TSTP Solution File: LCL786_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL786_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 : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:07 EDT 2024
% Result : Theorem 24.33s 3.92s
% Output : Refutation 24.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 740
% Syntax : Number of formulae : 2319 ( 283 unt; 88 typ; 0 def)
% Number of atoms : 6401 (1391 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7507 (3337 ~;3319 |; 155 &)
% ( 558 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 106 ( 53 >; 53 *; 0 +; 0 <<)
% Number of predicates : 534 ( 532 usr; 527 prp; 0-3 aty)
% Number of functors : 78 ( 78 usr; 22 con; 0-6 aty)
% Number of variables : 5918 (5769 !; 99 ?;5918 :)
% ( 50 !>; 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,
fun1: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * X1 ) > fun1(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun1(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun1(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun1(dB,fun1(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun1(dB,fun1(nat,dB)) ).
tff(func_def_11,type,
subst: fun1(dB,fun1(dB,fun1(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun1(X0,fun1(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun1(X1,fun1(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun1(X0,bool)) > fun1(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun1(X0,bool) * fun1(list(X0),bool) ) > fun1(list(X0),bool) ) ).
tff(func_def_19,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
collect:
!>[X0: $tType] : ( fun1(X0,bool) > fun1(X0,bool) ) ).
tff(func_def_22,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_23,type,
atom: nat > type ).
tff(func_def_24,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_25,type,
type_case:
!>[X0: $tType] : ( ( fun1(nat,X0) * fun1(type,fun1(type,X0)) * type ) > X0 ) ).
tff(func_def_26,type,
type_size: type > nat ).
tff(func_def_27,type,
typing: fun1(nat,type) > fun1(dB,fun1(type,bool)) ).
tff(func_def_28,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_29,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_30,type,
fEx:
!>[X0: $tType] : fun1(fun1(X0,bool),bool) ).
tff(func_def_31,type,
fFalse: bool ).
tff(func_def_32,type,
fTrue: bool ).
tff(func_def_33,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_34,type,
fequal:
!>[X0: $tType] : fun1(X0,fun1(X0,bool)) ).
tff(func_def_35,type,
member:
!>[X0: $tType] : fun1(X0,fun1(fun1(X0,bool),bool)) ).
tff(func_def_36,type,
t1: type ).
tff(func_def_37,type,
t_a: type ).
tff(func_def_38,type,
t: type ).
tff(func_def_39,type,
a: dB ).
tff(func_def_40,type,
as: list(dB) ).
tff(func_def_41,type,
e: fun1(nat,type) ).
tff(func_def_42,type,
ea: fun1(nat,type) ).
tff(func_def_43,type,
i: nat ).
tff(func_def_44,type,
ia: nat ).
tff(func_def_45,type,
n: nat ).
tff(func_def_46,type,
rs: list(dB) ).
tff(func_def_47,type,
t2: dB ).
tff(func_def_48,type,
u: dB ).
tff(func_def_49,type,
ua: dB ).
tff(func_def_50,type,
sK2: type > type ).
tff(func_def_51,type,
sK3: type > type ).
tff(func_def_52,type,
sK4: type > nat ).
tff(func_def_53,type,
sK5: dB > dB ).
tff(func_def_54,type,
sK6: dB > list(dB) ).
tff(func_def_55,type,
sK7: dB > nat ).
tff(func_def_56,type,
sK8: dB > dB ).
tff(func_def_57,type,
sK9: dB > dB ).
tff(func_def_58,type,
sK10: dB > list(dB) ).
tff(func_def_59,type,
sK11: ( dB * fun1(nat,type) ) > type ).
tff(func_def_60,type,
sK12: ( dB * fun1(nat,type) ) > type ).
tff(func_def_61,type,
sK13: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_62,type,
sK14: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_63,type,
sK15: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_64,type,
sK16: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_65,type,
sK17: ( type * list(dB) * nat * fun1(nat,type) ) > list(type) ).
tff(func_def_66,type,
sK18: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_67,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_68,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X1 ) ).
tff(func_def_69,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X1 ) ).
tff(func_def_70,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun1(X0,fun1(X1,X0)) > X0 ) ).
tff(func_def_71,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun1(X0,X1) ) > X0 ) ).
tff(func_def_72,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun1(X0,X1) ) > list(X0) ) ).
tff(func_def_73,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun1(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_74,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun1(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_75,type,
sK27: ( type * type * list(dB) * fun1(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_6,type,
sP0: dB > $o ).
tff(pred_def_7,type,
sP1: dB > $o ).
tff(f19799,plain,
$false,
inference(avatar_sat_refutation,[],[f550,f555,f560,f565,f569,f573,f577,f582,f587,f592,f596,f600,f604,f614,f618,f622,f627,f631,f635,f639,f643,f647,f651,f655,f669,f675,f679,f683,f696,f702,f706,f710,f716,f722,f728,f734,f740,f744,f748,f753,f761,f765,f770,f775,f780,f785,f789,f793,f797,f801,f818,f822,f827,f835,f839,f844,f850,f863,f867,f871,f875,f880,f884,f894,f898,f902,f906,f912,f918,f922,f926,f935,f940,f945,f951,f955,f960,f964,f969,f977,f986,f1009,f1014,f1022,f1027,f1032,f1037,f1046,f1052,f1059,f1065,f1071,f1076,f1080,f1095,f1101,f1105,f1111,f1115,f1121,f1126,f1130,f1134,f1138,f1158,f1163,f1178,f1184,f1194,f1200,f1206,f1211,f1219,f1223,f1228,f1235,f1240,f1247,f1253,f1258,f1263,f1270,f1276,f1280,f1286,f1292,f1299,f1309,f1326,f1331,f1339,f1345,f1350,f1354,f1358,f1362,f1443,f1447,f1451,f1495,f1501,f1515,f1519,f1548,f1554,f1558,f1572,f1578,f1592,f1599,f1607,f1614,f1618,f1626,f1632,f1645,f1651,f1659,f1665,f1670,f1677,f1687,f1693,f1702,f1708,f1719,f1725,f1731,f1736,f1777,f1865,f1871,f1884,f1888,f1896,f1912,f1918,f1926,f1942,f1946,f1951,f1957,f1984,f2000,f2006,f2017,f2021,f2030,f2038,f2052,f2066,f2070,f2079,f2085,f2095,f2103,f2111,f2123,f2128,f2132,f2136,f2144,f2158,f2169,f2249,f2253,f2258,f2267,f2272,f2281,f2287,f2294,f2299,f2304,f2308,f2788,f2811,f2834,f2839,f2850,f2854,f2858,f2862,f2866,f2870,f2878,f2882,f2897,f2902,f2907,f2911,f2915,f2920,f2924,f2928,f3003,f3008,f3013,f3017,f3040,f3067,f3068,f3069,f3070,f3071,f3072,f3073,f3074,f3075,f3076,f3077,f3078,f3079,f3080,f3081,f3082,f3083,f3084,f3643,f3698,f3702,f3706,f3714,f3718,f3722,f3726,f3730,f3735,f3740,f3759,f3790,f3798,f3803,f3807,f3812,f3838,f3842,f3846,f3851,f3856,f3873,f3878,f3882,f3886,f3890,f3894,f3898,f3988,f4005,f4009,f4013,f4017,f4166,f4170,f4174,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4586,f4590,f4594,f4658,f4662,f4666,f4670,f4674,f4730,f4743,f4747,f4751,f4799,f4803,f4807,f4811,f4848,f4852,f4856,f4878,f4883,f4887,f4891,f4895,f4899,f5025,f5029,f5033,f5037,f5041,f5058,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5137,f5141,f5204,f5229,f5233,f5237,f5241,f5245,f5249,f5253,f5257,f5261,f5266,f5270,f5274,f5480,f5535,f5546,f5550,f5554,f5887,f5891,f5895,f5899,f5903,f5907,f6058,f6102,f6106,f6110,f6114,f6118,f6122,f6126,f6132,f6136,f6140,f6144,f6567,f6571,f6637,f6642,f6646,f6650,f6654,f6658,f6662,f6666,f6670,f6674,f6678,f7054,f7073,f7077,f7081,f7085,f7089,f7384,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f8081,f8086,f8103,f8107,f8111,f8115,f8119,f8123,f8608,f8701,f8705,f8792,f8796,f8800,f8805,f8809,f8813,f8817,f8821,f8826,f8845,f8850,f8953,f9421,f9425,f9429,f9433,f9437,f9458,f9463,f9606,f9610,f9615,f9619,f9623,f9627,f9631,f9635,f9639,f9643,f9647,f9651,f9655,f9661,f9665,f10757,f10761,f10765,f10769,f10774,f10778,f10782,f10786,f10790,f10794,f10799,f11494,f11498,f11502,f11506,f11510,f11535,f11539,f11543,f11547,f11947,f12069,f12073,f12077,f12081,f12086,f12261,f12265,f12269,f12523,f12527,f12557,f12585,f12589,f12593,f12597,f12601,f12605,f12746,f13818,f13822,f13826,f13830,f13834,f13840,f14345,f14349,f14353,f14357,f14361,f14365,f14369,f14373,f14377,f14381,f14385,f14389,f14394,f14413,f14417,f14422,f17145,f17149,f17153,f17157,f17517,f17521,f17525,f17529,f17533,f17537,f17541,f17545,f17550,f17554,f19652,f19656,f19660,f19680,f19684,f19688,f19692,f19797,f19798]) ).
tff(f19798,plain,
( ~ spl28_4
| ~ spl28_19
| ~ spl28_127
| ~ spl28_313
| ~ spl28_518 ),
inference(avatar_split_clause,[],[f19668,f19650,f4880,f1296,f633,f562]) ).
tff(f562,plain,
( spl28_4
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_4])]) ).
tff(f633,plain,
( spl28_19
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_19])]) ).
tff(f1296,plain,
( spl28_127
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_127])]) ).
tff(f4880,plain,
( spl28_313
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_313])]) ).
tff(f19650,plain,
( spl28_518
<=> ! [X0: list(dB)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,X0,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_518])]) ).
tff(f19668,plain,
( ~ pp(fTrue)
| ~ spl28_19
| ~ spl28_127
| ~ spl28_313
| ~ spl28_518 ),
inference(forward_demodulation,[],[f19661,f1479]) ).
tff(f1479,plain,
( ( fTrue = aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)) )
| ~ spl28_19
| ~ spl28_127 ),
inference(resolution,[],[f634,f1298]) ).
tff(f1298,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl28_127 ),
inference(avatar_component_clause,[],[f1296]) ).
tff(f634,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl28_19 ),
inference(avatar_component_clause,[],[f633]) ).
tff(f19661,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl28_313
| ~ spl28_518 ),
inference(resolution,[],[f19651,f4882]) ).
tff(f4882,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl28_313 ),
inference(avatar_component_clause,[],[f4880]) ).
tff(f19651,plain,
( ! [X0: list(dB)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,X0,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0))) )
| ~ spl28_518 ),
inference(avatar_component_clause,[],[f19650]) ).
tff(f19797,plain,
( spl28_525
| ~ spl28_94
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1319,f1307,f1078,f19795]) ).
tff(f19795,plain,
( spl28_525
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun1(list(X0),X1),X3: X0,X2: fun1(X0,fun1(list(X0),X1))] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK19(X1,list(X0),X4,aa(X0,fun1(list(X0),X1),X2,X3))),X3)) != aa(list(X0),X1,X4,sK19(X1,list(X0),X4,aa(X0,fun1(list(X0),X1),X2,X3))) )
| ( aa(X0,fun1(list(X0),X1),X2,X3) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_525])]) ).
tff(f1078,plain,
( spl28_94
<=> ! [X1: $tType,X0: $tType,X3: fun1(X1,X0),X2: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_94])]) ).
tff(f1307,plain,
( spl28_128
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun1(X1,fun1(list(X1),X0)),X3: X1,X2: list(X1)] : ( aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_128])]) ).
tff(f1319,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(list(X0),X1)),X3: X0,X4: fun1(list(X0),X1),X5: X1] :
( ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),sK19(X1,list(X0),X4,aa(X0,fun1(list(X0),X1),X2,X3))),X3)) != aa(list(X0),X1,X4,sK19(X1,list(X0),X4,aa(X0,fun1(list(X0),X1),X2,X3))) )
| ( aa(X0,fun1(list(X0),X1),X2,X3) = X4 ) )
| ~ spl28_94
| ~ spl28_128 ),
inference(superposition,[],[f1079,f1308]) ).
tff(f1308,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl28_128 ),
inference(avatar_component_clause,[],[f1307]) ).
tff(f1079,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl28_94 ),
inference(avatar_component_clause,[],[f1078]) ).
tff(f19692,plain,
( spl28_524
| ~ spl28_152
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1985,f1982,f1612,f19690]) ).
tff(f19690,plain,
( spl28_524
<=> ! [X3: type,X4: nat,X0: fun1(nat,type),X5: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,nat,dB,lift,X4),X5)),X4),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_524])]) ).
tff(f1612,plain,
( spl28_152
<=> ! [X4: fun1(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_152])]) ).
tff(f1982,plain,
( spl28_184
<=> ! [X2: dB,X3: fun1(nat,type),X4: type,X0: nat,X5: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_184])]) ).
tff(f1985,plain,
( ! [X2: dB,X3: type,X0: fun1(nat,type),X1: type,X4: nat,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,nat,dB,lift,X4),X5)),X4),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),X5)) )
| ~ spl28_152
| ~ spl28_184 ),
inference(resolution,[],[f1983,f1613]) ).
tff(f1613,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3)) )
| ~ spl28_152 ),
inference(avatar_component_clause,[],[f1612]) ).
tff(f1983,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2))) )
| ~ spl28_184 ),
inference(avatar_component_clause,[],[f1982]) ).
tff(f19688,plain,
( spl28_523
| ~ spl28_125
| ~ spl28_161 ),
inference(avatar_split_clause,[],[f1679,f1675,f1284,f19686]) ).
tff(f19686,plain,
( spl28_523
<=> ! [X0: fun1(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| ( aa(type,type,combc(type,type,type,fun,X2),X1) = aa(type,type,combc(type,type,type,fun,sK14(aa(type,type,combc(type,type,type,fun,X2),X1),X3,X0)),sK13(aa(type,type,combc(type,type,type,fun,X2),X1),X3,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_523])]) ).
tff(f1284,plain,
( spl28_125
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun,sK14(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_125])]) ).
tff(f1675,plain,
( spl28_161
<=> ! [X0: type,X3: fun1(nat,type),X2: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_161])]) ).
tff(f1679,plain,
( ! [X2: type,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| ( aa(type,type,combc(type,type,type,fun,X2),X1) = aa(type,type,combc(type,type,type,fun,sK14(aa(type,type,combc(type,type,type,fun,X2),X1),X3,X0)),sK13(aa(type,type,combc(type,type,type,fun,X2),X1),X3,X0)) ) )
| ~ spl28_125
| ~ spl28_161 ),
inference(resolution,[],[f1676,f1285]) ).
tff(f1285,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun,sK14(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) )
| ~ spl28_125 ),
inference(avatar_component_clause,[],[f1284]) ).
tff(f1676,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1)) )
| ~ spl28_161 ),
inference(avatar_component_clause,[],[f1675]) ).
tff(f19684,plain,
( spl28_522
| ~ spl28_125
| ~ spl28_141 ),
inference(avatar_split_clause,[],[f1504,f1499,f1284,f19682]) ).
tff(f19682,plain,
( spl28_522
<=> ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| ( sK14(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun,sK14(sK14(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))),sK13(sK14(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_522])]) ).
tff(f1499,plain,
( spl28_141
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),sK14(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_141])]) ).
tff(f1504,plain,
( ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| ( sK14(X1,abs(X2),X0) = aa(type,type,combc(type,type,type,fun,sK14(sK14(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))),sK13(sK14(X1,abs(X2),X0),X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))) ) )
| ~ spl28_125
| ~ spl28_141 ),
inference(resolution,[],[f1500,f1285]) ).
tff(f1500,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),sK14(X0,X1,X2)),X1))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1))) )
| ~ spl28_141 ),
inference(avatar_component_clause,[],[f1499]) ).
tff(f19680,plain,
( spl28_521
| ~ spl28_132
| ~ spl28_141 ),
inference(avatar_split_clause,[],[f1503,f1499,f1343,f19678]) ).
tff(f19678,plain,
( spl28_521
<=> ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)),zero_zero(nat),sK11(X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0))))),sK12(X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_521])]) ).
tff(f1343,plain,
( spl28_132
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),sK12(X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_132])]) ).
tff(f1503,plain,
( ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(abs(X2))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)),zero_zero(nat),sK11(X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0))))),sK12(X2,shift(type,X0,zero_zero(nat),sK13(X1,abs(X2),X0)))),X2)) )
| ~ spl28_132
| ~ spl28_141 ),
inference(resolution,[],[f1500,f1344]) ).
tff(f1344,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),sK12(X1,X2)),X1)) )
| ~ spl28_132 ),
inference(avatar_component_clause,[],[f1343]) ).
tff(f19660,plain,
( spl28_520
| ~ spl28_153
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5105,f5056,f1616,f19658]) ).
tff(f19658,plain,
( spl28_520
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,abs(X0)) )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_520])]) ).
tff(f1616,plain,
( spl28_153
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_153])]) ).
tff(f5056,plain,
( spl28_323
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_323])]) ).
tff(f5105,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,abs(X0)) )
| ~ sP1(X0) )
| ~ spl28_153
| ~ spl28_323 ),
inference(resolution,[],[f5057,f1617]) ).
tff(f1617,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl28_153 ),
inference(avatar_component_clause,[],[f1616]) ).
tff(f5057,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( fTrue = aa(dB,bool,it,X0) ) )
| ~ spl28_323 ),
inference(avatar_component_clause,[],[f5056]) ).
tff(f19656,plain,
( spl28_519
| ~ spl28_148
| ~ spl28_172 ),
inference(avatar_split_clause,[],[f1873,f1869,f1576,f19654]) ).
tff(f19654,plain,
( spl28_519
<=> ! [X0: list(dB)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK16(t1,X0,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_519])]) ).
tff(f1576,plain,
( spl28_148
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_148])]) ).
tff(f1869,plain,
( spl28_172
<=> ! [X0: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun,X0,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_172])]) ).
tff(f1873,plain,
( ! [X0: list(dB)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK16(t1,X0,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0))) )
| ~ spl28_148
| ~ spl28_172 ),
inference(resolution,[],[f1870,f1577]) ).
tff(f1577,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl28_148 ),
inference(avatar_component_clause,[],[f1576]) ).
tff(f1870,plain,
( ! [X0: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun,X0,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) )
| ~ spl28_172 ),
inference(avatar_component_clause,[],[f1869]) ).
tff(f19652,plain,
( spl28_518
| ~ spl28_146
| ~ spl28_172 ),
inference(avatar_split_clause,[],[f1872,f1869,f1556,f19650]) ).
tff(f1556,plain,
( spl28_146
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_146])]) ).
tff(f1872,plain,
( ! [X0: list(dB)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,X0,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0))) )
| ~ spl28_146
| ~ spl28_172 ),
inference(resolution,[],[f1870,f1557]) ).
tff(f1557,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl28_146 ),
inference(avatar_component_clause,[],[f1556]) ).
tff(f17554,plain,
( spl28_517
| ~ spl28_22
| ~ spl28_278 ),
inference(avatar_split_clause,[],[f4464,f4168,f645,f17552]) ).
tff(f17552,plain,
( spl28_517
<=> ! [X0: nat,X1: nat] :
( ( atom(X0) != atom(X1) )
| ( sK4(atom(X0)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_517])]) ).
tff(f645,plain,
( spl28_22
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( atom(X0) != atom(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_22])]) ).
tff(f4168,plain,
( spl28_278
<=> ! [X0: nat] : ( atom(X0) = atom(sK4(atom(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_278])]) ).
tff(f4464,plain,
( ! [X0: nat,X1: nat] :
( ( atom(X0) != atom(X1) )
| ( sK4(atom(X0)) = X1 ) )
| ~ spl28_22
| ~ spl28_278 ),
inference(superposition,[],[f646,f4169]) ).
tff(f4169,plain,
( ! [X0: nat] : ( atom(X0) = atom(sK4(atom(X0))) )
| ~ spl28_278 ),
inference(avatar_component_clause,[],[f4168]) ).
tff(f646,plain,
( ! [X0: nat,X1: nat] :
( ( atom(X0) != atom(X1) )
| ( X0 = X1 ) )
| ~ spl28_22 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f17550,plain,
( spl28_516
| ~ spl28_80
| ~ spl28_348
| ~ spl28_515 ),
inference(avatar_split_clause,[],[f17546,f17543,f5544,f975,f17548]) ).
tff(f17548,plain,
( spl28_516
<=> ! [X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK14(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X3),zero_zero(nat)),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_516])]) ).
tff(f975,plain,
( spl28_80
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_80])]) ).
tff(f5544,plain,
( spl28_348
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun1(X0,fun1(X3,fun1(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun1(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),aa(X0,fun1(X3,fun1(X1,X2)),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_348])]) ).
tff(f17543,plain,
( spl28_515
<=> ! [X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK14(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_515])]) ).
tff(f17546,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK14(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X3),zero_zero(nat)),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_515 ),
inference(forward_demodulation,[],[f17544,f5589]) ).
tff(f5589,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X2,X7: X0,X4: fun1(X3,fun1(X2,fun1(X0,X1))),X5: X3] : ( aa(X2,X1,combc(X2,X0,X1,aa(X3,fun1(X2,fun1(X0,X1)),X4,X5),X7),X6) = aa(X3,X1,combc(X3,X0,X1,combc(X3,X2,fun1(X0,X1),X4,X6),X7),X5) )
| ~ spl28_80
| ~ spl28_348 ),
inference(superposition,[],[f5545,f976]) ).
tff(f976,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) )
| ~ spl28_80 ),
inference(avatar_component_clause,[],[f975]) ).
tff(f5545,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun1(X0,fun1(X3,fun1(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun1(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),aa(X0,fun1(X3,fun1(X1,X2)),X4,X6),X5),X7) )
| ~ spl28_348 ),
inference(avatar_component_clause,[],[f5544]) ).
tff(f17544,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK14(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) )
| ~ spl28_515 ),
inference(avatar_component_clause,[],[f17543]) ).
tff(f17545,plain,
( spl28_515
| ~ spl28_141
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1995,f1982,f1499,f17543]) ).
tff(f1995,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK13(X1,X2,X0)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK14(X1,X2,X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2))) )
| ~ spl28_141
| ~ spl28_184 ),
inference(resolution,[],[f1983,f1500]) ).
tff(f17541,plain,
( spl28_514
| ~ spl28_137
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1838,f1775,f1441,f17539]) ).
tff(f17539,plain,
( spl28_514
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: fun1(X0,list(X0)),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun1(X0,list(X0)),fun1(X0,list(X0)),aa(fun1(X0,fun1(list(X0),list(X0))),fun1(fun1(X0,list(X0)),fun1(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_514])]) ).
tff(f1441,plain,
( spl28_137
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_137])]) ).
tff(f1775,plain,
( spl28_170
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun1(X2,fun1(X1,X0)),X4: fun1(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X2,fun1(X1,X0)),fun1(fun1(X2,X1),fun1(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_170])]) ).
tff(f1838,plain,
( ! [X0: $tType,X2: fun1(X0,list(X0)),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun1(X0,list(X0)),fun1(X0,list(X0)),aa(fun1(X0,fun1(list(X0),list(X0))),fun1(fun1(X0,list(X0)),fun1(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) )
| ~ spl28_137
| ~ spl28_170 ),
inference(superposition,[],[f1442,f1776]) ).
tff(f1776,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X2,fun1(X1,X0)),fun1(fun1(X2,X1),fun1(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl28_170 ),
inference(avatar_component_clause,[],[f1775]) ).
tff(f1442,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X2 = X4 ) )
| ~ spl28_137 ),
inference(avatar_component_clause,[],[f1441]) ).
tff(f17537,plain,
( spl28_513
| ~ spl28_106
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1794,f1775,f1161,f17535]) ).
tff(f17535,plain,
( spl28_513
<=> ! [X0: $tType,X5: $tType,X6: fun1(type,fun1(X0,X5)),X4: fun1(nat,X0),X3: type,X2: type,X1: fun1(type,fun1(type,X0))] : ( aa(type,X5,aa(fun1(type,X0),fun1(type,X5),aa(fun1(type,fun1(X0,X5)),fun1(fun1(type,X0),fun1(type,X5)),combs(type,X0,X5),X6),aa(type,fun1(type,X0),X1,X2)),X3) = aa(X0,X5,aa(type,fun1(X0,X5),X6,X3),type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_513])]) ).
tff(f1161,plain,
( spl28_106
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: fun1(type,fun1(type,X0)),X2: type,X1: type] : ( aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_106])]) ).
tff(f1794,plain,
( ! [X5: $tType,X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,X0)),X6: fun1(type,fun1(X0,X5)),X4: fun1(nat,X0)] : ( aa(type,X5,aa(fun1(type,X0),fun1(type,X5),aa(fun1(type,fun1(X0,X5)),fun1(fun1(type,X0),fun1(type,X5)),combs(type,X0,X5),X6),aa(type,fun1(type,X0),X1,X2)),X3) = aa(X0,X5,aa(type,fun1(X0,X5),X6,X3),type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2))) )
| ~ spl28_106
| ~ spl28_170 ),
inference(superposition,[],[f1776,f1162]) ).
tff(f1162,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,fun1(type,X0)),X1: type,X4: fun1(nat,X0)] : ( aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun,X1),X2)) )
| ~ spl28_106 ),
inference(avatar_component_clause,[],[f1161]) ).
tff(f17533,plain,
( spl28_512
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1786,f1775,f975,f17531]) ).
tff(f17531,plain,
( spl28_512
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun1(X3,fun1(X0,fun1(X1,X2))),X6: X0,X7: fun1(X0,X1)] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2)),combs(X0,X1,X2),aa(X3,fun1(X0,fun1(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),combc(X3,X0,fun1(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_512])]) ).
tff(f1786,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun1(X0,X1),X4: fun1(X3,fun1(X0,fun1(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2)),combs(X0,X1,X2),aa(X3,fun1(X0,fun1(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),combc(X3,X0,fun1(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl28_80
| ~ spl28_170 ),
inference(superposition,[],[f1776,f976]) ).
tff(f17529,plain,
( spl28_511
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1785,f1775,f975,f17527]) ).
tff(f17527,plain,
( spl28_511
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun1(X0,fun1(X3,fun1(X1,X2))),X6: X0,X7: fun1(X0,X1)] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun1(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),aa(X0,fun1(X3,fun1(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_511])]) ).
tff(f1785,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun1(X0,X1),X4: fun1(X0,fun1(X3,fun1(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun1(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),aa(X0,fun1(X3,fun1(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl28_80
| ~ spl28_170 ),
inference(superposition,[],[f1776,f976]) ).
tff(f17525,plain,
( spl28_510
| ~ spl28_80
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1742,f1734,f975,f17523]) ).
tff(f17523,plain,
( spl28_510
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,aa(X2,fun1(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun1(X0,X1),X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_510])]) ).
tff(f1734,plain,
( spl28_169
<=> ! [X1: $tType,X0: $tType,X4: fun1(X1,X0),X3: X1,X2: list(X1)] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_169])]) ).
tff(f1742,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,aa(X2,fun1(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun1(X0,X1),X3,X4),X6)) )
| ~ spl28_80
| ~ spl28_169 ),
inference(superposition,[],[f1735,f976]) ).
tff(f1735,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl28_169 ),
inference(avatar_component_clause,[],[f1734]) ).
tff(f17521,plain,
( spl28_509
| ~ spl28_106
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1537,f1517,f1161,f17519]) ).
tff(f17519,plain,
( spl28_509
<=> ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(type,X0)),X3: fun1(type,X1),X4: type,X6: fun1(nat,X0),X5: type] : ( type_case(X0,X6,aa(fun1(type,X1),fun1(type,fun1(type,X0)),aa(fun1(X1,fun1(type,X0)),fun1(fun1(type,X1),fun1(type,fun1(type,X0))),combb(X1,fun1(type,X0),type),X2),X3),aa(type,type,combc(type,type,type,fun,X5),X4)) = aa(type,X0,aa(X1,fun1(type,X0),X2,aa(type,X1,X3,X4)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_509])]) ).
tff(f1517,plain,
( spl28_143
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun1(X1,X0),X4: fun1(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_143])]) ).
tff(f1537,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(type,X0)),X3: fun1(type,X1),X6: fun1(nat,X0),X4: type,X5: type] : ( type_case(X0,X6,aa(fun1(type,X1),fun1(type,fun1(type,X0)),aa(fun1(X1,fun1(type,X0)),fun1(fun1(type,X1),fun1(type,fun1(type,X0))),combb(X1,fun1(type,X0),type),X2),X3),aa(type,type,combc(type,type,type,fun,X5),X4)) = aa(type,X0,aa(X1,fun1(type,X0),X2,aa(type,X1,X3,X4)),X5) )
| ~ spl28_106
| ~ spl28_143 ),
inference(superposition,[],[f1162,f1518]) ).
tff(f1518,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X1,X0)] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) )
| ~ spl28_143 ),
inference(avatar_component_clause,[],[f1517]) ).
tff(f17517,plain,
( spl28_508
| ~ spl28_106
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1371,f1356,f1161,f17515]) ).
tff(f17515,plain,
( spl28_508
<=> ! [X0: $tType,X5: list(type),X3: type,X4: fun1(nat,fun1(X0,X0)),X6: X0,X2: type,X1: fun1(type,fun1(type,fun1(X0,X0)))] : ( foldr(type,X0,aa(type,fun1(type,fun1(X0,X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3),X6) = aa(X0,X0,type_case(fun1(X0,X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),foldr(type,X0,aa(type,fun1(type,fun1(X0,X0)),X1,X2),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_508])]) ).
tff(f1356,plain,
( spl28_135
<=> ! [X1: $tType,X0: $tType,X5: fun1(X0,fun1(X1,X1)),X4: X0,X3: list(X0),X2: X1] : ( aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_135])]) ).
tff(f1371,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,fun1(X0,X0))),X6: X0,X4: fun1(nat,fun1(X0,X0)),X5: list(type)] : ( foldr(type,X0,aa(type,fun1(type,fun1(X0,X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3),X6) = aa(X0,X0,type_case(fun1(X0,X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),foldr(type,X0,aa(type,fun1(type,fun1(X0,X0)),X1,X2),X5,X6)) )
| ~ spl28_106
| ~ spl28_135 ),
inference(superposition,[],[f1357,f1162]) ).
tff(f1357,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) )
| ~ spl28_135 ),
inference(avatar_component_clause,[],[f1356]) ).
tff(f17157,plain,
( spl28_507
| ~ spl28_80
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1741,f1734,f975,f17155]) ).
tff(f17155,plain,
( spl28_507
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun1(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_507])]) ).
tff(f1741,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun1(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) )
| ~ spl28_80
| ~ spl28_169 ),
inference(superposition,[],[f1735,f976]) ).
tff(f17153,plain,
( spl28_506
| ~ spl28_152
| ~ spl28_165 ),
inference(avatar_split_clause,[],[f1712,f1706,f1612,f17151]) ).
tff(f17151,plain,
( spl28_506
<=> ! [X2: type,X3: type,X4: dB,X0: fun1(nat,type),X6: list(type),X5: list(dB),X1: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,X6,X3)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_506])]) ).
tff(f1706,plain,
( spl28_165
<=> ! [X4: fun1(nat,type),X0: list(dB),X3: dB,X2: list(type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_165])]) ).
tff(f1712,plain,
( ! [X2: type,X3: type,X0: fun1(nat,type),X1: nat,X6: list(type),X4: dB,X5: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,X6,X3)),X4)) )
| ~ spl28_152
| ~ spl28_165 ),
inference(resolution,[],[f1707,f1613]) ).
tff(f1707,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl28_165 ),
inference(avatar_component_clause,[],[f1706]) ).
tff(f17149,plain,
( spl28_505
| ~ spl28_148
| ~ spl28_150 ),
inference(avatar_split_clause,[],[f1601,f1597,f1576,f17147]) ).
tff(f17147,plain,
( spl28_505
<=> ! [X2: list(dB),X4: dB,X0: fun1(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(foldr(type,type,fun,sK16(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_505])]) ).
tff(f1597,plain,
( spl28_150
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK18(X0,X1,X2,X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_150])]) ).
tff(f1601,plain,
( ! [X2: list(dB),X3: dB,X0: fun1(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(foldr(type,type,fun,sK16(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) )
| ~ spl28_148
| ~ spl28_150 ),
inference(resolution,[],[f1598,f1577]) ).
tff(f1598,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK18(X0,X1,X2,X3)),X1)) )
| ~ spl28_150 ),
inference(avatar_component_clause,[],[f1597]) ).
tff(f17145,plain,
( spl28_504
| ~ spl28_146
| ~ spl28_150 ),
inference(avatar_split_clause,[],[f1600,f1597,f1556,f17143]) ).
tff(f17143,plain,
( spl28_504
<=> ! [X2: list(dB),X4: dB,X0: fun1(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(foldr(type,type,fun,sK15(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_504])]) ).
tff(f1600,plain,
( ! [X2: list(dB),X3: dB,X0: fun1(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(foldr(type,type,fun,sK15(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) )
| ~ spl28_146
| ~ spl28_150 ),
inference(resolution,[],[f1598,f1557]) ).
tff(f14422,plain,
( spl28_503
| ~ spl28_80
| ~ spl28_348
| ~ spl28_502 ),
inference(avatar_split_clause,[],[f14418,f14415,f5544,f975,f14420]) ).
tff(f14420,plain,
( spl28_503
<=> ! [X2: dB,X3: dB,X4: dB,X0: dB,X5: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_503])]) ).
tff(f14415,plain,
( spl28_502
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_502])]) ).
tff(f14418,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) ) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_502 ),
inference(forward_demodulation,[],[f14416,f5589]) ).
tff(f14416,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl28_502 ),
inference(avatar_component_clause,[],[f14415]) ).
tff(f14417,plain,
( spl28_502
| ~ spl28_103
| ~ spl28_203 ),
inference(avatar_split_clause,[],[f2148,f2142,f1132,f14415]) ).
tff(f1132,plain,
( spl28_103
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_103])]) ).
tff(f2142,plain,
( spl28_203
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_203])]) ).
tff(f2148,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl28_103
| ~ spl28_203 ),
inference(superposition,[],[f1133,f2143]) ).
tff(f2143,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl28_203 ),
inference(avatar_component_clause,[],[f2142]) ).
tff(f1133,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X1 = X3 ) )
| ~ spl28_103 ),
inference(avatar_component_clause,[],[f1132]) ).
tff(f14413,plain,
( spl28_501
| ~ spl28_19
| ~ spl28_215 ),
inference(avatar_split_clause,[],[f2778,f2301,f633,f14410]) ).
tff(f14410,plain,
( spl28_501
<=> ( fTrue = aa(fun1(dB,bool),bool,fEx(dB),it) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_501])]) ).
tff(f2301,plain,
( spl28_215
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_215])]) ).
tff(f2778,plain,
( ( fTrue = aa(fun1(dB,bool),bool,fEx(dB),it) )
| ~ spl28_19
| ~ spl28_215 ),
inference(resolution,[],[f2303,f634]) ).
tff(f2303,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),it))
| ~ spl28_215 ),
inference(avatar_component_clause,[],[f2301]) ).
tff(f14394,plain,
( spl28_500
| ~ spl28_80
| ~ spl28_348
| ~ spl28_499 ),
inference(avatar_split_clause,[],[f14390,f14387,f5544,f975,f14392]) ).
tff(f14392,plain,
( spl28_500
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_500])]) ).
tff(f14387,plain,
( spl28_499
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X2) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_499])]) ).
tff(f14390,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) ) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_499 ),
inference(forward_demodulation,[],[f14388,f5589]) ).
tff(f14388,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl28_499 ),
inference(avatar_component_clause,[],[f14387]) ).
tff(f14389,plain,
( spl28_499
| ~ spl28_104
| ~ spl28_203 ),
inference(avatar_split_clause,[],[f2146,f2142,f1136,f14387]) ).
tff(f1136,plain,
( spl28_104
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_104])]) ).
tff(f2146,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl28_104
| ~ spl28_203 ),
inference(superposition,[],[f1137,f2143]) ).
tff(f1137,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X0 = X2 ) )
| ~ spl28_104 ),
inference(avatar_component_clause,[],[f1136]) ).
tff(f14385,plain,
( spl28_498
| ~ spl28_120
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1904,f1894,f1256,f14383]) ).
tff(f14383,plain,
( spl28_498
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK17(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_498])]) ).
tff(f1256,plain,
( spl28_120
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_120])]) ).
tff(f1894,plain,
( spl28_176
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK18(X0,X1,X2,X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_176])]) ).
tff(f1904,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK17(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) )
| ~ spl28_120
| ~ spl28_176 ),
inference(resolution,[],[f1895,f1257]) ).
tff(f1257,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) )
| ~ spl28_120 ),
inference(avatar_component_clause,[],[f1256]) ).
tff(f1895,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK18(X0,X1,X2,X3))),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2))) )
| ~ spl28_176 ),
inference(avatar_component_clause,[],[f1894]) ).
tff(f14381,plain,
( spl28_497
| ~ spl28_136
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1823,f1775,f1360,f14379]) ).
