TSTP Solution File: LCL787_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL787_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 : n029.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 07:53:09 EDT 2024
% Result : Theorem 18.74s 3.01s
% Output : Refutation 18.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 740
% Syntax : Number of formulae : 2331 ( 292 unt; 87 typ; 0 def)
% Number of atoms : 6390 (1321 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7478 (3332 ~;3294 |; 159 &)
% ( 560 <=>; 133 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 103 ( 50 >; 53 *; 0 +; 0 <<)
% Number of predicates : 536 ( 534 usr; 529 prp; 0-3 aty)
% Number of functors : 77 ( 77 usr; 24 con; 0-6 aty)
% Number of variables : 5747 (5605 !; 92 ?;5747 :)
% ( 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).
tff(func_def_19,type,
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] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_22,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_23,type,
atom: nat > type ).
tff(func_def_24,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_25,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_26,type,
type_size: type > nat ).
tff(func_def_27,type,
typing: fun(nat,type) > fun(dB,fun(type,bool)) ).
tff(func_def_28,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_29,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_30,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_31,type,
fFalse: bool ).
tff(func_def_32,type,
fTrue: bool ).
tff(func_def_33,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_34,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_35,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(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,
ts: list(type) ).
tff(func_def_40,type,
a: dB ).
tff(func_def_41,type,
as: list(dB) ).
tff(func_def_42,type,
e: fun(nat,type) ).
tff(func_def_43,type,
ea: fun(nat,type) ).
tff(func_def_44,type,
i: nat ).
tff(func_def_45,type,
ia: nat ).
tff(func_def_46,type,
n: nat ).
tff(func_def_47,type,
rs: list(dB) ).
tff(func_def_48,type,
t2: dB ).
tff(func_def_49,type,
u: dB ).
tff(func_def_50,type,
ua: dB ).
tff(func_def_51,type,
sK2: list(type) ).
tff(func_def_52,type,
sK3: dB > dB ).
tff(func_def_53,type,
sK4: dB > list(dB) ).
tff(func_def_54,type,
sK5: dB > nat ).
tff(func_def_55,type,
sK6: dB > dB ).
tff(func_def_56,type,
sK7: dB > dB ).
tff(func_def_57,type,
sK8: dB > list(dB) ).
tff(func_def_58,type,
sK9: ( dB * fun(nat,type) ) > type ).
tff(func_def_59,type,
sK10: ( dB * fun(nat,type) ) > type ).
tff(func_def_60,type,
sK11: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_61,type,
sK12: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_62,type,
sK13: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_63,type,
sK14: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_64,type,
sK15: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_65,type,
sK16: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_66,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_67,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_68,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_69,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_70,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_71,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_72,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_73,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_74,type,
sK25: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_6,type,
sP0: dB > $o ).
tff(pred_def_7,type,
sP1: dB > $o ).
tff(f17742,plain,
$false,
inference(avatar_sat_refutation,[],[f547,f552,f557,f562,f566,f570,f574,f579,f584,f589,f593,f597,f601,f611,f615,f619,f624,f628,f632,f636,f640,f644,f648,f652,f666,f672,f676,f680,f693,f699,f703,f707,f713,f719,f725,f731,f737,f742,f747,f751,f755,f760,f770,f774,f779,f784,f789,f794,f798,f802,f806,f810,f829,f833,f838,f846,f850,f855,f861,f874,f878,f882,f886,f890,f895,f905,f909,f914,f918,f922,f929,f933,f942,f946,f951,f957,f961,f966,f970,f975,f984,f988,f1013,f1018,f1026,f1031,f1036,f1042,f1050,f1056,f1063,f1069,f1075,f1080,f1085,f1099,f1105,f1109,f1115,f1119,f1124,f1128,f1132,f1148,f1153,f1168,f1174,f1184,f1190,f1196,f1201,f1209,f1214,f1218,f1225,f1230,f1237,f1243,f1248,f1256,f1260,f1266,f1270,f1276,f1282,f1289,f1297,f1305,f1315,f1322,f1329,f1346,f1351,f1359,f1365,f1370,f1374,f1378,f1382,f1492,f1496,f1500,f1519,f1525,f1539,f1543,f1547,f1576,f1582,f1596,f1602,f1616,f1620,f1627,f1637,f1644,f1652,f1658,f1671,f1678,f1686,f1693,f1703,f1709,f1718,f1724,f1738,f1743,f1751,f1756,f1795,f1881,f1893,f1897,f1913,f1921,f1928,f1934,f1942,f1959,f1963,f1967,f1973,f2000,f2018,f2024,f2028,f2039,f2048,f2056,f2070,f2084,f2089,f2097,f2103,f2113,f2121,f2129,f2134,f2146,f2150,f2154,f2162,f2176,f2188,f2192,f2271,f2276,f2285,f2290,f2299,f2305,f2310,f2317,f2322,f2817,f2840,f2863,f2868,f2879,f2883,f2887,f2891,f2895,f2899,f2907,f2911,f2926,f2931,f2936,f2940,f2944,f2949,f2953,f2957,f3033,f3038,f3042,f3047,f3051,f3081,f3113,f3114,f3115,f3116,f3117,f3118,f3119,f3120,f3121,f3122,f3123,f3124,f3125,f3126,f3127,f3128,f3129,f3130,f3131,f3132,f3133,f3134,f3135,f3710,f3768,f3772,f3776,f3784,f3788,f3792,f3796,f3801,f3806,f3824,f3846,f3854,f3859,f3863,f3868,f3894,f3899,f3904,f3909,f3914,f3930,f3934,f3938,f3942,f3946,f4024,f4028,f4032,f4036,f4040,f4208,f4213,f4217,f4221,f4233,f4253,f4257,f4261,f4265,f4269,f4273,f4277,f4282,f4286,f4290,f4294,f4298,f4528,f4641,f4645,f4649,f4653,f4718,f4722,f4726,f4730,f4734,f4815,f4819,f4823,f4870,f4909,f4913,f4949,f4954,f4959,f4963,f4967,f4971,f5003,f5008,f5012,f5016,f5020,f5052,f5148,f5152,f5156,f5161,f5165,f5169,f5203,f5207,f5211,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5279,f5392,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5451,f5714,f5725,f5729,f5733,f5737,f5741,f6094,f6098,f6102,f6106,f6110,f6114,f6143,f6309,f6313,f6317,f6321,f6325,f6331,f6335,f6339,f6343,f6347,f6351,f6775,f6779,f6784,f6789,f6861,f6865,f6869,f6873,f6877,f6881,f6885,f6891,f6895,f6899,f7210,f7278,f7282,f7286,f7290,f7294,f7298,f7514,f7721,f7725,f7729,f7733,f7737,f7742,f7746,f7750,f7754,f7758,f8247,f8292,f8296,f8300,f8359,f8380,f8384,f8388,f8392,f8396,f8898,f8965,f8969,f9056,f9060,f9064,f9068,f9072,f9078,f9082,f9087,f9106,f9111,f9703,f9707,f9711,f9715,f9719,f9723,f9728,f9733,f9876,f9880,f9884,f9888,f9894,f9898,f9902,f9906,f9910,f9914,f9918,f9922,f9926,f9930,f10690,f11021,f11025,f11029,f11033,f11037,f11041,f11047,f11051,f11055,f11060,f11777,f11781,f11785,f11789,f11793,f11797,f11801,f11805,f11809,f11813,f12331,f12335,f12339,f12343,f12348,f12521,f12525,f12529,f12695,f12699,f12703,f12708,f12729,f12735,f12739,f12760,f12788,f12792,f12796,f12800,f12804,f12809,f14005,f14009,f14013,f14029,f14033,f14495,f14499,f14503,f14507,f14511,f14515,f14519,f14523,f14527,f14531,f14535,f14539,f14544,f14562,f14566,f14571,f17312,f17316,f17320,f17324,f17701,f17716,f17720,f17724,f17728,f17732,f17736,f17740,f17741]) ).
