avatar_split_clause,[],[f620,f598,f572,f677]) ).
tff(f677,plain,
( spl36_30
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_30])]) ).
tff(f620,plain,
( sP1(ua)
| ~ spl36_9
| ~ spl36_15 ),
inference(resolution,[],[f599,f574]) ).
tff(f673,plain,
spl36_29,
inference(avatar_split_clause,[],[f400,f671]) ).
tff(f400,plain,
! [X0: dB,X1: nat] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0)),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: dB,X1: nat] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0)),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X20: dB,X18: nat] : ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X18)),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_beta__cases_I1_J) ).
tff(f669,plain,
spl36_28,
inference(avatar_split_clause,[],[f381,f667]) ).
tff(f381,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X19: dB] :
( pp(aa(dB,bool,it,X19))
=> pp(aa(dB,bool,it,abs(X19))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Lambda) ).
tff(f665,plain,
spl36_27,
inference(avatar_split_clause,[],[f517,f663]) ).
tff(f663,plain,
( spl36_27
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_27])]) ).
tff(f517,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f386]) ).
tff(f386,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,[],[f293]) ).
tff(f661,plain,
spl36_26,
inference(avatar_split_clause,[],[f448,f659]) ).
tff(f659,plain,
( spl36_26
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK20(X0,X1,X2)) = X0 )
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_26])]) ).
tff(f448,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK20(X0,X1,X2)) = X0 )
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f317]) ).
tff(f657,plain,
spl36_25,
inference(avatar_split_clause,[],[f438,f655]) ).
tff(f655,plain,
( spl36_25
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( abs(sK14(X0,X1,X2)) = X2 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_25])]) ).
tff(f438,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( abs(sK14(X0,X1,X2)) = X2 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f307]) ).
tff(f653,plain,
( spl36_24
| ~ spl36_10
| ~ spl36_15 ),
inference(avatar_split_clause,[],[f619,f598,f577,f650]) ).
tff(f650,plain,
( spl36_24
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_24])]) ).
tff(f619,plain,
( sP1(u)
| ~ spl36_10
| ~ spl36_15 ),
inference(resolution,[],[f599,f579]) ).
tff(f641,plain,
spl36_23,
inference(avatar_split_clause,[],[f516,f639]) ).
tff(f516,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f387]) ).
tff(f387,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f637,plain,
spl36_22,
inference(avatar_split_clause,[],[f399,f635]) ).
tff(f635,plain,
( spl36_22
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_22])]) ).
tff(f399,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X36: list(X0)] : ( map(X0,X0,combi(X0),X36) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_map__ident) ).
tff(f633,plain,
spl36_21,
inference(avatar_split_clause,[],[f391,f631]) ).
tff(f391,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f625,plain,
( spl36_20
| ~ spl36_8
| ~ spl36_15 ),
inference(avatar_split_clause,[],[f618,f598,f567,f622]) ).
tff(f622,plain,
( spl36_20
<=> sP1(t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_20])]) ).
tff(f618,plain,
( sP1(t2)
| ~ spl36_8
| ~ spl36_15 ),
inference(resolution,[],[f599,f569]) ).
tff(f616,plain,
spl36_19,
inference(avatar_split_clause,[],[f418,f614]) ).
tff(f614,plain,
( spl36_19
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_19])]) ).
tff(f418,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X39: nat,X40: nat] :
( ( var(X40) = var(X39) )
<=> ( X39 = X40 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dB_Osimps_I1_J) ).
tff(f612,plain,
spl36_18,
inference(avatar_split_clause,[],[f416,f610]) ).
tff(f610,plain,
( spl36_18
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_18])]) ).
tff(f416,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X37: dB,X38: dB] :
( ( abs(X38) = abs(X37) )
<=> ( X37 = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dB_Osimps_I3_J) ).
tff(f608,plain,
spl36_17,
inference(avatar_split_clause,[],[f398,f606]) ).
tff(f398,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X0: $tType,X87: X0] : ( aa(X0,X0,combi(X0),X87) = X87 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f604,plain,
spl36_16,
inference(avatar_split_clause,[],[f394,f602]) ).
tff(f394,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f127,f275,f274]) ).
tff(f127,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,[],[f70]) ).
tff(f70,axiom,
! [X59: dB] :
( pp(aa(dB,bool,it,X59))
<=> ( ? [X70: dB,X71: dB,X72: list(dB)] :
( pp(aa(dB,bool,it,X71))
& 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,X70),X71),zero_zero(nat)),X72)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X70)),X71),X72) = X59 ) )
| ? [X70: dB] :
( pp(aa(dB,bool,it,X70))
& ( abs(X70) = X59 ) )
| ? [X68: list(dB),X69: nat] :
( listsp(dB,it,X68)
& ( foldl(dB,dB,app,var(X69),X68) = X59 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_IT_Osimps) ).