tff(f14379,plain,
( spl28_497
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun1(X1,X0),X5: list(X0),X2: fun1(X1,fun1(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun1(X1,X0),fun1(X1,X1),aa(fun1(X1,fun1(X0,X1)),fun1(fun1(X1,X0),fun1(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_497])]) ).
tff(f1360,plain,
( spl28_136
<=> ! [X1: $tType,X0: $tType,X5: fun1(X0,fun1(X1,X0)),X4: X0,X3: X1,X2: list(X1)] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_136])]) ).
tff(f1823,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,X1)),X3: X1,X4: fun1(X1,X0),X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun1(X1,X0),fun1(X1,X1),aa(fun1(X1,fun1(X0,X1)),fun1(fun1(X1,X0),fun1(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) )
| ~ spl28_136
| ~ spl28_170 ),
inference(superposition,[],[f1361,f1776]) ).
tff(f1361,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl28_136 ),
inference(avatar_component_clause,[],[f1360]) ).
tff(f14377,plain,
( spl28_496
| ~ spl28_128
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1810,f1775,f1307,f14375]) ).
tff(f14375,plain,
( spl28_496
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun1(X0,list(X0)),X3: X0,X2: fun1(X0,fun1(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun1(X0,list(X0)),fun1(X0,X1),aa(fun1(X0,fun1(list(X0),X1)),fun1(fun1(X0,list(X0)),fun1(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_496])]) ).
tff(f1810,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(list(X0),X1)),X3: X0,X4: fun1(X0,list(X0)),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun1(X0,list(X0)),fun1(X0,X1),aa(fun1(X0,fun1(list(X0),X1)),fun1(fun1(X0,list(X0)),fun1(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) )
| ~ spl28_128
| ~ spl28_170 ),
inference(superposition,[],[f1776,f1308]) ).
tff(f14373,plain,
( spl28_495
| ~ spl28_20
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1781,f1775,f637,f14371]) ).
tff(f14371,plain,
( spl28_495
<=> ! [X1: $tType,X0: $tType,X3: fun1(fun1(X0,X1),X0),X2: fun1(X0,X1)] : ( aa(fun1(X0,X1),X1,aa(fun1(fun1(X0,X1),X0),fun1(fun1(X0,X1),X1),aa(fun1(fun1(X0,X1),fun1(X0,X1)),fun1(fun1(fun1(X0,X1),X0),fun1(fun1(X0,X1),X1)),combs(fun1(X0,X1),X0,X1),combi(fun1(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun1(X0,X1),X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_495])]) ).
tff(f637,plain,
( spl28_20
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_20])]) ).
tff(f1781,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,X1),X3: fun1(fun1(X0,X1),X0)] : ( aa(fun1(X0,X1),X1,aa(fun1(fun1(X0,X1),X0),fun1(fun1(X0,X1),X1),aa(fun1(fun1(X0,X1),fun1(X0,X1)),fun1(fun1(fun1(X0,X1),X0),fun1(fun1(X0,X1),X1)),combs(fun1(X0,X1),X0,X1),combi(fun1(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun1(X0,X1),X0,X3,X2)) )
| ~ spl28_20
| ~ spl28_170 ),
inference(superposition,[],[f1776,f638]) ).
tff(f638,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl28_20 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f14369,plain,
( spl28_494
| ~ spl28_148
| ~ spl28_155 ),
inference(avatar_split_clause,[],[f1634,f1630,f1576,f14367]) ).
tff(f14367,plain,
( spl28_494
<=> ! [X5: list(dB),X4: type,X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun,sK16(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_494])]) ).
tff(f1630,plain,
( spl28_155
<=> ! [X4: fun1(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_155])]) ).
tff(f1634,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun,sK16(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) )
| ~ spl28_148
| ~ spl28_155 ),
inference(resolution,[],[f1631,f1577]) ).
tff(f1631,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl28_155 ),
inference(avatar_component_clause,[],[f1630]) ).
tff(f14365,plain,
( spl28_493
| ~ spl28_146
| ~ spl28_155 ),
inference(avatar_split_clause,[],[f1633,f1630,f1556,f14363]) ).
tff(f14363,plain,
( spl28_493
<=> ! [X5: list(dB),X4: type,X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun,sK15(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_493])]) ).
tff(f1633,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun,sK15(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) )
| ~ spl28_146
| ~ spl28_155 ),
inference(resolution,[],[f1631,f1557]) ).
tff(f14361,plain,
( spl28_492
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1395,f1360,f14359]) ).
tff(f14359,plain,
( spl28_492
<=> ! [X1: $tType,X0: $tType,X5: list(X1),X3: X0,X4: X1,X2: fun1(X0,fun1(X1,X0)),X6: X1] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun1(X1,X0),X2,aa(X1,X0,aa(X0,fun1(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_492])]) ).
tff(f1395,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,X0)),X3: X0,X6: X1,X4: X1,X5: list(X1)] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun1(X1,X0),X2,aa(X1,X0,aa(X0,fun1(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) )
| ~ spl28_136 ),
inference(superposition,[],[f1361,f1361]) ).
tff(f14357,plain,
( spl28_491
| ~ spl28_19
| ~ spl28_26 ),
inference(avatar_split_clause,[],[f1476,f673,f633,f14355]) ).
tff(f14355,plain,
( spl28_491
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,sK9(X0)) )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_491])]) ).
tff(f673,plain,
( spl28_26
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_26])]) ).
tff(f1476,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,sK9(X0)) )
| ~ sP0(X0) )
| ~ spl28_19
| ~ spl28_26 ),
inference(resolution,[],[f634,f674]) ).
tff(f674,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) )
| ~ spl28_26 ),
inference(avatar_component_clause,[],[f673]) ).
tff(f14353,plain,
( spl28_490
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1388,f1360,f975,f14351]) ).
tff(f14351,plain,
( spl28_490
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun1(X2,fun1(X0,fun1(X1,X0)))] : ( foldl(X0,X1,aa(X2,fun1(X0,fun1(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun1(X0,fun1(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun1(X1,X0),combc(X2,X0,fun1(X1,X0),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_490])]) ).
tff(f1388,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,fun1(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,aa(X2,fun1(X0,fun1(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun1(X0,fun1(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun1(X1,X0),combc(X2,X0,fun1(X1,X0),X3,X5),X4),X6),X7) )
| ~ spl28_80
| ~ spl28_136 ),
inference(superposition,[],[f1361,f976]) ).
tff(f14349,plain,
( spl28_489
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1375,f1356,f14347]) ).
tff(f14347,plain,
( spl28_489
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X6: X0,X5: X1,X2: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun1(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun1(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_489])]) ).
tff(f1375,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,X1)),X3: list(X0),X6: X0,X4: X0,X5: X1] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun1(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun1(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) )
| ~ spl28_135 ),
inference(superposition,[],[f1357,f1357]) ).
tff(f14345,plain,
( spl28_488
| ~ spl28_80
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1373,f1356,f975,f14343]) ).
tff(f14343,plain,
( spl28_488
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun1(X2,fun1(X0,fun1(X1,X1)))] : ( foldr(X0,X1,aa(X2,fun1(X0,fun1(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun1(X1,X1),combc(X2,X0,fun1(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun1(X0,fun1(X1,X1)),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_488])]) ).
tff(f1373,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,fun1(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,aa(X2,fun1(X0,fun1(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun1(X1,X1),combc(X2,X0,fun1(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun1(X0,fun1(X1,X1)),X3,X4),X6,X7)) )
| ~ spl28_80
| ~ spl28_135 ),
inference(superposition,[],[f1357,f976]) ).
tff(f13840,plain,
( spl28_487
| ~ spl28_176
| ~ spl28_189 ),
inference(avatar_split_clause,[],[f2032,f2028,f1894,f13838]) ).
tff(f13838,plain,
( spl28_487
<=> ! [X4: dB,X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(X1,X2,X3,X0)),X4))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_487])]) ).
tff(f2028,plain,
( spl28_189
<=> ! [X4: fun1(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_189])]) ).
tff(f2032,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK18(X1,X2,X3,X0)),X4))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3))) )
| ~ spl28_176
| ~ spl28_189 ),
inference(resolution,[],[f2029,f1895]) ).
tff(f2029,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl28_189 ),
inference(avatar_component_clause,[],[f2028]) ).
tff(f13834,plain,
( spl28_486
| ~ spl28_69
| ~ spl28_80
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1770,f1734,f975,f916,f13832]) ).
tff(f13832,plain,
( spl28_486
<=> ! [X0: type,X1: list(type)] :
( ( map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),aa(type,list(type),combc(type,list(type),list(type),cons(type),X1),sK3(X0))) = aa(type,list(type),combc(type,list(type),list(type),cons(type),map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),X1)),X0) )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_486])]) ).
tff(f916,plain,
( spl28_69
<=> ! [X0: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK2(X0)),sK3(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_69])]) ).
tff(f1770,plain,
( ! [X0: type,X1: list(type)] :
( ( map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),aa(type,list(type),combc(type,list(type),list(type),cons(type),X1),sK3(X0))) = aa(type,list(type),combc(type,list(type),list(type),cons(type),map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),X1)),X0) )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_80
| ~ spl28_169 ),
inference(forward_demodulation,[],[f1750,f976]) ).
tff(f1750,plain,
( ! [X0: type,X1: list(type)] :
( ( map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),aa(type,list(type),combc(type,list(type),list(type),cons(type),X1),sK3(X0))) = aa(list(type),list(type),aa(type,fun1(list(type),list(type)),cons(type),X0),map(type,type,aa(type,fun1(type,type),fun,sK2(X0)),X1)) )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_169 ),
inference(superposition,[],[f1735,f917]) ).
tff(f917,plain,
( ! [X0: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK2(X0)),sK3(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69 ),
inference(avatar_component_clause,[],[f916]) ).
tff(f13830,plain,
( spl28_485
| ~ spl28_118
| ~ spl28_167 ),
inference(avatar_split_clause,[],[f1726,f1723,f1245,f13828]) ).
tff(f13828,plain,
( spl28_485
<=> ! [X4: list(type),X0: fun1(nat,type),X3: list(dB),X2: type,X1: nat] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_485])]) ).
tff(f1245,plain,
( spl28_118
<=> ! [X4: fun1(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_118])]) ).
tff(f1723,plain,
( spl28_167
<=> ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_167])]) ).
tff(f1726,plain,
( ! [X2: type,X3: list(dB),X0: fun1(nat,type),X1: nat,X4: list(type)] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl28_118
| ~ spl28_167 ),
inference(resolution,[],[f1724,f1246]) ).
tff(f1246,plain,
( ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) )
| ~ spl28_118 ),
inference(avatar_component_clause,[],[f1245]) ).
tff(f1724,plain,
( ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X2,X1),X0))
| listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(X2)),fEx(type)),X1) )
| ~ spl28_167 ),
inference(avatar_component_clause,[],[f1723]) ).
tff(f13826,plain,
( spl28_484
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1387,f1360,f975,f13824]) ).
tff(f13824,plain,
( spl28_484
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun1(X0,fun1(X2,fun1(X1,X0)))] : ( foldl(X0,X1,combc(X0,X2,fun1(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun1(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun1(X1,X0),aa(X0,fun1(X2,fun1(X1,X0)),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_484])]) ).
tff(f1387,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,fun1(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,combc(X0,X2,fun1(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun1(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun1(X1,X0),aa(X0,fun1(X2,fun1(X1,X0)),X3,X5),X4),X6),X7) )
| ~ spl28_80
| ~ spl28_136 ),
inference(superposition,[],[f1361,f976]) ).
tff(f13822,plain,
( spl28_483
| ~ spl28_80
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1372,f1356,f975,f13820]) ).
tff(f13820,plain,
( spl28_483
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun1(X0,fun1(X2,fun1(X1,X1)))] : ( foldr(X0,X1,combc(X0,X2,fun1(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun1(X1,X1),aa(X0,fun1(X2,fun1(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun1(X1,X1),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_483])]) ).
tff(f1372,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,fun1(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,combc(X0,X2,fun1(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun1(X1,X1),aa(X0,fun1(X2,fun1(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun1(X1,X1),X3,X4),X6,X7)) )
| ~ spl28_80
| ~ spl28_135 ),
inference(superposition,[],[f1357,f976]) ).
tff(f13818,plain,
( spl28_482
| ~ spl28_32
| ~ spl28_70 ),
inference(avatar_split_clause,[],[f928,f920,f708,f13816]) ).
tff(f13816,plain,
( spl28_482
<=> ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK5(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK7(foldl(dB,dB,app,var(X0),X1))),sK6(foldl(dB,dB,app,var(X0),X1))) )
| sP0(foldl(dB,dB,app,var(X0),X1))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_482])]) ).
tff(f708,plain,
( spl28_32
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_32])]) ).
tff(f920,plain,
( spl28_70
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_70])]) ).
tff(f928,plain,
( ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK5(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK7(foldl(dB,dB,app,var(X0),X1))),sK6(foldl(dB,dB,app,var(X0),X1))) )
| sP0(foldl(dB,dB,app,var(X0),X1))
| ~ listsp(dB,it,X1) )
| ~ spl28_32
| ~ spl28_70 ),
inference(resolution,[],[f921,f709]) ).
tff(f709,plain,
( ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) )
| ~ spl28_32 ),
inference(avatar_component_clause,[],[f708]) ).
tff(f921,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( abs(sK5(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| sP0(X0) )
| ~ spl28_70 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f12746,plain,
( spl28_481
| ~ spl28_4
| ~ spl28_217
| ~ spl28_420 ),
inference(avatar_split_clause,[],[f12532,f8951,f2786,f562,f12744]) ).
tff(f12744,plain,
( spl28_481
<=> ! [X0: nat] : sP1(abs(abs(abs(var(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_481])]) ).
tff(f2786,plain,
( spl28_217
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_217])]) ).
tff(f8951,plain,
( spl28_420
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_420])]) ).
tff(f12532,plain,
( ! [X0: nat] :
( ~ pp(fTrue)
| sP1(abs(abs(abs(var(X0))))) )
| ~ spl28_217
| ~ spl28_420 ),
inference(superposition,[],[f2787,f8952]) ).
tff(f8952,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl28_420 ),
inference(avatar_component_clause,[],[f8951]) ).
tff(f2787,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl28_217 ),
inference(avatar_component_clause,[],[f2786]) ).
tff(f12605,plain,
( spl28_480
| ~ spl28_115
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1902,f1894,f1226,f12603]) ).
tff(f12603,plain,
( spl28_480
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_480])]) ).
tff(f1226,plain,
( spl28_115
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_115])]) ).
tff(f1902,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl28_115
| ~ spl28_176 ),
inference(resolution,[],[f1895,f1227]) ).
tff(f1227,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl28_115 ),
inference(avatar_component_clause,[],[f1226]) ).
tff(f12601,plain,
( spl28_479
| ~ spl28_117
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1901,f1894,f1238,f12599]) ).
tff(f12599,plain,
( spl28_479
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK16(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_479])]) ).
tff(f1238,plain,
( spl28_117
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_117])]) ).
tff(f1901,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK16(aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl28_117
| ~ spl28_176 ),
inference(resolution,[],[f1895,f1239]) ).
tff(f1239,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl28_117 ),
inference(avatar_component_clause,[],[f1238]) ).
tff(f12597,plain,
( spl28_478
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1796,f1775,f975,f12595]) ).
tff(f12595,plain,
( spl28_478
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: X0,X7: fun1(X0,fun1(X1,X6))] : ( aa(X0,X6,aa(fun1(X0,X1),fun1(X0,X6),aa(fun1(X0,fun1(X1,X6)),fun1(fun1(X0,X1),fun1(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun1(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun1(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_478])]) ).
tff(f1796,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X7: fun1(X0,fun1(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun1(X0,X1),fun1(X0,X6),aa(fun1(X0,fun1(X1,X6)),fun1(fun1(X0,X1),fun1(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun1(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun1(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) )
| ~ spl28_80
| ~ spl28_170 ),
inference(superposition,[],[f1776,f976]) ).
tff(f12593,plain,
( spl28_477
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1795,f1775,f975,f12591]) ).
tff(f12591,plain,
( spl28_477
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X4: X2,X5: X0,X7: fun1(X0,fun1(X1,X6))] : ( aa(X0,X6,aa(fun1(X0,X1),fun1(X0,X6),aa(fun1(X0,fun1(X1,X6)),fun1(fun1(X0,X1),fun1(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun1(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun1(X2,X1),X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_477])]) ).
tff(f1795,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X7: fun1(X0,fun1(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun1(X0,X1),fun1(X0,X6),aa(fun1(X0,fun1(X1,X6)),fun1(fun1(X0,X1),fun1(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun1(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun1(X2,X1),X3,X5),X4)) )
| ~ spl28_80
| ~ spl28_170 ),
inference(superposition,[],[f1776,f976]) ).
tff(f12589,plain,
( spl28_476
| ~ spl28_80
| ~ spl28_136
| ~ spl28_155 ),
inference(avatar_split_clause,[],[f1641,f1630,f1360,f975,f12587]) ).
tff(f12587,plain,
( spl28_476
<=> ! [X3: fun1(nat,type),X4: type,X0: nat,X5: type,X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ( X4 = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_476])]) ).
tff(f1641,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ( X4 = X5 ) )
| ~ spl28_80
| ~ spl28_136
| ~ spl28_155 ),
inference(forward_demodulation,[],[f1640,f976]) ).
tff(f1640,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl28_80
| ~ spl28_136
| ~ spl28_155 ),
inference(forward_demodulation,[],[f1638,f976]) ).
tff(f1638,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl28_136
| ~ spl28_155 ),
inference(superposition,[],[f1631,f1361]) ).
tff(f12585,plain,
( spl28_475
| ~ spl28_80
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1541,f1517,f975,f12583]) ).
tff(f12583,plain,
( spl28_475
<=> ! [X1: $tType,X3: $tType,X0: $tType,X2: $tType,X5: fun1(X0,X3),X4: fun1(X3,fun1(X1,X2)),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun1(X0,X3),fun1(X0,fun1(X1,X2)),aa(fun1(X3,fun1(X1,X2)),fun1(fun1(X0,X3),fun1(X0,fun1(X1,X2))),combb(X3,fun1(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),X4,aa(X0,X3,X5,X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_475])]) ).
tff(f1541,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun1(X3,fun1(X1,X2)),X5: fun1(X0,X3)] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun1(X0,X3),fun1(X0,fun1(X1,X2)),aa(fun1(X3,fun1(X1,X2)),fun1(fun1(X0,X3),fun1(X0,fun1(X1,X2))),combb(X3,fun1(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),X4,aa(X0,X3,X5,X6)),X7) )
| ~ spl28_80
| ~ spl28_143 ),
inference(superposition,[],[f976,f1518]) ).
tff(f12557,plain,
( spl28_474
| ~ spl28_127
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1993,f1982,f1296,f12555]) ).
tff(f12555,plain,
( spl28_474
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_474])]) ).
tff(f1993,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) )
| ~ spl28_127
| ~ spl28_184 ),
inference(resolution,[],[f1983,f1298]) ).
tff(f12527,plain,
( spl28_473
| ~ spl28_135
| ~ spl28_139 ),
inference(avatar_split_clause,[],[f1489,f1449,f1356,f12525]) ).
tff(f12525,plain,
( spl28_473
<=> ! [X0: $tType,X4: $tType,X5: fun1(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK26(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_473])]) ).
tff(f1449,plain,
( spl28_139
<=> ! [X1: $tType,X0: $tType,X3: fun1(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_139])]) ).
tff(f1489,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun1(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK26(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) )
| ~ spl28_135
| ~ spl28_139 ),
inference(superposition,[],[f1450,f1357]) ).
tff(f1450,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( map(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl28_139 ),
inference(avatar_component_clause,[],[f1449]) ).
tff(f12523,plain,
( spl28_472
| ~ spl28_135
| ~ spl28_138 ),
inference(avatar_split_clause,[],[f1485,f1445,f1356,f12521]) ).
tff(f12521,plain,
( spl28_472
<=> ! [X0: $tType,X4: $tType,X5: fun1(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK24(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_472])]) ).
tff(f1445,plain,
( spl28_138
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun1(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_138])]) ).
tff(f1485,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun1(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK24(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) )
| ~ spl28_135
| ~ spl28_138 ),
inference(superposition,[],[f1446,f1357]) ).
tff(f1446,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( map(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl28_138 ),
inference(avatar_component_clause,[],[f1445]) ).
tff(f12269,plain,
( spl28_471
| ~ spl28_118
| ~ spl28_177 ),
inference(avatar_split_clause,[],[f1913,f1910,f1245,f12267]) ).
tff(f12267,plain,
( spl28_471
<=> ! [X5: type,X4: list(type),X0: fun1(nat,type),X3: list(dB),X2: nat,X1: dB] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_471])]) ).
tff(f1910,plain,
( spl28_177
<=> ! [X2: nat,X4: dB,X0: list(type),X5: fun1(nat,type),X3: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_177])]) ).
tff(f1913,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: dB,X4: list(type),X5: type] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl28_118
| ~ spl28_177 ),
inference(resolution,[],[f1911,f1246]) ).
tff(f1911,plain,
( ! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun1(nat,type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4)) )
| ~ spl28_177 ),
inference(avatar_component_clause,[],[f1910]) ).
tff(f12265,plain,
( spl28_470
| ~ spl28_69
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1859,f1775,f975,f916,f12263]) ).
tff(f12263,plain,
( spl28_470
<=> ! [X1: $tType,X2: fun1(type,fun1(type,X1)),X0: type] :
( ( aa(type,X1,aa(fun1(type,type),fun1(type,X1),aa(fun1(type,fun1(type,X1)),fun1(fun1(type,type),fun1(type,X1)),combs(type,type,X1),X2),aa(type,fun1(type,type),fun,sK2(X0))),sK3(X0)) = aa(type,X1,combc(type,type,X1,X2,X0),sK3(X0)) )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_470])]) ).
tff(f1859,plain,
( ! [X1: $tType,X2: fun1(type,fun1(type,X1)),X0: type] :
( ( aa(type,X1,aa(fun1(type,type),fun1(type,X1),aa(fun1(type,fun1(type,X1)),fun1(fun1(type,type),fun1(type,X1)),combs(type,type,X1),X2),aa(type,fun1(type,type),fun,sK2(X0))),sK3(X0)) = aa(type,X1,combc(type,type,X1,X2,X0),sK3(X0)) )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_80
| ~ spl28_170 ),
inference(forward_demodulation,[],[f1805,f976]) ).
tff(f1805,plain,
( ! [X1: $tType,X2: fun1(type,fun1(type,X1)),X0: type] :
( ( aa(type,X1,aa(fun1(type,type),fun1(type,X1),aa(fun1(type,fun1(type,X1)),fun1(fun1(type,type),fun1(type,X1)),combs(type,type,X1),X2),aa(type,fun1(type,type),fun,sK2(X0))),sK3(X0)) = aa(type,X1,aa(type,fun1(type,X1),X2,sK3(X0)),X0) )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_170 ),
inference(superposition,[],[f1776,f917]) ).
tff(f12261,plain,
( spl28_469
| ~ spl28_77
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1857,f1775,f975,f958,f12259]) ).
tff(f12259,plain,
( spl28_469
<=> ! [X2: $tType,X0: dB,X3: fun1(nat,fun1(dB,X2)),X1: nat] : ( aa(nat,X2,aa(fun1(nat,dB),fun1(nat,X2),aa(fun1(nat,fun1(dB,X2)),fun1(fun1(nat,dB),fun1(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_469])]) ).
tff(f958,plain,
( spl28_77
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_77])]) ).
tff(f1857,plain,
( ! [X2: $tType,X3: fun1(nat,fun1(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun1(nat,dB),fun1(nat,X2),aa(fun1(nat,fun1(dB,X2)),fun1(fun1(nat,dB),fun1(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) )
| ~ spl28_77
| ~ spl28_80
| ~ spl28_170 ),
inference(forward_demodulation,[],[f1802,f976]) ).
tff(f1802,plain,
( ! [X2: $tType,X3: fun1(nat,fun1(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun1(nat,dB),fun1(nat,X2),aa(fun1(nat,fun1(dB,X2)),fun1(fun1(nat,dB),fun1(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1))),X1) = aa(dB,X2,aa(nat,fun1(dB,X2),X3,X1),X0) )
| ~ spl28_77
| ~ spl28_170 ),
inference(superposition,[],[f1776,f959]) ).
tff(f959,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl28_77 ),
inference(avatar_component_clause,[],[f958]) ).
tff(f12086,plain,
( spl28_468
| ~ spl28_80
| ~ spl28_348
| ~ spl28_467 ),
inference(avatar_split_clause,[],[f12082,f12079,f5544,f975,f12084]) ).
tff(f12084,plain,
( spl28_468
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_468])]) ).
tff(f12079,plain,
( spl28_467
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_467])]) ).
tff(f12082,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_467 ),
inference(forward_demodulation,[],[f12080,f5589]) ).
tff(f12080,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl28_467 ),
inference(avatar_component_clause,[],[f12079]) ).
tff(f12081,plain,
( spl28_467
| ~ spl28_18
| ~ spl28_186 ),
inference(avatar_split_clause,[],[f2008,f2004,f629,f12079]) ).
tff(f629,plain,
( spl28_18
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_18])]) ).
tff(f2004,plain,
( spl28_186
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_186])]) ).
tff(f2008,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl28_18
| ~ spl28_186 ),
inference(resolution,[],[f2005,f630]) ).
tff(f630,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl28_18 ),
inference(avatar_component_clause,[],[f629]) ).
tff(f2005,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_186 ),
inference(avatar_component_clause,[],[f2004]) ).
tff(f12077,plain,
( spl28_466
| ~ spl28_80
| ~ spl28_181 ),
inference(avatar_split_clause,[],[f1976,f1944,f975,f12075]) ).
tff(f12075,plain,
( spl28_466
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun1(list(X3),list(X3)),cons(X3),sK25(X0,X3,X5,X4,X2,X1)),sK26(X0,X3,X5,X4,X2,X1)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_466])]) ).
tff(f1944,plain,
( spl28_181
<=> ! [X1: $tType,X0: $tType,X3: fun1(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),sK25(X0,X1,X2,X3,X4,X5)),sK26(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_181])]) ).
tff(f1976,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun1(list(X3),list(X3)),cons(X3),sK25(X0,X3,X5,X4,X2,X1)),sK26(X0,X3,X5,X4,X2,X1)) = X5 ) )
| ~ spl28_80
| ~ spl28_181 ),
inference(superposition,[],[f1945,f976]) ).
tff(f1945,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),sK25(X0,X1,X2,X3,X4,X5)),sK26(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl28_181 ),
inference(avatar_component_clause,[],[f1944]) ).
tff(f12073,plain,
( spl28_465
| ~ spl28_80
| ~ spl28_180 ),
inference(avatar_split_clause,[],[f1968,f1940,f975,f12071]) ).
tff(f12071,plain,
( spl28_465
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun1(list(X3),list(X3)),cons(X3),sK23(X3,X0,X2,X1,X5,X4)),sK24(X3,X0,X2,X1,X5,X4)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_465])]) ).
tff(f1940,plain,
( spl28_180
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun1(X0,X1),X2: list(X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_180])]) ).
tff(f1968,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun1(list(X3),list(X3)),cons(X3),sK23(X3,X0,X2,X1,X5,X4)),sK24(X3,X0,X2,X1,X5,X4)) = X5 ) )
| ~ spl28_80
| ~ spl28_180 ),
inference(superposition,[],[f1941,f976]) ).
tff(f1941,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl28_180 ),
inference(avatar_component_clause,[],[f1940]) ).
tff(f12069,plain,
( spl28_464
| ~ spl28_62
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1849,f1775,f878,f12067]) ).
tff(f12067,plain,
( spl28_464
<=> ! [X0: $tType,X3: fun1(X0,nat),X2: X0,X1: fun1(X0,fun1(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun1(nat,type),X1,X2)),aa(X0,type,aa(fun1(X0,nat),fun1(X0,type),aa(fun1(X0,fun1(nat,type)),fun1(fun1(X0,nat),fun1(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_464])]) ).
tff(f878,plain,
( spl28_62
<=> ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_62])]) ).
tff(f1849,plain,
( ! [X0: $tType,X2: X0,X3: fun1(X0,nat),X1: fun1(X0,fun1(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun1(nat,type),X1,X2)),aa(X0,type,aa(fun1(X0,nat),fun1(X0,type),aa(fun1(X0,fun1(nat,type)),fun1(fun1(X0,nat),fun1(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2))))
| ~ spl28_62
| ~ spl28_170 ),
inference(superposition,[],[f879,f1776]) ).
tff(f879,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl28_62 ),
inference(avatar_component_clause,[],[f878]) ).
tff(f11947,plain,
( spl28_463
| ~ spl28_4
| ~ spl28_217
| ~ spl28_412 ),
inference(avatar_split_clause,[],[f11515,f8802,f2786,f562,f11944]) ).
tff(f11944,plain,
( spl28_463
<=> sP1(abs(abs(abs(abs(ua))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_463])]) ).
tff(f8802,plain,
( spl28_412
<=> ( fTrue = aa(dB,bool,it,abs(abs(ua))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_412])]) ).
tff(f11515,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(ua)))))
| ~ spl28_217
| ~ spl28_412 ),
inference(superposition,[],[f2787,f8804]) ).
tff(f8804,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl28_412 ),
inference(avatar_component_clause,[],[f8802]) ).
tff(f11547,plain,
( spl28_462
| ~ spl28_161
| ~ spl28_189 ),
inference(avatar_split_clause,[],[f2031,f2028,f1675,f11545]) ).
tff(f11545,plain,
( spl28_462
<=> ! [X4: dB,X0: fun1(nat,type),X3: type,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_462])]) ).
tff(f2031,plain,
( ! [X2: dB,X3: type,X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) )
| ~ spl28_161
| ~ spl28_189 ),
inference(resolution,[],[f2029,f1676]) ).
tff(f11543,plain,
( spl28_461
| ~ spl28_62
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1860,f1775,f975,f878,f11541]) ).
tff(f11541,plain,
( spl28_461
<=> ! [X0: $tType,X3: nat,X2: fun1(nat,X0),X1: fun1(nat,fun1(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(nat,X0),fun1(nat,type),aa(fun1(nat,fun1(X0,type)),fun1(fun1(nat,X0),fun1(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_461])]) ).
tff(f1860,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: fun1(nat,fun1(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(nat,X0),fun1(nat,type),aa(fun1(nat,fun1(X0,type)),fun1(fun1(nat,X0),fun1(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3)))
| ~ spl28_62
| ~ spl28_80
| ~ spl28_170 ),
inference(forward_demodulation,[],[f1815,f976]) ).
tff(f1815,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: fun1(nat,fun1(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(nat,X0),fun1(nat,type),aa(fun1(nat,fun1(X0,type)),fun1(fun1(nat,X0),fun1(nat,type)),combs(nat,X0,type),X1),X2)),aa(X0,type,aa(nat,fun1(X0,type),X1,X3),aa(nat,X0,X2,X3))),var(X3)))
| ~ spl28_62
| ~ spl28_170 ),
inference(superposition,[],[f879,f1776]) ).
tff(f11539,plain,
( spl28_460
| ~ spl28_139
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1760,f1734,f1449,f11537]) ).
tff(f11537,plain,
( spl28_460
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun1(X1,X0),X6: fun1(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK26(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_460])]) ).
tff(f1760,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: fun1(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK26(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl28_139
| ~ spl28_169 ),
inference(superposition,[],[f1450,f1735]) ).
tff(f11535,plain,
( spl28_459
| ~ spl28_138
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1759,f1734,f1445,f11533]) ).
tff(f11533,plain,
( spl28_459
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun1(X1,X0),X6: fun1(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK24(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_459])]) ).
tff(f1759,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: fun1(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK24(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl28_138
| ~ spl28_169 ),
inference(superposition,[],[f1446,f1735]) ).
tff(f11510,plain,
( spl28_458
| ~ spl28_120
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1585,f1576,f1256,f11508]) ).
tff(f11508,plain,
( spl28_458
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK17(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_458])]) ).
tff(f1585,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK17(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl28_120
| ~ spl28_148 ),
inference(resolution,[],[f1577,f1257]) ).
tff(f11506,plain,
( spl28_457
| ~ spl28_120
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1565,f1556,f1256,f11504]) ).
tff(f11504,plain,
( spl28_457
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK17(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_457])]) ).
tff(f1565,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK17(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl28_120
| ~ spl28_146 ),
inference(resolution,[],[f1557,f1257]) ).
tff(f11502,plain,
( spl28_456
| ~ spl28_106
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1311,f1307,f1161,f11500]) ).
tff(f11500,plain,
( spl28_456
<=> ! [X0: $tType,X3: type,X4: fun1(nat,fun1(list(type),X0)),X6: X0,X5: list(type),X2: type,X1: fun1(type,fun1(type,fun1(list(type),X0)))] : ( list_case(X0,type,X6,aa(type,fun1(type,fun1(list(type),X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3)) = aa(list(type),X0,type_case(fun1(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_456])]) ).
tff(f1311,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,fun1(list(type),X0))),X6: X0,X4: fun1(nat,fun1(list(type),X0)),X5: list(type)] : ( list_case(X0,type,X6,aa(type,fun1(type,fun1(list(type),X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3)) = aa(list(type),X0,type_case(fun1(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),X5) )
| ~ spl28_106
| ~ spl28_128 ),
inference(superposition,[],[f1308,f1162]) ).
tff(f11498,plain,
( spl28_455
| ~ spl28_94
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1172,f1161,f1078,f11496]) ).
tff(f11496,plain,
( spl28_455
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: fun1(type,X0),X2: type,X1: fun1(type,fun1(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,sK19(X0,type,aa(type,fun1(type,X0),X1,X2),X3)),X2)) != aa(type,X0,X3,sK19(X0,type,aa(type,fun1(type,X0),X1,X2),X3)) )
| ( aa(type,fun1(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_455])]) ).
tff(f1172,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,X0),X1: fun1(type,fun1(type,X0)),X4: fun1(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,sK19(X0,type,aa(type,fun1(type,X0),X1,X2),X3)),X2)) != aa(type,X0,X3,sK19(X0,type,aa(type,fun1(type,X0),X1,X2),X3)) )
| ( aa(type,fun1(type,X0),X1,X2) = X3 ) )
| ~ spl28_94
| ~ spl28_106 ),
inference(superposition,[],[f1079,f1162]) ).
tff(f11494,plain,
( spl28_454
| ~ spl28_94
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1171,f1161,f1078,f11492]) ).
tff(f11492,plain,
( spl28_454
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: fun1(type,X0),X2: type,X1: fun1(type,fun1(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,sK19(X0,type,X3,aa(type,fun1(type,X0),X1,X2))),X2)) != aa(type,X0,X3,sK19(X0,type,X3,aa(type,fun1(type,X0),X1,X2))) )
| ( aa(type,fun1(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_454])]) ).
tff(f1171,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,X0),X1: fun1(type,fun1(type,X0)),X4: fun1(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,sK19(X0,type,X3,aa(type,fun1(type,X0),X1,X2))),X2)) != aa(type,X0,X3,sK19(X0,type,X3,aa(type,fun1(type,X0),X1,X2))) )
| ( aa(type,fun1(type,X0),X1,X2) = X3 ) )
| ~ spl28_94
| ~ spl28_106 ),
inference(superposition,[],[f1079,f1162]) ).
tff(f10799,plain,
( spl28_453
| ~ spl28_80
| ~ spl28_348
| ~ spl28_452 ),
inference(avatar_split_clause,[],[f10795,f10792,f5544,f975,f10797]) ).
tff(f10797,plain,
( spl28_453
<=> ! [X4: nat,X0: fun1(nat,type),X3: nat,X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_453])]) ).
tff(f10792,plain,
( spl28_452
<=> ! [X4: nat,X0: fun1(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X4)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_452])]) ).
tff(f10795,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_452 ),
inference(forward_demodulation,[],[f10793,f5589]) ).
tff(f10793,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl28_452 ),
inference(avatar_component_clause,[],[f10792]) ).
tff(f10794,plain,
( spl28_452
| ~ spl28_62
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1989,f1982,f878,f10792]) ).
tff(f1989,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl28_62
| ~ spl28_184 ),
inference(resolution,[],[f1983,f879]) ).
tff(f10790,plain,
( spl28_451
| ~ spl28_27
| ~ spl28_80
| ~ spl28_181 ),
inference(avatar_split_clause,[],[f1980,f1944,f975,f677,f10788]) ).
tff(f10788,plain,
( spl28_451
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK25(X0,X0,X1,combi(X0),X3,X2)),sK26(X0,X0,X1,combi(X0),X3,X2)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_451])]) ).
tff(f677,plain,
( spl28_27
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_27])]) ).
tff(f1980,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK25(X0,X0,X1,combi(X0),X3,X2)),sK26(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl28_27
| ~ spl28_80
| ~ spl28_181 ),
inference(forward_demodulation,[],[f1978,f976]) ).
tff(f1978,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK25(X0,X0,X1,combi(X0),X3,X2)),sK26(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl28_27
| ~ spl28_181 ),
inference(superposition,[],[f1945,f678]) ).
tff(f678,plain,
( ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 )
| ~ spl28_27 ),
inference(avatar_component_clause,[],[f677]) ).
tff(f10786,plain,
( spl28_450
| ~ spl28_27
| ~ spl28_80
| ~ spl28_180 ),
inference(avatar_split_clause,[],[f1972,f1940,f975,f677,f10784]) ).