tff(f17741,plain,
( ~ spl26_4
| ~ spl26_19
| ~ spl26_126
| ~ spl26_309
| ~ spl26_520 ),
inference(avatar_split_clause,[],[f17712,f17699,f4951,f1286,f630,f559]) ).
tff(f559,plain,
( spl26_4
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
tff(f630,plain,
( spl26_19
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_19])]) ).
tff(f1286,plain,
( spl26_126
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_126])]) ).
tff(f4951,plain,
( spl26_309
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_309])]) ).
tff(f17699,plain,
( spl26_520
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),X0,var(i),shift(type,e,i,t))),a))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,X0),var(i)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_520])]) ).
tff(f17712,plain,
( ~ pp(fTrue)
| ~ spl26_19
| ~ spl26_126
| ~ spl26_309
| ~ spl26_520 ),
inference(forward_demodulation,[],[f17702,f4978]) ).
tff(f4978,plain,
( ( fTrue = aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a) )
| ~ spl26_19
| ~ spl26_309 ),
inference(resolution,[],[f4953,f631]) ).
tff(f631,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f4953,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl26_309 ),
inference(avatar_component_clause,[],[f4951]) ).
tff(f17702,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl26_126
| ~ spl26_520 ),
inference(resolution,[],[f17700,f1288]) ).
tff(f1288,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl26_126 ),
inference(avatar_component_clause,[],[f1286]) ).
tff(f17700,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,X0),var(i))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),X0,var(i),shift(type,e,i,t))),a)) )
| ~ spl26_520 ),
inference(avatar_component_clause,[],[f17699]) ).
tff(f17740,plain,
( spl26_527
| ~ spl26_140
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1855,f1793,f1490,f17738]) ).
tff(f17738,plain,
( spl26_527
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: fun(X0,list(X0)),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_527])]) ).
tff(f1490,plain,
( spl26_140
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_140])]) ).
tff(f1793,plain,
( spl26_171
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_171])]) ).
tff(f1855,plain,
( ! [X0: $tType,X2: fun(X0,list(X0)),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ( X1 = X3 ) )
| ~ spl26_140
| ~ spl26_171 ),
inference(superposition,[],[f1491,f1794]) ).
tff(f1794,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl26_171 ),
inference(avatar_component_clause,[],[f1793]) ).
tff(f1491,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X2 = X4 ) )
| ~ spl26_140 ),
inference(avatar_component_clause,[],[f1490]) ).
tff(f17736,plain,
( spl26_526
| ~ spl26_105
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1812,f1793,f1151,f17734]) ).
tff(f17734,plain,
( spl26_526
<=> ! [X0: $tType,X5: $tType,X6: fun(type,fun(X0,X5)),X4: fun(nat,X0),X3: type,X2: type,X1: fun(type,fun(type,X0))] : ( aa(type,X5,aa(fun(type,X0),fun(type,X5),aa(fun(type,fun(X0,X5)),fun(fun(type,X0),fun(type,X5)),combs(type,X0,X5),X6),aa(type,fun(type,X0),X1,X2)),X3) = aa(X0,X5,aa(type,fun(X0,X5),X6,X3),type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_526])]) ).
tff(f1151,plain,
( spl26_105
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,fun(type,X0)),X2: type,X1: type] : ( aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_105])]) ).
tff(f1812,plain,
( ! [X5: $tType,X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,X0)),X6: fun(type,fun(X0,X5)),X4: fun(nat,X0)] : ( aa(type,X5,aa(fun(type,X0),fun(type,X5),aa(fun(type,fun(X0,X5)),fun(fun(type,X0),fun(type,X5)),combs(type,X0,X5),X6),aa(type,fun(type,X0),X1,X2)),X3) = aa(X0,X5,aa(type,fun(X0,X5),X6,X3),type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2))) )
| ~ spl26_105
| ~ spl26_171 ),
inference(superposition,[],[f1794,f1152]) ).
tff(f1152,plain,
( ! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2)) )
| ~ spl26_105 ),
inference(avatar_component_clause,[],[f1151]) ).
tff(f17732,plain,
( spl26_525
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1804,f1793,f986,f17730]) ).
tff(f17730,plain,
( spl26_525
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X6: X0,X7: fun(X0,X1)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),aa(X3,fun(X0,fun(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_525])]) ).
tff(f986,plain,
( spl26_82
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_82])]) ).
tff(f1804,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),aa(X3,fun(X0,fun(X1,X2)),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl26_82
| ~ spl26_171 ),
inference(superposition,[],[f1794,f987]) ).
tff(f987,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl26_82 ),
inference(avatar_component_clause,[],[f986]) ).
tff(f17728,plain,
( spl26_524
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1803,f1793,f986,f17726]) ).
tff(f17726,plain,
( spl26_524
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X3,X4: fun(X0,fun(X3,fun(X1,X2))),X6: X0,X7: fun(X0,X1)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_524])]) ).
tff(f1803,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),combc(X0,X3,fun(X1,X2),X4,X5)),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),aa(X0,X1,X7,X6)) )
| ~ spl26_82
| ~ spl26_171 ),
inference(superposition,[],[f1794,f987]) ).
tff(f17724,plain,
( spl26_523
| ~ spl26_82
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1762,f1754,f986,f17722]) ).
tff(f17722,plain,
( spl26_523
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,aa(X2,fun(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun(X0,X1),X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_523])]) ).
tff(f1754,plain,
( spl26_170
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_170])]) ).
tff(f1762,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,aa(X2,fun(X0,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)),map(X0,X1,aa(X2,fun(X0,X1),X3,X4),X6)) )
| ~ spl26_82
| ~ spl26_170 ),
inference(superposition,[],[f1755,f987]) ).
tff(f1755,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl26_170 ),
inference(avatar_component_clause,[],[f1754]) ).