tff(f600,plain,
spl36_15,
inference(avatar_split_clause,[],[f393,f598]) ).
tff(f393,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f596,plain,
spl36_14,
inference(avatar_split_clause,[],[f397,f594]) ).
tff(f594,plain,
( spl36_14
<=> ! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_14])]) ).
tff(f397,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X42: nat,X20: dB] : ( liftn(zero_zero(nat),X20,X42) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_liftn__0) ).
tff(f592,plain,
spl36_13,
inference(avatar_split_clause,[],[f377,f590]) ).
tff(f377,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X21: nat] : pp(aa(dB,bool,it,var(X21))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Var__IT) ).
tff(f588,plain,
spl36_12,
inference(avatar_split_clause,[],[f376,f586]) ).
tff(f586,plain,
( spl36_12
<=> ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_12])]) ).
tff(f376,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X43: nat] : ( zero_zero(nat) = size_size(dB,var(X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_dB_Osize_I4_J) ).
tff(f584,plain,
spl36_11,
inference(avatar_split_clause,[],[f375,f582]) ).
tff(f582,plain,
( spl36_11
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_11])]) ).
tff(f375,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X43: nat] : ( zero_zero(nat) = dB_size(var(X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dB_Osize_I1_J) ).
tff(f580,plain,
spl36_10,
inference(avatar_split_clause,[],[f358,f577]) ).
tff(f358,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
tff(f575,plain,
spl36_9,
inference(avatar_split_clause,[],[f357,f572]) ).
tff(f357,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
tff(f570,plain,
spl36_8,
inference(avatar_split_clause,[],[f356,f567]) ).
tff(f356,plain,
pp(aa(dB,bool,it,t2)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
tff(f565,plain,
~ spl36_7,
inference(avatar_split_clause,[],[f351,f562]) ).
tff(f351,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f560,plain,
spl36_6,
inference(avatar_split_clause,[],[f395,f558]) ).
tff(f558,plain,
( spl36_6
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_6])]) ).
tff(f395,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X44: dB,X43: nat] : ( abs(X44) != var(X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_dB_Osimps_I6_J) ).
tff(f556,plain,
spl36_5,
inference(avatar_split_clause,[],[f388,f554]) ).
tff(f554,plain,
( spl36_5
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_5])]) ).
tff(f388,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f552,plain,
~ spl36_4,
inference(avatar_split_clause,[],[f355,f549]) ).
tff(f549,plain,
( spl36_4
<=> ( n = i ) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_4])]) ).
tff(f355,plain,
n != i,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
n != i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_False) ).
tff(f547,plain,
spl36_3,
inference(avatar_split_clause,[],[f354,f544]) ).
tff(f354,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f542,plain,
spl36_2,
inference(avatar_split_clause,[],[f353,f539]) ).
tff(f539,plain,
( spl36_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_2])]) ).
tff(f353,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f537,plain,
~ spl36_1,
inference(avatar_split_clause,[],[f352,f534]) ).
tff(f534,plain,
( spl36_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl36_1])]) ).
tff(f352,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL828_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 13:21:12 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (13512)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (13519)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.42 % (13515)WARNING: value z3 for option sas not known
% 0.22/0.43 % (13519)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % (13513)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.43 % (13514)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.43 % (13516)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.43 % (13515)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)
% 0.22/0.43 % (13517)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)
% 0.22/0.43 % (13518)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)
% 0.22/0.44 % Exception at run slice level
% 0.22/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44 % Exception at run slice level
% 0.22/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44 % Exception at run slice level
% 0.22/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.45 % (13520)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.45 % (13521)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)
% 0.22/0.45 % (13522)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)
% 0.22/0.46 % (13520)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.46 % (13521)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.46 % Exception at run slice level
% 0.22/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.48 % (13530)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)
% 1.78/0.66 % (13517)First to succeed.
% 1.78/0.69 % (13517)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13512"
% 1.78/0.69 % (13517)Refutation found. Thanks to Tanya!
% 1.78/0.69 % SZS status Theorem for theBenchmark
% 1.78/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.18/0.70 % (13517)------------------------------
% 2.18/0.70 % (13517)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.18/0.70 % (13517)Termination reason: Refutation
% 2.18/0.70
% 2.18/0.70 % (13517)Memory used [KB]: 4107
% 2.18/0.70 % (13517)Time elapsed: 0.265 s
% 2.18/0.70 % (13517)Instructions burned: 699 (million)
% 2.18/0.70 % (13512)Success in time 0.316 s
%------------------------------------------------------------------------------