tff(f10784,plain,
( spl28_450
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X0,X3,X2,X1,combi(X0))),sK24(X0,X0,X3,X2,X1,combi(X0))) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_450])]) ).
tff(f1972,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X0,X3,X2,X1,combi(X0))),sK24(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl28_27
| ~ spl28_80
| ~ spl28_180 ),
inference(forward_demodulation,[],[f1970,f976]) ).
tff(f1970,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X0,X3,X2,X1,combi(X0))),sK24(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl28_27
| ~ spl28_180 ),
inference(superposition,[],[f1941,f678]) ).
tff(f10782,plain,
( spl28_449
| ~ spl28_49
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1814,f1775,f795,f10780]) ).
tff(f10780,plain,
( spl28_449
<=> ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X4: X0,X3: fun1(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X0,fun1(X1,bool)),fun1(fun1(X0,X1),fun1(X0,bool)),combs(X0,X1,bool),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_449])]) ).
tff(f795,plain,
( spl28_49
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_49])]) ).
tff(f1814,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X3: fun1(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X0,fun1(X1,bool)),fun1(fun1(X0,X1),fun1(X0,bool)),combs(X0,X1,bool),X2),X3))) )
| ~ spl28_49
| ~ spl28_170 ),
inference(superposition,[],[f796,f1776]) ).
tff(f796,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun1(X0,bool),bool,fEx(X0),X2)) )
| ~ spl28_49 ),
inference(avatar_component_clause,[],[f795]) ).
tff(f10778,plain,
( spl28_448
| ~ spl28_134
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1756,f1734,f1352,f10776]) ).
tff(f10776,plain,
( spl28_448
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun1(X1,X0),X6: fun1(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK25(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_448])]) ).
tff(f1352,plain,
( spl28_134
<=> ! [X1: $tType,X0: $tType,X3: fun1(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK25(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_134])]) ).
tff(f1756,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: fun1(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK25(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl28_134
| ~ spl28_169 ),
inference(superposition,[],[f1353,f1735]) ).
tff(f1353,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(X1,X0,X3,sK25(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl28_134 ),
inference(avatar_component_clause,[],[f1352]) ).
tff(f10774,plain,
( spl28_447
| ~ spl28_4
| ~ spl28_217
| ~ spl28_406 ),
inference(avatar_split_clause,[],[f10131,f8605,f2786,f562,f10771]) ).
tff(f10771,plain,
( spl28_447
<=> sP1(abs(abs(abs(abs(u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_447])]) ).
tff(f8605,plain,
( spl28_406
<=> ( fTrue = aa(dB,bool,it,abs(abs(u))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_406])]) ).
tff(f10131,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(u)))))
| ~ spl28_217
| ~ spl28_406 ),
inference(superposition,[],[f2787,f8607]) ).
tff(f8607,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl28_406 ),
inference(avatar_component_clause,[],[f8605]) ).
tff(f10769,plain,
( spl28_446
| ~ spl28_133
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1755,f1734,f1348,f10767]) ).
tff(f10767,plain,
( spl28_446
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun1(X1,X0),X6: fun1(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK23(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_446])]) ).
tff(f1348,plain,
( spl28_133
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun1(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK23(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_133])]) ).
tff(f1755,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: fun1(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK23(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl28_133
| ~ spl28_169 ),
inference(superposition,[],[f1349,f1735]) ).
tff(f1349,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(X0,X1,X5,sK23(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl28_133 ),
inference(avatar_component_clause,[],[f1348]) ).
tff(f10765,plain,
( spl28_445
| ~ spl28_135
| ~ spl28_142 ),
inference(avatar_split_clause,[],[f1521,f1513,f1356,f10763]) ).
tff(f10763,plain,
( spl28_445
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_445])]) ).
tff(f1513,plain,
( spl28_142
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_142])]) ).
tff(f1521,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) )
| ~ spl28_135
| ~ spl28_142 ),
inference(superposition,[],[f1514,f1357]) ).
tff(f1514,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 = X3 ) )
| ~ spl28_142 ),
inference(avatar_component_clause,[],[f1513]) ).
tff(f10761,plain,
( spl28_444
| ~ spl28_80
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1313,f1307,f975,f10759]) ).
tff(f10759,plain,
( spl28_444
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun1(X2,fun1(X0,fun1(list(X0),X1)))] : ( list_case(X1,X0,X7,aa(X2,fun1(X0,fun1(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun1(list(X0),X1),combc(X2,X0,fun1(list(X0),X1),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_444])]) ).
tff(f1313,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,fun1(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,aa(X2,fun1(X0,fun1(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun1(list(X0),X1),combc(X2,X0,fun1(list(X0),X1),X3,X5),X4),X6) )
| ~ spl28_80
| ~ spl28_128 ),
inference(superposition,[],[f1308,f976]) ).
tff(f10757,plain,
( spl28_443
| ~ spl28_80
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1312,f1307,f975,f10755]) ).
tff(f10755,plain,
( spl28_443
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun1(X0,fun1(X2,fun1(list(X0),X1)))] : ( list_case(X1,X0,X7,combc(X0,X2,fun1(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun1(list(X0),X1),aa(X0,fun1(X2,fun1(list(X0),X1)),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_443])]) ).
tff(f1312,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,fun1(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,combc(X0,X2,fun1(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun1(list(X0),X1),aa(X0,fun1(X2,fun1(list(X0),X1)),X3,X5),X4),X6) )
| ~ spl28_80
| ~ spl28_128 ),
inference(superposition,[],[f1308,f976]) ).
tff(f9665,plain,
( spl28_442
| ~ spl28_108
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1897,f1894,f1182,f9663]) ).
tff(f9663,plain,
( spl28_442
<=> ! [X4: dB,X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,X3,X0))),X4))
| ~ beta(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_442])]) ).
tff(f1182,plain,
( spl28_108
<=> ! [X0: dB,X3: fun1(nat,type),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_108])]) ).
tff(f1897,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,X3,X0))),X4))
| ~ beta(X3,X4) )
| ~ spl28_108
| ~ spl28_176 ),
inference(resolution,[],[f1895,f1183]) ).
tff(f1183,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) )
| ~ spl28_108 ),
inference(avatar_component_clause,[],[f1182]) ).
tff(f9661,plain,
( spl28_441
| ~ spl28_102
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1844,f1775,f1128,f9659]) ).
tff(f9659,plain,
( spl28_441
<=> ! [X0: type,X3: type,X2: type,X1: fun1(type,type)] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_441])]) ).
tff(f1128,plain,
( spl28_102
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_102])]) ).
tff(f1844,plain,
( ! [X2: type,X3: type,X0: type,X1: fun1(type,type)] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) )
| ~ spl28_102
| ~ spl28_170 ),
inference(superposition,[],[f1129,f1776]) ).
tff(f1129,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) )
| ( X0 = X2 ) )
| ~ spl28_102 ),
inference(avatar_component_clause,[],[f1128]) ).
tff(f9655,plain,
( spl28_440
| ~ spl28_104
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1828,f1775,f1136,f9653]) ).
tff(f9653,plain,
( spl28_440
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun1(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_440])]) ).
tff(f1828,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun1(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) )
| ~ spl28_104
| ~ spl28_170 ),
inference(superposition,[],[f1137,f1776]) ).
tff(f9651,plain,
( spl28_439
| ~ spl28_13
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1811,f1775,f602,f9649]) ).
tff(f9649,plain,
( spl28_439
<=> ! [X1: $tType,X0: $tType,X4: fun1(X1,X0),X3: X1,X2: fun1(X1,fun1(X0,bool))] :
( ( fFalse = aa(X1,bool,aa(fun1(X1,X0),fun1(X1,bool),aa(fun1(X1,fun1(X0,bool)),fun1(fun1(X1,X0),fun1(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun1(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_439])]) ).
tff(f602,plain,
( spl28_13
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_13])]) ).
tff(f1811,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,bool)),X3: X1,X4: fun1(X1,X0)] :
( ( fFalse = aa(X1,bool,aa(fun1(X1,X0),fun1(X1,bool),aa(fun1(X1,fun1(X0,bool)),fun1(fun1(X1,X0),fun1(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun1(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) )
| ~ spl28_13
| ~ spl28_170 ),
inference(superposition,[],[f1776,f603]) ).
tff(f603,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl28_13 ),
inference(avatar_component_clause,[],[f602]) ).
tff(f9647,plain,
( spl28_438
| ~ spl28_106
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1806,f1775,f1161,f9645]) ).
tff(f9645,plain,
( spl28_438
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: fun1(type,type),X2: type,X1: fun1(type,fun1(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,aa(type,type,X3,X2)),X2)) = aa(type,X0,aa(fun1(type,type),fun1(type,X0),aa(fun1(type,fun1(type,X0)),fun1(fun1(type,type),fun1(type,X0)),combs(type,type,X0),X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_438])]) ).
tff(f1806,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,type),X1: fun1(type,fun1(type,X0)),X4: fun1(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,aa(type,type,X3,X2)),X2)) = aa(type,X0,aa(fun1(type,type),fun1(type,X0),aa(fun1(type,fun1(type,X0)),fun1(fun1(type,type),fun1(type,X0)),combs(type,type,X0),X1),X3),X2) )
| ~ spl28_106
| ~ spl28_170 ),
inference(superposition,[],[f1776,f1162]) ).
tff(f9643,plain,
( spl28_437
| ~ spl28_13
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1801,f1775,f602,f9641]) ).
tff(f9641,plain,
( spl28_437
<=> ! [X3: $tType,X0: $tType,X4: fun1(X0,fun1(bool,X3)),X2: X0,X1: fun1(X0,bool)] :
( ( aa(X0,X3,aa(fun1(X0,bool),fun1(X0,X3),aa(fun1(X0,fun1(bool,X3)),fun1(fun1(X0,bool),fun1(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun1(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_437])]) ).
tff(f1801,plain,
( ! [X0: $tType,X3: $tType,X2: X0,X1: fun1(X0,bool),X4: fun1(X0,fun1(bool,X3))] :
( ( aa(X0,X3,aa(fun1(X0,bool),fun1(X0,X3),aa(fun1(X0,fun1(bool,X3)),fun1(fun1(X0,bool),fun1(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun1(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl28_13
| ~ spl28_170 ),
inference(superposition,[],[f1776,f603]) ).
tff(f9639,plain,
( spl28_436
| ~ spl28_13
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1780,f1775,f602,f9637]) ).
tff(f9637,plain,
( spl28_436
<=> ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X4: X0,X3: fun1(X0,X1)] :
( ( fFalse = aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X0,fun1(X1,bool)),fun1(fun1(X0,X1),fun1(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_436])]) ).
tff(f1780,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X3: fun1(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X0,fun1(X1,bool)),fun1(fun1(X0,X1),fun1(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) )
| ~ spl28_13
| ~ spl28_170 ),
inference(superposition,[],[f1776,f603]) ).
tff(f9635,plain,
( spl28_435
| ~ spl28_163
| ~ spl28_165 ),
inference(avatar_split_clause,[],[f1711,f1706,f1691,f9633]) ).
tff(f9633,plain,
( spl28_435
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK17(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_435])]) ).
tff(f1691,plain,
( spl28_163
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_163])]) ).
tff(f1711,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK17(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X4))) )
| ~ spl28_163
| ~ spl28_165 ),
inference(resolution,[],[f1707,f1692]) ).
tff(f1692,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1))) )
| ~ spl28_163 ),
inference(avatar_component_clause,[],[f1691]) ).
tff(f9631,plain,
( spl28_434
| ~ spl28_115
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1584,f1576,f1226,f9629]) ).
tff(f9629,plain,
( spl28_434
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_434])]) ).
tff(f1584,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl28_115
| ~ spl28_148 ),
inference(resolution,[],[f1577,f1227]) ).
tff(f9627,plain,
( spl28_433
| ~ spl28_117
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1583,f1576,f1238,f9625]) ).
tff(f9625,plain,
( spl28_433
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_433])]) ).
tff(f1583,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun,sK16(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl28_117
| ~ spl28_148 ),
inference(resolution,[],[f1577,f1239]) ).
tff(f9623,plain,
( spl28_432
| ~ spl28_115
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1564,f1556,f1226,f9621]) ).
tff(f9621,plain,
( spl28_432
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_432])]) ).
tff(f1564,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl28_115
| ~ spl28_146 ),
inference(resolution,[],[f1557,f1227]) ).
tff(f9619,plain,
( spl28_431
| ~ spl28_117
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1563,f1556,f1238,f9617]) ).
tff(f9617,plain,
( spl28_431
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_431])]) ).
tff(f1563,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK16(foldr(type,type,fun,sK15(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl28_117
| ~ spl28_146 ),
inference(resolution,[],[f1557,f1239]) ).
tff(f9615,plain,
( spl28_430
| ~ spl28_4
| ~ spl28_217
| ~ spl28_399 ),
inference(avatar_split_clause,[],[f9442,f8083,f2786,f562,f9612]) ).
tff(f9612,plain,
( spl28_430
<=> sP1(abs(abs(abs(abs(t2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_430])]) ).
tff(f8083,plain,
( spl28_399
<=> ( fTrue = aa(dB,bool,it,abs(abs(t2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_399])]) ).
tff(f9442,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(t2)))))
| ~ spl28_217
| ~ spl28_399 ),
inference(superposition,[],[f2787,f8085]) ).
tff(f8085,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t2))) )
| ~ spl28_399 ),
inference(avatar_component_clause,[],[f8083]) ).
tff(f9610,plain,
( spl28_429
| ~ spl28_110
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1394,f1360,f1198,f9608]) ).
tff(f9608,plain,
( spl28_429
<=> ! [X0: dB,X3: list(nat),X2: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_429])]) ).
tff(f1198,plain,
( spl28_110
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_110])]) ).
tff(f1394,plain,
( ! [X2: dB,X3: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),X2,X3) )
| ~ spl28_110
| ~ spl28_136 ),
inference(superposition,[],[f1361,f1199]) ).
tff(f1199,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl28_110 ),
inference(avatar_component_clause,[],[f1198]) ).
tff(f9606,plain,
( spl28_428
| ~ spl28_135
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1390,f1360,f1356,f9604]) ).
tff(f9604,plain,
( spl28_428
<=> ! [X0: $tType,X3: list(X0),X4: X0,X5: list(X0),X2: X0,X1: fun1(X0,fun1(X0,X0))] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_428])]) ).
tff(f1390,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun1(X0,fun1(X0,X0)),X4: X0,X5: list(X0)] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) )
| ~ spl28_135
| ~ spl28_136 ),
inference(superposition,[],[f1361,f1357]) ).
tff(f9463,plain,
( spl28_427
| ~ spl28_80
| ~ spl28_348
| ~ spl28_426 ),
inference(avatar_split_clause,[],[f9459,f9456,f5544,f975,f9461]) ).
tff(f9461,plain,
( spl28_427
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_427])]) ).
tff(f9456,plain,
( spl28_426
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_426])]) ).
tff(f9459,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_426 ),
inference(forward_demodulation,[],[f9457,f5589]) ).
tff(f9457,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl28_426 ),
inference(avatar_component_clause,[],[f9456]) ).
tff(f9458,plain,
( spl28_426
| ~ spl28_18
| ~ spl28_183 ),
inference(avatar_split_clause,[],[f1959,f1955,f629,f9456]) ).
tff(f1955,plain,
( spl28_183
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_183])]) ).
tff(f1959,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl28_18
| ~ spl28_183 ),
inference(resolution,[],[f1956,f630]) ).
tff(f1956,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl28_183 ),
inference(avatar_component_clause,[],[f1955]) ).
tff(f9437,plain,
( spl28_425
| ~ spl28_80
| ~ spl28_179 ),
inference(avatar_split_clause,[],[f1928,f1924,f975,f9435]) ).
tff(f9435,plain,
( spl28_425
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) = aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_425])]) ).
tff(f1924,plain,
( spl28_179
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_179])]) ).
tff(f1928,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) = aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl28_80
| ~ spl28_179 ),
inference(superposition,[],[f1925,f976]) ).
tff(f1925,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl28_179 ),
inference(avatar_component_clause,[],[f1924]) ).
tff(f9433,plain,
( spl28_424
| ~ spl28_65
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1835,f1775,f896,f9431]) ).
tff(f9431,plain,
( spl28_424
<=> ! [X0: $tType,X2: fun1(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun1(X0,list(X0)),fun1(X0,list(X0)),aa(fun1(X0,fun1(list(X0),list(X0))),fun1(fun1(X0,list(X0)),fun1(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_424])]) ).
tff(f896,plain,
( spl28_65
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_65])]) ).
tff(f1835,plain,
( ! [X0: $tType,X2: fun1(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun1(X0,list(X0)),fun1(X0,list(X0)),aa(fun1(X0,fun1(list(X0),list(X0))),fun1(fun1(X0,list(X0)),fun1(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ~ spl28_65
| ~ spl28_170 ),
inference(superposition,[],[f897,f1776]) ).
tff(f897,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X1),X2) != X2 )
| ~ spl28_65 ),
inference(avatar_component_clause,[],[f896]) ).
tff(f9429,plain,
( spl28_423
| ~ spl28_29
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1739,f1734,f694,f9427]) ).
tff(f9427,plain,
( spl28_423
<=> ! [X0: $tType,X4: list(nat),X3: X0,X2: nat,X1: fun1(nat,X0)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_423])]) ).
tff(f694,plain,
( spl28_29
<=> ! [X0: $tType,X2: fun1(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_29])]) ).
tff(f1739,plain,
( ! [X0: $tType,X2: nat,X3: X0,X1: fun1(nat,X0),X4: list(nat)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) )
| ~ spl28_29
| ~ spl28_169 ),
inference(superposition,[],[f1735,f695]) ).
tff(f695,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 )
| ~ spl28_29 ),
inference(avatar_component_clause,[],[f694]) ).
tff(f9425,plain,
( spl28_422
| ~ spl28_133
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1383,f1356,f1348,f9423]) ).
tff(f9423,plain,
( spl28_422
<=> ! [X0: $tType,X4: $tType,X5: fun1(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK23(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_422])]) ).
tff(f1383,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun1(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK23(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) )
| ~ spl28_133
| ~ spl28_135 ),
inference(superposition,[],[f1349,f1357]) ).
tff(f9421,plain,
( spl28_421
| ~ spl28_134
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1382,f1356,f1352,f9419]) ).
tff(f9419,plain,
( spl28_421
<=> ! [X0: $tType,X4: $tType,X5: fun1(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK25(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_421])]) ).
tff(f1382,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun1(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK25(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) )
| ~ spl28_134
| ~ spl28_135 ),
inference(superposition,[],[f1353,f1357]) ).
tff(f8953,plain,
( spl28_420
| ~ spl28_113
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5112,f5056,f1217,f8951]) ).
tff(f1217,plain,
( spl28_113
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_113])]) ).
tff(f5112,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl28_113
| ~ spl28_323 ),
inference(resolution,[],[f5057,f1218]) ).
tff(f1218,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl28_113 ),
inference(avatar_component_clause,[],[f1217]) ).
tff(f8850,plain,
( spl28_419
| ~ spl28_80
| ~ spl28_348
| ~ spl28_418 ),
inference(avatar_split_clause,[],[f8846,f8843,f5544,f975,f8848]) ).
tff(f8848,plain,
( spl28_419
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_419])]) ).
tff(f8843,plain,
( spl28_418
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_418])]) ).
tff(f8846,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0)) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_418 ),
inference(forward_demodulation,[],[f8844,f5589]) ).
tff(f8844,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl28_418 ),
inference(avatar_component_clause,[],[f8843]) ).
tff(f8845,plain,
( spl28_418
| ~ spl28_89
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1994,f1982,f1049,f8843]) ).
tff(f1049,plain,
( spl28_89
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_89])]) ).
tff(f1994,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl28_89
| ~ spl28_184 ),
inference(resolution,[],[f1983,f1051]) ).
tff(f1051,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl28_89 ),
inference(avatar_component_clause,[],[f1049]) ).
tff(f8826,plain,
( spl28_417
| ~ spl28_80
| ~ spl28_348
| ~ spl28_416 ),
inference(avatar_split_clause,[],[f8822,f8819,f5544,f975,f8824]) ).
tff(f8824,plain,
( spl28_417
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_417])]) ).
tff(f8819,plain,
( spl28_416
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_416])]) ).
tff(f8822,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl28_80
| ~ spl28_348
| ~ spl28_416 ),
inference(forward_demodulation,[],[f8820,f5589]) ).
tff(f8820,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl28_416 ),
inference(avatar_component_clause,[],[f8819]) ).
tff(f8821,plain,
( spl28_416
| ~ spl28_91
| ~ spl28_184 ),
inference(avatar_split_clause,[],[f1992,f1982,f1062,f8819]) ).
tff(f1062,plain,
( spl28_91
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_91])]) ).
tff(f1992,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl28_91
| ~ spl28_184 ),
inference(resolution,[],[f1983,f1064]) ).
tff(f1064,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs)))
| ~ spl28_91 ),
inference(avatar_component_clause,[],[f1062]) ).
tff(f8817,plain,
( spl28_415
| ~ spl28_13
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1745,f1734,f602,f8815]) ).
tff(f8815,plain,
( spl28_415
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: fun1(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun1(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_415])]) ).
tff(f1745,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun1(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun1(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl28_13
| ~ spl28_169 ),
inference(superposition,[],[f1735,f603]) ).
tff(f8813,plain,
( spl28_414
| ~ spl28_148
| ~ spl28_165 ),
inference(avatar_split_clause,[],[f1710,f1706,f1576,f8811]) ).
tff(f8811,plain,
( spl28_414
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK16(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_414])]) ).
tff(f1710,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK16(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl28_148
| ~ spl28_165 ),
inference(resolution,[],[f1707,f1577]) ).
tff(f8809,plain,
( spl28_413
| ~ spl28_146
| ~ spl28_165 ),
inference(avatar_split_clause,[],[f1709,f1706,f1556,f8807]) ).
tff(f8807,plain,
( spl28_413
<=> ! [X4: list(dB),X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_413])]) ).
tff(f1709,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl28_146
| ~ spl28_165 ),
inference(resolution,[],[f1707,f1557]) ).
tff(f8805,plain,
( spl28_412
| ~ spl28_235
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5110,f5056,f2917,f8802]) ).
tff(f2917,plain,
( spl28_235
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_235])]) ).
tff(f5110,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl28_235
| ~ spl28_323 ),
inference(resolution,[],[f5057,f2919]) ).
tff(f2919,plain,
( sP1(abs(abs(ua)))
| ~ spl28_235 ),
inference(avatar_component_clause,[],[f2917]) ).
tff(f8800,plain,
( spl28_411
| ~ spl28_80
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1321,f1307,f975,f8798]) ).
tff(f8798,plain,
( spl28_411
<=> ! [X0: $tType,X1: $tType,X2: $tType,X6: fun1(X1,X2),X4: X0,X5: list(X0),X3: fun1(X0,fun1(list(X0),fun1(X1,X2))),X7: X1] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun1(list(X0),fun1(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun1(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_411])]) ).
tff(f1321,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(list(X0),fun1(X1,X2))),X6: fun1(X1,X2),X7: X1,X4: X0,X5: list(X0)] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun1(list(X0),fun1(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun1(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) )
| ~ spl28_80
| ~ spl28_128 ),
inference(superposition,[],[f976,f1308]) ).
tff(f8796,plain,
( spl28_410
| ~ spl28_80
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1089,f1078,f975,f8794]) ).
tff(f8794,plain,
( spl28_410
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK19(X1,X0,aa(X2,fun1(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK19(X1,X0,aa(X2,fun1(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun1(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_410])]) ).
tff(f1089,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK19(X1,X0,aa(X2,fun1(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK19(X1,X0,aa(X2,fun1(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun1(X0,X1),X3,X4) = X5 ) )
| ~ spl28_80
| ~ spl28_94 ),
inference(superposition,[],[f1079,f976]) ).
tff(f8792,plain,
( spl28_409
| ~ spl28_80
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1084,f1078,f975,f8790]) ).
tff(f8790,plain,
( spl28_409
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X3: fun1(X2,fun1(X0,X1)),X5: fun1(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK19(X1,X0,X5,aa(X2,fun1(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK19(X1,X0,X5,aa(X2,fun1(X0,X1),X3,X4))) )
| ( aa(X2,fun1(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_409])]) ).
tff(f1084,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK19(X1,X0,X5,aa(X2,fun1(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK19(X1,X0,X5,aa(X2,fun1(X0,X1),X3,X4))) )
| ( aa(X2,fun1(X0,X1),X3,X4) = X5 ) )
| ~ spl28_80
| ~ spl28_94 ),
inference(superposition,[],[f1079,f976]) ).
tff(f8705,plain,
( spl28_408
| ~ spl28_49
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1827,f1775,f795,f8703]) ).
tff(f8703,plain,
( spl28_408
<=> ! [X1: $tType,X0: $tType,X4: fun1(X1,X0),X3: X1,X2: fun1(X1,fun1(X0,bool))] :
( ~ pp(aa(X1,bool,aa(fun1(X1,X0),fun1(X1,bool),aa(fun1(X1,fun1(X0,bool)),fun1(fun1(X1,X0),fun1(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(X1,fun1(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_408])]) ).
tff(f1827,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,bool)),X3: X1,X4: fun1(X1,X0)] :
( ~ pp(aa(X1,bool,aa(fun1(X1,X0),fun1(X1,bool),aa(fun1(X1,fun1(X0,bool)),fun1(fun1(X1,X0),fun1(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(X1,fun1(X0,bool),X2,X3))) )
| ~ spl28_49
| ~ spl28_170 ),
inference(superposition,[],[f796,f1776]) ).
tff(f8701,plain,
( spl28_407
| ~ spl28_29
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1783,f1775,f694,f8699]) ).
tff(f8699,plain,
( spl28_407
<=> ! [X1: $tType,X0: $tType,X2: fun1(nat,fun1(X0,X1)),X4: fun1(X0,X1),X5: fun1(nat,X0),X3: nat] : ( aa(nat,X1,aa(fun1(nat,X0),fun1(nat,X1),aa(fun1(nat,fun1(X0,X1)),fun1(fun1(nat,X0),fun1(nat,X1)),combs(nat,X0,X1),shift(fun1(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_407])]) ).
tff(f1783,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(nat,fun1(X0,X1)),X3: nat,X4: fun1(X0,X1),X5: fun1(nat,X0)] : ( aa(nat,X1,aa(fun1(nat,X0),fun1(nat,X1),aa(fun1(nat,fun1(X0,X1)),fun1(fun1(nat,X0),fun1(nat,X1)),combs(nat,X0,X1),shift(fun1(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) )
| ~ spl28_29
| ~ spl28_170 ),
inference(superposition,[],[f1776,f695]) ).
tff(f8608,plain,
( spl28_406
| ~ spl28_228
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5109,f5056,f2875,f8605]) ).
tff(f2875,plain,
( spl28_228
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_228])]) ).
tff(f5109,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl28_228
| ~ spl28_323 ),
inference(resolution,[],[f5057,f2877]) ).
tff(f2877,plain,
( sP1(abs(abs(u)))
| ~ spl28_228 ),
inference(avatar_component_clause,[],[f2875]) ).
tff(f8123,plain,
( spl28_405
| ~ spl28_29
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1856,f1775,f975,f694,f8121]) ).
tff(f8121,plain,
( spl28_405
<=> ! [X0: $tType,X4: $tType,X3: X0,X5: fun1(nat,fun1(X0,X4)),X2: nat,X1: fun1(nat,X0)] : ( aa(nat,X4,aa(fun1(nat,X0),fun1(nat,X4),aa(fun1(nat,fun1(X0,X4)),fun1(fun1(nat,X0),fun1(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_405])]) ).
tff(f1856,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun1(nat,X0),X5: fun1(nat,fun1(X0,X4))] : ( aa(nat,X4,aa(fun1(nat,X0),fun1(nat,X4),aa(fun1(nat,fun1(X0,X4)),fun1(fun1(nat,X0),fun1(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) )
| ~ spl28_29
| ~ spl28_80
| ~ spl28_170 ),
inference(forward_demodulation,[],[f1793,f976]) ).
tff(f1793,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun1(nat,X0),X5: fun1(nat,fun1(X0,X4))] : ( aa(nat,X4,aa(fun1(nat,X0),fun1(nat,X4),aa(fun1(nat,fun1(X0,X4)),fun1(fun1(nat,X0),fun1(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(X0,X4,aa(nat,fun1(X0,X4),X5,X2),X3) )
| ~ spl28_29
| ~ spl28_170 ),
inference(superposition,[],[f1776,f695]) ).
tff(f8119,plain,
( spl28_404
| ~ spl28_101
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1846,f1775,f1124,f8117]) ).
tff(f8117,plain,
( spl28_404
<=> ! [X0: type,X3: type,X2: type,X1: fun1(type,type)] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_404])]) ).
tff(f1124,plain,
( spl28_101
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_101])]) ).
tff(f1846,plain,
( ! [X2: type,X3: type,X0: type,X1: fun1(type,type)] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) )
| ( X0 = X2 ) )
| ~ spl28_101
| ~ spl28_170 ),
inference(superposition,[],[f1125,f1776]) ).
tff(f1125,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) )
| ( X1 = X3 ) )
| ~ spl28_101 ),
inference(avatar_component_clause,[],[f1124]) ).
tff(f8115,plain,
( spl28_403
| ~ spl28_103
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1830,f1775,f1132,f8113]) ).
tff(f8113,plain,
( spl28_403
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun1(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_403])]) ).
tff(f1830,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun1(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) )
| ~ spl28_103
| ~ spl28_170 ),
inference(superposition,[],[f1133,f1776]) ).
tff(f8111,plain,
( spl28_402
| ~ spl28_80
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1807,f1775,f975,f8109]) ).
tff(f8109,plain,
( spl28_402
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X2,X0)] : ( aa(X2,X1,aa(fun1(X2,X0),fun1(X2,X1),aa(fun1(X2,fun1(X0,X1)),fun1(fun1(X2,X0),fun1(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_402])]) ).
tff(f1807,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X2,X0)] : ( aa(X2,X1,aa(fun1(X2,X0),fun1(X2,X1),aa(fun1(X2,fun1(X0,X1)),fun1(fun1(X2,X0),fun1(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) )
| ~ spl28_80
| ~ spl28_170 ),
inference(superposition,[],[f1776,f976]) ).
tff(f8107,plain,
( spl28_401
| ~ spl28_80
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1088,f1078,f975,f8105]) ).
tff(f8105,plain,
( spl28_401
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun1(X2,X1),X3,sK19(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK19(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_401])]) ).
tff(f1088,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun1(X2,X1),X3,sK19(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK19(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl28_80
| ~ spl28_94 ),
inference(superposition,[],[f1079,f976]) ).
tff(f8103,plain,
( spl28_400
| ~ spl28_80
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1083,f1078,f975,f8101]) ).
tff(f8101,plain,
( spl28_400
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun1(X0,X1),X4: X2,X3: fun1(X0,fun1(X2,X1))] :
( ( aa(X2,X1,aa(X0,fun1(X2,X1),X3,sK19(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK19(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_400])]) ).
tff(f1083,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X0,fun1(X2,X1)),X4: X2,X5: fun1(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun1(X2,X1),X3,sK19(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK19(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl28_80
| ~ spl28_94 ),
inference(superposition,[],[f1079,f976]) ).
tff(f8086,plain,
( spl28_399
| ~ spl28_221
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5108,f5056,f2836,f8083]) ).
tff(f2836,plain,
( spl28_221
<=> sP1(abs(abs(t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_221])]) ).
tff(f5108,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t2))) )
| ~ spl28_221
| ~ spl28_323 ),
inference(resolution,[],[f5057,f2838]) ).
tff(f2838,plain,
( sP1(abs(abs(t2)))
| ~ spl28_221 ),
inference(avatar_component_clause,[],[f2836]) ).
tff(f8081,plain,
( spl28_398
| ~ spl28_142
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1761,f1734,f1513,f8079]) ).
tff(f8079,plain,
( spl28_398
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun1(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_398])]) ).
tff(f1761,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) )
| ~ spl28_142
| ~ spl28_169 ),
inference(superposition,[],[f1514,f1735]) ).
tff(f7553,plain,
( spl28_397
| ~ spl28_103
| ~ spl28_179 ),
inference(avatar_split_clause,[],[f1931,f1924,f1132,f7551]) ).
tff(f7551,plain,
( spl28_397
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_397])]) ).
tff(f1931,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl28_103
| ~ spl28_179 ),
inference(superposition,[],[f1133,f1925]) ).
tff(f7549,plain,
( spl28_396
| ~ spl28_104
| ~ spl28_179 ),
inference(avatar_split_clause,[],[f1929,f1924,f1136,f7547]) ).
tff(f7547,plain,
( spl28_396
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_396])]) ).
tff(f1929,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) )
| ~ spl28_104
| ~ spl28_179 ),
inference(superposition,[],[f1137,f1925]) ).
tff(f7545,plain,
( spl28_395
| ~ spl28_73
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1900,f1894,f938,f7543]) ).
tff(f7543,plain,
( spl28_395
<=> ! [X0: fun1(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,var(X3),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_395])]) ).
tff(f938,plain,
( spl28_73
<=> ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_73])]) ).
tff(f1900,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun,X1),sK18(X1,X2,var(X3),X0)) ) )
| ~ spl28_73
| ~ spl28_176 ),
inference(resolution,[],[f1895,f939]) ).
tff(f939,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl28_73 ),
inference(avatar_component_clause,[],[f938]) ).
tff(f7541,plain,
( spl28_394
| ~ spl28_132
| ~ spl28_176 ),
inference(avatar_split_clause,[],[f1898,f1894,f1343,f7539]) ).
tff(f7539,plain,
( spl28_394
<=> ! [X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X3,X0))),sK12(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_394])]) ).
tff(f1898,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X3,X0))),sK12(X3,X0)),X3)) )
| ~ spl28_132
| ~ spl28_176 ),
inference(resolution,[],[f1895,f1344]) ).
tff(f7537,plain,
( spl28_393
| ~ spl28_20
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1791,f1775,f637,f7535]) ).
tff(f7535,plain,
( spl28_393
<=> ! [X2: $tType,X0: $tType,X3: fun1(X0,fun1(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun1(X0,X0),fun1(X0,X2),aa(fun1(X0,fun1(X0,X2)),fun1(fun1(X0,X0),fun1(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun1(X0,X2),X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_393])]) ).
tff(f1791,plain,
( ! [X0: $tType,X2: $tType,X3: fun1(X0,fun1(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun1(X0,X0),fun1(X0,X2),aa(fun1(X0,fun1(X0,X2)),fun1(fun1(X0,X0),fun1(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun1(X0,X2),X3,X1),X1) )
| ~ spl28_20
| ~ spl28_170 ),
inference(superposition,[],[f1776,f638]) ).
tff(f7533,plain,
( spl28_392
| ~ spl28_137
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1757,f1734,f1441,f7531]) ).
tff(f7531,plain,
( spl28_392
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun1(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_392])]) ).
tff(f1757,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) )
| ~ spl28_137
| ~ spl28_169 ),
inference(superposition,[],[f1442,f1735]) ).
tff(f7529,plain,
( spl28_391
| ~ spl28_57
| ~ spl28_157 ),
inference(avatar_split_clause,[],[f1654,f1649,f848,f7527]) ).
tff(f7527,plain,
( spl28_391
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X1,X2)) != foldl(dB,dB,app,X3,map(dB,dB,combc(dB,nat,dB,lift,X0),X2)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_391])]) ).
tff(f848,plain,
( spl28_57
<=> ! [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,[spl28_57])]) ).
tff(f1649,plain,
( spl28_157
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_157])]) ).
tff(f1654,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X1,X2)) != foldl(dB,dB,app,X3,map(dB,dB,combc(dB,nat,dB,lift,X0),X2)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl28_57
| ~ spl28_157 ),
inference(superposition,[],[f849,f1650]) ).
tff(f1650,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl28_157 ),
inference(avatar_component_clause,[],[f1649]) ).
tff(f849,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) )
| ( X0 = X2 ) )
| ~ spl28_57 ),
inference(avatar_component_clause,[],[f848]) ).
tff(f7525,plain,
( spl28_390
| ~ spl28_62
| ~ spl28_80
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1544,f1517,f975,f878,f7523]) ).
tff(f7523,plain,
( spl28_390
<=> ! [X0: $tType,X3: nat,X2: fun1(nat,X0),X1: fun1(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(X0,type),fun1(nat,type),combc(fun1(X0,type),fun1(nat,X0),fun1(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_390])]) ).
tff(f1544,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: fun1(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(X0,type),fun1(nat,type),combc(fun1(X0,type),fun1(nat,X0),fun1(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl28_62
| ~ spl28_80
| ~ spl28_143 ),
inference(forward_demodulation,[],[f1536,f976]) ).
tff(f1536,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: fun1(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun1(nat,X0),fun1(nat,type),aa(fun1(X0,type),fun1(fun1(nat,X0),fun1(nat,type)),combb(X0,type,nat),X1),X2)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl28_62
| ~ spl28_143 ),
inference(superposition,[],[f879,f1518]) ).
tff(f7521,plain,
( spl28_389
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1165,f1161,f7519]) ).