tff(f17720,plain,
( spl26_522
| ~ spl26_105
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1565,f1545,f1151,f17718]) ).
tff(f17718,plain,
( spl26_522
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,fun(type,X0)),X3: fun(type,X1),X4: type,X6: fun(nat,X0),X5: type] : ( type_case(X0,X6,aa(fun(type,X1),fun(type,fun(type,X0)),aa(fun(X1,fun(type,X0)),fun(fun(type,X1),fun(type,fun(type,X0))),combb(X1,fun(type,X0),type),X2),X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),X2,aa(type,X1,X3,X4)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_522])]) ).
tff(f1545,plain,
( spl26_147
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_147])]) ).
tff(f1565,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(type,X0)),X3: fun(type,X1),X6: fun(nat,X0),X4: type,X5: type] : ( type_case(X0,X6,aa(fun(type,X1),fun(type,fun(type,X0)),aa(fun(X1,fun(type,X0)),fun(fun(type,X1),fun(type,fun(type,X0))),combb(X1,fun(type,X0),type),X2),X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),X2,aa(type,X1,X3,X4)),X5) )
| ~ spl26_105
| ~ spl26_147 ),
inference(superposition,[],[f1152,f1546]) ).
tff(f1546,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) )
| ~ spl26_147 ),
inference(avatar_component_clause,[],[f1545]) ).
tff(f17716,plain,
( spl26_521
| ~ spl26_105
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1391,f1376,f1151,f17714]) ).
tff(f17714,plain,
( spl26_521
<=> ! [X0: $tType,X5: list(type),X3: type,X4: fun(nat,fun(X0,X0)),X6: X0,X2: type,X1: fun(type,fun(type,fun(X0,X0)))] : ( foldr(type,X0,aa(type,fun(type,fun(X0,X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3),X6) = aa(X0,X0,type_case(fun(X0,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),foldr(type,X0,aa(type,fun(type,fun(X0,X0)),X1,X2),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_521])]) ).
tff(f1376,plain,
( spl26_138
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X1)),X4: X0,X3: list(X0),X2: X1] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_138])]) ).
tff(f1391,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,fun(X0,X0))),X6: X0,X4: fun(nat,fun(X0,X0)),X5: list(type)] : ( foldr(type,X0,aa(type,fun(type,fun(X0,X0)),X1,X2),aa(type,list(type),combc(type,list(type),list(type),cons(type),X5),X3),X6) = aa(X0,X0,type_case(fun(X0,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),foldr(type,X0,aa(type,fun(type,fun(X0,X0)),X1,X2),X5,X6)) )
| ~ spl26_105
| ~ spl26_138 ),
inference(superposition,[],[f1377,f1152]) ).
tff(f1377,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) )
| ~ spl26_138 ),
inference(avatar_component_clause,[],[f1376]) ).
tff(f17701,plain,
( spl26_520
| ~ spl26_175
| ~ spl26_178 ),
inference(avatar_split_clause,[],[f1929,f1926,f1895,f17699]) ).
tff(f1895,plain,
( spl26_175
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK16(X0,X1,X2,X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_175])]) ).
tff(f1926,plain,
( spl26_178
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),X0)),var(i)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_178])]) ).
tff(f1929,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),X0,var(i),shift(type,e,i,t))),a))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,X0),var(i)))) )
| ~ spl26_175
| ~ spl26_178 ),
inference(resolution,[],[f1927,f1896]) ).
tff(f1896,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK16(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))) )
| ~ spl26_175 ),
inference(avatar_component_clause,[],[f1895]) ).
tff(f1927,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),X0)),var(i)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),a)) )
| ~ spl26_178 ),
inference(avatar_component_clause,[],[f1926]) ).
tff(f17324,plain,
( spl26_519
| ~ spl26_82
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1761,f1754,f986,f17322]) ).
tff(f17322,plain,
( spl26_519
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X6: list(X0),X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_519])]) ).
tff(f1761,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X6: list(X0),X4: X2,X5: X0] : ( map(X0,X1,combc(X0,X2,X1,X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)),map(X0,X1,combc(X0,X2,X1,X3,X4),X6)) )
| ~ spl26_82
| ~ spl26_170 ),
inference(superposition,[],[f1755,f987]) ).
tff(f17320,plain,
( spl26_518
| ~ spl26_156
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1731,f1722,f1642,f17318]) ).
tff(f17318,plain,
( spl26_518
<=> ! [X2: type,X3: type,X4: dB,X0: fun(nat,type),X6: list(type),X5: list(dB),X1: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,X6,X3)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_518])]) ).
tff(f1642,plain,
( spl26_156
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_156])]) ).
tff(f1722,plain,
( spl26_166
<=> ! [X4: fun(nat,type),X0: list(dB),X3: dB,X2: list(type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_166])]) ).
tff(f1731,plain,
( ! [X2: type,X3: type,X0: fun(nat,type),X1: nat,X6: list(type),X4: dB,X5: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X3),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X1),X4),X5)))
| ~ pp(aa(list(type),bool,typings(shift(type,X0,X1,X2),X5),X6))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,X6,X3)),X4)) )
| ~ spl26_156
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1643]) ).
tff(f1643,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3)) )
| ~ spl26_156 ),
inference(avatar_component_clause,[],[f1642]) ).
tff(f1723,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl26_166 ),
inference(avatar_component_clause,[],[f1722]) ).
tff(f17316,plain,
( spl26_517
| ~ spl26_151
| ~ spl26_154 ),
inference(avatar_split_clause,[],[f1631,f1625,f1600,f17314]) ).
tff(f17314,plain,
( spl26_517
<=> ! [X2: list(dB),X4: dB,X0: fun(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(foldr(type,type,fun1,sK14(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_517])]) ).
tff(f1600,plain,
( spl26_151
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_151])]) ).
tff(f1625,plain,
( spl26_154
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK16(X0,X1,X2,X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_154])]) ).
tff(f1631,plain,
( ! [X2: list(dB),X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(foldr(type,type,fun1,sK14(X1,X2,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X0),X1),X3,X4,X0)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X3),X4),X2))) )
| ~ spl26_151
| ~ spl26_154 ),
inference(resolution,[],[f1626,f1601]) ).
tff(f1601,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl26_151 ),
inference(avatar_component_clause,[],[f1600]) ).
tff(f1626,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK16(X0,X1,X2,X3)),X1)) )
| ~ spl26_154 ),
inference(avatar_component_clause,[],[f1625]) ).
tff(f17312,plain,
( spl26_516
| ~ spl26_149
| ~ spl26_154 ),
inference(avatar_split_clause,[],[f1630,f1625,f1580,f17310]) ).
tff(f17310,plain,
( spl26_516
<=> ! [X2: list(dB),X4: dB,X0: fun(nat,type),X3: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(foldr(type,type,fun1,sK13(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,[spl26_516])]) ).