tff(f7519,plain,
( spl28_389
<=> ! [X0: $tType,X3: type,X4: fun1(nat,fun1(type,X0)),X6: fun1(nat,X0),X5: type,X2: type,X1: fun1(type,fun1(type,fun1(type,X0)))] : ( type_case(X0,X6,aa(type,fun1(type,fun1(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun,X5),X3)) = aa(type,X0,type_case(fun1(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_389])]) ).
tff(f1165,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,fun1(type,X0))),X6: fun1(nat,X0),X4: fun1(nat,fun1(type,X0)),X5: type] : ( type_case(X0,X6,aa(type,fun1(type,fun1(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun,X5),X3)) = aa(type,X0,type_case(fun1(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)),X5) )
| ~ spl28_106 ),
inference(superposition,[],[f1162,f1162]) ).
tff(f7384,plain,
( spl28_388
| ~ spl28_4
| ~ spl28_217
| ~ spl28_346 ),
inference(avatar_split_clause,[],[f7059,f5477,f2786,f562,f7381]) ).
tff(f7381,plain,
( spl28_388
<=> sP1(abs(abs(abs(ua)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_388])]) ).
tff(f5477,plain,
( spl28_346
<=> ( fTrue = aa(dB,bool,it,abs(ua)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_346])]) ).
tff(f7059,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(ua))))
| ~ spl28_217
| ~ spl28_346 ),
inference(superposition,[],[f2787,f5479]) ).
tff(f5479,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl28_346 ),
inference(avatar_component_clause,[],[f5477]) ).
tff(f7089,plain,
( spl28_387
| ~ spl28_80
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1753,f1734,f975,f7087]) ).
tff(f7087,plain,
( spl28_387
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun1(X1,X0)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_387])]) ).
tff(f1753,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) )
| ~ spl28_80
| ~ spl28_169 ),
inference(superposition,[],[f1735,f976]) ).
tff(f7085,plain,
( spl28_386
| ~ spl28_49
| ~ spl28_163 ),
inference(avatar_split_clause,[],[f1696,f1691,f795,f7083]) ).
tff(f7083,plain,
( spl28_386
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK17(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_386])]) ).
tff(f1696,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK17(X1,X3,X2,X0),X1)))) )
| ~ spl28_49
| ~ spl28_163 ),
inference(resolution,[],[f1692,f796]) ).
tff(f7081,plain,
( spl28_385
| ~ spl28_108
| ~ spl28_161 ),
inference(avatar_split_clause,[],[f1680,f1675,f1182,f7079]) ).
tff(f7079,plain,
( spl28_385
<=> ! [X4: dB,X0: fun1(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X2),X1)),X4))
| ~ beta(abs(X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_385])]) ).
tff(f1680,plain,
( ! [X2: type,X3: dB,X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X2),X1)),X4))
| ~ beta(abs(X3),X4) )
| ~ spl28_108
| ~ spl28_161 ),
inference(resolution,[],[f1676,f1183]) ).
tff(f7077,plain,
( spl28_384
| ~ spl28_135
| ~ spl28_137 ),
inference(avatar_split_clause,[],[f1453,f1441,f1356,f7075]) ).
tff(f7075,plain,
( spl28_384
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_384])]) ).
tff(f1453,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) )
| ~ spl28_135
| ~ spl28_137 ),
inference(superposition,[],[f1442,f1357]) ).
tff(f7073,plain,
( spl28_383
| ~ spl28_29
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1385,f1360,f694,f7071]) ).
tff(f7071,plain,
( spl28_383
<=> ! [X0: $tType,X2: nat,X4: X0,X5: list(X0),X3: fun1(X0,nat),X1: fun1(nat,fun1(X0,nat))] : ( foldl(nat,X0,shift(fun1(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun1(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_383])]) ).
tff(f1385,plain,
( ! [X0: $tType,X2: nat,X3: fun1(X0,nat),X1: fun1(nat,fun1(X0,nat)),X4: X0,X5: list(X0)] : ( foldl(nat,X0,shift(fun1(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun1(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) )
| ~ spl28_29
| ~ spl28_136 ),
inference(superposition,[],[f1361,f695]) ).
tff(f7054,plain,
( spl28_382
| ~ spl28_29
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1370,f1356,f694,f7052]) ).
tff(f7052,plain,
( spl28_382
<=> ! [X0: $tType,X3: fun1(X0,X0),X4: list(nat),X5: X0,X2: nat,X1: fun1(nat,fun1(X0,X0))] : ( foldr(nat,X0,shift(fun1(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun1(X0,X0),X1,X2,X3),X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_382])]) ).
tff(f1370,plain,
( ! [X0: $tType,X2: nat,X3: fun1(X0,X0),X1: fun1(nat,fun1(X0,X0)),X4: list(nat),X5: X0] : ( foldr(nat,X0,shift(fun1(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun1(X0,X0),X1,X2,X3),X4,X5)) )
| ~ spl28_29
| ~ spl28_135 ),
inference(superposition,[],[f1357,f695]) ).
tff(f6678,plain,
( spl28_381
| ~ spl28_49
| ~ spl28_161 ),
inference(avatar_split_clause,[],[f1681,f1675,f795,f6676]) ).
tff(f6676,plain,
( spl28_381
<=> ! [X0: fun1(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X2),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_381])]) ).
tff(f1681,plain,
( ! [X2: type,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun,X2),X1)))) )
| ~ spl28_49
| ~ spl28_161 ),
inference(resolution,[],[f1676,f796]) ).
tff(f6674,plain,
( spl28_380
| ~ spl28_49
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1586,f1576,f795,f6672]) ).
tff(f6672,plain,
( spl28_380
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK16(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_380])]) ).
tff(f1586,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK16(X1,X3,X2,X0),X1)))) )
| ~ spl28_49
| ~ spl28_148 ),
inference(resolution,[],[f1577,f796]) ).
tff(f6670,plain,
( spl28_379
| ~ spl28_108
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1579,f1576,f1182,f6668]) ).
tff(f6668,plain,
( spl28_379
<=> ! [X4: dB,X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK16(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_379])]) ).
tff(f1579,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK16(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) )
| ~ spl28_108
| ~ spl28_148 ),
inference(resolution,[],[f1577,f1183]) ).
tff(f6666,plain,
( spl28_378
| ~ spl28_49
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1566,f1556,f795,f6664]) ).
tff(f6664,plain,
( spl28_378
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK15(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_378])]) ).
tff(f1566,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK15(X1,X3,X2,X0),X1)))) )
| ~ spl28_49
| ~ spl28_146 ),
inference(resolution,[],[f1557,f796]) ).
tff(f6662,plain,
( spl28_377
| ~ spl28_108
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1559,f1556,f1182,f6660]) ).
tff(f6660,plain,
( spl28_377
<=> ! [X4: dB,X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK15(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_377])]) ).
tff(f1559,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun,sK15(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) )
| ~ spl28_108
| ~ spl28_146 ),
inference(resolution,[],[f1557,f1183]) ).
tff(f6658,plain,
( spl28_376
| ~ spl28_49
| ~ spl28_80
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1543,f1517,f975,f795,f6656]) ).
tff(f6656,plain,
( spl28_376
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun1(X0,X1),X2: fun1(X1,bool)] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),aa(fun1(X1,bool),fun1(X0,bool),combc(fun1(X1,bool),fun1(X0,X1),fun1(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_376])]) ).
tff(f1543,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,bool),X3: fun1(X0,X1),X4: X0] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),aa(fun1(X1,bool),fun1(X0,bool),combc(fun1(X1,bool),fun1(X0,X1),fun1(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) )
| ~ spl28_49
| ~ spl28_80
| ~ spl28_143 ),
inference(forward_demodulation,[],[f1535,f976]) ).
tff(f1535,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,bool),X3: fun1(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X1,bool),fun1(fun1(X0,X1),fun1(X0,bool)),combb(X1,bool,X0),X2),X3))) )
| ~ spl28_49
| ~ spl28_143 ),
inference(superposition,[],[f796,f1518]) ).
tff(f6654,plain,
( spl28_375
| ~ spl28_66
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1431,f1360,f975,f900,f6652]) ).
tff(f6652,plain,
( spl28_375
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_375])]) ).
tff(f900,plain,
( spl28_66
<=> ! [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,[spl28_66])]) ).
tff(f1431,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl28_66
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1408,f976]) ).
tff(f1408,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl28_66
| ~ spl28_136 ),
inference(superposition,[],[f901,f1361]) ).
tff(f901,plain,
( ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) )
| ( X0 = X2 ) )
| ~ spl28_66 ),
inference(avatar_component_clause,[],[f900]) ).
tff(f6650,plain,
( spl28_374
| ~ spl28_67
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1427,f1360,f975,f904,f6648]) ).
tff(f6648,plain,
( spl28_374
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_374])]) ).
tff(f904,plain,
( spl28_67
<=> ! [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,[spl28_67])]) ).
tff(f1427,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl28_67
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1404,f976]) ).
tff(f1404,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl28_67
| ~ spl28_136 ),
inference(superposition,[],[f905,f1361]) ).
tff(f905,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) )
| ( X0 = X2 ) )
| ~ spl28_67 ),
inference(avatar_component_clause,[],[f904]) ).
tff(f6646,plain,
( spl28_373
| ~ spl28_77
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1393,f1360,f958,f6644]) ).
tff(f6644,plain,
( spl28_373
<=> ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_373])]) ).
tff(f1393,plain,
( ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun1(nat,dB),subst,X0),X0,X2) )
| ~ spl28_77
| ~ spl28_136 ),
inference(superposition,[],[f1361,f959]) ).
tff(f6642,plain,
( spl28_372
| ~ spl28_4
| ~ spl28_217
| ~ spl28_343 ),
inference(avatar_split_clause,[],[f6516,f5263,f2786,f562,f6639]) ).
tff(f6639,plain,
( spl28_372
<=> sP1(abs(abs(abs(u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_372])]) ).
tff(f5263,plain,
( spl28_343
<=> ( fTrue = aa(dB,bool,it,abs(u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_343])]) ).
tff(f6516,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(u))))
| ~ spl28_217
| ~ spl28_343 ),
inference(superposition,[],[f2787,f5265]) ).
tff(f5265,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl28_343 ),
inference(avatar_component_clause,[],[f5263]) ).
tff(f6637,plain,
( spl28_371
| ~ spl28_80
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1166,f1161,f975,f6635]) ).
tff(f6635,plain,
( spl28_371
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: type,X6: fun1(nat,X0),X5: type,X2: fun1(X1,fun1(type,fun1(type,X0)))] : ( type_case(X0,X6,aa(X1,fun1(type,fun1(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun,X5),X4)) = aa(type,X0,aa(X1,fun1(type,X0),combc(X1,type,fun1(type,X0),X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_371])]) ).
tff(f1166,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(type,fun1(type,X0))),X3: X1,X6: fun1(nat,X0),X4: type,X5: type] : ( type_case(X0,X6,aa(X1,fun1(type,fun1(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun,X5),X4)) = aa(type,X0,aa(X1,fun1(type,X0),combc(X1,type,fun1(type,X0),X2,X4),X3),X5) )
| ~ spl28_80
| ~ spl28_106 ),
inference(superposition,[],[f1162,f976]) ).
tff(f6571,plain,
( spl28_370
| ~ spl28_108
| ~ spl28_152 ),
inference(avatar_split_clause,[],[f1619,f1612,f1182,f6569]) ).
tff(f6569,plain,
( spl28_370
<=> ! [X3: nat,X4: type,X0: fun1(nat,type),X5: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1),X5))
| ~ beta(aa(dB,dB,combc(dB,nat,dB,lift,X3),X2),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_370])]) ).
tff(f1619,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1),X5))
| ~ beta(aa(dB,dB,combc(dB,nat,dB,lift,X3),X2),X5) )
| ~ spl28_108
| ~ spl28_152 ),
inference(resolution,[],[f1613,f1183]) ).
tff(f6567,plain,
( spl28_369
| ~ spl28_13
| ~ spl28_80
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1542,f1517,f975,f602,f6565]) ).
tff(f6565,plain,
( spl28_369
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun1(X0,X1),X2: fun1(X1,bool)] :
( ( fTrue = aa(X0,bool,aa(fun1(X1,bool),fun1(X0,bool),combc(fun1(X1,bool),fun1(X0,X1),fun1(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_369])]) ).
tff(f1542,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,bool),X3: fun1(X0,X1),X4: X0] :
( ( fTrue = aa(X0,bool,aa(fun1(X1,bool),fun1(X0,bool),combc(fun1(X1,bool),fun1(X0,X1),fun1(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_143 ),
inference(forward_demodulation,[],[f1530,f976]) ).
tff(f1530,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,bool),X3: fun1(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun1(X0,X1),fun1(X0,bool),aa(fun1(X1,bool),fun1(fun1(X0,X1),fun1(X0,bool)),combb(X1,bool,X0),X2),X3),X4) ) )
| ~ spl28_13
| ~ spl28_143 ),
inference(superposition,[],[f1518,f603]) ).
tff(f6144,plain,
( spl28_368
| ~ spl28_64
| ~ spl28_181 ),
inference(avatar_split_clause,[],[f1973,f1944,f891,f6142]) ).
tff(f6142,plain,
( spl28_368
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK25(dB,X0,X2,X1,as,a)),sK26(dB,X0,X2,X1,as,a)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_368])]) ).
tff(f891,plain,
( spl28_64
<=> ( rs = aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),a),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_64])]) ).
tff(f1973,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK25(dB,X0,X2,X1,as,a)),sK26(dB,X0,X2,X1,as,a)) = X2 ) )
| ~ spl28_64
| ~ spl28_181 ),
inference(superposition,[],[f1945,f893]) ).
tff(f893,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl28_64 ),
inference(avatar_component_clause,[],[f891]) ).
tff(f6140,plain,
( spl28_367
| ~ spl28_64
| ~ spl28_180 ),
inference(avatar_split_clause,[],[f1965,f1940,f891,f6138]) ).
tff(f6138,plain,
( spl28_367
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,dB,as,a,X2,X1)),sK24(X0,dB,as,a,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_367])]) ).
tff(f1965,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,dB,as,a,X2,X1)),sK24(X0,dB,as,a,X2,X1)) = X2 ) )
| ~ spl28_64
| ~ spl28_180 ),
inference(superposition,[],[f1941,f893]) ).
tff(f6136,plain,
( spl28_366
| ~ spl28_71
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1834,f1775,f924,f6134]) ).
tff(f6134,plain,
( spl28_366
<=> ! [X2: nat,X0: dB,X1: fun1(dB,dB),X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_366])]) ).
tff(f924,plain,
( spl28_71
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_71])]) ).
tff(f1834,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: fun1(dB,dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) )
| ~ spl28_71
| ~ spl28_170 ),
inference(superposition,[],[f925,f1776]) ).
tff(f925,plain,
( ! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) )
| ~ spl28_71 ),
inference(avatar_component_clause,[],[f924]) ).
tff(f6132,plain,
( spl28_365
| ~ spl28_132
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1560,f1556,f1343,f6130]) ).
tff(f6130,plain,
( spl28_365
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X2,X0))),sK12(X2,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_365])]) ).
tff(f1560,plain,
( ! [X2: dB,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X2,X0))),sK12(X2,X0)),X2)) )
| ~ spl28_132
| ~ spl28_146 ),
inference(resolution,[],[f1557,f1344]) ).
tff(f6126,plain,
( spl28_364
| ~ spl28_49
| ~ spl28_141 ),
inference(avatar_split_clause,[],[f1509,f1499,f795,f6124]) ).
tff(f6124,plain,
( spl28_364
<=> ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK13(X1,X2,X0))),sK14(X1,X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_364])]) ).
tff(f1509,plain,
( ! [X2: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK13(X1,X2,X0))),sK14(X1,X2,X0)))) )
| ~ spl28_49
| ~ spl28_141 ),
inference(resolution,[],[f1500,f796]) ).
tff(f6122,plain,
( spl28_363
| ~ spl28_108
| ~ spl28_141 ),
inference(avatar_split_clause,[],[f1502,f1499,f1182,f6120]) ).
tff(f6120,plain,
( spl28_363
<=> ! [X0: fun1(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK13(X1,X2,X0))),sK14(X1,X2,X0)),X3))
| ~ beta(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_363])]) ).
tff(f1502,plain,
( ! [X2: dB,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK13(X1,X2,X0))),sK14(X1,X2,X0)),X3))
| ~ beta(X2,X3) )
| ~ spl28_108
| ~ spl28_141 ),
inference(resolution,[],[f1500,f1183]) ).
tff(f6118,plain,
( spl28_362
| ~ spl28_13
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1379,f1356,f602,f6116]) ).
tff(f6116,plain,
( spl28_362
<=> ! [X0: $tType,X4: bool,X3: X0,X2: list(X0),X1: fun1(X0,fun1(bool,bool))] :
( ( fFalse = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_362])]) ).
tff(f1379,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: fun1(X0,fun1(bool,bool)),X4: bool] :
( ( fFalse = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) )
| ~ spl28_13
| ~ spl28_135 ),
inference(superposition,[],[f1357,f603]) ).
tff(f6114,plain,
( spl28_361
| ~ spl28_13
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1378,f1356,f602,f6112]) ).
tff(f6112,plain,
( spl28_361
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun1(X0,fun1(bool,bool))] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_361])]) ).
tff(f1378,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun1(X0,fun1(bool,bool)),X4: bool] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) )
| ~ spl28_13
| ~ spl28_135 ),
inference(superposition,[],[f1357,f603]) ).
tff(f6110,plain,
( spl28_360
| ~ spl28_13
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1376,f1356,f602,f6108]) ).
tff(f6108,plain,
( spl28_360
<=> ! [X0: $tType,X2: list(X0),X4: X0,X3: bool,X1: fun1(X0,fun1(bool,bool))] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_360])]) ).
tff(f1376,plain,
( ! [X0: $tType,X2: list(X0),X3: bool,X1: fun1(X0,fun1(bool,bool)),X4: X0] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun1(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) )
| ~ spl28_13
| ~ spl28_135 ),
inference(superposition,[],[f1357,f603]) ).
tff(f6106,plain,
( spl28_359
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1315,f1307,f6104]) ).
tff(f6104,plain,
( spl28_359
<=> ! [X1: $tType,X0: $tType,X5: X1,X6: X1,X4: list(X0),X3: X0,X2: fun1(X0,fun1(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_359])]) ).
tff(f1315,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ~ spl28_128 ),
inference(superposition,[],[f1308,f1308]) ).
tff(f6102,plain,
( spl28_358
| ~ spl28_80
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1173,f1161,f975,f6100]) ).
tff(f6100,plain,
( spl28_358
<=> ! [X1: $tType,X0: $tType,X5: fun1(nat,fun1(X0,X1)),X3: type,X4: type,X6: X0,X2: fun1(type,fun1(type,fun1(X0,X1)))] : ( aa(type,X1,combc(type,X0,X1,aa(type,fun1(type,fun1(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun1(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun,X4),X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_358])]) ).
tff(f1173,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(type,fun1(type,fun1(X0,X1))),X3: type,X6: X0,X4: type,X5: fun1(nat,fun1(X0,X1))] : ( aa(type,X1,combc(type,X0,X1,aa(type,fun1(type,fun1(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun1(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun,X4),X3)),X6) )
| ~ spl28_80
| ~ spl28_106 ),
inference(superposition,[],[f976,f1162]) ).
tff(f6058,plain,
( spl28_357
| ~ spl28_4
| ~ spl28_217
| ~ spl28_333 ),
inference(avatar_split_clause,[],[f5807,f5201,f2786,f562,f6055]) ).
tff(f6055,plain,
( spl28_357
<=> sP1(abs(abs(abs(t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_357])]) ).
tff(f5201,plain,
( spl28_333
<=> ( fTrue = aa(dB,bool,it,abs(t2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_333])]) ).
tff(f5807,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(t2))))
| ~ spl28_217
| ~ spl28_333 ),
inference(superposition,[],[f2787,f5203]) ).
tff(f5203,plain,
( ( fTrue = aa(dB,bool,it,abs(t2)) )
| ~ spl28_333 ),
inference(avatar_component_clause,[],[f5201]) ).
tff(f5907,plain,
( spl28_356
| ~ spl28_132
| ~ spl28_161 ),
inference(avatar_split_clause,[],[f1678,f1675,f1343,f5905]) ).
tff(f5905,plain,
( spl28_356
<=> ! [X0: fun1(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X3,X0))),sK12(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_356])]) ).
tff(f1678,plain,
( ! [X2: type,X3: dB,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X3,X0))),sK12(X3,X0)),X3)) )
| ~ spl28_132
| ~ spl28_161 ),
inference(resolution,[],[f1676,f1344]) ).
tff(f5903,plain,
( spl28_355
| ~ spl28_57
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1438,f1360,f975,f848,f5901]) ).
tff(f5901,plain,
( spl28_355
<=> ! [X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_355])]) ).
tff(f1438,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) )
| ~ spl28_57
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1415,f976]) ).
tff(f1415,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),X1) != foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ( X0 = X3 ) )
| ~ spl28_57
| ~ spl28_136 ),
inference(superposition,[],[f849,f1361]) ).
tff(f5899,plain,
( spl28_354
| ~ spl28_54
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1424,f1360,f975,f833,f5897]) ).
tff(f5897,plain,
( spl28_354
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_354])]) ).
tff(f833,plain,
( spl28_54
<=> ! [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,[spl28_54])]) ).
tff(f1424,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl28_54
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1401,f976]) ).
tff(f1401,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl28_54
| ~ spl28_136 ),
inference(superposition,[],[f834,f1361]) ).
tff(f834,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl28_54 ),
inference(avatar_component_clause,[],[f833]) ).
tff(f5895,plain,
( spl28_353
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1421,f1360,f975,f602,f5893]) ).
tff(f5893,plain,
( spl28_353
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: bool,X1: fun1(bool,fun1(X0,bool))] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_353])]) ).
tff(f1421,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun1(bool,fun1(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1398,f976]) ).
tff(f1398,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun1(bool,fun1(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun1(X0,bool),X1,X2),X4),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl28_13
| ~ spl28_136 ),
inference(superposition,[],[f1361,f603]) ).
tff(f5891,plain,
( spl28_352
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1420,f1360,f975,f602,f5889]) ).
tff(f5889,plain,
( spl28_352
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun1(bool,fun1(X0,bool))] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_352])]) ).
tff(f1420,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun1(bool,fun1(X0,bool)),X4: list(X0)] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1396,f976]) ).
tff(f1396,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun1(bool,fun1(X0,bool)),X4: list(X0)] :
( ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ( fTrue = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun1(X0,bool),X1,X2),X3),X4) ) )
| ~ spl28_13
| ~ spl28_136 ),
inference(superposition,[],[f1361,f603]) ).
tff(f5887,plain,
( spl28_351
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1419,f1360,f975,f602,f5885]) ).
tff(f5885,plain,
( spl28_351
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun1(bool,fun1(X0,bool))] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_351])]) ).
tff(f1419,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun1(bool,fun1(X0,bool)),X4: list(X0)] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1392,f976]) ).
tff(f1392,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun1(bool,fun1(X0,bool)),X4: list(X0)] :
( ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) )
| ( fTrue = aa(X0,bool,aa(bool,fun1(X0,bool),X1,X2),X3) ) )
| ~ spl28_13
| ~ spl28_136 ),
inference(superposition,[],[f1361,f603]) ).
tff(f5554,plain,
( spl28_350
| ~ spl28_80
| ~ spl28_143 ),
inference(avatar_split_clause,[],[f1528,f1517,f975,f5552]) ).
tff(f5552,plain,
( spl28_350
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun1(X0,X1),X5: X0,X3: fun1(X1,X2)] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun1(X1,X2),fun1(X0,X2),combc(fun1(X1,X2),fun1(X0,X1),fun1(X0,X2),combb(X1,X2,X0),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_350])]) ).
tff(f1528,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X1,X2),X4: fun1(X0,X1),X5: X0] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun1(X1,X2),fun1(X0,X2),combc(fun1(X1,X2),fun1(X0,X1),fun1(X0,X2),combb(X1,X2,X0),X4),X3),X5) )
| ~ spl28_80
| ~ spl28_143 ),
inference(superposition,[],[f1518,f976]) ).
tff(f5550,plain,
( spl28_349
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f990,f975,f5548]) ).
tff(f5548,plain,
( spl28_349
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun1(X3,fun1(X0,fun1(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun1(X0,fun1(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),combc(X3,X0,fun1(X1,X2),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_349])]) ).
tff(f990,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun1(X3,fun1(X0,fun1(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun1(X0,fun1(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),combc(X3,X0,fun1(X1,X2),X4,X6),X5),X7) )
| ~ spl28_80 ),
inference(superposition,[],[f976,f976]) ).
tff(f5546,plain,
( spl28_348
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f989,f975,f5544]) ).
tff(f989,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun1(X0,fun1(X3,fun1(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun1(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun1(X1,X2),aa(X0,fun1(X3,fun1(X1,X2)),X4,X6),X5),X7) )
| ~ spl28_80 ),
inference(superposition,[],[f976,f976]) ).
tff(f5535,plain,
( spl28_347
| ~ spl28_80
| ~ spl28_142 ),
inference(avatar_split_clause,[],[f1522,f1513,f975,f5533]) ).
tff(f5533,plain,
( spl28_347
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_347])]) ).
tff(f1522,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) )
| ~ spl28_80
| ~ spl28_142 ),
inference(superposition,[],[f1514,f976]) ).
tff(f5480,plain,
( spl28_346
| ~ spl28_81
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5120,f5056,f983,f5477]) ).
tff(f983,plain,
( spl28_81
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_81])]) ).
tff(f5120,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl28_81
| ~ spl28_323 ),
inference(resolution,[],[f5057,f985]) ).
tff(f985,plain,
( sP1(abs(ua))
| ~ spl28_81 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f5274,plain,
( spl28_345
| ~ spl28_73
| ~ spl28_148 ),
inference(avatar_split_clause,[],[f1582,f1576,f938,f5272]) ).
tff(f5272,plain,
( spl28_345
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK16(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_345])]) ).
tff(f1582,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK16(X1,X3,var(X2),X0),X1) ) )
| ~ spl28_73
| ~ spl28_148 ),
inference(resolution,[],[f1577,f939]) ).
tff(f5270,plain,
( spl28_344
| ~ spl28_73
| ~ spl28_146 ),
inference(avatar_split_clause,[],[f1562,f1556,f938,f5268]) ).
tff(f5268,plain,
( spl28_344
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK15(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_344])]) ).
tff(f1562,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK15(X1,X3,var(X2),X0),X1) ) )
| ~ spl28_73
| ~ spl28_146 ),
inference(resolution,[],[f1557,f939]) ).
tff(f5266,plain,
( spl28_343
| ~ spl28_74
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5119,f5056,f942,f5263]) ).
tff(f942,plain,
( spl28_74
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_74])]) ).
tff(f5119,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl28_74
| ~ spl28_323 ),
inference(resolution,[],[f5057,f944]) ).
tff(f944,plain,
( sP1(abs(u))
| ~ spl28_74 ),
inference(avatar_component_clause,[],[f942]) ).
tff(f5261,plain,
( spl28_342
| ~ spl28_27
| ~ spl28_139 ),
inference(avatar_split_clause,[],[f1491,f1449,f677,f5259]) ).
tff(f5259,plain,
( spl28_342
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK26(X0,X0,X1,combi(X0),X3,X2)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_342])]) ).
tff(f1491,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK26(X0,X0,X1,combi(X0),X3,X2)) = X3 ) )
| ~ spl28_27
| ~ spl28_139 ),
inference(superposition,[],[f1450,f678]) ).
tff(f5257,plain,
( spl28_341
| ~ spl28_80
| ~ spl28_139 ),
inference(avatar_split_clause,[],[f1490,f1449,f975,f5255]) ).
tff(f5255,plain,
( spl28_341
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK26(X0,X3,X5,X4,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_341])]) ).
tff(f1490,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK26(X0,X3,X5,X4,X2,X1)) = X2 ) )
| ~ spl28_80
| ~ spl28_139 ),
inference(superposition,[],[f1450,f976]) ).
tff(f5253,plain,
( spl28_340
| ~ spl28_27
| ~ spl28_138 ),
inference(avatar_split_clause,[],[f1487,f1445,f677,f5251]) ).
tff(f5251,plain,
( spl28_340
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK24(X0,X0,X3,X2,X1,combi(X0))) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_340])]) ).
tff(f1487,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK24(X0,X0,X3,X2,X1,combi(X0))) = X3 ) )
| ~ spl28_27
| ~ spl28_138 ),
inference(superposition,[],[f1446,f678]) ).
tff(f5249,plain,
( spl28_339
| ~ spl28_80
| ~ spl28_138 ),
inference(avatar_split_clause,[],[f1486,f1445,f975,f5247]) ).
tff(f5247,plain,
( spl28_339
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK24(X3,X0,X2,X1,X5,X4)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_339])]) ).
tff(f1486,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK24(X3,X0,X2,X1,X5,X4)) = X2 ) )
| ~ spl28_80
| ~ spl28_138 ),
inference(superposition,[],[f1446,f976]) ).
tff(f5245,plain,
( spl28_338
| ~ spl28_80
| ~ spl28_137 ),
inference(avatar_split_clause,[],[f1454,f1441,f975,f5243]) ).
tff(f5243,plain,
( spl28_338
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_338])]) ).
tff(f1454,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) )
| ~ spl28_80
| ~ spl28_137 ),
inference(superposition,[],[f1442,f976]) ).
tff(f5241,plain,
( spl28_337
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1391,f1360,f975,f5239]) ).
tff(f5239,plain,
( spl28_337
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: list(X0),X2: fun1(X1,fun1(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_337])]) ).
tff(f1391,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,X1)),X3: X1,X4: X0,X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) )
| ~ spl28_80
| ~ spl28_136 ),
inference(superposition,[],[f1361,f976]) ).
tff(f5237,plain,
( spl28_336
| ~ spl28_49
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1381,f1356,f795,f5235]) ).
tff(f5235,plain,
( spl28_336
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun1(X0,fun1(bool,bool))] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun1(bool,bool),bool,fEx(bool),aa(X0,fun1(bool,bool),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_336])]) ).
tff(f1381,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun1(X0,fun1(bool,bool)),X4: bool] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun1(bool,bool),bool,fEx(bool),aa(X0,fun1(bool,bool),X1,X2))) )
| ~ spl28_49
| ~ spl28_135 ),
inference(superposition,[],[f796,f1357]) ).
tff(f5233,plain,
( spl28_335
| ~ spl28_80
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1377,f1356,f975,f5231]) ).
tff(f5231,plain,
( spl28_335
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X1),X5: X0,X2: fun1(X1,fun1(X0,X0))] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_335])]) ).
tff(f1377,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,X0)),X3: X1,X4: list(X1),X5: X0] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) )
| ~ spl28_80
| ~ spl28_135 ),
inference(superposition,[],[f1357,f976]) ).
tff(f5229,plain,
( spl28_334
| ~ spl28_49
| ~ spl28_118 ),
inference(avatar_split_clause,[],[f1248,f1245,f795,f5227]) ).
tff(f5227,plain,
( spl28_334
<=> ! [X4: type,X0: fun1(nat,type),X3: nat,X2: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun1(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_334])]) ).
tff(f1248,plain,
( ! [X2: list(type),X3: nat,X0: fun1(nat,type),X1: list(dB),X4: type] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun1(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) )
| ~ spl28_49
| ~ spl28_118 ),
inference(resolution,[],[f1246,f796]) ).
tff(f5204,plain,
( spl28_333
| ~ spl28_68
| ~ spl28_323 ),
inference(avatar_split_clause,[],[f5118,f5056,f909,f5201]) ).
tff(f909,plain,
( spl28_68
<=> sP1(abs(t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_68])]) ).
tff(f5118,plain,
( ( fTrue = aa(dB,bool,it,abs(t2)) )
| ~ spl28_68
| ~ spl28_323 ),
inference(resolution,[],[f5057,f911]) ).
tff(f911,plain,
( sP1(abs(t2))
| ~ spl28_68 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f5141,plain,
( spl28_332
| ~ spl28_73
| ~ spl28_163 ),
inference(avatar_split_clause,[],[f1694,f1691,f938,f5139]) ).
tff(f5139,plain,
( spl28_332
<=> ! [X0: fun1(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK17(X1,X3,X2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_332])]) ).
tff(f1694,plain,
( ! [X2: nat,X3: list(dB),X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun,sK17(X1,X3,X2,X0),X1) ) )
| ~ spl28_73
| ~ spl28_163 ),
inference(resolution,[],[f1692,f939]) ).
tff(f5137,plain,
( spl28_331
| ~ spl28_73
| ~ spl28_141 ),
inference(avatar_split_clause,[],[f1505,f1499,f938,f5135]) ).
tff(f5135,plain,
( spl28_331
<=> ! [X2: nat,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK13(X1,var(X2),X0)),X2) = sK14(X1,var(X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_331])]) ).
tff(f1505,plain,
( ! [X2: nat,X0: fun1(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK13(X1,var(X2),X0)),X2) = sK14(X1,var(X2),X0) ) )
| ~ spl28_73
| ~ spl28_141 ),
inference(resolution,[],[f1500,f939]) ).
tff(f5104,plain,
( spl28_330
| ~ spl28_32
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1422,f1360,f975,f708,f5102]) ).
tff(f5102,plain,
( spl28_330
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_330])]) ).
tff(f1422,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl28_32
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1399,f976]) ).
tff(f1399,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl28_32
| ~ spl28_136 ),
inference(superposition,[],[f709,f1361]) ).
tff(f5100,plain,
( spl28_329
| ~ spl28_27
| ~ spl28_134 ),
inference(avatar_split_clause,[],[f1368,f1352,f677,f5098]) ).
tff(f5098,plain,
( spl28_329
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK25(X0,X0,X1,combi(X0),X3,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_329])]) ).
tff(f1368,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK25(X0,X0,X1,combi(X0),X3,X2)) = X2 ) )
| ~ spl28_27
| ~ spl28_134 ),
inference(superposition,[],[f1353,f678]) ).
tff(f5096,plain,
( spl28_328
| ~ spl28_80
| ~ spl28_134 ),
inference(avatar_split_clause,[],[f1367,f1352,f975,f5094]) ).
tff(f5094,plain,
( spl28_328
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK25(X0,X3,X5,X4,X2,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_328])]) ).
tff(f1367,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK25(X0,X3,X5,X4,X2,X1)) = X1 ) )
| ~ spl28_80
| ~ spl28_134 ),
inference(superposition,[],[f1353,f976]) ).
tff(f5092,plain,
( spl28_327
| ~ spl28_27
| ~ spl28_133 ),
inference(avatar_split_clause,[],[f1365,f1348,f677,f5090]) ).
tff(f5090,plain,
( spl28_327
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK23(X0,X0,X3,X2,X1,combi(X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_327])]) ).
tff(f1365,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK23(X0,X0,X3,X2,X1,combi(X0))) = X2 ) )
| ~ spl28_27
| ~ spl28_133 ),
inference(superposition,[],[f1349,f678]) ).
tff(f5088,plain,
( spl28_326
| ~ spl28_80
| ~ spl28_133 ),
inference(avatar_split_clause,[],[f1364,f1348,f975,f5086]) ).
tff(f5086,plain,
( spl28_326
<=> ! [X0: $tType,X3: $tType,X4: fun1(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK23(X3,X0,X2,X1,X5,X4)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_326])]) ).
tff(f1364,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun1(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK23(X3,X0,X2,X1,X5,X4)) = X1 ) )
| ~ spl28_80
| ~ spl28_133 ),
inference(superposition,[],[f1349,f976]) ).
tff(f5084,plain,
( spl28_325
| ~ spl28_13
| ~ spl28_80
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1322,f1307,f975,f602,f5082]) ).
tff(f5082,plain,
( spl28_325
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: fun1(X0,fun1(list(X0),bool)),X1: bool] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_325])]) ).
tff(f1322,plain,
( ! [X0: $tType,X2: fun1(X0,fun1(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_128 ),
inference(forward_demodulation,[],[f1317,f976]) ).
tff(f1317,plain,
( ! [X0: $tType,X2: fun1(X0,fun1(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(list(X0),bool,aa(X0,fun1(list(X0),bool),X2,X4),X3) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl28_13
| ~ spl28_128 ),
inference(superposition,[],[f1308,f603]) ).
tff(f5080,plain,
( spl28_324
| ~ spl28_108
| ~ spl28_127 ),
inference(avatar_split_clause,[],[f1302,f1296,f1182,f5078]) ).
tff(f5078,plain,
( spl28_324
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),X0))
| ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_324])]) ).
tff(f1302,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),X0))
| ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as),X0) )
| ~ spl28_108
| ~ spl28_127 ),
inference(resolution,[],[f1298,f1183]) ).
tff(f5058,plain,
( spl28_323
| ~ spl28_18
| ~ spl28_19 ),
inference(avatar_split_clause,[],[f1463,f633,f629,f5056]) ).
tff(f1463,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) )
| ~ spl28_18
| ~ spl28_19 ),
inference(resolution,[],[f634,f630]) ).
tff(f5041,plain,
( spl28_322
| ~ spl28_130
| ~ spl28_186 ),
inference(avatar_split_clause,[],[f2007,f2004,f1329,f5039]) ).
tff(f5039,plain,
( spl28_322
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0))))
| ~ pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_322])]) ).
tff(f1329,plain,
( spl28_130
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_130])]) ).
tff(f2007,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0))))
| ~ pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) )
| ~ spl28_130
| ~ spl28_186 ),
inference(resolution,[],[f2005,f1330]) ).
tff(f1330,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))))
| ~ sP0(X0) )
| ~ spl28_130 ),
inference(avatar_component_clause,[],[f1329]) ).
tff(f5037,plain,
( spl28_321
| ~ spl28_46
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1848,f1775,f783,f5035]) ).
tff(f5035,plain,
( spl28_321
<=> ! [X2: nat,X0: type,X1: fun1(type,type)] : ( atom(X2) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_321])]) ).
tff(f783,plain,
( spl28_46
<=> ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_46])]) ).
tff(f1848,plain,
( ! [X2: nat,X0: type,X1: fun1(type,type)] : ( atom(X2) != aa(type,type,aa(fun1(type,type),fun1(type,type),aa(fun1(type,fun1(type,type)),fun1(fun1(type,type),fun1(type,type)),combs(type,type,type),fun),X1),X0) )
| ~ spl28_46
| ~ spl28_170 ),
inference(superposition,[],[f784,f1776]) ).
tff(f784,plain,
( ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ~ spl28_46 ),
inference(avatar_component_clause,[],[f783]) ).
tff(f5033,plain,
( spl28_320
| ~ spl28_47
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1833,f1775,f787,f5031]) ).
tff(f5031,plain,
( spl28_320
<=> ! [X2: dB,X0: dB,X1: fun1(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_320])]) ).
tff(f787,plain,
( spl28_47
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_47])]) ).
tff(f1833,plain,
( ! [X2: dB,X0: dB,X1: fun1(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl28_47
| ~ spl28_170 ),
inference(superposition,[],[f788,f1776]) ).
tff(f788,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) )
| ~ spl28_47 ),
inference(avatar_component_clause,[],[f787]) ).
tff(f5029,plain,
( spl28_319
| ~ spl28_48
| ~ spl28_170 ),
inference(avatar_split_clause,[],[f1832,f1775,f791,f5027]) ).
tff(f5027,plain,
( spl28_319
<=> ! [X2: nat,X0: dB,X1: fun1(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_319])]) ).
tff(f791,plain,
( spl28_48
<=> ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_48])]) ).
tff(f1832,plain,
( ! [X2: nat,X0: dB,X1: fun1(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun1(dB,dB),fun1(dB,dB),aa(fun1(dB,fun1(dB,dB)),fun1(fun1(dB,dB),fun1(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl28_48
| ~ spl28_170 ),
inference(superposition,[],[f792,f1776]) ).
tff(f792,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) )
| ~ spl28_48 ),
inference(avatar_component_clause,[],[f791]) ).
tff(f5025,plain,
( spl28_318
| ~ spl28_29
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1310,f1307,f694,f5023]) ).
tff(f5023,plain,
( spl28_318
<=> ! [X0: $tType,X5: X0,X4: list(nat),X3: fun1(list(nat),X0),X2: nat,X1: fun1(nat,fun1(list(nat),X0))] : ( list_case(X0,nat,X5,shift(fun1(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_318])]) ).
tff(f1310,plain,
( ! [X0: $tType,X2: nat,X3: fun1(list(nat),X0),X1: fun1(nat,fun1(list(nat),X0)),X4: list(nat),X5: X0] : ( list_case(X0,nat,X5,shift(fun1(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) )
| ~ spl28_29
| ~ spl28_128 ),
inference(superposition,[],[f1308,f695]) ).
tff(f4899,plain,
( spl28_317
| ~ spl28_49
| ~ spl28_152 ),
inference(avatar_split_clause,[],[f1620,f1612,f795,f4897]) ).
tff(f4897,plain,
( spl28_317
<=> ! [X4: type,X0: fun1(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_317])]) ).
tff(f1620,plain,
( ! [X2: dB,X3: nat,X0: fun1(nat,type),X1: type,X4: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) )
| ~ spl28_49
| ~ spl28_152 ),
inference(resolution,[],[f1613,f796]) ).
tff(f4895,plain,
( spl28_316
| ~ spl28_65
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1384,f1356,f896,f4893]) ).
tff(f4893,plain,
( spl28_316
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_316])]) ).
tff(f1384,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ~ spl28_65
| ~ spl28_135 ),
inference(superposition,[],[f897,f1357]) ).
tff(f4891,plain,
( spl28_315
| ~ spl28_28
| ~ spl28_130 ),
inference(avatar_split_clause,[],[f1332,f1329,f681,f4889]) ).
tff(f4889,plain,
( spl28_315
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_315])]) ).
tff(f681,plain,
( spl28_28
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_28])]) ).
tff(f1332,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0)))) )
| ~ spl28_28
| ~ spl28_130 ),
inference(resolution,[],[f1330,f682]) ).
tff(f682,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl28_28 ),
inference(avatar_component_clause,[],[f681]) ).
tff(f4887,plain,
( spl28_314
| ~ spl28_80
| ~ spl28_128 ),
inference(avatar_split_clause,[],[f1316,f1307,f975,f4885]) ).
tff(f4885,plain,
( spl28_314
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: list(X0),X3: X0,X2: fun1(X0,fun1(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_314])]) ).
tff(f1316,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(list(X0),X1)),X3: X0,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) )
| ~ spl28_80
| ~ spl28_128 ),
inference(superposition,[],[f1308,f976]) ).
tff(f4883,plain,
( spl28_313
| ~ spl28_115
| ~ spl28_127 ),
inference(avatar_split_clause,[],[f1301,f1296,f1226,f4880]) ).
tff(f1301,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl28_115
| ~ spl28_127 ),
inference(resolution,[],[f1298,f1227]) ).
tff(f4878,plain,
( spl28_312
| ~ spl28_117
| ~ spl28_127 ),
inference(avatar_split_clause,[],[f1300,f1296,f1238,f4875]) ).
tff(f4875,plain,
( spl28_312
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK16(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_312])]) ).
tff(f1300,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK16(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl28_117
| ~ spl28_127 ),
inference(resolution,[],[f1298,f1239]) ).
tff(f4856,plain,
( spl28_311
| ~ spl28_47
| ~ spl28_203 ),
inference(avatar_split_clause,[],[f2151,f2142,f787,f4854]) ).
tff(f4854,plain,
( spl28_311
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_311])]) ).
tff(f2151,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl28_47
| ~ spl28_203 ),
inference(superposition,[],[f788,f2143]) ).
tff(f4852,plain,
( spl28_310
| ~ spl28_48
| ~ spl28_203 ),
inference(avatar_split_clause,[],[f2150,f2142,f791,f4850]) ).
tff(f4850,plain,
( spl28_310
<=> ! [X4: nat,X0: dB,X3: dB,X2: dB,X1: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_310])]) ).
tff(f2150,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl28_48
| ~ spl28_203 ),
inference(superposition,[],[f792,f2143]) ).
tff(f4848,plain,
( spl28_309
| ~ spl28_17
| ~ spl28_130 ),
inference(avatar_split_clause,[],[f1333,f1329,f625,f4846]) ).
tff(f4846,plain,
( spl28_309
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_309])]) ).
tff(f625,plain,
( spl28_17
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_17])]) ).
tff(f1333,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))) )
| ~ spl28_17
| ~ spl28_130 ),
inference(resolution,[],[f1330,f626]) ).
tff(f626,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl28_17 ),
inference(avatar_component_clause,[],[f625]) ).
tff(f4811,plain,
( spl28_308
| ~ spl28_130
| ~ spl28_183 ),
inference(avatar_split_clause,[],[f1958,f1955,f1329,f4809]) ).
tff(f4809,plain,
( spl28_308
<=> ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0)))
| ~ pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_308])]) ).
tff(f1958,plain,
( ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0)))
| ~ pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) )
| ~ spl28_130
| ~ spl28_183 ),
inference(resolution,[],[f1956,f1330]) ).
tff(f4807,plain,
( spl28_307
| ~ spl28_71
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1429,f1360,f975,f924,f4805]) ).
tff(f4805,plain,
( spl28_307
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_307])]) ).
tff(f1429,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl28_71
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1406,f976]) ).
tff(f1406,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X4) )
| ~ spl28_71
| ~ spl28_136 ),
inference(superposition,[],[f925,f1361]) ).
tff(f4803,plain,
( spl28_306
| ~ spl28_4
| ~ spl28_213 ),
inference(avatar_split_clause,[],[f2501,f2292,f562,f4801]) ).
tff(f4801,plain,
( spl28_306
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_306])]) ).
tff(f2292,plain,
( spl28_213
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_213])]) ).
tff(f2501,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl28_4
| ~ spl28_213 ),
inference(superposition,[],[f564,f2293]) ).
tff(f2293,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl28_213 ),
inference(avatar_component_clause,[],[f2292]) ).
tff(f564,plain,
( pp(fTrue)
| ~ spl28_4 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f4799,plain,
( spl28_305
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1167,f1161,f4797]) ).
tff(f4797,plain,
( spl28_305
<=> ! [X0: $tType,X3: type,X4: fun1(nat,X0),X5: fun1(nat,X0),X2: type,X1: fun1(type,fun1(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_305])]) ).
tff(f1167,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,X0)),X4: fun1(nat,X0),X5: fun1(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) )
| ~ spl28_106 ),
inference(superposition,[],[f1162,f1162]) ).
tff(f4751,plain,
( spl28_304
| ~ spl28_80
| ~ spl28_110 ),
inference(avatar_split_clause,[],[f1201,f1198,f975,f4749]) ).
tff(f4749,plain,
( spl28_304
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_304])]) ).
tff(f1201,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 )
| ~ spl28_80
| ~ spl28_110 ),
inference(superposition,[],[f1199,f976]) ).
tff(f4747,plain,
( spl28_303
| ~ spl28_13
| ~ spl28_80
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1174,f1161,f975,f602,f4745]) ).
tff(f4745,plain,
( spl28_303
<=> ! [X2: type,X0: fun1(nat,bool),X1: fun1(type,fun1(type,bool)),X3: type] :
( ( fFalse = aa(type,bool,combc(type,type,bool,X1,X2),X3) )
| ( fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_303])]) ).
tff(f1174,plain,
( ! [X2: type,X3: type,X0: fun1(nat,bool),X1: fun1(type,fun1(type,bool))] :
( ( fFalse = aa(type,bool,combc(type,type,bool,X1,X2),X3) )
| ( fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun,X2),X3)) ) )
| ~ spl28_13
| ~ spl28_80
| ~ spl28_106 ),
inference(forward_demodulation,[],[f1169,f976]) ).
tff(f1169,plain,
( ! [X2: type,X3: type,X0: fun1(nat,bool),X1: fun1(type,fun1(type,bool))] :
( ( fFalse = aa(type,bool,aa(type,fun1(type,bool),X1,X3),X2) )
| ( fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun,X2),X3)) ) )
| ~ spl28_13
| ~ spl28_106 ),
inference(superposition,[],[f1162,f603]) ).
tff(f4743,plain,
( spl28_302
| ~ spl28_62
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f1004,f975,f878,f4741]) ).
tff(f4741,plain,
( spl28_302
<=> ! [X0: $tType,X3: nat,X2: X0,X1: fun1(X0,fun1(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun1(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_302])]) ).
tff(f1004,plain,
( ! [X0: $tType,X2: X0,X3: nat,X1: fun1(X0,fun1(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun1(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3)))
| ~ spl28_62
| ~ spl28_80 ),
inference(superposition,[],[f879,f976]) ).
tff(f4730,plain,
( spl28_301
| ~ spl28_15
| ~ spl28_19 ),
inference(avatar_split_clause,[],[f1465,f633,f616,f4728]) ).
tff(f4728,plain,
( spl28_301
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_301])]) ).
tff(f616,plain,
( spl28_15
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_15])]) ).
tff(f1465,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) )
| ~ spl28_15
| ~ spl28_19 ),
inference(resolution,[],[f634,f617]) ).
tff(f617,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl28_15 ),
inference(avatar_component_clause,[],[f616]) ).
tff(f4674,plain,
( spl28_300
| ~ spl28_59
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1433,f1360,f975,f865,f4672]) ).
tff(f4672,plain,
( spl28_300
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_300])]) ).
tff(f865,plain,
( spl28_59
<=> ! [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,[spl28_59])]) ).
tff(f1433,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl28_59
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1410,f976]) ).
tff(f1410,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl28_59
| ~ spl28_136 ),
inference(superposition,[],[f866,f1361]) ).
tff(f866,plain,
( ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) )
| ( X1 = X3 ) )
| ~ spl28_59 ),
inference(avatar_component_clause,[],[f865]) ).
tff(f4670,plain,
( spl28_299
| ~ spl28_60
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1425,f1360,f975,f869,f4668]) ).
tff(f4668,plain,
( spl28_299
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_299])]) ).
tff(f869,plain,
( spl28_60
<=> ! [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,[spl28_60])]) ).
tff(f1425,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl28_60
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1402,f976]) ).
tff(f1402,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl28_60
| ~ spl28_136 ),
inference(superposition,[],[f870,f1361]) ).
tff(f870,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) )
| ( X1 = X3 ) )
| ~ spl28_60 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f4666,plain,
( spl28_298
| ~ spl28_28
| ~ spl28_112 ),
inference(avatar_split_clause,[],[f1212,f1209,f681,f4664]) ).
tff(f4664,plain,
( spl28_298
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),var(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_298])]) ).
tff(f1209,plain,
( spl28_112
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_112])]) ).
tff(f1212,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),var(X2)))) )
| ~ spl28_28
| ~ spl28_112 ),
inference(resolution,[],[f1210,f682]) ).
tff(f1210,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl28_112 ),
inference(avatar_component_clause,[],[f1209]) ).
tff(f4662,plain,
( spl28_297
| ~ spl28_13
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1090,f1078,f602,f4660]) ).
tff(f4660,plain,
( spl28_297
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK19(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK19(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_297])]) ).
tff(f1090,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK19(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK19(bool,X0,X1,X2)) ) )
| ~ spl28_13
| ~ spl28_94 ),
inference(superposition,[],[f1079,f603]) ).
tff(f4658,plain,
( spl28_296
| ~ spl28_13
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1085,f1078,f602,f4656]) ).
tff(f4656,plain,
( spl28_296
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK19(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK19(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_296])]) ).
tff(f1085,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK19(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK19(bool,X0,X2,X1)) ) )
| ~ spl28_13
| ~ spl28_94 ),
inference(superposition,[],[f1079,f603]) ).
tff(f4594,plain,
( spl28_295
| ~ spl28_17
| ~ spl28_112 ),
inference(avatar_split_clause,[],[f1213,f1209,f625,f4592]) ).
tff(f4592,plain,
( spl28_295
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_295])]) ).
tff(f1213,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X0),X1),var(X2))) )
| ~ spl28_17
| ~ spl28_112 ),
inference(resolution,[],[f1210,f626]) ).
tff(f4590,plain,
( spl28_294
| ~ spl28_49
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f996,f975,f795,f4588]) ).
tff(f4588,plain,
( spl28_294
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun1(X1,fun1(X0,bool))] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(X1,fun1(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_294])]) ).
tff(f996,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),aa(X1,fun1(X0,bool),X2,X3))) )
| ~ spl28_49
| ~ spl28_80 ),
inference(superposition,[],[f796,f976]) ).
tff(f4586,plain,
( spl28_293
| ~ spl28_49
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f995,f975,f795,f4584]) ).
tff(f4584,plain,
( spl28_293
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun1(X0,fun1(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_293])]) ).
tff(f995,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),X3))
| pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) )
| ~ spl28_49
| ~ spl28_80 ),
inference(superposition,[],[f796,f976]) ).
tff(f4234,plain,
( spl28_292
| ~ spl28_65
| ~ spl28_169 ),
inference(avatar_split_clause,[],[f1754,f1734,f896,f4232]) ).
tff(f4232,plain,
( spl28_292
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun1(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_292])]) ).
tff(f1754,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ~ spl28_65
| ~ spl28_169 ),
inference(superposition,[],[f897,f1735]) ).
tff(f4230,plain,
( spl28_291
| ~ spl28_89
| ~ spl28_155 ),
inference(avatar_split_clause,[],[f1636,f1630,f1049,f4228]) ).
tff(f4228,plain,
( spl28_291
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_291])]) ).
tff(f1636,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) )
| ~ spl28_89
| ~ spl28_155 ),
inference(resolution,[],[f1631,f1051]) ).
tff(f4226,plain,
( spl28_290
| ~ spl28_91
| ~ spl28_155 ),
inference(avatar_split_clause,[],[f1635,f1630,f1062,f4224]) ).
tff(f4224,plain,
( spl28_290
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t1 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_290])]) ).
tff(f1635,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t1 = X0 ) )
| ~ spl28_91
| ~ spl28_155 ),
inference(resolution,[],[f1631,f1064]) ).
tff(f4222,plain,
( spl28_289
| ~ spl28_89
| ~ spl28_108 ),
inference(avatar_split_clause,[],[f1187,f1182,f1049,f4220]) ).
tff(f4220,plain,
( spl28_289
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),X0))
| ~ beta(foldl(dB,dB,app,var(i),rs),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_289])]) ).
tff(f1187,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),X0))
| ~ beta(foldl(dB,dB,app,var(i),rs),X0) )
| ~ spl28_89
| ~ spl28_108 ),
inference(resolution,[],[f1183,f1051]) ).
tff(f4218,plain,
( spl28_288
| ~ spl28_91
| ~ spl28_108 ),
inference(avatar_split_clause,[],[f1186,f1182,f1062,f4216]) ).
tff(f4216,plain,
( spl28_288
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),X0))
| ~ beta(foldl(dB,dB,app,var(i),rs),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_288])]) ).
tff(f1186,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),X0))
| ~ beta(foldl(dB,dB,app,var(i),rs),X0) )
| ~ spl28_91
| ~ spl28_108 ),
inference(resolution,[],[f1183,f1064]) ).
tff(f4214,plain,
( spl28_287
| ~ spl28_26
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2802,f2786,f673,f4212]) ).
tff(f4212,plain,
( spl28_287
<=> ! [X0: dB] :
( sP1(abs(abs(sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_287])]) ).
tff(f2802,plain,
( ! [X0: dB] :
( sP1(abs(abs(sK9(X0))))
| ~ sP0(X0) )
| ~ spl28_26
| ~ spl28_217 ),
inference(resolution,[],[f2787,f674]) ).
tff(f4210,plain,
( spl28_286
| ~ spl28_80
| ~ spl28_106 ),
inference(avatar_split_clause,[],[f1168,f1161,f975,f4208]) ).
tff(f4208,plain,
( spl28_286
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: type,X2: type,X1: fun1(type,fun1(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_286])]) ).
tff(f1168,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun1(type,fun1(type,X0)),X4: fun1(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2) )
| ~ spl28_80
| ~ spl28_106 ),
inference(superposition,[],[f1162,f976]) ).
tff(f4206,plain,
( spl28_285
| ~ spl28_80
| ~ spl28_104 ),
inference(avatar_split_clause,[],[f1152,f1136,f975,f4204]) ).
tff(f4204,plain,
( spl28_285
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_285])]) ).
tff(f1152,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) )
| ~ spl28_80
| ~ spl28_104 ),
inference(superposition,[],[f1137,f976]) ).
tff(f4202,plain,
( spl28_284
| ~ spl28_80
| ~ spl28_103 ),
inference(avatar_split_clause,[],[f1149,f1132,f975,f4200]) ).
tff(f4200,plain,
( spl28_284
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_284])]) ).
tff(f1149,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) )
| ~ spl28_80
| ~ spl28_103 ),
inference(superposition,[],[f1133,f976]) ).
tff(f4198,plain,
( spl28_283
| ~ spl28_80
| ~ spl28_102 ),
inference(avatar_split_clause,[],[f1145,f1128,f975,f4196]) ).
tff(f4196,plain,
( spl28_283
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,combc(type,type,type,fun,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_283])]) ).
tff(f1145,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,combc(type,type,type,fun,X1),X0) )
| ( X1 = X3 ) )
| ~ spl28_80
| ~ spl28_102 ),
inference(superposition,[],[f1129,f976]) ).
tff(f4194,plain,
( spl28_282
| ~ spl28_80
| ~ spl28_101 ),
inference(avatar_split_clause,[],[f1140,f1124,f975,f4192]) ).
tff(f4192,plain,
( spl28_282
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,combc(type,type,type,fun,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_282])]) ).
tff(f1140,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != aa(type,type,combc(type,type,type,fun,X1),X0) )
| ( X0 = X2 ) )
| ~ spl28_80
| ~ spl28_101 ),
inference(superposition,[],[f1125,f976]) ).
tff(f4190,plain,
( spl28_281
| ~ spl28_13
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f991,f975,f602,f4188]) ).
tff(f4188,plain,
( spl28_281
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun1(X1,fun1(X0,bool))] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun1(X0,bool),X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_281])]) ).
tff(f991,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,fun1(X0,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun1(X0,bool),X2,X3),X4) ) )
| ~ spl28_13
| ~ spl28_80 ),
inference(superposition,[],[f976,f603]) ).
tff(f4186,plain,
( spl28_280
| ~ spl28_13
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f987,f975,f602,f4184]) ).
tff(f4184,plain,
( spl28_280
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun1(X0,fun1(X1,bool))] :
( ( fFalse = aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_280])]) ).
tff(f987,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X0,fun1(X1,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun1(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) )
| ~ spl28_13
| ~ spl28_80 ),
inference(superposition,[],[f976,f603]) ).
tff(f4174,plain,
( spl28_279
| ~ spl28_50
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1435,f1360,f975,f799,f4172]) ).
tff(f4172,plain,
( spl28_279
<=> ! [X4: list(dB),X0: dB,X3: nat,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_279])]) ).
tff(f799,plain,
( spl28_50
<=> ! [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,[spl28_50])]) ).
tff(f1435,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ~ spl28_50
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1412,f976]) ).
tff(f1412,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X0)),X2),X1) )
| ~ spl28_50
| ~ spl28_136 ),
inference(superposition,[],[f800,f1361]) ).
tff(f800,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) )
| ~ spl28_50 ),
inference(avatar_component_clause,[],[f799]) ).
tff(f4170,plain,
( spl28_278
| ~ spl28_216 ),
inference(avatar_split_clause,[],[f2784,f2306,f4168]) ).
tff(f2306,plain,
( spl28_216
<=> ! [X0: type,X1: nat] :
( ( atom(X1) != X0 )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_216])]) ).
tff(f2784,plain,
( ! [X0: nat] : ( atom(X0) = atom(sK4(atom(X0))) )
| ~ spl28_216 ),
inference(equality_resolution,[],[f2307]) ).
tff(f2307,plain,
( ! [X0: type,X1: nat] :
( ( atom(X1) != X0 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_216 ),
inference(avatar_component_clause,[],[f2306]) ).
tff(f4166,plain,
( spl28_277
| ~ spl28_50
| ~ spl28_80
| ~ spl28_136 ),
inference(avatar_split_clause,[],[f1423,f1360,f975,f799,f4164]) ).
tff(f4164,plain,
( spl28_277
<=> ! [X4: list(dB),X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_277])]) ).
tff(f1423,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl28_50
| ~ spl28_80
| ~ spl28_136 ),
inference(forward_demodulation,[],[f1400,f976]) ).
tff(f1400,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(X0)),X2),X1) != foldl(dB,dB,app,abs(X3),X4) )
| ~ spl28_50
| ~ spl28_136 ),
inference(superposition,[],[f800,f1361]) ).
tff(f4017,plain,
( spl28_276
| ~ spl28_64
| ~ spl28_142 ),
inference(avatar_split_clause,[],[f1520,f1513,f891,f4015]) ).
tff(f4015,plain,
( spl28_276
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_276])]) ).
tff(f1520,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) )
| ~ spl28_64
| ~ spl28_142 ),
inference(superposition,[],[f1514,f893]) ).
tff(f4013,plain,
( spl28_275
| ~ spl28_20
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1087,f1078,f637,f4011]) ).
tff(f4011,plain,
( spl28_275
<=> ! [X0: $tType,X1: fun1(X0,X0)] :
( ( sK19(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK19(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_275])]) ).
tff(f1087,plain,
( ! [X0: $tType,X1: fun1(X0,X0)] :
( ( sK19(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK19(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl28_20
| ~ spl28_94 ),
inference(superposition,[],[f1079,f638]) ).
tff(f4009,plain,
( spl28_274
| ~ spl28_13
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1086,f1078,f602,f4007]) ).
tff(f4007,plain,
( spl28_274
<=> ! [X0: $tType,X2: fun1(bool,X0),X1: fun1(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK19(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_274])]) ).
tff(f1086,plain,
( ! [X0: $tType,X2: fun1(bool,X0),X1: fun1(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK19(X0,bool,X1,X2) ) )
| ~ spl28_13
| ~ spl28_94 ),
inference(superposition,[],[f1079,f603]) ).
tff(f4005,plain,
( spl28_273
| ~ spl28_20
| ~ spl28_94 ),
inference(avatar_split_clause,[],[f1082,f1078,f637,f4003]) ).
tff(f4003,plain,
( spl28_273
<=> ! [X0: $tType,X1: fun1(X0,X0)] :
( ( sK19(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK19(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_273])]) ).
tff(f1082,plain,
( ! [X0: $tType,X1: fun1(X0,X0)] :
( ( sK19(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK19(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl28_20
| ~ spl28_94 ),
inference(superposition,[],[f1079,f638]) ).
tff(f3988,plain,
( spl28_272
| ~ spl28_49
| ~ spl28_87 ),
inference(avatar_split_clause,[],[f1039,f1035,f795,f3986]) ).
tff(f3986,plain,
( spl28_272
<=> ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,fun1(X0,bool),bool,member(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_272])]) ).
tff(f1035,plain,
( spl28_87
<=> ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun1(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_87])]) ).
tff(f1039,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,fun1(X0,bool),bool,member(X0),X1))) )
| ~ spl28_49
| ~ spl28_87 ),
inference(resolution,[],[f1036,f796]) ).
tff(f1036,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun1(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl28_87 ),
inference(avatar_component_clause,[],[f1035]) ).
tff(f3898,plain,
( spl28_271
| ~ spl28_47
| ~ spl28_179 ),
inference(avatar_split_clause,[],[f1934,f1924,f787,f3896]) ).
tff(f3896,plain,
( spl28_271
<=> ! [X2: dB,X0: nat,X1: dB,X3: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_271])]) ).
tff(f1934,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl28_47
| ~ spl28_179 ),
inference(superposition,[],[f788,f1925]) ).
tff(f3894,plain,
( spl28_270
| ~ spl28_48
| ~ spl28_179 ),
inference(avatar_split_clause,[],[f1933,f1924,f791,f3892]) ).
tff(f3892,plain,
( spl28_270
<=> ! [X2: dB,X0: nat,X1: dB,X3: nat] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_270])]) ).
tff(f1933,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl28_48
| ~ spl28_179 ),
inference(superposition,[],[f792,f1925]) ).
tff(f3890,plain,
( spl28_269
| ~ spl28_64
| ~ spl28_139 ),
inference(avatar_split_clause,[],[f1488,f1449,f891,f3888]) ).
tff(f3888,plain,
( spl28_269
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK26(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_269])]) ).
tff(f1488,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK26(dB,X0,X2,X1,as,a)) ) )
| ~ spl28_64
| ~ spl28_139 ),
inference(superposition,[],[f1450,f893]) ).
tff(f3886,plain,
( spl28_268
| ~ spl28_64
| ~ spl28_138 ),
inference(avatar_split_clause,[],[f1484,f1445,f891,f3884]) ).
tff(f3884,plain,
( spl28_268
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK24(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_268])]) ).
tff(f1484,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK24(X0,dB,as,a,X2,X1)) ) )
| ~ spl28_64
| ~ spl28_138 ),
inference(superposition,[],[f1446,f893]) ).
tff(f3882,plain,
( spl28_267
| ~ spl28_64
| ~ spl28_137 ),
inference(avatar_split_clause,[],[f1452,f1441,f891,f3880]) ).
tff(f3880,plain,
( spl28_267
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_267])]) ).
tff(f1452,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) )
| ~ spl28_64
| ~ spl28_137 ),
inference(superposition,[],[f1442,f893]) ).
tff(f3878,plain,
( spl28_266
| ~ spl28_89
| ~ spl28_117 ),
inference(avatar_split_clause,[],[f1242,f1238,f1049,f3875]) ).
tff(f3875,plain,
( spl28_266
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK16(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_266])]) ).
tff(f1242,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK16(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl28_89
| ~ spl28_117 ),
inference(resolution,[],[f1239,f1051]) ).
tff(f3873,plain,
( spl28_265
| ~ spl28_91
| ~ spl28_117 ),
inference(avatar_split_clause,[],[f1241,f1238,f1062,f3870]) ).
tff(f3870,plain,
( spl28_265
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK16(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_265])]) ).
tff(f1241,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK16(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl28_91
| ~ spl28_117 ),
inference(resolution,[],[f1239,f1064]) ).
tff(f3856,plain,
( spl28_264
| ~ spl28_89
| ~ spl28_115 ),
inference(avatar_split_clause,[],[f1230,f1226,f1049,f3853]) ).
tff(f3853,plain,
( spl28_264
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_264])]) ).
tff(f1230,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl28_89
| ~ spl28_115 ),
inference(resolution,[],[f1227,f1051]) ).
tff(f3851,plain,
( spl28_263
| ~ spl28_91
| ~ spl28_115 ),
inference(avatar_split_clause,[],[f1229,f1226,f1062,f3848]) ).
tff(f3848,plain,
( spl28_263
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_263])]) ).
tff(f1229,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl28_91
| ~ spl28_115 ),
inference(resolution,[],[f1227,f1064]) ).
tff(f3846,plain,
( spl28_262
| ~ spl28_69
| ~ spl28_102 ),
inference(avatar_split_clause,[],[f1144,f1128,f916,f3844]) ).
tff(f3844,plain,
( spl28_262
<=> ! [X2: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) != X0 )
| ( sK3(X0) = X2 )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_262])]) ).
tff(f1144,plain,
( ! [X2: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) != X0 )
| ( sK3(X0) = X2 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_102 ),
inference(superposition,[],[f1129,f917]) ).
tff(f3842,plain,
( spl28_261
| ~ spl28_69
| ~ spl28_101 ),
inference(avatar_split_clause,[],[f1139,f1124,f916,f3840]) ).
tff(f3840,plain,
( spl28_261
<=> ! [X2: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) != X0 )
| ( sK2(X0) = X1 )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_261])]) ).
tff(f1139,plain,
( ! [X2: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) != X0 )
| ( sK2(X0) = X1 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_101 ),
inference(superposition,[],[f1125,f917]) ).
tff(f3838,plain,
( spl28_260
| ~ spl28_29
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f988,f975,f694,f3836]) ).
tff(f3836,plain,
( spl28_260
<=> ! [X1: $tType,X0: $tType,X2: fun1(nat,fun1(X0,X1)),X3: nat,X4: fun1(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun1(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_260])]) ).
tff(f988,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(nat,fun1(X0,X1)),X3: nat,X4: fun1(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun1(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) )
| ~ spl28_29
| ~ spl28_80 ),
inference(superposition,[],[f976,f695]) ).
tff(f3812,plain,
( spl28_259
| ~ spl28_64
| ~ spl28_134 ),
inference(avatar_split_clause,[],[f1366,f1352,f891,f3810]) ).
tff(f3810,plain,
( spl28_259
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK25(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_259])]) ).
tff(f1366,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK25(dB,X0,X2,X1,as,a)) ) )
| ~ spl28_64
| ~ spl28_134 ),
inference(superposition,[],[f1353,f893]) ).
tff(f3807,plain,
( spl28_258
| ~ spl28_64
| ~ spl28_133 ),
inference(avatar_split_clause,[],[f1363,f1348,f891,f3805]) ).
tff(f3805,plain,
( spl28_258
<=> ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK23(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_258])]) ).
tff(f1363,plain,
( ! [X0: $tType,X2: list(X0),X1: fun1(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK23(X0,dB,as,a,X2,X1)) ) )
| ~ spl28_64
| ~ spl28_133 ),
inference(superposition,[],[f1349,f893]) ).
tff(f3803,plain,
( spl28_257
| ~ spl28_89
| ~ spl28_120 ),
inference(avatar_split_clause,[],[f1265,f1256,f1049,f3800]) ).
tff(f3800,plain,
( spl28_257
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK17(t_a,rs,i,shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_257])]) ).
tff(f1265,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK17(t_a,rs,i,shift(type,ea,ia,t))))
| ~ spl28_89
| ~ spl28_120 ),
inference(resolution,[],[f1257,f1051]) ).
tff(f3798,plain,
( spl28_256
| ~ spl28_91
| ~ spl28_120 ),
inference(avatar_split_clause,[],[f1264,f1256,f1062,f3795]) ).
tff(f3795,plain,
( spl28_256
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK17(t1,rs,i,shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_256])]) ).
tff(f1264,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK17(t1,rs,i,shift(type,e,i,t))))
| ~ spl28_91
| ~ spl28_120 ),
inference(resolution,[],[f1257,f1064]) ).
tff(f3790,plain,
( spl28_255
| ~ spl28_77
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f992,f975,f958,f3788]) ).
tff(f3788,plain,
( spl28_255
<=> ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),X1),var(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_255])]) ).
tff(f992,plain,
( ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X0),X1),var(X1)) = X0 )
| ~ spl28_77
| ~ spl28_80 ),
inference(superposition,[],[f976,f959]) ).
tff(f3759,plain,
( spl28_254
| ~ spl28_18
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2789,f2786,f629,f3757]) ).
tff(f3757,plain,
( spl28_254
<=> ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_254])]) ).
tff(f2789,plain,
( ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) )
| ~ spl28_18
| ~ spl28_217 ),
inference(resolution,[],[f2787,f630]) ).
tff(f3740,plain,
( spl28_253
| ~ spl28_49
| ~ spl28_91 ),
inference(avatar_split_clause,[],[f1066,f1062,f795,f3737]) ).
tff(f3737,plain,
( spl28_253
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_253])]) ).
tff(f1066,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1)))
| ~ spl28_49
| ~ spl28_91 ),
inference(resolution,[],[f1064,f796]) ).
tff(f3735,plain,
( spl28_252
| ~ spl28_49
| ~ spl28_89 ),
inference(avatar_split_clause,[],[f1053,f1049,f795,f3732]) ).
tff(f3732,plain,
( spl28_252
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_252])]) ).
tff(f1053,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a)))
| ~ spl28_49
| ~ spl28_89 ),
inference(resolution,[],[f1051,f796]) ).
tff(f3730,plain,
( spl28_251
| ~ spl28_28
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f1015,f1012,f681,f3728]) ).
tff(f3728,plain,
( spl28_251
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_251])]) ).
tff(f1012,plain,
( spl28_83
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_83])]) ).
tff(f1015,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) )
| ~ spl28_28
| ~ spl28_83 ),
inference(resolution,[],[f1013,f682]) ).
tff(f1013,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_83 ),
inference(avatar_component_clause,[],[f1012]) ).
tff(f3726,plain,
( spl28_250
| ~ spl28_71
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f999,f975,f924,f3724]) ).
tff(f3724,plain,
( spl28_250
<=> ! [X2: nat,X0: dB,X1: dB,X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_250])]) ).
tff(f999,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: dB] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) )
| ~ spl28_71
| ~ spl28_80 ),
inference(superposition,[],[f925,f976]) ).
tff(f3722,plain,
( spl28_249
| ~ spl28_69
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f994,f975,f916,f3720]) ).
tff(f3720,plain,
( spl28_249
<=> ! [X0: type] :
( ( aa(type,type,combc(type,type,type,fun,sK3(X0)),sK2(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_249])]) ).
tff(f994,plain,
( ! [X0: type] :
( ( aa(type,type,combc(type,type,type,fun,sK3(X0)),sK2(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_69
| ~ spl28_80 ),
inference(superposition,[],[f976,f917]) ).
tff(f3718,plain,
( spl28_248
| ~ spl28_28
| ~ spl28_75 ),
inference(avatar_split_clause,[],[f978,f949,f681,f3716]) ).
tff(f3716,plain,
( spl28_248
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK5(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_248])]) ).
tff(f949,plain,
( spl28_75
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_75])]) ).
tff(f978,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK5(X0))) )
| ~ spl28_28
| ~ spl28_75 ),
inference(resolution,[],[f950,f682]) ).
tff(f950,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK5(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl28_75 ),
inference(avatar_component_clause,[],[f949]) ).
tff(f3714,plain,
( spl28_247
| ~ spl28_49
| ~ spl28_62 ),
inference(avatar_split_clause,[],[f885,f878,f795,f3712]) ).
tff(f3712,plain,
( spl28_247
<=> ! [X0: fun1(nat,type),X1: nat] : pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_247])]) ).
tff(f885,plain,
( ! [X0: fun1(nat,type),X1: nat] : pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1))))
| ~ spl28_49
| ~ spl28_62 ),
inference(resolution,[],[f879,f796]) ).
tff(f3706,plain,
( spl28_246
| ~ spl28_17
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f1016,f1012,f625,f3704]) ).
tff(f3704,plain,
( spl28_246
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_246])]) ).
tff(f1016,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) )
| ~ spl28_17
| ~ spl28_83 ),
inference(resolution,[],[f1013,f626]) ).
tff(f3702,plain,
( spl28_245
| ~ spl28_17
| ~ spl28_75 ),
inference(avatar_split_clause,[],[f979,f949,f625,f3700]) ).