tff(f1580,plain,
( spl26_149
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_149])]) ).
tff(f1630,plain,
( ! [X2: list(dB),X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(foldr(type,type,fun1,sK13(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))) )
| ~ spl26_149
| ~ spl26_154 ),
inference(resolution,[],[f1626,f1581]) ).
tff(f1581,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl26_149 ),
inference(avatar_component_clause,[],[f1580]) ).
tff(f14571,plain,
( spl26_515
| ~ spl26_82
| ~ spl26_352
| ~ spl26_514 ),
inference(avatar_split_clause,[],[f14567,f14564,f5723,f986,f14569]) ).
tff(f14569,plain,
( spl26_515
<=> ! [X2: dB,X3: dB,X4: dB,X0: dB,X5: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_515])]) ).
tff(f5723,plain,
( spl26_352
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X0,fun(X3,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_352])]) ).
tff(f14564,plain,
( spl26_514
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_514])]) ).
tff(f14567,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X0) = X4 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_514 ),
inference(forward_demodulation,[],[f14565,f5776]) ).
tff(f5776,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X2,X7: X0,X4: fun(X3,fun(X2,fun(X0,X1))),X5: X3] : ( aa(X2,X1,combc(X2,X0,X1,aa(X3,fun(X2,fun(X0,X1)),X4,X5),X7),X6) = aa(X3,X1,combc(X3,X0,X1,combc(X3,X2,fun(X0,X1),X4,X6),X7),X5) )
| ~ spl26_82
| ~ spl26_352 ),
inference(superposition,[],[f5724,f987]) ).
tff(f5724,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) )
| ~ spl26_352 ),
inference(avatar_component_clause,[],[f5723]) ).
tff(f14565,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl26_514 ),
inference(avatar_component_clause,[],[f14564]) ).
tff(f14566,plain,
( spl26_514
| ~ spl26_102
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f2166,f2160,f1126,f14564]) ).
tff(f1126,plain,
( spl26_102
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_102])]) ).
tff(f2160,plain,
( spl26_204
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_204])]) ).
tff(f2166,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),X2) = X4 ) )
| ~ spl26_102
| ~ spl26_204 ),
inference(superposition,[],[f1127,f2161]) ).
tff(f2161,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl26_204 ),
inference(avatar_component_clause,[],[f2160]) ).
tff(f1127,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X1 = X3 ) )
| ~ spl26_102 ),
inference(avatar_component_clause,[],[f1126]) ).
tff(f14562,plain,
( spl26_513
| ~ spl26_244
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5023,f4969,f3708,f14560]) ).
tff(f14560,plain,
( spl26_513
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(abs(var(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_513])]) ).
tff(f3708,plain,
( spl26_244
<=> ! [X0: nat] : sP1(abs(abs(var(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_244])]) ).
tff(f4969,plain,
( spl26_313
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_313])]) ).
tff(f5023,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(abs(var(X0)))) )
| ~ spl26_244
| ~ spl26_313 ),
inference(resolution,[],[f4970,f3709]) ).
tff(f3709,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl26_244 ),
inference(avatar_component_clause,[],[f3708]) ).
tff(f4970,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( fTrue = aa(dB,bool,it,X0) ) )
| ~ spl26_313 ),
inference(avatar_component_clause,[],[f4969]) ).
tff(f14544,plain,
( spl26_512
| ~ spl26_82
| ~ spl26_352
| ~ spl26_511 ),
inference(avatar_split_clause,[],[f14540,f14537,f5723,f986,f14542]) ).
tff(f14542,plain,
( spl26_512
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_512])]) ).
tff(f14537,plain,
( spl26_511
<=> ! [X3: dB,X4: dB,X0: dB,X5: dB,X2: dB,X1: nat] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_511])]) ).
tff(f14540,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X1),X3) = X5 )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) ) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_511 ),
inference(forward_demodulation,[],[f14538,f5776]) ).
tff(f14538,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl26_511 ),
inference(avatar_component_clause,[],[f14537]) ).
tff(f14539,plain,
( spl26_511
| ~ spl26_103
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f2164,f2160,f1130,f14537]) ).
tff(f1130,plain,
( spl26_103
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_103])]) ).
tff(f2164,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB,X5: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) )
| ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X2) = X5 ) )
| ~ spl26_103
| ~ spl26_204 ),
inference(superposition,[],[f1131,f2161]) ).
tff(f1131,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 = X2 ) )
| ~ spl26_103 ),
inference(avatar_component_clause,[],[f1130]) ).
tff(f14535,plain,
( spl26_510
| ~ spl26_119
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1905,f1895,f1246,f14533]) ).
tff(f14533,plain,
( spl26_510
<=> ! [X4: list(dB),X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_510])]) ).
tff(f1246,plain,
( spl26_119
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_119])]) ).
tff(f1905,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,var(X3),X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK15(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,var(X3),X4),X0)),X4,X3,X0))) )
| ~ spl26_119
| ~ spl26_175 ),
inference(resolution,[],[f1896,f1247]) ).
tff(f1247,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl26_119 ),
inference(avatar_component_clause,[],[f1246]) ).
tff(f14531,plain,
( spl26_509
| ~ spl26_139
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1840,f1793,f1380,f14529]) ).
tff(f14529,plain,
( spl26_509
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun(X1,X0),X5: list(X0),X2: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_509])]) ).
tff(f1380,plain,
( spl26_139
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X0)),X4: X0,X3: X1,X2: list(X1)] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_139])]) ).
tff(f1840,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X1)),X3: X1,X4: fun(X1,X0),X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),aa(X1,X0,X4,X3))) = foldl(X1,X0,X2,aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),X2),X4),X3),X5) )
| ~ spl26_139
| ~ spl26_171 ),
inference(superposition,[],[f1381,f1794]) ).
tff(f1381,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl26_139 ),
inference(avatar_component_clause,[],[f1380]) ).
tff(f14527,plain,
( spl26_508
| ~ spl26_131
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1827,f1793,f1327,f14525]) ).
tff(f14525,plain,
( spl26_508
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: fun(X0,list(X0)),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun(X0,list(X0)),fun(X0,X1),aa(fun(X0,fun(list(X0),X1)),fun(fun(X0,list(X0)),fun(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_508])]) ).
tff(f1327,plain,
( spl26_131
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_131])]) ).
tff(f1827,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: fun(X0,list(X0)),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),X4,X3)),X3)) = aa(X0,X1,aa(fun(X0,list(X0)),fun(X0,X1),aa(fun(X0,fun(list(X0),X1)),fun(fun(X0,list(X0)),fun(X0,X1)),combs(X0,list(X0),X1),X2),X4),X3) )
| ~ spl26_131
| ~ spl26_171 ),
inference(superposition,[],[f1794,f1328]) ).
tff(f1328,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl26_131 ),
inference(avatar_component_clause,[],[f1327]) ).