tff(f3700,plain,
( spl28_245
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_245])]) ).
tff(f979,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK5(X0)) )
| ~ spl28_17
| ~ spl28_75 ),
inference(resolution,[],[f950,f626]) ).
tff(f3698,plain,
( spl28_244
| ~ spl28_28
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f970,f967,f681,f3696]) ).
tff(f3696,plain,
( spl28_244
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_244])]) ).
tff(f967,plain,
( spl28_79
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_79])]) ).
tff(f970,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) )
| ~ spl28_28
| ~ spl28_79 ),
inference(resolution,[],[f968,f682]) ).
tff(f968,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_79 ),
inference(avatar_component_clause,[],[f967]) ).
tff(f3643,plain,
( spl28_243
| ~ spl28_15
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2791,f2786,f616,f3641]) ).
tff(f3641,plain,
( spl28_243
<=> ! [X0: nat] : sP1(abs(abs(var(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_243])]) ).
tff(f2791,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl28_15
| ~ spl28_217 ),
inference(resolution,[],[f2787,f617]) ).
tff(f3084,plain,
( ~ spl28_4
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3041]) ).
tff(f3041,plain,
( $false
| ~ spl28_4
| ~ spl28_220 ),
inference(resolution,[],[f2833,f564]) ).
tff(f2833,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl28_220 ),
inference(avatar_component_clause,[],[f2832]) ).
tff(f2832,plain,
( spl28_220
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_220])]) ).
tff(f3083,plain,
( ~ spl28_40
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3042]) ).
tff(f3042,plain,
( $false
| ~ spl28_40
| ~ spl28_220 ),
inference(resolution,[],[f2833,f752]) ).
tff(f752,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl28_40 ),
inference(avatar_component_clause,[],[f751]) ).
tff(f751,plain,
( spl28_40
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_40])]) ).
tff(f3082,plain,
( ~ spl28_15
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3044]) ).
tff(f3044,plain,
( $false
| ~ spl28_15
| ~ spl28_220 ),
inference(resolution,[],[f2833,f617]) ).
tff(f3081,plain,
( ~ spl28_8
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3047]) ).
tff(f3047,plain,
( $false
| ~ spl28_8
| ~ spl28_220 ),
inference(resolution,[],[f2833,f581]) ).
tff(f581,plain,
( pp(aa(dB,bool,it,t2))
| ~ spl28_8 ),
inference(avatar_component_clause,[],[f579]) ).
tff(f579,plain,
( spl28_8
<=> pp(aa(dB,bool,it,t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_8])]) ).
tff(f3080,plain,
( ~ spl28_10
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3048]) ).
tff(f3048,plain,
( $false
| ~ spl28_10
| ~ spl28_220 ),
inference(resolution,[],[f2833,f591]) ).
tff(f591,plain,
( pp(aa(dB,bool,it,u))
| ~ spl28_10 ),
inference(avatar_component_clause,[],[f589]) ).
tff(f589,plain,
( spl28_10
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_10])]) ).
tff(f3079,plain,
( ~ spl28_9
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3049]) ).
tff(f3049,plain,
( $false
| ~ spl28_9
| ~ spl28_220 ),
inference(resolution,[],[f2833,f586]) ).
tff(f586,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl28_9 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f584,plain,
( spl28_9
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_9])]) ).
tff(f3078,plain,
( ~ spl28_220
| ~ spl28_238 ),
inference(avatar_contradiction_clause,[],[f3053]) ).
tff(f3053,plain,
( $false
| ~ spl28_220
| ~ spl28_238 ),
inference(resolution,[],[f2833,f3002]) ).
tff(f3002,plain,
( ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl28_238 ),
inference(avatar_component_clause,[],[f3001]) ).
tff(f3001,plain,
( spl28_238
<=> ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_238])]) ).
tff(f3077,plain,
( ~ spl28_62
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3054]) ).
tff(f3054,plain,
( $false
| ~ spl28_62
| ~ spl28_220 ),
inference(resolution,[],[f2833,f879]) ).
tff(f3076,plain,
( ~ spl28_91
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3055]) ).
tff(f3055,plain,
( $false
| ~ spl28_91
| ~ spl28_220 ),
inference(resolution,[],[f2833,f1064]) ).
tff(f3075,plain,
( ~ spl28_127
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3056]) ).
tff(f3056,plain,
( $false
| ~ spl28_127
| ~ spl28_220 ),
inference(resolution,[],[f2833,f1298]) ).
tff(f3074,plain,
( ~ spl28_89
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3057]) ).
tff(f3057,plain,
( $false
| ~ spl28_89
| ~ spl28_220 ),
inference(resolution,[],[f2833,f1051]) ).
tff(f3073,plain,
( ~ spl28_34
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3058]) ).
tff(f3058,plain,
( $false
| ~ spl28_34
| ~ spl28_220 ),
inference(resolution,[],[f2833,f721]) ).
tff(f721,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl28_34 ),
inference(avatar_component_clause,[],[f719]) ).
tff(f719,plain,
( spl28_34
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_34])]) ).
tff(f3072,plain,
( ~ spl28_36
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3059]) ).
tff(f3059,plain,
( $false
| ~ spl28_36
| ~ spl28_220 ),
inference(resolution,[],[f2833,f733]) ).
tff(f733,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl28_36 ),
inference(avatar_component_clause,[],[f731]) ).
tff(f731,plain,
( spl28_36
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_36])]) ).
tff(f3071,plain,
( ~ spl28_220
| ~ spl28_231 ),
inference(avatar_contradiction_clause,[],[f3062]) ).
tff(f3062,plain,
( $false
| ~ spl28_220
| ~ spl28_231 ),
inference(resolution,[],[f2833,f2901]) ).
tff(f2901,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl28_231 ),
inference(avatar_component_clause,[],[f2899]) ).
tff(f2899,plain,
( spl28_231
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_231])]) ).
tff(f3070,plain,
( ~ spl28_220
| ~ spl28_232 ),
inference(avatar_contradiction_clause,[],[f3063]) ).
tff(f3063,plain,
( $false
| ~ spl28_220
| ~ spl28_232 ),
inference(resolution,[],[f2833,f2906]) ).
tff(f2906,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl28_232 ),
inference(avatar_component_clause,[],[f2904]) ).
tff(f2904,plain,
( spl28_232
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_232])]) ).
tff(f3069,plain,
( ~ spl28_220
| ~ spl28_233 ),
inference(avatar_contradiction_clause,[],[f3064]) ).
tff(f3064,plain,
( $false
| ~ spl28_220
| ~ spl28_233 ),
inference(resolution,[],[f2833,f2910]) ).
tff(f2910,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl28_233 ),
inference(avatar_component_clause,[],[f2909]) ).
tff(f2909,plain,
( spl28_233
<=> ! [X0: $tType,X1: X0] : pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_233])]) ).
tff(f3068,plain,
( ~ spl28_219
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3065]) ).
tff(f3065,plain,
( $false
| ~ spl28_219
| ~ spl28_220 ),
inference(resolution,[],[f2833,f2830]) ).
tff(f2830,plain,
( pp(aa(fun1(bool,bool),bool,fEx(bool),combi(bool)))
| ~ spl28_219 ),
inference(avatar_component_clause,[],[f2828]) ).
tff(f2828,plain,
( spl28_219
<=> pp(aa(fun1(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_219])]) ).
tff(f3067,plain,
( ~ spl28_215
| ~ spl28_220 ),
inference(avatar_contradiction_clause,[],[f3066]) ).
tff(f3066,plain,
( $false
| ~ spl28_215
| ~ spl28_220 ),
inference(resolution,[],[f2833,f2303]) ).
tff(f3040,plain,
( spl28_220
| spl28_242
| ~ spl28_49
| ~ spl28_53 ),
inference(avatar_split_clause,[],[f830,f825,f795,f3038,f2832]) ).
tff(f3038,plain,
( spl28_242
<=> ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun1(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_242])]) ).
tff(f825,plain,
( spl28_53
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_53])]) ).
tff(f830,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun1(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) )
| ~ spl28_49
| ~ spl28_53 ),
inference(resolution,[],[f826,f796]) ).
tff(f826,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl28_53 ),
inference(avatar_component_clause,[],[f825]) ).
tff(f3017,plain,
( spl28_241
| ~ spl28_65
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f1002,f975,f896,f3015]) ).
tff(f3015,plain,
( spl28_241
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_241])]) ).
tff(f1002,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 )
| ~ spl28_65
| ~ spl28_80 ),
inference(superposition,[],[f897,f976]) ).
tff(f3013,plain,
( spl28_240
| ~ spl28_64
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f993,f975,f891,f3010]) ).
tff(f3010,plain,
( spl28_240
<=> ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_240])]) ).
tff(f993,plain,
( ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) )
| ~ spl28_64
| ~ spl28_80 ),
inference(superposition,[],[f976,f893]) ).
tff(f3008,plain,
( spl28_239
| ~ spl28_17
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f971,f967,f625,f3006]) ).
tff(f3006,plain,
( spl28_239
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_239])]) ).
tff(f971,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl28_17
| ~ spl28_79 ),
inference(resolution,[],[f968,f626]) ).
tff(f3003,plain,
( spl28_238
| ~ spl28_29
| ~ spl28_62 ),
inference(avatar_split_clause,[],[f886,f878,f694,f3001]) ).
tff(f886,plain,
( ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl28_29
| ~ spl28_62 ),
inference(superposition,[],[f879,f695]) ).
tff(f2928,plain,
( spl28_237
| ~ spl28_36
| ~ spl28_108 ),
inference(avatar_split_clause,[],[f1189,f1182,f731,f2926]) ).
tff(f2926,plain,
( spl28_237
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| ~ beta(u,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_237])]) ).
tff(f1189,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| ~ beta(u,X0) )
| ~ spl28_36
| ~ spl28_108 ),
inference(resolution,[],[f1183,f733]) ).
tff(f2924,plain,
( spl28_236
| ~ spl28_34
| ~ spl28_108 ),
inference(avatar_split_clause,[],[f1188,f1182,f719,f2922]) ).
tff(f2922,plain,
( spl28_236
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| ~ beta(ua,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_236])]) ).
tff(f1188,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| ~ beta(ua,X0) )
| ~ spl28_34
| ~ spl28_108 ),
inference(resolution,[],[f1183,f721]) ).
tff(f2920,plain,
( spl28_235
| ~ spl28_9
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2799,f2786,f584,f2917]) ).
tff(f2799,plain,
( sP1(abs(abs(ua)))
| ~ spl28_9
| ~ spl28_217 ),
inference(resolution,[],[f2787,f586]) ).
tff(f2915,plain,
( spl28_234
| ~ spl28_29
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f814,f795,f694,f2913]) ).
tff(f2913,plain,
( spl28_234
<=> ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun1(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_234])]) ).
tff(f814,plain,
( ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun1(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) )
| ~ spl28_29
| ~ spl28_49 ),
inference(superposition,[],[f796,f695]) ).
tff(f2911,plain,
( spl28_233
| ~ spl28_40
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f811,f795,f751,f2909]) ).
tff(f811,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun1(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl28_40
| ~ spl28_49 ),
inference(resolution,[],[f796,f752]) ).
tff(f2907,plain,
( spl28_232
| ~ spl28_36
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f810,f795,f731,f2904]) ).
tff(f810,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl28_36
| ~ spl28_49 ),
inference(resolution,[],[f796,f733]) ).
tff(f2902,plain,
( spl28_231
| ~ spl28_34
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f809,f795,f719,f2899]) ).
tff(f809,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl28_34
| ~ spl28_49 ),
inference(resolution,[],[f796,f721]) ).
tff(f2897,plain,
( spl28_230
| ~ spl28_13
| ~ spl28_31 ),
inference(avatar_split_clause,[],[f711,f704,f602,f2895]) ).
tff(f2895,plain,
( spl28_230
<=> ! [X2: nat,X0: fun1(nat,bool),X1: fun1(type,fun1(type,bool))] :
( ( fFalse = aa(nat,bool,X0,X2) )
| ( fTrue = type_case(bool,X0,X1,atom(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_230])]) ).
tff(f704,plain,
( spl28_31
<=> ! [X0: $tType,X3: fun1(nat,X0),X2: fun1(type,fun1(type,X0)),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_31])]) ).
tff(f711,plain,
( ! [X2: nat,X0: fun1(nat,bool),X1: fun1(type,fun1(type,bool))] :
( ( fFalse = aa(nat,bool,X0,X2) )
| ( fTrue = type_case(bool,X0,X1,atom(X2)) ) )
| ~ spl28_13
| ~ spl28_31 ),
inference(superposition,[],[f705,f603]) ).
tff(f705,plain,
( ! [X0: $tType,X2: fun1(type,fun1(type,X0)),X3: fun1(nat,X0),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) )
| ~ spl28_31 ),
inference(avatar_component_clause,[],[f704]) ).
tff(f2882,plain,
( spl28_229
| ~ spl28_13
| ~ spl28_29 ),
inference(avatar_split_clause,[],[f697,f694,f602,f2880]) ).
tff(f2880,plain,
( spl28_229
<=> ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_229])]) ).
tff(f697,plain,
( ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) )
| ~ spl28_13
| ~ spl28_29 ),
inference(superposition,[],[f695,f603]) ).
tff(f2878,plain,
( spl28_228
| ~ spl28_10
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2798,f2786,f589,f2875]) ).
tff(f2798,plain,
( sP1(abs(abs(u)))
| ~ spl28_10
| ~ spl28_217 ),
inference(resolution,[],[f2787,f591]) ).
tff(f2870,plain,
( spl28_227
| ~ spl28_46
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f1003,f975,f783,f2868]) ).
tff(f2868,plain,
( spl28_227
<=> ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,combc(type,type,type,fun,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_227])]) ).
tff(f1003,plain,
( ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,combc(type,type,type,fun,X1),X0) )
| ~ spl28_46
| ~ spl28_80 ),
inference(superposition,[],[f784,f976]) ).
tff(f2866,plain,
( spl28_226
| ~ spl28_47
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f998,f975,f787,f2864]) ).
tff(f2864,plain,
( spl28_226
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_226])]) ).
tff(f998,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl28_47
| ~ spl28_80 ),
inference(superposition,[],[f788,f976]) ).
tff(f2862,plain,
( spl28_225
| ~ spl28_48
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f997,f975,f791,f2860]) ).
tff(f2860,plain,
( spl28_225
<=> ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_225])]) ).
tff(f997,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl28_48
| ~ spl28_80 ),
inference(superposition,[],[f792,f976]) ).
tff(f2858,plain,
( spl28_224
| ~ spl28_28
| ~ spl28_54 ),
inference(avatar_split_clause,[],[f855,f833,f681,f2856]) ).
tff(f2856,plain,
( spl28_224
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_224])]) ).
tff(f855,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl28_28
| ~ spl28_54 ),
inference(resolution,[],[f834,f682]) ).
tff(f2854,plain,
( spl28_223
| ~ spl28_28
| ~ spl28_51 ),
inference(avatar_split_clause,[],[f851,f816,f681,f2852]) ).
tff(f2852,plain,
( spl28_223
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(abs(sK5(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_223])]) ).
tff(f816,plain,
( spl28_51
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_51])]) ).
tff(f851,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(abs(sK5(X0))) )
| ~ spl28_28
| ~ spl28_51 ),
inference(resolution,[],[f817,f682]) ).
tff(f817,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK5(X0)))
| sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) )
| ~ spl28_51 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f2850,plain,
( spl28_222
| ~ spl28_17
| ~ spl28_51 ),
inference(avatar_split_clause,[],[f852,f816,f625,f2848]) ).
tff(f2848,plain,
( spl28_222
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_222])]) ).
tff(f852,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(sK5(X0)) )
| ~ spl28_17
| ~ spl28_51 ),
inference(resolution,[],[f817,f626]) ).
tff(f2839,plain,
( spl28_221
| ~ spl28_8
| ~ spl28_217 ),
inference(avatar_split_clause,[],[f2797,f2786,f579,f2836]) ).
tff(f2797,plain,
( sP1(abs(abs(t2)))
| ~ spl28_8
| ~ spl28_217 ),
inference(resolution,[],[f2787,f581]) ).
tff(f2834,plain,
( spl28_219
| spl28_220
| ~ spl28_20
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f813,f795,f637,f2832,f2828]) ).
tff(f813,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun1(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl28_20
| ~ spl28_49 ),
inference(superposition,[],[f796,f638]) ).
tff(f2811,plain,
( spl28_218
| ~ spl28_13
| ~ spl28_20 ),
inference(avatar_split_clause,[],[f663,f637,f602,f2809]) ).
tff(f2809,plain,
( spl28_218
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_218])]) ).
tff(f663,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl28_13
| ~ spl28_20 ),
inference(superposition,[],[f638,f603]) ).
tff(f2788,plain,
( spl28_217
| ~ spl28_28
| ~ spl28_38 ),
inference(avatar_split_clause,[],[f755,f742,f681,f2786]) ).
tff(f742,plain,
( spl28_38
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_38])]) ).
tff(f755,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl28_28
| ~ spl28_38 ),
inference(resolution,[],[f743,f682]) ).
tff(f743,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl28_38 ),
inference(avatar_component_clause,[],[f742]) ).
tff(f2308,plain,
( spl28_216
| ~ spl28_46
| ~ spl28_69 ),
inference(avatar_split_clause,[],[f927,f916,f783,f2306]) ).
tff(f927,plain,
( ! [X0: type,X1: nat] :
( ( atom(X1) != X0 )
| ( atom(sK4(X0)) = X0 ) )
| ~ spl28_46
| ~ spl28_69 ),
inference(superposition,[],[f784,f917]) ).
tff(f2304,plain,
( spl28_215
| ~ spl28_15
| ~ spl28_49 ),
inference(avatar_split_clause,[],[f804,f795,f616,f2301]) ).
tff(f804,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),it))
| ~ spl28_15
| ~ spl28_49 ),
inference(resolution,[],[f796,f617]) ).
tff(f2299,plain,
( spl28_214
| ~ spl28_9
| ~ spl28_19 ),
inference(avatar_split_clause,[],[f1473,f633,f584,f2296]) ).
tff(f2296,plain,
( spl28_214
<=> ( aa(dB,bool,it,ua) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_214])]) ).
tff(f1473,plain,
( ( aa(dB,bool,it,ua) = fTrue )
| ~ spl28_9
| ~ spl28_19 ),
inference(resolution,[],[f634,f586]) ).
tff(f2294,plain,
( spl28_213
| ~ spl28_13 ),
inference(avatar_split_clause,[],[f605,f602,f2292]) ).
tff(f605,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl28_13 ),
inference(superposition,[],[f603,f603]) ).
tff(f2287,plain,
( spl28_212
| ~ spl28_80
| ~ spl28_211 ),
inference(avatar_split_clause,[],[f2283,f2279,f975,f2285]) ).
tff(f2285,plain,
( spl28_212
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( collect(list(X0),aa(fun1(fun1(X0,bool),bool),fun1(list(X0),bool),combc(fun1(fun1(X0,bool),bool),fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),combb(fun1(X0,bool),bool,list(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun1(X0,bool),list(fun1(X0,bool)),combc(fun1(X0,bool),list(fun1(X0,bool)),list(fun1(X0,bool)),cons(fun1(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_212])]) ).
tff(f2279,plain,
( spl28_211
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_211])]) ).
tff(f2283,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( collect(list(X0),aa(fun1(fun1(X0,bool),bool),fun1(list(X0),bool),combc(fun1(fun1(X0,bool),bool),fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),combb(fun1(X0,bool),bool,list(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun1(X0,bool),list(fun1(X0,bool)),combc(fun1(X0,bool),list(fun1(X0,bool)),list(fun1(X0,bool)),cons(fun1(X0,bool)),X1),X2)) )
| ~ spl28_80
| ~ spl28_211 ),
inference(forward_demodulation,[],[f2282,f976]) ).
tff(f2282,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = collect(list(X0),aa(fun1(fun1(X0,bool),bool),fun1(list(X0),bool),combc(fun1(fun1(X0,bool),bool),fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),combb(fun1(X0,bool),bool,list(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) )
| ~ spl28_80
| ~ spl28_211 ),
inference(forward_demodulation,[],[f2280,f976]) ).
tff(f2280,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) )
| ~ spl28_211 ),
inference(avatar_component_clause,[],[f2279]) ).
tff(f2281,plain,
spl28_211,
inference(avatar_split_clause,[],[f496,f2279]) ).
tff(f496,plain,
! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ),
inference(definition_unfolding,[],[f402,f405]) ).
tff(f405,plain,
! [X0: $tType,X2: fun1(X0,bool),X1: fun1(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: fun1(list(X0),bool),X2: fun1(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X2))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X74: fun1(list(X0),bool),X63: fun1(X0,bool)] : ( set_Cons(X0,X63,X74) = collect(list(X0),aa(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool),aa(fun1(fun1(X0,bool),bool),fun1(fun1(list(X0),fun1(X0,bool)),fun1(list(X0),bool)),combb(fun1(X0,bool),bool,list(X0)),fEx(X0)),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool)),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,bool))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool),list(X0)),aa(fun1(fun1(list(X0),bool),bool),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,bool)),combb(fun1(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))))),combb(fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),bool))),list(X0)),combs(X0,fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),aa(fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(list(X0),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))))),combb(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),list(X0)),aa(fun1(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(list(X0),fun1(bool,bool))),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(list(X0),fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool)))),aa(fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),fun1(fun1(list(X0),fun1(X0,fun1(list(X0),bool))),fun1(list(X0),fun1(X0,fun1(list(X0),fun1(bool,bool))))),combb(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool))),list(X0)),aa(fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),fun1(fun1(X0,fun1(list(X0),bool)),fun1(X0,fun1(list(X0),fun1(bool,bool)))),combb(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool)),X0),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(list(X0),bool),fun1(list(X0),fun1(bool,bool))),combb(bool,fun1(bool,bool),list(X0)),fconj))),combc(list(X0),fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)),aa(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),aa(fun1(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool)))),fun1(fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(list(X0),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))))),combb(fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),fun1(fun1(X0,fun1(list(X0),list(X0))),fun1(X0,fun1(list(X0),bool))),list(X0)),combb(fun1(list(X0),list(X0)),fun1(list(X0),bool),X0)),aa(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),aa(fun1(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool))),fun1(fun1(list(X0),fun1(list(X0),bool)),fun1(list(X0),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)))),combb(fun1(list(X0),bool),fun1(fun1(list(X0),list(X0)),fun1(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun1(list(X0),bool),fun1(list(X0),bool),aa(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool))),fun1(fun1(X0,fun1(bool,bool)),fun1(X0,fun1(fun1(list(X0),bool),fun1(list(X0),bool)))),combb(fun1(bool,bool),fun1(fun1(list(X0),bool),fun1(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),combc(X0,fun1(X0,bool),bool,member(X0),X63))),combc(list(X0),fun1(list(X0),bool),bool,member(list(X0)),X74)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_set__Cons__def) ).
tff(f402,plain,
! [X0: $tType,X2: fun1(X0,bool),X1: list(fun1(X0,bool))] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: list(fun1(X0,bool)),X2: fun1(X0,bool)] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X75: list(fun1(X0,bool)),X63: fun1(X0,bool)] : ( listset(X0,aa(list(fun1(X0,bool)),list(fun1(X0,bool)),aa(fun1(X0,bool),fun1(list(fun1(X0,bool)),list(fun1(X0,bool))),cons(fun1(X0,bool)),X63),X75)) = set_Cons(X0,X63,listset(X0,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_listset_Osimps_I2_J) ).
tff(f2272,plain,
( spl28_210
| ~ spl28_80
| ~ spl28_209 ),
inference(avatar_split_clause,[],[f2268,f2265,f975,f2270]) ).
tff(f2270,plain,
( spl28_210
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_210])]) ).
tff(f2265,plain,
( spl28_209
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_209])]) ).
tff(f2268,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl28_80
| ~ spl28_209 ),
inference(forward_demodulation,[],[f2266,f976]) ).
tff(f2266,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl28_209 ),
inference(avatar_component_clause,[],[f2265]) ).
tff(f2267,plain,
spl28_209,
inference(avatar_split_clause,[],[f454,f2265]) ).
tff(f454,plain,
! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0))
<=> pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X13: list(type),X12: list(dB),X4: dB,X11: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X11,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X4),X12)),X13))
<=> pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X11),X4))),typings(X11,X12)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_typings_Osimps_I2_J) ).
tff(f2258,plain,
( spl28_208
| ~ spl28_80
| ~ spl28_207 ),
inference(avatar_split_clause,[],[f2254,f2251,f975,f2256]) ).
tff(f2256,plain,
( spl28_208
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_208])]) ).
tff(f2251,plain,
( spl28_207
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_207])]) ).
tff(f2254,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl28_80
| ~ spl28_207 ),
inference(forward_demodulation,[],[f2252,f976]) ).
tff(f2252,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0)) )
| ~ spl28_207 ),
inference(avatar_component_clause,[],[f2251]) ).
tff(f2253,plain,
spl28_207,
inference(avatar_split_clause,[],[f453,f2251]) ).
tff(f453,plain,
! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
inference(cnf_transformation,[],[f316]) ).
tff(f2249,plain,
( spl28_206
| ~ spl28_10
| ~ spl28_19 ),
inference(avatar_split_clause,[],[f1472,f633,f589,f2246]) ).
tff(f2246,plain,
( spl28_206
<=> ( aa(dB,bool,it,u) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_206])]) ).
tff(f1472,plain,
( ( aa(dB,bool,it,u) = fTrue )
| ~ spl28_10
| ~ spl28_19 ),
inference(resolution,[],[f634,f591]) ).
tff(f2169,plain,
spl28_205,
inference(avatar_split_clause,[],[f477,f2167]) ).
tff(f2167,plain,
( spl28_205
<=> ! [X1: $tType,X0: $tType,X3: list(X1),X4: X0,X5: fun1(X0,fun1(X1,X0)),X2: X1] :
( ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK20(X0,X1,X5))),sK21(X0,X1,X5)) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK21(X0,X1,X5))),sK20(X0,X1,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_205])]) ).
tff(f477,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun1(X0,fun1(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK20(X0,X1,X5))),sK21(X0,X1,X5)) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK21(X0,X1,X5))),sK20(X0,X1,X5)) ) ),
inference(cnf_transformation,[],[f322]) ).
tff(f322,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun1(X0,fun1(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK20(X0,X1,X5))),sK21(X0,X1,X5)) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK21(X0,X1,X5))),sK20(X0,X1,X5)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f261,f321]) ).
tff(f321,plain,
! [X1: $tType,X0: $tType,X5: fun1(X0,fun1(X1,X0))] :
( ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK20(X0,X1,X5))),sK21(X0,X1,X5)) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,sK22(X0,X1,X5)),sK21(X0,X1,X5))),sK20(X0,X1,X5)) ) ),
introduced(choice_axiom,[]) ).
tff(f261,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun1(X0,fun1(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X2),X3) )
| ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X7)),X6) ) ),
inference(ennf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun1(X0,fun1(X1,X0))] :
( ! [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X6)),X7) = aa(X1,X0,aa(X0,fun1(X1,X0),X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun1(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X2),X3) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X1: $tType,X0: $tType,X9: X0,X55: list(X0),X7: X1,X56: fun1(X1,fun1(X0,X1))] :
( ! [X59: X0,X60: X0,X61: X1] : ( aa(X0,X1,aa(X1,fun1(X0,X1),X56,aa(X0,X1,aa(X1,fun1(X0,X1),X56,X61),X59)),X60) = aa(X0,X1,aa(X1,fun1(X0,X1),X56,aa(X0,X1,aa(X1,fun1(X0,X1),X56,X61),X60)),X59) )
=> ( aa(X0,X1,aa(X1,fun1(X0,X1),X56,foldl(X1,X0,X56,X7,X55)),X9) = foldl(X1,X0,X56,aa(X0,X1,aa(X1,fun1(X0,X1),X56,X7),X9),X55) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_foldl__fun__comm) ).
tff(f2158,plain,
spl28_204,
inference(avatar_split_clause,[],[f486,f2156]) ).
tff(f2156,plain,
( spl28_204
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun1(X2,X1),X6: fun1(X0,fun1(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_204])]) ).
tff(f486,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun1(X0,fun1(X1,X0)),X4: fun1(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun1(X2,X1),X5: X0,X6: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X55: list(X2),X56: fun1(X2,X1),X46: X0,X67: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X67,X46,map(X2,X1,X56,X55)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X67),X56),X46,X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_foldl__map) ).
tff(f2144,plain,
( spl28_203
| ~ spl28_80
| ~ spl28_202 ),
inference(avatar_split_clause,[],[f2140,f2134,f975,f2142]) ).
tff(f2134,plain,
( spl28_202
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_202])]) ).
tff(f2140,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl28_80
| ~ spl28_202 ),
inference(forward_demodulation,[],[f2139,f976]) ).
tff(f2139,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl28_80
| ~ spl28_202 ),
inference(forward_demodulation,[],[f2138,f976]) ).
tff(f2138,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) )
| ~ spl28_80
| ~ spl28_202 ),
inference(forward_demodulation,[],[f2137,f976]) ).
tff(f2137,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) )
| ~ spl28_80
| ~ spl28_202 ),
inference(forward_demodulation,[],[f2135,f976]) ).
tff(f2135,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) )
| ~ spl28_202 ),
inference(avatar_component_clause,[],[f2134]) ).
tff(f2136,plain,
spl28_202,
inference(avatar_split_clause,[],[f428,f2134]) ).
tff(f428,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X47: nat,X48: dB,X49: dB,X29: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X29),X49)),X48),X47) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X29),X48),X47)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X49),X48),X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_subst__App) ).
tff(f2132,plain,
spl28_201,
inference(avatar_split_clause,[],[f537,f2130]) ).
tff(f2130,plain,
( spl28_201
<=> ! [X5: type,X3: fun1(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_201])]) ).
tff(f537,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f536,f470]) ).
tff(f470,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X94: X0,X95: X1,X93: fun1(X0,fun1(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X93,X95),X94) = aa(X1,X2,aa(X0,fun1(X1,X2),X93,X94),X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f536,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f535,f470]) ).
tff(f535,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f534,f470]) ).
tff(f534,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f488,f470]) ).
tff(f488,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(flattening,[],[f264]) ).
tff(f264,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun1(type,type),fun,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X24: dB,X6: type,X10: nat,X11: fun1(nat,type),X4: dB,X40: type,X41: type] :
( ( t = aa(type,type,aa(type,fun1(type,type),fun,X41),X40) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X11,X10,X41)),X4),X6))
=> ( pp(aa(dB,bool,it,X24))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X24),X41))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X24),X10))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_MI1) ).
tff(f2128,plain,
( spl28_200
| ~ spl28_8
| ~ spl28_19 ),
inference(avatar_split_clause,[],[f1471,f633,f579,f2125]) ).
tff(f2125,plain,
( spl28_200
<=> ( aa(dB,bool,it,t2) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_200])]) ).
tff(f1471,plain,
( ( aa(dB,bool,it,t2) = fTrue )
| ~ spl28_8
| ~ spl28_19 ),
inference(resolution,[],[f634,f581]) ).
tff(f2123,plain,
spl28_199,
inference(avatar_split_clause,[],[f533,f2121]) ).
tff(f2121,plain,
( spl28_199
<=> ! [X5: type,X3: fun1(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_199])]) ).
tff(f533,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f532,f470]) ).
tff(f532,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f531,f470]) ).
tff(f531,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f530,f470]) ).
tff(f530,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f487,f470]) ).
tff(f487,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(flattening,[],[f262]) ).
tff(f262,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun1(type,type),fun,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X24: dB,X6: type,X10: nat,X11: fun1(nat,type),X4: dB,X40: type,X41: type] :
( ( t = aa(type,type,aa(type,fun1(type,type),fun,X41),X40) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X11,X10,X40)),X4),X6))
=> ( pp(aa(dB,bool,it,X24))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X24),X40))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X24),X10))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_MI2) ).
tff(f2111,plain,
( spl28_198
| ~ spl28_80
| ~ spl28_197 ),
inference(avatar_split_clause,[],[f2107,f2101,f975,f2109]) ).
tff(f2109,plain,
( spl28_198
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),splice(X0,X3,X1)),X2)),X4) = splice(X0,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_198])]) ).
tff(f2101,plain,
( spl28_197
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_197])]) ).
tff(f2107,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),splice(X0,X3,X1)),X2)),X4) = splice(X0,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X1),X2)) )
| ~ spl28_80
| ~ spl28_197 ),
inference(forward_demodulation,[],[f2106,f976]) ).
tff(f2106,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),splice(X0,X3,X1)),X2)),X4) = splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X1),X2)) )
| ~ spl28_80
| ~ spl28_197 ),
inference(forward_demodulation,[],[f2105,f976]) ).
tff(f2105,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),splice(X0,X3,X1)),X2)),X4) )
| ~ spl28_80
| ~ spl28_197 ),
inference(forward_demodulation,[],[f2104,f976]) ).
tff(f2104,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))),X4) )
| ~ spl28_80
| ~ spl28_197 ),
inference(forward_demodulation,[],[f2102,f976]) ).
tff(f2102,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) )
| ~ spl28_197 ),
inference(avatar_component_clause,[],[f2101]) ).
tff(f2103,plain,
spl28_197,
inference(avatar_split_clause,[],[f460,f2101]) ).
tff(f460,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X65: list(X0),X66: X0,X53: list(X0),X54: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X54),X53),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X66),X65)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X54),aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X66),splice(X0,X53,X65))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_splice_Osimps_I3_J) ).
tff(f2095,plain,
spl28_196,
inference(avatar_split_clause,[],[f457,f2093]) ).
tff(f2093,plain,
( spl28_196
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_196])]) ).
tff(f457,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f318]) ).
tff(f318,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(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(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(flattening,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(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(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X62: fun1(X0,bool),X63: fun1(X0,bool),X64: list(X0)] :
( listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X63)),X62),X64)
<=> ( listsp(X0,X62,X64)
& listsp(X0,X63,X64) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_listsp__conj__eq) ).
tff(f2085,plain,
( spl28_195
| ~ spl28_80
| ~ spl28_194 ),
inference(avatar_split_clause,[],[f2081,f2077,f975,f2083]) ).
tff(f2083,plain,
( spl28_195
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_195])]) ).
tff(f2077,plain,
( spl28_194
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_194])]) ).
tff(f2081,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl28_80
| ~ spl28_194 ),
inference(forward_demodulation,[],[f2080,f976]) ).
tff(f2080,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) )
| ~ spl28_80
| ~ spl28_194 ),
inference(forward_demodulation,[],[f2078,f976]) ).
tff(f2078,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) )
| ~ spl28_194 ),
inference(avatar_component_clause,[],[f2077]) ).
tff(f2079,plain,
spl28_194,
inference(avatar_split_clause,[],[f427,f2077]) ).
tff(f427,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X10: nat,X24: dB,X12: list(dB),X4: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X4,X12)),X24),X10) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X24),X10),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X24),X10),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_subst__map) ).
tff(f2070,plain,
spl28_193,
inference(avatar_split_clause,[],[f456,f2068]) ).
tff(f2068,plain,
( spl28_193
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_193])]) ).
tff(f456,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f318]) ).
tff(f2066,plain,
spl28_192,
inference(avatar_split_clause,[],[f455,f2064]) ).
tff(f2064,plain,
( spl28_192
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_192])]) ).
tff(f455,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun1(X0,bool),fun1(X0,bool),aa(fun1(X0,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,bool)),combs(X0,bool,bool),aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f318]) ).
tff(f2052,plain,
spl28_191,
inference(avatar_split_clause,[],[f543,f2050]) ).
tff(f2050,plain,
( spl28_191
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun1(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_191])]) ).
tff(f543,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f542,f470]) ).
tff(f542,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f491,f470]) ).
tff(f491,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
& ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f269,f331]) ).
tff(f331,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
=> ( pp(aa(list(type),bool,typings(X6,X3),sK27(X0,X2,X3,X6)))
& ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f269,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f268]) ).
tff(f268,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( pp(aa(list(type),bool,typings(X6,X4),X1))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X5: type,X13: list(type),X6: type,X34: list(dB),X12: list(dB),X10: nat,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,foldl(dB,dB,app,var(X10),X12),X34)),X6))
=> ( pp(aa(list(type),bool,typings(X11,X12),X13))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,var(X10),X12)),X5))
=> ? [X35: list(type)] :
( pp(aa(list(type),bool,typings(X11,X34),X35))
& ( foldr(type,type,fun,X35,X6) = X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_var__app__types) ).
tff(f2038,plain,
spl28_190,
inference(avatar_split_clause,[],[f545,f2036]) ).
tff(f2036,plain,
( spl28_190
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun1(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_190])]) ).
tff(f545,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f544,f470]) ).
tff(f544,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f490,f470]) ).
tff(f490,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun,sK27(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f332]) ).
tff(f2030,plain,
( spl28_189
| ~ spl28_80
| ~ spl28_188 ),
inference(avatar_split_clause,[],[f2026,f2019,f975,f2028]) ).
tff(f2019,plain,
( spl28_188
<=> ! [X2: type,X4: fun1(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_188])]) ).
tff(f2026,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl28_80
| ~ spl28_188 ),
inference(forward_demodulation,[],[f2025,f976]) ).
tff(f2025,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl28_80
| ~ spl28_188 ),
inference(forward_demodulation,[],[f2024,f976]) ).
tff(f2024,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl28_80
| ~ spl28_188 ),
inference(forward_demodulation,[],[f2023,f976]) ).
tff(f2023,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl28_80
| ~ spl28_188 ),
inference(forward_demodulation,[],[f2022,f976]) ).
tff(f2022,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl28_80
| ~ spl28_188 ),
inference(forward_demodulation,[],[f2020,f976]) ).
tff(f2020,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl28_188 ),
inference(avatar_component_clause,[],[f2019]) ).
tff(f2021,plain,
spl28_188,
inference(avatar_split_clause,[],[f466,f2019]) ).
tff(f466,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X4: dB,X5: type,X6: type,X7: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X7),aa(type,type,aa(type,fun1(type,type),fun,X6),X5)))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X4),X6))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),aa(dB,dB,aa(dB,fun1(dB,dB),app,X7),X4)),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_App) ).
tff(f2017,plain,
( spl28_187
| ~ spl28_26
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f691,f681,f673,f2015]) ).
tff(f2015,plain,
( spl28_187
<=> ! [X0: dB] :
( sP1(abs(sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_187])]) ).
tff(f691,plain,
( ! [X0: dB] :
( sP1(abs(sK9(X0)))
| ~ sP0(X0) )
| ~ spl28_26
| ~ spl28_28 ),
inference(resolution,[],[f682,f674]) ).
tff(f2006,plain,
( spl28_186
| ~ spl28_80
| ~ spl28_185 ),
inference(avatar_split_clause,[],[f2002,f1998,f975,f2004]) ).
tff(f1998,plain,
( spl28_185
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_185])]) ).
tff(f2002,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_80
| ~ spl28_185 ),
inference(forward_demodulation,[],[f2001,f976]) ).
tff(f2001,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl28_80
| ~ spl28_185 ),
inference(forward_demodulation,[],[f1999,f976]) ).
tff(f1999,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl28_185 ),
inference(avatar_component_clause,[],[f1998]) ).
tff(f2000,plain,
spl28_185,
inference(avatar_split_clause,[],[f419,f1998]) ).
tff(f419,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(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,fun1(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X36: list(dB),X7: dB,X42: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X42),X7),zero_zero(nat)),X36)))
=> ( pp(aa(dB,bool,it,X7))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X42)),X7),X36))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Beta) ).
tff(f1984,plain,
spl28_184,
inference(avatar_split_clause,[],[f541,f1982]) ).
tff(f541,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2))) ),
inference(forward_demodulation,[],[f540,f470]) ).
tff(f540,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f539,f470]) ).
tff(f539,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f538,f470]) ).
tff(f538,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f525,f470]) ).
tff(f525,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f489]) ).
tff(f489,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X6: fun1(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f266]) ).
tff(f266,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
=> ( ( shift(type,X3,X0,X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X10: nat,X5: type,X24: dB,X52: fun1(nat,type),X6: type,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),X6))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X52),X24),X5))
=> ( ( shift(type,X52,X10,X5) = X11 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X52),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X24),X10)),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_subst__lemma) ).
tff(f1957,plain,
( spl28_183
| ~ spl28_80
| ~ spl28_182 ),
inference(avatar_split_clause,[],[f1953,f1949,f975,f1955]) ).
tff(f1949,plain,
( spl28_182
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_182])]) ).
tff(f1953,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl28_80
| ~ spl28_182 ),
inference(forward_demodulation,[],[f1952,f976]) ).
tff(f1952,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl28_80
| ~ spl28_182 ),
inference(forward_demodulation,[],[f1950,f976]) ).
tff(f1950,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl28_182 ),
inference(avatar_component_clause,[],[f1949]) ).
tff(f1951,plain,
spl28_182,
inference(avatar_split_clause,[],[f501,f1949]) ).
tff(f501,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f369]) ).
tff(f369,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f285,f286]) ).
tff(f286,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f285,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f284]) ).
tff(f284,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f270]) ).
tff(f270,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1946,plain,
spl28_181,
inference(avatar_split_clause,[],[f482,f1944]) ).
tff(f482,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),sK25(X0,X1,X2,X3,X4,X5)),sK26(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ( ( map(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK25(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),sK25(X0,X1,X2,X3,X4,X5)),sK26(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f328,f329]) ).
tff(f329,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
=> ( ( map(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK25(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),sK25(X0,X1,X2,X3,X4,X5)),sK26(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f328,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(rectify,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
<=> ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType,X1: $tType,X70: list(X1),X56: fun1(X1,X0),X55: list(X0),X9: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X9),X55) = map(X1,X0,X56,X70) )
<=> ? [X72: X1,X73: list(X1)] :
( ( map(X1,X0,X56,X73) = X55 )
& ( aa(X1,X0,X56,X72) = X9 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X72),X73) = X70 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Cons__eq__map__conv) ).
tff(f1942,plain,
spl28_180,
inference(avatar_split_clause,[],[f478,f1940]) ).
tff(f478,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ( ( map(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK23(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f324,f325]) ).
tff(f325,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
=> ( ( map(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK23(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f324,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(rectify,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X1: $tType,X0: $tType,X70: list(X0),X71: X0,X55: list(X1),X56: fun1(X1,X0)] :
( ( map(X1,X0,X56,X55) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X71),X70) )
<=> ? [X72: X1,X73: list(X1)] :
( ( map(X1,X0,X56,X73) = X70 )
& ( aa(X1,X0,X56,X72) = X71 )
& ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X72),X73) = X55 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_map__eq__Cons__conv) ).
tff(f1926,plain,
( spl28_179
| ~ spl28_80
| ~ spl28_178 ),
inference(avatar_split_clause,[],[f1922,f1916,f975,f1924]) ).
tff(f1916,plain,
( spl28_178
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_178])]) ).
tff(f1922,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl28_80
| ~ spl28_178 ),
inference(forward_demodulation,[],[f1921,f976]) ).
tff(f1921,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)) )
| ~ spl28_80
| ~ spl28_178 ),
inference(forward_demodulation,[],[f1920,f976]) ).
tff(f1920,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl28_80
| ~ spl28_178 ),
inference(forward_demodulation,[],[f1919,f976]) ).
tff(f1919,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl28_80
| ~ spl28_178 ),
inference(forward_demodulation,[],[f1917,f976]) ).
tff(f1917,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) )
| ~ spl28_178 ),
inference(avatar_component_clause,[],[f1916]) ).
tff(f1918,plain,
spl28_178,
inference(avatar_split_clause,[],[f404,f1916]) ).
tff(f404,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X47: nat,X29: dB,X48: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X48),X29)),X47) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X48),X47)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X29),X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_lift_Osimps_I2_J) ).
tff(f1912,plain,
spl28_177,
inference(avatar_split_clause,[],[f529,f1910]) ).
tff(f529,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ),
inference(forward_demodulation,[],[f476,f470]) ).
tff(f476,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0)) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X13: list(type),X12: list(dB),X10: nat,X6: type,X24: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X24),X6))
=> ( pp(aa(list(type),bool,typings(shift(type,X11,X10,X6),X12),X13))
=> pp(aa(list(type),bool,typings(X11,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X24),X10),X12)),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_substs__lemma) ).
tff(f1896,plain,
( spl28_176
| ~ spl28_80
| ~ spl28_175 ),
inference(avatar_split_clause,[],[f1892,f1886,f975,f1894]) ).
tff(f1886,plain,
( spl28_175
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_175])]) ).
tff(f1892,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK18(X0,X1,X2,X3))),X2)) )
| ~ spl28_80
| ~ spl28_175 ),
inference(forward_demodulation,[],[f1891,f976]) ).
tff(f1891,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK18(X0,X1,X2,X3))),X2)) )
| ~ spl28_80
| ~ spl28_175 ),
inference(forward_demodulation,[],[f1890,f976]) ).
tff(f1890,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK18(X0,X1,X2,X3))),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl28_80
| ~ spl28_175 ),
inference(forward_demodulation,[],[f1889,f976]) ).
tff(f1889,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl28_80
| ~ spl28_175 ),
inference(forward_demodulation,[],[f1887,f976]) ).
tff(f1887,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl28_175 ),
inference(avatar_component_clause,[],[f1886]) ).
tff(f1888,plain,
spl28_175,
inference(avatar_split_clause,[],[f438,f1886]) ).
tff(f438,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK18(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f248,f304]) ).
tff(f304,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0))) )
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK18(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK18(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f248,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0))
=> ~ ! [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0)))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X6: type,X24: dB,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X24)),X6))
=> ~ ! [X25: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),aa(type,type,aa(type,fun1(type,type),fun,X25),X6)))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X24),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_typing__elims_I2_J) ).
tff(f1884,plain,
( spl28_173
| ~ spl28_174
| ~ spl28_13 ),
inference(avatar_split_clause,[],[f610,f602,f1881,f1878]) ).
tff(f1878,plain,
( spl28_173
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_173])]) ).
tff(f1881,plain,
( spl28_174
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_174])]) ).
tff(f610,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl28_13 ),
inference(equality_factoring,[],[f603]) ).
tff(f1871,plain,
( spl28_172
| ~ spl28_80
| ~ spl28_171 ),
inference(avatar_split_clause,[],[f1867,f1863,f975,f1869]) ).
tff(f1863,plain,
( spl28_171
<=> ! [X0: list(type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a)),foldr(type,type,fun,X0,t1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_171])]) ).
tff(f1867,plain,
( ! [X0: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun,X0,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) )
| ~ spl28_80
| ~ spl28_171 ),
inference(forward_demodulation,[],[f1866,f976]) ).
tff(f1866,plain,
( ! [X0: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun,X0,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) )
| ~ spl28_80
| ~ spl28_171 ),
inference(forward_demodulation,[],[f1864,f976]) ).
tff(f1864,plain,
( ! [X0: list(type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a)),foldr(type,type,fun,X0,t1))) )
| ~ spl28_171 ),
inference(avatar_component_clause,[],[f1863]) ).
tff(f1865,plain,
( spl28_171
| spl28_1 ),
inference(avatar_split_clause,[],[f492,f547,f1863]) ).
tff(f547,plain,
( spl28_1
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl28_1])]) ).
tff(f492,plain,
! [X0: list(type)] :
( thesis
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a)),foldr(type,type,fun,X0,t1))) ),
inference(definition_unfolding,[],[f334,f339]) ).
tff(f339,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True) ).
tff(f334,plain,
! [X0: list(type)] :
( thesis
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t1))) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: list(type)] :
( thesis
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t1))) ),
inference(flattening,[],[f220]) ).
tff(f220,plain,
! [X0: list(type)] :
( thesis
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t1))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t1)))
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
=> thesis ) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X96: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X96,t1)))
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X96))
=> thesis ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f1777,plain,
spl28_170,
inference(avatar_split_clause,[],[f475,f1775]) ).
tff(f475,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X2,fun1(X1,X0)),fun1(fun1(X2,X1),fun1(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X2,fun1(X1,X0)),fun1(fun1(X2,X1),fun1(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X94: X0,X95: fun1(X0,X1),X93: fun1(X0,fun1(X1,X2))] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X0,fun1(X1,X2)),fun1(fun1(X0,X1),fun1(X0,X2)),combs(X0,X1,X2),X93),X95),X94) = aa(X1,X2,aa(X0,fun1(X1,X2),X93,X94),aa(X0,X1,X95,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1736,plain,
( spl28_169
| ~ spl28_80
| ~ spl28_168 ),
inference(avatar_split_clause,[],[f1732,f1729,f975,f1734]) ).
tff(f1729,plain,
( spl28_168
<=> ! [X1: $tType,X0: $tType,X4: fun1(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_168])]) ).
tff(f1732,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl28_80
| ~ spl28_168 ),
inference(forward_demodulation,[],[f1730,f976]) ).
tff(f1730,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) )
| ~ spl28_168 ),
inference(avatar_component_clause,[],[f1729]) ).
tff(f1731,plain,
spl28_168,
inference(avatar_split_clause,[],[f459,f1729]) ).
tff(f459,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X1: $tType,X55: list(X1),X9: X1,X56: fun1(X1,X0)] : ( map(X1,X0,X56,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X9),X55)) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),aa(X1,X0,X56,X9)),map(X1,X0,X56,X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_map_Osimps_I2_J) ).
tff(f1725,plain,
( spl28_167
| ~ spl28_80
| ~ spl28_166 ),
inference(avatar_split_clause,[],[f1720,f1717,f975,f1723]) ).
tff(f1717,plain,
( spl28_166
<=> ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_166])]) ).
tff(f1720,plain,
( ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl28_80
| ~ spl28_166 ),
inference(forward_demodulation,[],[f1718,f976]) ).
tff(f1718,plain,
( ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl28_166 ),
inference(avatar_component_clause,[],[f1717]) ).
tff(f1719,plain,
spl28_166,
inference(avatar_split_clause,[],[f414,f1717]) ).
tff(f414,plain,
! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: list(type),X1: list(dB),X2: fun1(nat,type)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: list(type),X1: list(dB),X2: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X2,X1),X0))
=> listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X13: list(type),X12: list(dB),X11: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X11,X12),X13))
=> listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X11)),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lists__typings) ).
tff(f1708,plain,
( spl28_165
| ~ spl28_80
| ~ spl28_164 ),
inference(avatar_split_clause,[],[f1704,f1700,f975,f1706]) ).
tff(f1700,plain,
( spl28_164
<=> ! [X2: list(type),X4: fun1(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_164])]) ).
tff(f1704,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl28_80
| ~ spl28_164 ),
inference(forward_demodulation,[],[f1703,f976]) ).
tff(f1703,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) )
| ~ spl28_80
| ~ spl28_164 ),
inference(forward_demodulation,[],[f1701,f976]) ).
tff(f1701,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) )
| ~ spl28_164 ),
inference(avatar_component_clause,[],[f1700]) ).
tff(f1702,plain,
spl28_164,
inference(avatar_split_clause,[],[f464,f1700]) ).
tff(f464,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1)))
=> ( pp(aa(list(type),bool,typings(X4,X0),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X12: list(dB),X6: type,X13: list(type),X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),foldr(type,type,fun,X13,X6)))
=> ( pp(aa(list(type),bool,typings(X11,X12),X13))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,X4,X12)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_list__app__typeI) ).
tff(f1693,plain,
( spl28_163
| ~ spl28_80
| ~ spl28_162 ),
inference(avatar_split_clause,[],[f1689,f1685,f975,f1691]) ).
tff(f1685,plain,
( spl28_162
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_162])]) ).
tff(f1689,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)),var(X2))) )
| ~ spl28_80
| ~ spl28_162 ),
inference(forward_demodulation,[],[f1688,f976]) ).
tff(f1688,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl28_80
| ~ spl28_162 ),
inference(forward_demodulation,[],[f1686,f976]) ).
tff(f1686,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl28_162 ),
inference(avatar_component_clause,[],[f1685]) ).
tff(f1687,plain,
spl28_162,
inference(avatar_split_clause,[],[f436,f1685]) ).
tff(f436,plain,
! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f247,f302]) ).
tff(f302,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK17(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f247,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(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: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X6: type,X12: list(dB),X10: nat,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,var(X10),X12)),X6))
=> ~ ! [X26: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),var(X10)),foldr(type,type,fun,X26,X6)))
=> ~ pp(aa(list(type),bool,typings(X11,X12),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_var__app__typesE) ).
tff(f1677,plain,
( spl28_161
| ~ spl28_80
| ~ spl28_160 ),
inference(avatar_split_clause,[],[f1673,f1668,f975,f1675]) ).
tff(f1668,plain,
( spl28_160
<=> ! [X0: type,X3: fun1(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_160])]) ).
tff(f1673,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1))) )
| ~ spl28_80
| ~ spl28_160 ),
inference(forward_demodulation,[],[f1672,f976]) ).
tff(f1672,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl28_80
| ~ spl28_160 ),
inference(forward_demodulation,[],[f1671,f976]) ).
tff(f1671,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl28_80
| ~ spl28_160 ),
inference(forward_demodulation,[],[f1669,f976]) ).
tff(f1669,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl28_160 ),
inference(avatar_component_clause,[],[f1668]) ).
tff(f1670,plain,
spl28_160,
inference(avatar_split_clause,[],[f435,f1668]) ).
tff(f435,plain,
! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: type,X1: dB,X2: type,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: type,X1: dB,X2: type,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0))) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X5: type,X4: dB,X6: type,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,zero_zero(nat),X6)),X4),X5))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),abs(X4)),aa(type,type,aa(type,fun1(type,type),fun,X6),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Abs) ).
tff(f1665,plain,
( spl28_159
| ~ spl28_80
| ~ spl28_158 ),
inference(avatar_split_clause,[],[f1661,f1657,f975,f1663]) ).
tff(f1663,plain,
( spl28_159
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_159])]) ).
tff(f1657,plain,
( spl28_158
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_158])]) ).
tff(f1661,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) )
| ~ spl28_80
| ~ spl28_158 ),
inference(forward_demodulation,[],[f1660,f976]) ).
tff(f1660,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) )
| ~ spl28_80
| ~ spl28_158 ),
inference(forward_demodulation,[],[f1658,f976]) ).
tff(f1658,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) )
| ~ spl28_158 ),
inference(avatar_component_clause,[],[f1657]) ).
tff(f1659,plain,
spl28_158,
inference(avatar_split_clause,[],[f429,f1657]) ).
tff(f429,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(X3,X2)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X28: nat,X29: dB,X48: dB,X51: dB] :
( beta(X51,X48)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X51),X29),X28),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X48),X29),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_subst__preserves__beta) ).
tff(f1651,plain,
( spl28_157
| ~ spl28_80
| ~ spl28_156 ),
inference(avatar_split_clause,[],[f1647,f1643,f975,f1649]) ).
tff(f1643,plain,
( spl28_156
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_156])]) ).
tff(f1647,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl28_80
| ~ spl28_156 ),
inference(forward_demodulation,[],[f1646,f976]) ).
tff(f1646,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl28_80
| ~ spl28_156 ),
inference(forward_demodulation,[],[f1644,f976]) ).
tff(f1644,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl28_156 ),
inference(avatar_component_clause,[],[f1643]) ).
tff(f1645,plain,
spl28_156,
inference(avatar_split_clause,[],[f403,f1643]) ).
tff(f403,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X10: nat,X12: list(dB),X4: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X4,X12)),X10) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X4),X10),map(dB,dB,combc(dB,nat,dB,lift,X10),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_lift__map) ).
tff(f1632,plain,
( spl28_155
| ~ spl28_80
| ~ spl28_154 ),
inference(avatar_split_clause,[],[f1628,f1624,f975,f1630]) ).
tff(f1624,plain,
( spl28_154
<=> ! [X4: fun1(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_154])]) ).
tff(f1628,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl28_80
| ~ spl28_154 ),
inference(forward_demodulation,[],[f1627,f976]) ).
tff(f1627,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl28_80
| ~ spl28_154 ),
inference(forward_demodulation,[],[f1625,f976]) ).
tff(f1625,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl28_154 ),
inference(avatar_component_clause,[],[f1624]) ).
tff(f1626,plain,
spl28_154,
inference(avatar_split_clause,[],[f465,f1624]) ).
tff(f465,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f255]) ).
tff(f255,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X5: type,X6: type,X12: list(dB),X10: nat,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,var(X10),X12)),X6))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,var(X10),X12)),X5))
=> ( X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_var__app__type__eq) ).
tff(f1618,plain,
( spl28_153
| ~ spl28_18
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f686,f681,f629,f1616]) ).
tff(f686,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl28_18
| ~ spl28_28 ),
inference(resolution,[],[f682,f630]) ).
tff(f1614,plain,
( spl28_152
| ~ spl28_80
| ~ spl28_151 ),
inference(avatar_split_clause,[],[f1610,f1605,f975,f1612]) ).
tff(f1605,plain,
( spl28_151
<=> ! [X4: fun1(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_151])]) ).
tff(f1610,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) )
| ~ spl28_80
| ~ spl28_151 ),
inference(forward_demodulation,[],[f1609,f976]) ).
tff(f1609,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl28_80
| ~ spl28_151 ),
inference(forward_demodulation,[],[f1608,f976]) ).
tff(f1608,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl28_80
| ~ spl28_151 ),
inference(forward_demodulation,[],[f1606,f976]) ).
tff(f1606,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl28_151 ),
inference(avatar_component_clause,[],[f1605]) ).
tff(f1607,plain,
spl28_151,
inference(avatar_split_clause,[],[f463,f1605]) ).
tff(f463,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X5: type,X10: nat,X6: type,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),X6))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X11,X10,X5)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X4),X10)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lift__type) ).
tff(f1599,plain,
( spl28_150
| ~ spl28_80
| ~ spl28_149 ),
inference(avatar_split_clause,[],[f1595,f1590,f975,f1597]) ).
tff(f1590,plain,
( spl28_149
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK18(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_149])]) ).
tff(f1595,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK18(X0,X1,X2,X3)),X1)) )
| ~ spl28_80
| ~ spl28_149 ),
inference(forward_demodulation,[],[f1594,f976]) ).
tff(f1594,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK18(X0,X1,X2,X3)),X1)) )
| ~ spl28_80
| ~ spl28_149 ),
inference(forward_demodulation,[],[f1593,f976]) ).
tff(f1593,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK18(X0,X1,X2,X3)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl28_80
| ~ spl28_149 ),
inference(forward_demodulation,[],[f1591,f976]) ).
tff(f1591,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK18(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl28_149 ),
inference(avatar_component_clause,[],[f1590]) ).
tff(f1592,plain,
spl28_149,
inference(avatar_split_clause,[],[f439,f1590]) ).
tff(f439,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK18(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f305]) ).
tff(f1578,plain,
( spl28_148
| ~ spl28_80
| ~ spl28_147 ),
inference(avatar_split_clause,[],[f1574,f1570,f975,f1576]) ).
tff(f1570,plain,
( spl28_147
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_147])]) ).
tff(f1574,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)),X2)) )
| ~ spl28_80
| ~ spl28_147 ),
inference(forward_demodulation,[],[f1573,f976]) ).
tff(f1573,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_80
| ~ spl28_147 ),
inference(forward_demodulation,[],[f1571,f976]) ).
tff(f1571,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_147 ),
inference(avatar_component_clause,[],[f1570]) ).
tff(f1572,plain,
spl28_147,
inference(avatar_split_clause,[],[f433,f1570]) ).
tff(f433,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f245,f300]) ).
tff(f300,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK16(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f245,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(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: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X6: type,X12: list(dB),X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,X4,X12)),X6))
=> ? [X26: list(type)] :
( pp(aa(list(type),bool,typings(X11,X12),X26))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),foldr(type,type,fun,X26,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_list__app__typeD) ).
tff(f1558,plain,
( spl28_146
| ~ spl28_80
| ~ spl28_144 ),
inference(avatar_split_clause,[],[f1550,f1546,f975,f1556]) ).
tff(f1546,plain,
( spl28_144
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_144])]) ).
tff(f1550,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)),X2)) )
| ~ spl28_80
| ~ spl28_144 ),
inference(forward_demodulation,[],[f1549,f976]) ).
tff(f1549,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_80
| ~ spl28_144 ),
inference(forward_demodulation,[],[f1547,f976]) ).
tff(f1547,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_144 ),
inference(avatar_component_clause,[],[f1546]) ).
tff(f1554,plain,
( spl28_145
| ~ spl28_17
| ~ spl28_26 ),
inference(avatar_split_clause,[],[f684,f673,f625,f1552]) ).
tff(f1552,plain,
( spl28_145
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_145])]) ).
tff(f684,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK9(X0)) )
| ~ spl28_17
| ~ spl28_26 ),
inference(resolution,[],[f674,f626]) ).
tff(f1548,plain,
spl28_144,
inference(avatar_split_clause,[],[f431,f1546]) ).
tff(f431,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f244,f298]) ).
tff(f298,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK15(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f244,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X6: type,X12: list(dB),X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),foldl(dB,dB,app,X4,X12)),X6))
=> ~ ! [X26: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),foldr(type,type,fun,X26,X6)))
=> ~ pp(aa(list(type),bool,typings(X11,X12),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list__app__typeE) ).
tff(f1519,plain,
spl28_143,
inference(avatar_split_clause,[],[f474,f1517]) ).
tff(f474,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X1,X0)] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X1,X0)] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X94: X0,X95: fun1(X0,X1),X93: fun1(X1,X2)] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X1,X2),fun1(fun1(X0,X1),fun1(X0,X2)),combb(X1,X2,X0),X93),X95),X94) = aa(X1,X2,X93,aa(X0,X1,X95,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1515,plain,
spl28_142,
inference(avatar_split_clause,[],[f468,f1513]) ).
tff(f468,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(flattening,[],[f319]) ).
tff(f319,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(nnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X43: list(X0),X44: X0,X45: list(X0),X46: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X46),X45) = aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X44),X43) )
<=> ( ( X43 = X45 )
& ( X44 = X46 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_list_Oinject) ).
tff(f1501,plain,
( spl28_141
| ~ spl28_80
| ~ spl28_140 ),
inference(avatar_split_clause,[],[f1497,f1493,f975,f1499]) ).
tff(f1493,plain,
( spl28_140
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),X1),sK14(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_140])]) ).
tff(f1497,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),sK14(X0,X1,X2)),X1)) )
| ~ spl28_80
| ~ spl28_140 ),
inference(forward_demodulation,[],[f1496,f976]) ).
tff(f1496,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),sK14(X0,X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_80
| ~ spl28_140 ),
inference(forward_demodulation,[],[f1494,f976]) ).
tff(f1494,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),X1),sK14(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_140 ),
inference(avatar_component_clause,[],[f1493]) ).
tff(f1495,plain,
spl28_140,
inference(avatar_split_clause,[],[f417,f1493]) ).
tff(f417,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),X1),sK14(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),X1),sK14(X0,X1,X2)))
& ( aa(type,type,aa(type,fun1(type,type),fun,sK13(X0,X1,X2)),sK14(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f237,f294]) ).
tff(f294,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 ) )
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK13(X0,X1,X2))),X1),sK14(X0,X1,X2)))
& ( aa(type,type,aa(type,fun1(type,type),fun,sK13(X0,X1,X2)),sK14(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f237,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 )
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X6: type,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),abs(X4)),X6))
=> ~ ! [X25: type,X85: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X25),X85) = X6 )
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X11,zero_zero(nat),X25)),X4),X85)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_typing__elims_I3_J) ).
tff(f1451,plain,
spl28_139,
inference(avatar_split_clause,[],[f484,f1449]) ).
tff(f484,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f330]) ).
tff(f1447,plain,
spl28_138,
inference(avatar_split_clause,[],[f480,f1445]) ).
tff(f480,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( map(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f1443,plain,
spl28_137,
inference(avatar_split_clause,[],[f467,f1441]) ).
tff(f467,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f1362,plain,
spl28_136,
inference(avatar_split_clause,[],[f528,f1360]) ).
tff(f528,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f473,f470]) ).
tff(f473,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType,X1: $tType,X55: list(X1),X9: X1,X46: X0,X56: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X56,X46,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X9),X55)) = foldl(X0,X1,X56,aa(X1,X0,aa(X0,fun1(X1,X0),X56,X46),X9),X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_foldl__Cons) ).
tff(f1358,plain,
spl28_135,
inference(avatar_split_clause,[],[f527,f1356]) ).
tff(f527,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ),
inference(forward_demodulation,[],[f472,f470]) ).
tff(f472,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X1: $tType,X0: $tType,X46: X0,X55: list(X1),X9: X1,X56: fun1(X1,fun1(X0,X0))] : ( foldr(X1,X0,X56,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X9),X55),X46) = aa(X0,X0,aa(X1,fun1(X0,X0),X56,X9),foldr(X1,X0,X56,X55,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_foldr_Osimps_I2_J) ).
tff(f1354,plain,
spl28_134,
inference(avatar_split_clause,[],[f483,f1352]) ).
tff(f483,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun1(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK25(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f330]) ).
tff(f1350,plain,
spl28_133,
inference(avatar_split_clause,[],[f479,f1348]) ).
tff(f479,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun1(X0,X1)] :
( ( aa(X0,X1,X5,sK23(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f1345,plain,
( spl28_132
| ~ spl28_80
| ~ spl28_131 ),
inference(avatar_split_clause,[],[f1341,f1337,f975,f1343]) ).
tff(f1337,plain,
( spl28_131
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),X1),sK12(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_131])]) ).
tff(f1341,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),sK12(X1,X2)),X1)) )
| ~ spl28_80
| ~ spl28_131 ),
inference(forward_demodulation,[],[f1340,f976]) ).
tff(f1340,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),sK12(X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_80
| ~ spl28_131 ),
inference(forward_demodulation,[],[f1338,f976]) ).
tff(f1338,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),X1),sK12(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_131 ),
inference(avatar_component_clause,[],[f1337]) ).
tff(f1339,plain,
spl28_131,
inference(avatar_split_clause,[],[f415,f1337]) ).
tff(f415,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),X1),sK12(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),X1),sK12(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f236,f292]) ).
tff(f292,plain,
! [X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X1,X2))),X1),sK12(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f236,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X6: type,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),abs(X4)),X6))
=> ~ ! [X85: type,X86: type] : ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X11,zero_zero(nat),X85)),X4),X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_abs__typeE) ).
tff(f1331,plain,
( spl28_130
| ~ spl28_80
| ~ spl28_129 ),
inference(avatar_split_clause,[],[f1327,f1324,f975,f1329]) ).
tff(f1324,plain,
( spl28_129
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_129])]) ).
tff(f1327,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))))
| ~ sP0(X0) )
| ~ spl28_80
| ~ spl28_129 ),
inference(forward_demodulation,[],[f1325,f976]) ).
tff(f1325,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) )
| ~ spl28_129 ),
inference(avatar_component_clause,[],[f1324]) ).
tff(f1326,plain,
spl28_129,
inference(avatar_split_clause,[],[f367,f1324]) ).
tff(f367,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1309,plain,
spl28_128,
inference(avatar_split_clause,[],[f526,f1307]) ).
tff(f526,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f471,f470]) ).
tff(f471,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X1: $tType,X45: list(X1),X46: X1,X57: fun1(X1,fun1(list(X1),X0)),X58: X0] : ( list_case(X0,X1,X58,X57,aa(list(X1),list(X1),aa(X1,fun1(list(X1),list(X1)),cons(X1),X46),X45)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X57,X46),X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_list_Osimps_I5_J) ).
tff(f1299,plain,
( spl28_127
| ~ spl28_80
| ~ spl28_126 ),
inference(avatar_split_clause,[],[f1294,f1289,f975,f1296]) ).
tff(f1289,plain,
( spl28_126
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a),as)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_126])]) ).
tff(f1294,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl28_80
| ~ spl28_126 ),
inference(forward_demodulation,[],[f1293,f976]) ).
tff(f1293,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a),as)))
| ~ spl28_80
| ~ spl28_126 ),
inference(forward_demodulation,[],[f1291,f976]) ).
tff(f1291,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a),as)),t1))
| ~ spl28_126 ),
inference(avatar_component_clause,[],[f1289]) ).
tff(f1292,plain,
spl28_126,
inference(avatar_split_clause,[],[f495,f1289]) ).
tff(f495,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(i)),a),as)),t1)),
inference(definition_unfolding,[],[f348,f339]) ).
tff(f348,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t1)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f1286,plain,
( spl28_125
| ~ spl28_80
| ~ spl28_124 ),
inference(avatar_split_clause,[],[f1282,f1278,f975,f1284]) ).
tff(f1278,plain,
( spl28_124
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK13(X0,X1,X2)),sK14(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_124])]) ).
tff(f1282,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun,sK14(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) )
| ~ spl28_80
| ~ spl28_124 ),
inference(forward_demodulation,[],[f1281,f976]) ).
tff(f1281,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun,sK14(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_80
| ~ spl28_124 ),
inference(forward_demodulation,[],[f1279,f976]) ).
tff(f1279,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK13(X0,X1,X2)),sK14(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl28_124 ),
inference(avatar_component_clause,[],[f1278]) ).
tff(f1280,plain,
spl28_124,
inference(avatar_split_clause,[],[f416,f1278]) ).
tff(f416,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK13(X0,X1,X2)),sK14(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1276,plain,
( spl28_123
| ~ spl28_80
| ~ spl28_122 ),
inference(avatar_split_clause,[],[f1272,f1268,f975,f1274]) ).
tff(f1274,plain,
( spl28_123
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_123])]) ).
tff(f1268,plain,
( spl28_122
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_122])]) ).
tff(f1272,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl28_80
| ~ spl28_122 ),
inference(forward_demodulation,[],[f1271,f976]) ).
tff(f1271,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl28_80
| ~ spl28_122 ),
inference(forward_demodulation,[],[f1269,f976]) ).
tff(f1269,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat)))
| ~ spl28_122 ),
inference(avatar_component_clause,[],[f1268]) ).
tff(f1270,plain,
spl28_122,
inference(avatar_split_clause,[],[f379,f1268]) ).
tff(f379,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X29: dB,X48: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X48)),X29),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X48),X29),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_beta) ).
tff(f1263,plain,
( ~ spl28_121
| ~ spl28_64
| ~ spl28_65 ),
inference(avatar_split_clause,[],[f907,f896,f891,f1260]) ).
tff(f1260,plain,
( spl28_121
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_121])]) ).
tff(f907,plain,
( ( as != rs )
| ~ spl28_64
| ~ spl28_65 ),
inference(superposition,[],[f897,f893]) ).
tff(f1258,plain,
( spl28_120
| ~ spl28_80
| ~ spl28_119 ),
inference(avatar_split_clause,[],[f1254,f1251,f975,f1256]) ).
tff(f1251,plain,
( spl28_119
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_119])]) ).
tff(f1254,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) )
| ~ spl28_80
| ~ spl28_119 ),
inference(forward_demodulation,[],[f1252,f976]) ).
tff(f1252,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl28_119 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f1253,plain,
spl28_119,
inference(avatar_split_clause,[],[f437,f1251]) ).
tff(f437,plain,
! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f1247,plain,
spl28_118,
inference(avatar_split_clause,[],[f462,f1245]) ).
tff(f462,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X4,X3),X2))
=> pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X5: type,X10: nat,X13: list(type),X12: list(dB),X11: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X11,X12),X13))
=> pp(aa(list(type),bool,typings(shift(type,X11,X10,X5),map(dB,dB,combc(dB,nat,dB,lift,X10),X12)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_lift__types) ).
tff(f1240,plain,
( spl28_117
| ~ spl28_80
| ~ spl28_116 ),
inference(avatar_split_clause,[],[f1236,f1233,f975,f1238]) ).
tff(f1233,plain,
( spl28_116
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_116])]) ).
tff(f1236,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl28_80
| ~ spl28_116 ),
inference(forward_demodulation,[],[f1234,f976]) ).
tff(f1234,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_116 ),
inference(avatar_component_clause,[],[f1233]) ).
tff(f1235,plain,
spl28_116,
inference(avatar_split_clause,[],[f434,f1233]) ).
tff(f434,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f301]) ).
tff(f1228,plain,
( spl28_115
| ~ spl28_80
| ~ spl28_114 ),
inference(avatar_split_clause,[],[f1224,f1221,f975,f1226]) ).
tff(f1221,plain,
( spl28_114
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_114])]) ).
tff(f1224,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl28_80
| ~ spl28_114 ),
inference(forward_demodulation,[],[f1222,f976]) ).
tff(f1222,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl28_114 ),
inference(avatar_component_clause,[],[f1221]) ).
tff(f1223,plain,
spl28_114,
inference(avatar_split_clause,[],[f432,f1221]) ).
tff(f432,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f299]) ).
tff(f1219,plain,
( spl28_113
| ~ spl28_15
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f687,f681,f616,f1217]) ).
tff(f687,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl28_15
| ~ spl28_28 ),
inference(resolution,[],[f682,f617]) ).
tff(f1211,plain,
( spl28_112
| ~ spl28_80
| ~ spl28_111 ),
inference(avatar_split_clause,[],[f1207,f1204,f975,f1209]) ).
tff(f1204,plain,
( spl28_111
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_111])]) ).
tff(f1207,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl28_80
| ~ spl28_111 ),
inference(forward_demodulation,[],[f1205,f976]) ).
tff(f1205,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl28_111 ),
inference(avatar_component_clause,[],[f1204]) ).
tff(f1206,plain,
spl28_111,
inference(avatar_split_clause,[],[f412,f1204]) ).
tff(f412,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X50: nat,X28: nat,X51: dB] :
( pp(aa(dB,bool,it,X51))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X51),var(X28)),X50))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subst__Var__IT) ).
tff(f1200,plain,
( spl28_110
| ~ spl28_80
| ~ spl28_109 ),
inference(avatar_split_clause,[],[f1196,f1192,f975,f1198]) ).
tff(f1192,plain,
( spl28_109
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_109])]) ).
tff(f1196,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl28_80
| ~ spl28_109 ),
inference(forward_demodulation,[],[f1195,f976]) ).
tff(f1195,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl28_80
| ~ spl28_109 ),
inference(forward_demodulation,[],[f1193,f976]) ).
tff(f1193,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl28_109 ),
inference(avatar_component_clause,[],[f1192]) ).
tff(f1194,plain,
spl28_109,
inference(avatar_split_clause,[],[f401,f1192]) ).
tff(f401,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X48: dB,X47: nat,X29: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X29),X47)),X48),X47) = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_subst__lift) ).