tff(f14523,plain,
( spl26_507
| ~ spl26_20
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1799,f1793,f634,f14521]) ).
tff(f14521,plain,
( spl26_507
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(X0,X1),X0),X2: fun(X0,X1)] : ( aa(fun(X0,X1),X1,aa(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1),aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1)),combs(fun(X0,X1),X0,X1),combi(fun(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_507])]) ).
tff(f634,plain,
( spl26_20
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_20])]) ).
tff(f1799,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(fun(X0,X1),X0)] : ( aa(fun(X0,X1),X1,aa(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1),aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(fun(X0,X1),X0),fun(fun(X0,X1),X1)),combs(fun(X0,X1),X0,X1),combi(fun(X0,X1))),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) )
| ~ spl26_20
| ~ spl26_171 ),
inference(superposition,[],[f1794,f635]) ).
tff(f635,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl26_20 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f14519,plain,
( spl26_506
| ~ spl26_151
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1660,f1656,f1600,f14517]) ).
tff(f14517,plain,
( spl26_506
<=> ! [X5: list(dB),X4: type,X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK14(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_506])]) ).
tff(f1656,plain,
( spl26_158
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_158])]) ).
tff(f1660,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK14(X4,X5,foldl(dB,dB,app,var(X2),X3),X0),X4) = X1 )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X4),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X5))) )
| ~ spl26_151
| ~ spl26_158 ),
inference(resolution,[],[f1657,f1601]) ).
tff(f1657,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl26_158 ),
inference(avatar_component_clause,[],[f1656]) ).
tff(f14515,plain,
( spl26_505
| ~ spl26_149
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1659,f1656,f1580,f14513]) ).
tff(f14513,plain,
( spl26_505
<=> ! [X5: list(dB),X4: type,X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK13(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,[spl26_505])]) ).
tff(f1659,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: type,X5: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( foldr(type,type,fun1,sK13(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))) )
| ~ spl26_149
| ~ spl26_158 ),
inference(resolution,[],[f1657,f1581]) ).
tff(f14511,plain,
( spl26_504
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1444,f1380,f14509]) ).
tff(f14509,plain,
( spl26_504
<=> ! [X1: $tType,X0: $tType,X5: list(X1),X3: X0,X4: X1,X2: fun(X0,fun(X1,X0)),X6: X1] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_504])]) ).
tff(f1444,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,X0)),X3: X0,X6: X1,X4: X1,X5: list(X1)] : ( foldl(X0,X1,X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4)),X6),X5) = foldl(X0,X1,X2,X3,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X5),X6)),X4)) )
| ~ spl26_139 ),
inference(superposition,[],[f1381,f1381]) ).
tff(f14507,plain,
( spl26_503
| ~ spl26_152
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5021,f4969,f1614,f14505]) ).
tff(f14505,plain,
( spl26_503
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,abs(X0)) )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_503])]) ).
tff(f1614,plain,
( spl26_152
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_152])]) ).
tff(f5021,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,abs(X0)) )
| ~ sP1(X0) )
| ~ spl26_152
| ~ spl26_313 ),
inference(resolution,[],[f4970,f1615]) ).
tff(f1615,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl26_152 ),
inference(avatar_component_clause,[],[f1614]) ).
tff(f14503,plain,
( spl26_502
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1437,f1380,f986,f14501]) ).
tff(f14501,plain,
( spl26_502
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun(X2,fun(X0,fun(X1,X0)))] : ( foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),combc(X2,X0,fun(X1,X0),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_502])]) ).
tff(f1437,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,aa(X2,fun(X0,fun(X1,X0)),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),combc(X2,X0,fun(X1,X0),X3,X5),X4),X6),X7) )
| ~ spl26_82
| ~ spl26_139 ),
inference(superposition,[],[f1381,f987]) ).
tff(f14499,plain,
( spl26_501
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1395,f1376,f14497]) ).
tff(f14497,plain,
( spl26_501
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X6: X0,X5: X1,X2: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_501])]) ).
tff(f1395,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,X1)),X3: list(X0),X6: X0,X4: X0,X5: X1] : ( foldr(X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)),X6),X5) = aa(X1,X1,aa(X0,fun(X1,X1),X2,X6),aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),foldr(X0,X1,X2,X3,X5))) )
| ~ spl26_138 ),
inference(superposition,[],[f1377,f1377]) ).
tff(f14495,plain,
( spl26_500
| ~ spl26_82
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1393,f1376,f986,f14493]) ).
tff(f14493,plain,
( spl26_500
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun(X2,fun(X0,fun(X1,X1)))] : ( foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),combc(X2,X0,fun(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_500])]) ).
tff(f1393,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),combc(X2,X0,fun(X1,X1),X3,X5),X4),foldr(X0,X1,aa(X2,fun(X0,fun(X1,X1)),X3,X4),X6,X7)) )
| ~ spl26_82
| ~ spl26_138 ),
inference(superposition,[],[f1377,f987]) ).
tff(f14033,plain,
( spl26_499
| ~ spl26_175
| ~ spl26_190 ),
inference(avatar_split_clause,[],[f2050,f2046,f1895,f14031]) ).
tff(f14031,plain,
( spl26_499
<=> ! [X4: dB,X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(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,[spl26_499])]) ).
tff(f2046,plain,
( spl26_190
<=> ! [X4: fun(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_190])]) ).
tff(f2050,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),sK16(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))) )
| ~ spl26_175
| ~ spl26_190 ),
inference(resolution,[],[f2047,f1896]) ).
tff(f2047,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl26_190 ),
inference(avatar_component_clause,[],[f2046]) ).
tff(f14029,plain,
( spl26_498
| ~ spl26_117
| ~ spl26_168 ),
inference(avatar_split_clause,[],[f1746,f1741,f1235,f14027]) ).
tff(f14027,plain,
( spl26_498
<=> ! [X4: list(type),X0: fun(nat,type),X3: list(dB),X2: type,X1: nat] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_498])]) ).
tff(f1235,plain,
( spl26_117
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_117])]) ).
tff(f1741,plain,
( spl26_168
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_168])]) ).
tff(f1746,plain,
( ! [X2: type,X3: list(dB),X0: fun(nat,type),X1: nat,X4: list(type)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,X0,X1,X2))),fEx(type)),map(dB,dB,combc(dB,nat,dB,lift,X1),X3))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl26_117
| ~ spl26_168 ),
inference(resolution,[],[f1742,f1236]) ).
tff(f1236,plain,
( ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) )
| ~ spl26_117 ),
inference(avatar_component_clause,[],[f1235]) ).
tff(f1742,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X2,X1),X0))
| listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1) )
| ~ spl26_168 ),
inference(avatar_component_clause,[],[f1741]) ).
tff(f14013,plain,
( spl26_497
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1436,f1380,f986,f14011]) ).
tff(f14011,plain,
( spl26_497
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: list(X1),X6: X1,X3: fun(X0,fun(X2,fun(X1,X0)))] : ( foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),aa(X0,fun(X2,fun(X1,X0)),X3,X5),X4),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_497])]) ).
tff(f1436,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,X0))),X6: X1,X7: list(X1),X4: X2,X5: X0] : ( foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),X5,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X7),X6)) = foldl(X0,X1,combc(X0,X2,fun(X1,X0),X3,X4),aa(X1,X0,aa(X2,fun(X1,X0),aa(X0,fun(X2,fun(X1,X0)),X3,X5),X4),X6),X7) )
| ~ spl26_82
| ~ spl26_139 ),
inference(superposition,[],[f1381,f987]) ).
tff(f14009,plain,
( spl26_496
| ~ spl26_82
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1392,f1376,f986,f14007]) ).
tff(f14007,plain,
( spl26_496
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X7: X1,X6: list(X0),X5: X0,X3: fun(X0,fun(X2,fun(X1,X1)))] : ( foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),aa(X0,fun(X2,fun(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_496])]) ).
tff(f1392,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5),X7) = aa(X1,X1,aa(X2,fun(X1,X1),aa(X0,fun(X2,fun(X1,X1)),X3,X5),X4),foldr(X0,X1,combc(X0,X2,fun(X1,X1),X3,X4),X6,X7)) )
| ~ spl26_82
| ~ spl26_138 ),
inference(superposition,[],[f1377,f987]) ).
tff(f14005,plain,
( spl26_495
| ~ spl26_32
| ~ spl26_71 ),
inference(avatar_split_clause,[],[f934,f927,f705,f14003]) ).
tff(f14003,plain,
( spl26_495
<=> ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK3(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK5(foldl(dB,dB,app,var(X0),X1))),sK4(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,[spl26_495])]) ).
tff(f705,plain,
( spl26_32
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_32])]) ).
tff(f927,plain,
( spl26_71
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK3(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_71])]) ).
tff(f934,plain,
( ! [X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = abs(sK3(foldl(dB,dB,app,var(X0),X1))) )
| ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(sK5(foldl(dB,dB,app,var(X0),X1))),sK4(foldl(dB,dB,app,var(X0),X1))) )
| sP0(foldl(dB,dB,app,var(X0),X1))
| ~ listsp(dB,it,X1) )
| ~ spl26_32
| ~ spl26_71 ),
inference(resolution,[],[f928,f706]) ).
tff(f706,plain,
( ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) )
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f705]) ).
tff(f928,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( abs(sK3(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| sP0(X0) )
| ~ spl26_71 ),
inference(avatar_component_clause,[],[f927]) ).
tff(f12809,plain,
( spl26_494
| ~ spl26_114
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1903,f1895,f1216,f12807]) ).
tff(f12807,plain,
( spl26_494
<=> ! [X4: list(dB),X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK13(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_494])]) ).
tff(f1216,plain,
( spl26_114
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_114])]) ).
tff(f1903,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK13(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl26_114
| ~ spl26_175 ),
inference(resolution,[],[f1896,f1217]) ).
tff(f1217,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3))) )
| ~ spl26_114 ),
inference(avatar_component_clause,[],[f1216]) ).
tff(f12804,plain,
( spl26_493
| ~ spl26_116
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1902,f1895,f1228,f12802]) ).
tff(f12802,plain,
( spl26_493
<=> ! [X4: list(dB),X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK14(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_493])]) ).
tff(f1228,plain,
( spl26_116
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_116])]) ).
tff(f1902,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),foldl(dB,dB,app,X3,X4))))
| pp(aa(list(type),bool,typings(X0,X4),sK14(aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,foldl(dB,dB,app,X3,X4),X0)),X4,X3,X0))) )
| ~ spl26_116
| ~ spl26_175 ),
inference(resolution,[],[f1896,f1229]) ).
tff(f1229,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl26_116 ),
inference(avatar_component_clause,[],[f1228]) ).
tff(f12800,plain,
( spl26_492
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1814,f1793,f986,f12798]) ).
tff(f12798,plain,
( spl26_492
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: X0,X7: fun(X0,fun(X1,X6))] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_492])]) ).
tff(f1814,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X7: fun(X0,fun(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),aa(X2,fun(X0,X1),X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,combc(X2,X0,X1,X3,X5),X4)) )
| ~ spl26_82
| ~ spl26_171 ),
inference(superposition,[],[f1794,f987]) ).
tff(f12796,plain,
( spl26_491
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1813,f1793,f986,f12794]) ).
tff(f12794,plain,
( spl26_491
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: X0,X7: fun(X0,fun(X1,X6))] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_491])]) ).
tff(f1813,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X7: fun(X0,fun(X1,X6)),X4: X2,X5: X0] : ( aa(X0,X6,aa(fun(X0,X1),fun(X0,X6),aa(fun(X0,fun(X1,X6)),fun(fun(X0,X1),fun(X0,X6)),combs(X0,X1,X6),X7),combc(X0,X2,X1,X3,X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,aa(X0,fun(X2,X1),X3,X5),X4)) )
| ~ spl26_82
| ~ spl26_171 ),
inference(superposition,[],[f1794,f987]) ).
tff(f12792,plain,
( spl26_490
| ~ spl26_82
| ~ spl26_139
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1667,f1656,f1380,f986,f12790]) ).
tff(f12790,plain,
( spl26_490
<=> ! [X3: fun(nat,type),X4: type,X0: nat,X5: type,X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ( X4 = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_490])]) ).
tff(f1667,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),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 ) )
| ~ spl26_82
| ~ spl26_139
| ~ spl26_158 ),
inference(forward_demodulation,[],[f1666,f987]) ).
tff(f1666,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl26_82
| ~ spl26_139
| ~ spl26_158 ),
inference(forward_demodulation,[],[f1664,f987]) ).
tff(f1664,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: list(dB),X4: type,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ( X4 = X5 ) )
| ~ spl26_139
| ~ spl26_158 ),
inference(superposition,[],[f1657,f1381]) ).
tff(f12788,plain,
( spl26_489
| ~ spl26_82
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1569,f1545,f986,f12786]) ).
tff(f12786,plain,
( spl26_489
<=> ! [X1: $tType,X3: $tType,X0: $tType,X2: $tType,X5: fun(X0,X3),X4: fun(X3,fun(X1,X2)),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X3,fun(X1,X2)),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combb(X3,fun(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),X4,aa(X0,X3,X5,X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_489])]) ).
tff(f1569,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X1,X2)),X5: fun(X0,X3)] : ( aa(X0,X2,combc(X0,X1,X2,aa(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X3,fun(X1,X2)),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combb(X3,fun(X1,X2),X0),X4),X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),X4,aa(X0,X3,X5,X6)),X7) )
| ~ spl26_82
| ~ spl26_147 ),
inference(superposition,[],[f987,f1546]) ).