tff(f1184,plain,
( spl28_108
| ~ spl28_80
| ~ spl28_107 ),
inference(avatar_split_clause,[],[f1180,f1176,f975,f1182]) ).
tff(f1176,plain,
( spl28_107
<=> ! [X0: dB,X3: fun1(nat,type),X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_107])]) ).
tff(f1180,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) )
| ~ spl28_80
| ~ spl28_107 ),
inference(forward_demodulation,[],[f1179,f976]) ).
tff(f1179,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) )
| ~ spl28_80
| ~ spl28_107 ),
inference(forward_demodulation,[],[f1177,f976]) ).
tff(f1177,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) )
| ~ spl28_107 ),
inference(avatar_component_clause,[],[f1176]) ).
tff(f1178,plain,
spl28_107,
inference(avatar_split_clause,[],[f430,f1176]) ).
tff(f430,plain,
! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(flattening,[],[f242]) ).
tff(f242,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
=> ( beta(X2,X0)
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X92: dB,X6: type,X4: dB,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X4),X6))
=> ( beta(X4,X92)
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),X92),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subject__reduction) ).
tff(f1163,plain,
( spl28_106
| ~ spl28_80
| ~ spl28_105 ),
inference(avatar_split_clause,[],[f1159,f1156,f975,f1161]) ).
tff(f1156,plain,
( spl28_105
<=> ! [X0: $tType,X4: fun1(nat,X0),X3: fun1(type,fun1(type,X0)),X2: type,X1: type] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun1(type,type),fun,X2),X1)) = aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_105])]) ).
tff(f1159,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,fun1(type,X0)),X1: type,X4: fun1(nat,X0)] : ( aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun,X1),X2)) )
| ~ spl28_80
| ~ spl28_105 ),
inference(forward_demodulation,[],[f1157,f976]) ).
tff(f1157,plain,
( ! [X0: $tType,X2: type,X3: fun1(type,fun1(type,X0)),X1: type,X4: fun1(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun1(type,type),fun,X2),X1)) = aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) )
| ~ spl28_105 ),
inference(avatar_component_clause,[],[f1156]) ).
tff(f1158,plain,
spl28_105,
inference(avatar_split_clause,[],[f458,f1156]) ).
tff(f458,plain,
! [X0: $tType,X2: type,X3: fun1(type,fun1(type,X0)),X1: type,X4: fun1(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun1(type,type),fun,X2),X1)) = aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: type,X2: type,X3: fun1(type,fun1(type,X0)),X4: fun1(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun1(type,type),fun,X2),X1)) = aa(type,X0,aa(type,fun1(type,X0),X3,X2),X1) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X16: type,X17: type,X57: fun1(type,fun1(type,X0)),X58: fun1(nat,X0)] : ( type_case(X0,X58,X57,aa(type,type,aa(type,fun1(type,type),fun,X17),X16)) = aa(type,X0,aa(type,fun1(type,X0),X57,X17),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_type_Osimps_I6_J) ).
tff(f1138,plain,
spl28_104,
inference(avatar_split_clause,[],[f451,f1136]) ).
tff(f451,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f314]) ).
tff(f314,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X20: dB,X21: dB,X22: dB,X23: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X23),X22) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X21),X20) )
<=> ( ( X20 = X22 )
& ( X21 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I2_J) ).
tff(f1134,plain,
spl28_103,
inference(avatar_split_clause,[],[f450,f1132]) ).
tff(f450,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f1130,plain,
spl28_102,
inference(avatar_split_clause,[],[f448,f1128]) ).
tff(f448,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) = aa(type,type,aa(type,fun1(type,type),fun,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) = aa(type,type,aa(type,fun1(type,type),fun,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ) ),
inference(nnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) = aa(type,type,aa(type,fun1(type,type),fun,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X14: type,X15: type,X16: type,X17: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X17),X16) = aa(type,type,aa(type,fun1(type,type),fun,X15),X14) )
<=> ( ( X14 = X16 )
& ( X15 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_type_Osimps_I2_J) ).
tff(f1126,plain,
spl28_101,
inference(avatar_split_clause,[],[f447,f1124]) ).
tff(f447,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X1),X0) != aa(type,type,aa(type,fun1(type,type),fun,X3),X2) ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1121,plain,
( spl28_100
| ~ spl28_80
| ~ spl28_99 ),
inference(avatar_split_clause,[],[f1117,f1113,f975,f1119]) ).
tff(f1119,plain,
( spl28_100
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_100])]) ).
tff(f1113,plain,
( spl28_99
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_99])]) ).
tff(f1117,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_99 ),
inference(forward_demodulation,[],[f1116,f976]) ).
tff(f1116,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_99 ),
inference(forward_demodulation,[],[f1114,f976]) ).
tff(f1114,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl28_99 ),
inference(avatar_component_clause,[],[f1113]) ).
tff(f1115,plain,
spl28_99,
inference(avatar_split_clause,[],[f411,f1113]) ).
tff(f411,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1)) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X49: dB,X29: dB,X48: dB] :
( beta(X48,X29)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X49),X48),aa(dB,dB,aa(dB,fun1(dB,dB),app,X49),X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_appR) ).
tff(f1111,plain,
( spl28_98
| ~ spl28_80
| ~ spl28_97 ),
inference(avatar_split_clause,[],[f1107,f1103,f975,f1109]) ).
tff(f1109,plain,
( spl28_98
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_98])]) ).
tff(f1103,plain,
( spl28_97
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_97])]) ).
tff(f1107,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_97 ),
inference(forward_demodulation,[],[f1106,f976]) ).
tff(f1106,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_97 ),
inference(forward_demodulation,[],[f1104,f976]) ).
tff(f1104,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl28_97 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f1105,plain,
spl28_97,
inference(avatar_split_clause,[],[f410,f1103]) ).
tff(f410,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0)) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X49: dB,X29: dB,X48: dB] :
( beta(X48,X29)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X48),X49),aa(dB,dB,aa(dB,fun1(dB,dB),app,X29),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_appL) ).
tff(f1101,plain,
( spl28_96
| ~ spl28_80
| ~ spl28_95 ),
inference(avatar_split_clause,[],[f1097,f1093,f975,f1099]) ).
tff(f1099,plain,
( spl28_96
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_96])]) ).
tff(f1093,plain,
( spl28_95
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_95])]) ).
tff(f1097,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_95 ),
inference(forward_demodulation,[],[f1096,f976]) ).
tff(f1096,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) )
| ~ spl28_80
| ~ spl28_95 ),
inference(forward_demodulation,[],[f1094,f976]) ).
tff(f1094,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) )
| ~ spl28_95 ),
inference(avatar_component_clause,[],[f1093]) ).
tff(f1095,plain,
spl28_95,
inference(avatar_split_clause,[],[f409,f1093]) ).
tff(f409,plain,
! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X28: nat,X48: dB,X51: dB] :
( beta(X51,X48)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X51),X28),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X48),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_lift__preserves__beta) ).
tff(f1080,plain,
spl28_94,
inference(avatar_split_clause,[],[f440,f1078]) ).
tff(f440,plain,
! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f249,f306]) ).
tff(f306,plain,
! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f249,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(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,X67: fun1(X0,X1),X56: fun1(X0,X1)] :
( ! [X59: X0] : ( aa(X0,X1,X56,X59) = aa(X0,X1,X67,X59) )
=> ( X56 = X67 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1076,plain,
( spl28_93
| ~ spl28_80
| ~ spl28_92 ),
inference(avatar_split_clause,[],[f1072,f1069,f975,f1074]) ).
tff(f1074,plain,
( spl28_93
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_93])]) ).
tff(f1069,plain,
( spl28_92
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_92])]) ).
tff(f1072,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK9(X0)),abs(sK8(X0))),sK10(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl28_80
| ~ spl28_92 ),
inference(forward_demodulation,[],[f1070,f976]) ).
tff(f1070,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl28_92 ),
inference(avatar_component_clause,[],[f1069]) ).
tff(f1071,plain,
spl28_92,
inference(avatar_split_clause,[],[f366,f1069]) ).
tff(f366,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1065,plain,
( spl28_91
| ~ spl28_80
| ~ spl28_90 ),
inference(avatar_split_clause,[],[f1060,f1056,f975,f1062]) ).
tff(f1056,plain,
( spl28_90
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_90])]) ).
tff(f1060,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs)))
| ~ spl28_80
| ~ spl28_90 ),
inference(forward_demodulation,[],[f1058,f976]) ).
tff(f1058,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1))
| ~ spl28_90 ),
inference(avatar_component_clause,[],[f1056]) ).
tff(f1059,plain,
spl28_90,
inference(avatar_split_clause,[],[f494,f1056]) ).
tff(f494,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)),
inference(definition_unfolding,[],[f347,f339]) ).
tff(f347,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nT) ).
tff(f1052,plain,
( spl28_89
| ~ spl28_80
| ~ spl28_88 ),
inference(avatar_split_clause,[],[f1047,f1043,f975,f1049]) ).
tff(f1043,plain,
( spl28_88
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_88])]) ).
tff(f1047,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl28_80
| ~ spl28_88 ),
inference(forward_demodulation,[],[f1045,f976]) ).
tff(f1045,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a))
| ~ spl28_88 ),
inference(avatar_component_clause,[],[f1043]) ).
tff(f1046,plain,
spl28_88,
inference(avatar_split_clause,[],[f493,f1043]) ).
tff(f493,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f346,f339]) ).
tff(f346,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(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,fun1(type,bool),typing(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(f1037,plain,
( spl28_87
| ~ spl28_80
| ~ spl28_86 ),
inference(avatar_split_clause,[],[f1033,f1030,f975,f1035]) ).
tff(f1030,plain,
( spl28_86
<=> ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_86])]) ).
tff(f1033,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun1(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl28_80
| ~ spl28_86 ),
inference(forward_demodulation,[],[f1031,f976]) ).
tff(f1031,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl28_86 ),
inference(avatar_component_clause,[],[f1030]) ).
tff(f1032,plain,
spl28_86,
inference(avatar_split_clause,[],[f423,f1030]) ).
tff(f423,plain,
! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: X0] :
( ( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: X0] :
( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X63: fun1(X0,bool),X9: X0] :
( pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X9),X63))
<=> pp(aa(X0,bool,X63,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f1027,plain,
( spl28_85
| ~ spl28_80
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f1023,f1020,f975,f1025]) ).
tff(f1025,plain,
( spl28_85
<=> ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun1(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_85])]) ).
tff(f1020,plain,
( spl28_84
<=> ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_84])]) ).
tff(f1023,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun1(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl28_80
| ~ spl28_84 ),
inference(forward_demodulation,[],[f1021,f976]) ).
tff(f1021,plain,
( ! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl28_84 ),
inference(avatar_component_clause,[],[f1020]) ).
tff(f1022,plain,
spl28_84,
inference(avatar_split_clause,[],[f422,f1020]) ).
tff(f422,plain,
! [X0: $tType,X2: X0,X1: fun1(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun1(X0,bool),bool,aa(X0,fun1(fun1(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1014,plain,
( spl28_83
| ~ spl28_80
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f1010,f1007,f975,f1012]) ).
tff(f1007,plain,
( spl28_82
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_82])]) ).
tff(f1010,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_80
| ~ spl28_82 ),
inference(forward_demodulation,[],[f1008,f976]) ).
tff(f1008,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_82 ),
inference(avatar_component_clause,[],[f1007]) ).
tff(f1009,plain,
spl28_82,
inference(avatar_split_clause,[],[f386,f1007]) ).
tff(f386,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(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(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X28: nat,X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X29),var(X28)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_app__Var__IT) ).
tff(f986,plain,
( spl28_81
| ~ spl28_9
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f690,f681,f584,f983]) ).
tff(f690,plain,
( sP1(abs(ua))
| ~ spl28_9
| ~ spl28_28 ),
inference(resolution,[],[f682,f586]) ).
tff(f977,plain,
spl28_80,
inference(avatar_split_clause,[],[f470,f975]) ).
tff(f969,plain,
( spl28_79
| ~ spl28_78 ),
inference(avatar_split_clause,[],[f965,f962,f967]) ).
tff(f962,plain,
( spl28_78
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_78])]) ).
tff(f965,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_78 ),
inference(forward_demodulation,[],[f963,f470]) ).
tff(f963,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl28_78 ),
inference(avatar_component_clause,[],[f962]) ).
tff(f964,plain,
spl28_78,
inference(avatar_split_clause,[],[f385,f962]) ).
tff(f385,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X28: nat,X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X29),X28))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_lift__IT) ).
tff(f960,plain,
( spl28_77
| ~ spl28_76 ),
inference(avatar_split_clause,[],[f956,f953,f958]) ).
tff(f953,plain,
( spl28_76
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_76])]) ).
tff(f956,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl28_76 ),
inference(forward_demodulation,[],[f954,f470]) ).
tff(f954,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl28_76 ),
inference(avatar_component_clause,[],[f953]) ).
tff(f955,plain,
spl28_76,
inference(avatar_split_clause,[],[f378,f953]) ).
tff(f378,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X49: dB,X47: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X47)),X49),X47) = X49 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subst__eq) ).
tff(f951,plain,
spl28_75,
inference(avatar_split_clause,[],[f361,f949]) ).
tff(f361,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,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,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) )
| ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f280,f282,f281]) ).
tff(f281,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f280,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,[],[f279]) ).
tff(f279,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,[],[f278]) ).
tff(f278,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,[],[f271]) ).
tff(f271,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(f945,plain,
( spl28_74
| ~ spl28_10
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f689,f681,f589,f942]) ).
tff(f689,plain,
( sP1(abs(u))
| ~ spl28_10
| ~ spl28_28 ),
inference(resolution,[],[f682,f591]) ).
tff(f940,plain,
( spl28_73
| ~ spl28_72 ),
inference(avatar_split_clause,[],[f936,f933,f938]) ).
tff(f933,plain,
( spl28_72
<=> ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_72])]) ).
tff(f936,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl28_72 ),
inference(forward_demodulation,[],[f934,f470]) ).
tff(f934,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) )
| ~ spl28_72 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f935,plain,
spl28_72,
inference(avatar_split_clause,[],[f418,f933]) ).
tff(f418,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X6: type,X10: nat,X11: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X11),var(X10)),X6))
=> ( aa(nat,type,X11,X10) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_typing__elims_I1_J) ).
tff(f926,plain,
spl28_71,
inference(avatar_split_clause,[],[f426,f924]) ).
tff(f426,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X36: list(dB),X37: nat,X4: dB,X7: dB] : ( foldl(dB,dB,app,var(X37),X36) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X7)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Abs__App__neq__Var__apps) ).
tff(f922,plain,
spl28_70,
inference(avatar_split_clause,[],[f359,f920]) ).
tff(f359,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f918,plain,
spl28_69,
inference(avatar_split_clause,[],[f358,f916]) ).
tff(f358,plain,
! [X0: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK2(X0)),sK3(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK2(X0)),sK3(X0)) = X0 )
| ( atom(sK4(X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f274,f276,f275]) ).
tff(f275,plain,
! [X0: type] :
( ? [X1: type,X2: type] : ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) = X0 )
=> ( aa(type,type,aa(type,fun1(type,type),fun,sK2(X0)),sK3(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f276,plain,
! [X0: type] :
( ? [X3: nat] : ( atom(X3) = X0 )
=> ( atom(sK4(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f274,plain,
! [X0: type] :
( ? [X1: type,X2: type] : ( aa(type,type,aa(type,fun1(type,type),fun,X1),X2) = X0 )
| ? [X3: nat] : ( atom(X3) = X0 ) ),
inference(rectify,[],[f225]) ).
tff(f225,plain,
! [X0: type] :
( ? [X2: type,X3: type] : ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) = X0 )
| ? [X1: nat] : ( atom(X1) = X0 ) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: type] :
( ! [X1: nat] : ( atom(X1) != X0 )
=> ~ ! [X2: type,X3: type] : ( aa(type,type,aa(type,fun1(type,type),fun,X2),X3) != X0 ) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X66: type] :
( ! [X76: nat] : ( atom(X76) != X66 )
=> ~ ! [X77: type,X78: type] : ( aa(type,type,aa(type,fun1(type,type),fun,X77),X78) != X66 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_type_Oexhaust) ).
tff(f912,plain,
( spl28_68
| ~ spl28_8
| ~ spl28_28 ),
inference(avatar_split_clause,[],[f688,f681,f579,f909]) ).
tff(f688,plain,
( sP1(abs(t2))
| ~ spl28_8
| ~ spl28_28 ),
inference(resolution,[],[f682,f581]) ).
tff(f906,plain,
spl28_67,
inference(avatar_split_clause,[],[f445,f904]) ).
tff(f445,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,[],[f311]) ).
tff(f311,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,[],[f310]) ).
tff(f310,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,[],[f190]) ).
tff(f190,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,[],[f25]) ).
tff(f25,axiom,
! [X36: list(dB),X37: nat,X38: list(dB),X39: nat] :
( ( foldl(dB,dB,app,var(X39),X38) = foldl(dB,dB,app,var(X37),X36) )
<=> ( ( X36 = X38 )
& ( X37 = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Var__apps__eq__Var__apps__conv) ).
tff(f902,plain,
spl28_66,
inference(avatar_split_clause,[],[f442,f900]) ).
tff(f442,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,[],[f309]) ).
tff(f309,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,[],[f308]) ).
tff(f308,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,[],[f189]) ).
tff(f189,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,[],[f81]) ).
tff(f81,axiom,
! [X36: list(dB),X7: dB,X38: list(dB),X42: dB] :
( ( foldl(dB,dB,app,abs(X42),X38) = foldl(dB,dB,app,abs(X7),X36) )
<=> ( ( X36 = X38 )
& ( X7 = X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Abs__apps__eq__Abs__apps__conv) ).
tff(f898,plain,
spl28_65,
inference(avatar_split_clause,[],[f399,f896]) ).
tff(f399,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X54: X0,X53: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun1(list(X0),list(X0)),cons(X0),X54),X53) != X53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_not__Cons__self) ).
tff(f894,plain,
spl28_64,
inference(avatar_split_clause,[],[f345,f891]) ).
tff(f345,plain,
rs = aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun1(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Cons) ).
tff(f884,plain,
( spl28_63
| ~ spl28_15
| ~ spl28_17 ),
inference(avatar_split_clause,[],[f656,f625,f616,f882]) ).
tff(f882,plain,
( spl28_63
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_63])]) ).
tff(f656,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl28_15
| ~ spl28_17 ),
inference(resolution,[],[f626,f617]) ).
tff(f880,plain,
( spl28_62
| ~ spl28_61 ),
inference(avatar_split_clause,[],[f876,f873,f878]) ).
tff(f873,plain,
( spl28_61
<=> ! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_61])]) ).
tff(f876,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl28_61 ),
inference(forward_demodulation,[],[f874,f470]) ).
tff(f874,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl28_61 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f875,plain,
spl28_61,
inference(avatar_split_clause,[],[f506,f873]) ).
tff(f506,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f413]) ).
tff(f413,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: type,X9: nat,X8: fun1(nat,type)] :
( ( aa(nat,type,X8,X9) = X6 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),var(X9)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_typing_OVar) ).
tff(f871,plain,
spl28_60,
inference(avatar_split_clause,[],[f444,f869]) ).
tff(f444,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,[],[f311]) ).
tff(f867,plain,
spl28_59,
inference(avatar_split_clause,[],[f441,f865]) ).
tff(f441,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,[],[f309]) ).
tff(f863,plain,
spl28_58,
inference(avatar_split_clause,[],[f356,f861]) ).
tff(f861,plain,
( spl28_58
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_58])]) ).
tff(f356,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X12: list(dB)] :
( listsp(dB,it,X12)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_lifts__IT) ).
tff(f850,plain,
spl28_57,
inference(avatar_split_clause,[],[f420,f848]) ).
tff(f420,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,[],[f296]) ).
tff(f296,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,[],[f174]) ).
tff(f174,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X7: dB,X12: list(dB),X42: dB] :
( ( foldl(dB,dB,app,X42,X12) = foldl(dB,dB,app,X7,X12) )
<=> ( X7 = X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_apps__eq__tail__conv) ).
tff(f844,plain,
( spl28_56
| ~ spl28_55 ),
inference(avatar_split_clause,[],[f840,f837,f842]) ).
tff(f842,plain,
( spl28_56
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_56])]) ).
tff(f837,plain,
( spl28_55
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_55])]) ).
tff(f840,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl28_55 ),
inference(forward_demodulation,[],[f838,f470]) ).
tff(f838,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1)) )
| ~ spl28_55 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f839,plain,
spl28_55,
inference(avatar_split_clause,[],[f408,f837]) ).
tff(f408,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X0: $tType,X66: X0,X54: X0] :
( ( X54 = X66 )
| ~ pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X54),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f835,plain,
spl28_54,
inference(avatar_split_clause,[],[f384,f833]) ).
tff(f384,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,[],[f227]) ).
tff(f227,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,[],[f142]) ).
tff(f142,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X37: nat,X38: list(dB)] :
( listsp(dB,it,X38)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X37),X38))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_IT_OVar) ).
tff(f827,plain,
( spl28_53
| ~ spl28_52 ),
inference(avatar_split_clause,[],[f823,f820,f825]) ).
tff(f820,plain,
( spl28_52
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_52])]) ).
tff(f823,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl28_52 ),
inference(forward_demodulation,[],[f821,f470]) ).
tff(f821,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl28_52 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f822,plain,
spl28_52,
inference(avatar_split_clause,[],[f380,f820]) ).
tff(f380,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X95: bool,X93: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X93),X95))
| ~ pp(X95)
| ~ pp(X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f818,plain,
spl28_51,
inference(avatar_split_clause,[],[f362,f816]) ).
tff(f362,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f801,plain,
spl28_50,
inference(avatar_split_clause,[],[f425,f799]) ).
tff(f425,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,[],[f177]) ).
tff(f177,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,[],[f88]) ).
tff(f88,axiom,
! [X36: list(dB),X42: dB,X12: list(dB),X37: nat] : ( foldl(dB,dB,app,var(X37),X12) != foldl(dB,dB,app,abs(X42),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Var__apps__neq__Abs__apps) ).
tff(f797,plain,
spl28_49,
inference(avatar_split_clause,[],[f407,f795]) ).
tff(f407,plain,
! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType,X1: X0,X2: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X54: X0,X93: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X93))
| ~ pp(aa(X0,bool,X93,X54)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f793,plain,
spl28_48,
inference(avatar_split_clause,[],[f397,f791]) ).
tff(f397,plain,
! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: dB,X1: dB,X2: nat] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X32: dB,X33: dB,X31: nat] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X33),X32) != var(X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dB_Osimps_I4_J) ).
tff(f789,plain,
spl28_47,
inference(avatar_split_clause,[],[f395,f787]) ).
tff(f395,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X82: dB,X83: dB,X84: dB] : ( abs(X82) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X84),X83) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_dB_Osimps_I8_J) ).
tff(f785,plain,
spl28_46,
inference(avatar_split_clause,[],[f393,f783]) ).
tff(f393,plain,
! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: type,X1: type,X2: nat] : ( atom(X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X68: type,X69: type,X31: nat] : ( atom(X31) != aa(type,type,aa(type,fun1(type,type),fun,X69),X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_type_Osimps_I3_J) ).
tff(f780,plain,
( spl28_45
| ~ spl28_44 ),
inference(avatar_split_clause,[],[f776,f773,f778]) ).
tff(f778,plain,
( spl28_45
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_45])]) ).
tff(f773,plain,
( spl28_44
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_44])]) ).
tff(f776,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl28_44 ),
inference(forward_demodulation,[],[f774,f470]) ).
tff(f774,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) )
| ~ spl28_44 ),
inference(avatar_component_clause,[],[f773]) ).
tff(f775,plain,
spl28_44,
inference(avatar_split_clause,[],[f382,f773]) ).
tff(f382,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X95: bool,X93: bool] :
( pp(X95)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X93),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f770,plain,
( spl28_43
| ~ spl28_42 ),
inference(avatar_split_clause,[],[f766,f763,f768]) ).
tff(f768,plain,
( spl28_43
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_43])]) ).
tff(f763,plain,
( spl28_42
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_42])]) ).
tff(f766,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl28_42 ),
inference(forward_demodulation,[],[f764,f470]) ).
tff(f764,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) )
| ~ spl28_42 ),
inference(avatar_component_clause,[],[f763]) ).
tff(f765,plain,
spl28_42,
inference(avatar_split_clause,[],[f381,f763]) ).
tff(f381,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X95: bool,X93: bool] :
( pp(X93)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X93),X95)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f761,plain,
spl28_41,
inference(avatar_split_clause,[],[f360,f759]) ).
tff(f759,plain,
( spl28_41
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_41])]) ).
tff(f360,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f753,plain,
( spl28_40
| ~ spl28_39 ),
inference(avatar_split_clause,[],[f749,f746,f751]) ).
tff(f746,plain,
( spl28_39
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_39])]) ).
tff(f749,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl28_39 ),
inference(forward_demodulation,[],[f747,f470]) ).
tff(f747,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X2))
| ~ spl28_39 ),
inference(avatar_component_clause,[],[f746]) ).
tff(f748,plain,
spl28_39,
inference(avatar_split_clause,[],[f505,f746]) ).
tff(f505,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f406]) ).
tff(f406,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X66: X0,X54: X0] :
( pp(aa(X0,bool,aa(X0,fun1(X0,bool),fequal(X0),X54),X66))
| ( X54 != X66 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f744,plain,
spl28_38,
inference(avatar_split_clause,[],[f357,f742]) ).
tff(f357,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X51: dB] :
( pp(aa(dB,bool,it,X51))
=> pp(aa(dB,bool,it,abs(X51))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Lambda) ).
tff(f740,plain,
( spl28_37
| ~ spl28_9
| ~ spl28_17 ),
inference(avatar_split_clause,[],[f659,f625,f584,f737]) ).
tff(f737,plain,
( spl28_37
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_37])]) ).
tff(f659,plain,
( sP1(ua)
| ~ spl28_9
| ~ spl28_17 ),
inference(resolution,[],[f626,f586]) ).
tff(f734,plain,
( spl28_36
| ~ spl28_35 ),
inference(avatar_split_clause,[],[f729,f725,f731]) ).
tff(f725,plain,
( spl28_35
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_35])]) ).
tff(f729,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl28_35 ),
inference(forward_demodulation,[],[f727,f470]) ).
tff(f727,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t))
| ~ spl28_35 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f728,plain,
spl28_35,
inference(avatar_split_clause,[],[f344,f725]) ).
tff(f344,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uT) ).
tff(f722,plain,
( spl28_34
| ~ spl28_33 ),
inference(avatar_split_clause,[],[f717,f713,f719]) ).
tff(f713,plain,
( spl28_33
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_33])]) ).
tff(f717,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl28_33 ),
inference(forward_demodulation,[],[f715,f470]) ).
tff(f715,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t))
| ~ spl28_33 ),
inference(avatar_component_clause,[],[f713]) ).
tff(f716,plain,
spl28_33,
inference(avatar_split_clause,[],[f343,f713]) ).
tff(f343,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t)),
inference(cnf_transformation,[],[f45]) ).
tff(f45,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Var_I4_J) ).
tff(f710,plain,
spl28_32,
inference(avatar_split_clause,[],[f500,f708]) ).
tff(f500,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f363]) ).
tff(f363,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,[],[f283]) ).
tff(f706,plain,
spl28_31,
inference(avatar_split_clause,[],[f424,f704]) ).
tff(f424,plain,
! [X0: $tType,X2: fun1(type,fun1(type,X0)),X3: fun1(nat,X0),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: nat,X2: fun1(type,fun1(type,X0)),X3: fun1(nat,X0)] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType,X19: nat,X57: fun1(type,fun1(type,X0)),X58: fun1(nat,X0)] : ( type_case(X0,X58,X57,atom(X19)) = aa(nat,X0,X58,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_type_Osimps_I5_J) ).
tff(f702,plain,
( spl28_30
| ~ spl28_10
| ~ spl28_17 ),
inference(avatar_split_clause,[],[f658,f625,f589,f699]) ).
tff(f699,plain,
( spl28_30
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_30])]) ).
tff(f658,plain,
( sP1(u)
| ~ spl28_10
| ~ spl28_17 ),
inference(resolution,[],[f626,f591]) ).
tff(f696,plain,
spl28_29,
inference(avatar_split_clause,[],[f516,f694]) ).
tff(f516,plain,
! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f461]) ).
tff(f461,plain,
! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X6: X0,X11: fun1(nat,X0),X30: nat,X10: nat] :
( ( X10 = X30 )
=> ( aa(nat,X0,shift(X0,X11,X10,X6),X30) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_shift__eq) ).
tff(f683,plain,
spl28_28,
inference(avatar_split_clause,[],[f499,f681]) ).
tff(f499,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f364]) ).
tff(f364,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f679,plain,
spl28_27,
inference(avatar_split_clause,[],[f377,f677]) ).
tff(f377,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType,X64: list(X0)] : ( map(X0,X0,combi(X0),X64) = X64 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_map__ident) ).
tff(f675,plain,
spl28_26,
inference(avatar_split_clause,[],[f368,f673]) ).
tff(f368,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f669,plain,
( spl28_25
| ~ spl28_8
| ~ spl28_17 ),
inference(avatar_split_clause,[],[f657,f625,f579,f666]) ).
tff(f666,plain,
( spl28_25
<=> sP1(t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_25])]) ).
tff(f657,plain,
( sP1(t2)
| ~ spl28_8
| ~ spl28_17 ),
inference(resolution,[],[f626,f581]) ).
tff(f655,plain,
spl28_24,
inference(avatar_split_clause,[],[f391,f653]) ).
tff(f653,plain,
( spl28_24
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_24])]) ).
tff(f391,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X18: nat,X19: nat] :
( ( var(X19) = var(X18) )
<=> ( X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dB_Osimps_I1_J) ).
tff(f651,plain,
spl28_23,
inference(avatar_split_clause,[],[f389,f649]) ).
tff(f649,plain,
( spl28_23
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_23])]) ).
tff(f389,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X80: dB,X81: dB] :
( ( abs(X81) = abs(X80) )
<=> ( X80 = X81 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_dB_Osimps_I3_J) ).
tff(f647,plain,
spl28_22,
inference(avatar_split_clause,[],[f387,f645]) ).
tff(f387,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( atom(X0) != atom(X1) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: nat,X1: nat] :
( ( ( atom(X0) = atom(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( atom(X0) != atom(X1) ) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: nat,X1: nat] :
( ( atom(X0) = atom(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X18: nat,X19: nat] :
( ( atom(X19) = atom(X18) )
<=> ( X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_type_Osimps_I1_J) ).
tff(f643,plain,
spl28_21,
inference(avatar_split_clause,[],[f383,f641]) ).
tff(f641,plain,
( spl28_21
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_21])]) ).
tff(f383,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: dB,X1: dB] :
( beta(X1,X0)
=> beta(abs(X1),abs(X0)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X29: dB,X48: dB] :
( beta(X48,X29)
=> beta(abs(X48),abs(X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_abs) ).
tff(f639,plain,
spl28_20,
inference(avatar_split_clause,[],[f376,f637]) ).
tff(f376,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X93: X0] : ( aa(X0,X0,combi(X0),X93) = X93 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f635,plain,
( spl28_19
| spl28_2
| ~ spl28_13 ),
inference(avatar_split_clause,[],[f606,f602,f552,f633]) ).
tff(f552,plain,
( spl28_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_2])]) ).
tff(f606,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl28_2
| ~ spl28_13 ),
inference(superposition,[],[f554,f603]) ).
tff(f554,plain,
( ~ pp(fFalse)
| spl28_2 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f631,plain,
spl28_18,
inference(avatar_split_clause,[],[f371,f629]) ).
tff(f371,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f129,f271,f270]) ).
tff(f129,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,[],[f91]) ).
tff(f91,axiom,
! [X46: dB] :
( pp(aa(dB,bool,it,X46))
<=> ( ? [X89: dB,X90: dB,X91: list(dB)] :
( pp(aa(dB,bool,it,X90))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X89),X90),zero_zero(nat)),X91)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X89)),X90),X91) = X46 ) )
| ? [X89: dB] :
( pp(aa(dB,bool,it,X89))
& ( abs(X89) = X46 ) )
| ? [X87: list(dB),X88: nat] :
( listsp(dB,it,X87)
& ( foldl(dB,dB,app,var(X88),X87) = X46 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_IT_Osimps) ).
tff(f627,plain,
spl28_17,
inference(avatar_split_clause,[],[f370,f625]) ).
tff(f370,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f288]) ).
tff(f622,plain,
spl28_16,
inference(avatar_split_clause,[],[f375,f620]) ).
tff(f620,plain,
( spl28_16
<=> ! [X0: $tType,X1: fun1(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_16])]) ).
tff(f375,plain,
! [X0: $tType,X1: fun1(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType,X1: fun1(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X79: fun1(X0,bool)] : ( collect(X0,X79) = X79 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f618,plain,
spl28_15,
inference(avatar_split_clause,[],[f352,f616]) ).
tff(f352,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,[],[f18]) ).
tff(f18,axiom,
! [X27: nat] : pp(aa(dB,bool,it,var(X27))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Var__IT) ).
tff(f614,plain,
spl28_14,
inference(avatar_split_clause,[],[f351,f612]) ).
tff(f612,plain,
( spl28_14
<=> ! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_14])]) ).
tff(f351,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X31: nat] : ( zero_zero(nat) = size_size(type,atom(X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_type_Osize_I3_J) ).
tff(f604,plain,
spl28_13,
inference(avatar_split_clause,[],[f353,f602]) ).
tff(f353,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X93: bool] :
( ( fFalse = X93 )
| ( fTrue = X93 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f600,plain,
spl28_12,
inference(avatar_split_clause,[],[f350,f598]) ).
tff(f598,plain,
( spl28_12
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_12])]) ).
tff(f350,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,[],[f74]) ).
tff(f74,axiom,
! [X31: nat] : ( zero_zero(nat) = dB_size(var(X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dB_Osize_I1_J) ).
tff(f596,plain,
spl28_11,
inference(avatar_split_clause,[],[f349,f594]) ).
tff(f594,plain,
( spl28_11
<=> ! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_11])]) ).
tff(f349,plain,
! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X31: nat] : ( zero_zero(nat) = type_size(atom(X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_type_Osize_I1_J) ).
tff(f592,plain,
spl28_10,
inference(avatar_split_clause,[],[f342,f589]) ).
tff(f342,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_uIT) ).
tff(f587,plain,
spl28_9,
inference(avatar_split_clause,[],[f341,f584]) ).
tff(f341,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Var_I3_J) ).
tff(f582,plain,
spl28_8,
inference(avatar_split_clause,[],[f340,f579]) ).
tff(f340,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(f577,plain,
spl28_7,
inference(avatar_split_clause,[],[f373,f575]) ).
tff(f575,plain,
( spl28_7
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_7])]) ).
tff(f373,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X82: dB,X31: nat] : ( var(X31) != abs(X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_dB_Osimps_I6_J) ).
tff(f573,plain,
spl28_6,
inference(avatar_split_clause,[],[f372,f571]) ).
tff(f571,plain,
( spl28_6
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_6])]) ).
tff(f372,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X29: dB,X28: nat] : ~ beta(var(X28),X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_beta__cases_I1_J) ).
tff(f569,plain,
spl28_5,
inference(avatar_split_clause,[],[f365,f567]) ).
tff(f567,plain,
( spl28_5
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_5])]) ).
tff(f365,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f565,plain,
spl28_4,
inference(avatar_split_clause,[],[f338,f562]) ).
tff(f338,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(f560,plain,
spl28_3,
inference(avatar_split_clause,[],[f337,f557]) ).
tff(f557,plain,
( spl28_3
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_3])]) ).
tff(f337,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(f555,plain,
~ spl28_2,
inference(avatar_split_clause,[],[f335,f552]) ).
tff(f335,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f550,plain,
~ spl28_1,
inference(avatar_split_clause,[],[f333,f547]) ).
tff(f333,plain,
~ thesis,
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
~ thesis,
inference(flattening,[],[f117]) ).
tff(f117,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f116]) ).
tff(f116,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL786_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n024.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 14:02:20 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (31286)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (31299)WARNING: value z3 for option sas not known
% 0.15/0.40 % (31301)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40 % (31298)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40 % (31303)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.40 % (31302)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.40 % (31297)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40 % (31299)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.40 % (31304)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % Exception at run slice level
% 0.15/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (31304)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (31319)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (31320)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)
% 0.22/0.42 % (31321)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)
% 0.22/0.43 % (31319)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % Exception at run slice level
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % (31320)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.45 % (31336)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)
% 24.03/3.84 % (31302)First to succeed.
% 24.33/3.91 % (31302)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31286"
% 24.33/3.92 % (31302)Refutation found. Thanks to Tanya!
% 24.33/3.92 % SZS status Theorem for theBenchmark
% 24.33/3.92 % SZS output start Proof for theBenchmark
% See solution above
% 24.33/3.94 % (31302)------------------------------
% 24.33/3.94 % (31302)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 24.33/3.94 % (31302)Termination reason: Refutation
% 24.33/3.94
% 24.33/3.94 % (31302)Memory used [KB]: 30599
% 24.33/3.94 % (31302)Time elapsed: 3.520 s
% 24.33/3.94 % (31302)Instructions burned: 6735 (million)
% 24.33/3.94 % (31286)Success in time 3.553 s
%------------------------------------------------------------------------------