tff(f12760,plain,
( spl26_488
| ~ spl26_128
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2011,f1998,f1302,f12758]) ).
tff(f12758,plain,
( spl26_488
<=> ! [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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_488])]) ).
tff(f1302,plain,
( spl26_128
<=> 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,[spl26_128])]) ).
tff(f1998,plain,
( spl26_185
<=> ! [X2: dB,X3: fun(nat,type),X4: type,X0: nat,X5: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_185])]) ).
tff(f2011,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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)),i),X0))) )
| ~ spl26_128
| ~ spl26_185 ),
inference(resolution,[],[f1999,f1304]) ).
tff(f1304,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)))
| ~ spl26_128 ),
inference(avatar_component_clause,[],[f1302]) ).
tff(f1999,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) )
| ~ spl26_185 ),
inference(avatar_component_clause,[],[f1998]) ).
tff(f12739,plain,
( spl26_487
| ~ spl26_82
| ~ spl26_352
| ~ spl26_485 ),
inference(avatar_split_clause,[],[f12730,f12727,f5723,f986,f12737]) ).
tff(f12737,plain,
( spl26_487
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_487])]) ).
tff(f12727,plain,
( spl26_485
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_485])]) ).
tff(f12730,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_485 ),
inference(forward_demodulation,[],[f12728,f5776]) ).
tff(f12728,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),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl26_485 ),
inference(avatar_component_clause,[],[f12727]) ).
tff(f12735,plain,
( spl26_486
| ~ spl26_19
| ~ spl26_216 ),
inference(avatar_split_clause,[],[f2808,f2319,f630,f12732]) ).
tff(f12732,plain,
( spl26_486
<=> ( fTrue = aa(fun(dB,bool),bool,fEx(dB),it) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_486])]) ).
tff(f2319,plain,
( spl26_216
<=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_216])]) ).
tff(f2808,plain,
( ( fTrue = aa(fun(dB,bool),bool,fEx(dB),it) )
| ~ spl26_19
| ~ spl26_216 ),
inference(resolution,[],[f2321,f631]) ).
tff(f2321,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl26_216 ),
inference(avatar_component_clause,[],[f2319]) ).
tff(f12729,plain,
( spl26_485
| ~ spl26_130
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2003,f1998,f1319,f12727]) ).
tff(f1319,plain,
( spl26_130
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_130])]) ).
tff(f2003,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),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl26_130
| ~ spl26_185 ),
inference(resolution,[],[f1999,f1321]) ).
tff(f1321,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl26_130 ),
inference(avatar_component_clause,[],[f1319]) ).
tff(f12708,plain,
( spl26_484
| ~ spl26_82
| ~ spl26_352
| ~ spl26_483 ),
inference(avatar_split_clause,[],[f12704,f12701,f5723,f986,f12706]) ).
tff(f12706,plain,
( spl26_484
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_484])]) ).
tff(f12701,plain,
( spl26_483
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_483])]) ).
tff(f12704,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_483 ),
inference(forward_demodulation,[],[f12702,f5776]) ).
tff(f12702,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),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl26_483 ),
inference(avatar_component_clause,[],[f12701]) ).
tff(f12703,plain,
( spl26_483
| ~ spl26_126
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2002,f1998,f1286,f12701]) ).
tff(f2002,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),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,a),var(i))),i),X0))) )
| ~ spl26_126
| ~ spl26_185 ),
inference(resolution,[],[f1999,f1288]) ).
tff(f12699,plain,
( spl26_482
| ~ spl26_138
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1513,f1498,f1376,f12697]) ).
tff(f12697,plain,
( spl26_482
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK24(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_482])]) ).
tff(f1498,plain,
( spl26_142
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK24(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_142])]) ).
tff(f1513,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK24(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) ) )
| ~ spl26_138
| ~ spl26_142 ),
inference(superposition,[],[f1499,f1377]) ).
tff(f1499,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( map(X1,X0,X3,sK24(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl26_142 ),
inference(avatar_component_clause,[],[f1498]) ).
tff(f12695,plain,
( spl26_481
| ~ spl26_138
| ~ spl26_141 ),
inference(avatar_split_clause,[],[f1509,f1494,f1376,f12693]) ).
tff(f12693,plain,
( spl26_481
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK22(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_481])]) ).
tff(f1494,plain,
( spl26_141
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_141])]) ).
tff(f1509,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = map(X4,X0,X5,sK22(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) ) )
| ~ spl26_138
| ~ spl26_141 ),
inference(superposition,[],[f1495,f1377]) ).
tff(f1495,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( map(X0,X1,X5,sK22(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl26_141 ),
inference(avatar_component_clause,[],[f1494]) ).
tff(f12529,plain,
( spl26_480
| ~ spl26_117
| ~ spl26_176 ),
inference(avatar_split_clause,[],[f1916,f1911,f1235,f12527]) ).
tff(f12527,plain,
( spl26_480
<=> ! [X5: type,X4: list(type),X0: fun(nat,type),X3: list(dB),X2: nat,X1: dB] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_480])]) ).
tff(f1911,plain,
( spl26_176
<=> ! [X2: nat,X4: dB,X0: list(type),X5: fun(nat,type),X3: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_176])]) ).
tff(f1916,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: dB,X4: list(type),X5: type] :
( pp(aa(list(type),bool,typings(X0,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X2),map(dB,dB,combc(dB,nat,dB,lift,X2),X3))),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X5),X1))
| ~ pp(aa(list(type),bool,typings(X0,X3),X4)) )
| ~ spl26_117
| ~ spl26_176 ),
inference(resolution,[],[f1912,f1236]) ).
tff(f1912,plain,
( ! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4)) )
| ~ spl26_176 ),
inference(avatar_component_clause,[],[f1911]) ).
tff(f12525,plain,
( spl26_479
| ~ spl26_78
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1874,f1793,f986,f964,f12523]) ).
tff(f12523,plain,
( spl26_479
<=> ! [X2: $tType,X0: dB,X3: fun(nat,fun(dB,X2)),X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_479])]) ).
tff(f964,plain,
( spl26_78
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_78])]) ).
tff(f1874,plain,
( ! [X2: $tType,X3: fun(nat,fun(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(nat,X2,combc(nat,dB,X2,X3,X0),X1) )
| ~ spl26_78
| ~ spl26_82
| ~ spl26_171 ),
inference(forward_demodulation,[],[f1820,f987]) ).
tff(f1820,plain,
( ! [X2: $tType,X3: fun(nat,fun(dB,X2)),X0: dB,X1: nat] : ( aa(nat,X2,aa(fun(nat,dB),fun(nat,X2),aa(fun(nat,fun(dB,X2)),fun(fun(nat,dB),fun(nat,X2)),combs(nat,dB,X2),X3),aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1))),X1) = aa(dB,X2,aa(nat,fun(dB,X2),X3,X1),X0) )
| ~ spl26_78
| ~ spl26_171 ),
inference(superposition,[],[f1794,f965]) ).
tff(f965,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl26_78 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f12521,plain,
( spl26_478
| ~ spl26_19
| ~ spl26_26 ),
inference(avatar_split_clause,[],[f1422,f670,f630,f12519]) ).
tff(f12519,plain,
( spl26_478
<=> ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,sK7(X0)) )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_478])]) ).
tff(f670,plain,
( spl26_26
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_26])]) ).
tff(f1422,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,sK7(X0)) )
| ~ sP0(X0) )
| ~ spl26_19
| ~ spl26_26 ),
inference(resolution,[],[f631,f671]) ).
tff(f671,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) )
| ~ spl26_26 ),
inference(avatar_component_clause,[],[f670]) ).
tff(f12348,plain,
( spl26_477
| ~ spl26_82
| ~ spl26_352
| ~ spl26_476 ),
inference(avatar_split_clause,[],[f12344,f12341,f5723,f986,f12346]) ).
tff(f12346,plain,
( spl26_477
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_477])]) ).
tff(f12341,plain,
( spl26_476
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_476])]) ).
tff(f12344,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_476 ),
inference(forward_demodulation,[],[f12342,f5776]) ).
tff(f12342,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl26_476 ),
inference(avatar_component_clause,[],[f12341]) ).
tff(f12343,plain,
( spl26_476
| ~ spl26_18
| ~ spl26_188 ),
inference(avatar_split_clause,[],[f2030,f2026,f626,f12341]) ).
tff(f626,plain,
( spl26_18
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_18])]) ).
tff(f2026,plain,
( spl26_188
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_188])]) ).
tff(f2030,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2)))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl26_18
| ~ spl26_188 ),
inference(resolution,[],[f2027,f627]) ).
tff(f627,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f2027,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_188 ),
inference(avatar_component_clause,[],[f2026]) ).
tff(f12339,plain,
( spl26_475
| ~ spl26_82
| ~ spl26_182 ),
inference(avatar_split_clause,[],[f1992,f1961,f986,f12337]) ).
tff(f12337,plain,
( spl26_475
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK23(X0,X3,X5,X4,X2,X1)),sK24(X0,X3,X5,X4,X2,X1)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_475])]) ).
tff(f1961,plain,
( spl26_182
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_182])]) ).
tff(f1992,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK23(X0,X3,X5,X4,X2,X1)),sK24(X0,X3,X5,X4,X2,X1)) = X5 ) )
| ~ spl26_82
| ~ spl26_182 ),
inference(superposition,[],[f1962,f987]) ).
tff(f1962,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl26_182 ),
inference(avatar_component_clause,[],[f1961]) ).
tff(f12335,plain,
( spl26_474
| ~ spl26_82
| ~ spl26_181 ),
inference(avatar_split_clause,[],[f1984,f1957,f986,f12333]) ).
tff(f12333,plain,
( spl26_474
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK21(X3,X0,X2,X1,X5,X4)),sK22(X3,X0,X2,X1,X5,X4)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_474])]) ).
tff(f1957,plain,
( spl26_181
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_181])]) ).
tff(f1984,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(list(X3),list(X3),aa(X3,fun(list(X3),list(X3)),cons(X3),sK21(X3,X0,X2,X1,X5,X4)),sK22(X3,X0,X2,X1,X5,X4)) = X5 ) )
| ~ spl26_82
| ~ spl26_181 ),
inference(superposition,[],[f1958,f987]) ).
tff(f1958,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl26_181 ),
inference(avatar_component_clause,[],[f1957]) ).
tff(f12331,plain,
( spl26_473
| ~ spl26_65
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1866,f1793,f893,f12329]) ).
tff(f12329,plain,
( spl26_473
<=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,aa(fun(X0,nat),fun(X0,type),aa(fun(X0,fun(nat,type)),fun(fun(X0,nat),fun(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_473])]) ).
tff(f893,plain,
( spl26_65
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_65])]) ).
tff(f1866,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,aa(fun(X0,nat),fun(X0,type),aa(fun(X0,fun(nat,type)),fun(fun(X0,nat),fun(X0,type)),combs(X0,nat,type),X1),X3),X2)),var(aa(X0,nat,X3,X2))))
| ~ spl26_65
| ~ spl26_171 ),
inference(superposition,[],[f894,f1794]) ).
tff(f894,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl26_65 ),
inference(avatar_component_clause,[],[f893]) ).
tff(f11813,plain,
( spl26_472
| ~ spl26_162
| ~ spl26_190 ),
inference(avatar_split_clause,[],[f2049,f2046,f1691,f11811]) ).
tff(f11811,plain,
( spl26_472
<=> ! [X4: dB,X0: fun(nat,type),X3: type,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_472])]) ).
tff(f1691,plain,
( spl26_162
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_162])]) ).
tff(f2049,plain,
( ! [X2: dB,X3: type,X0: fun(nat,type),X1: type,X4: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X3),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X3),X4)) )
| ~ spl26_162
| ~ spl26_190 ),
inference(resolution,[],[f2047,f1692]) ).
tff(f1692,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1)) )
| ~ spl26_162 ),
inference(avatar_component_clause,[],[f1691]) ).
tff(f11809,plain,
( spl26_471
| ~ spl26_65
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1876,f1793,f986,f893,f11807]) ).
tff(f11807,plain,
( spl26_471
<=> ! [X0: $tType,X3: nat,X2: fun(nat,X0),X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_471])]) ).
tff(f1876,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(nat,type,combc(nat,X0,type,X1,aa(nat,X0,X2,X3)),X3)),var(X3)))
| ~ spl26_65
| ~ spl26_82
| ~ spl26_171 ),
inference(forward_demodulation,[],[f1832,f987]) ).
tff(f1832,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(nat,fun(X0,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(nat,fun(X0,type)),fun(fun(nat,X0),fun(nat,type)),combs(nat,X0,type),X1),X2)),aa(X0,type,aa(nat,fun(X0,type),X1,X3),aa(nat,X0,X2,X3))),var(X3)))
| ~ spl26_65
| ~ spl26_171 ),
inference(superposition,[],[f894,f1794]) ).
tff(f11805,plain,
( spl26_470
| ~ spl26_4
| ~ spl26_217
| ~ spl26_407 ),
inference(avatar_split_clause,[],[f11526,f8245,f2815,f559,f11803]) ).
tff(f11803,plain,
( spl26_470
<=> ! [X0: nat] : sP1(abs(abs(abs(var(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_470])]) ).
tff(f2815,plain,
( spl26_217
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_217])]) ).
tff(f8245,plain,
( spl26_407
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_407])]) ).
tff(f11526,plain,
( ! [X0: nat] :
( ~ pp(fTrue)
| sP1(abs(abs(abs(var(X0))))) )
| ~ spl26_217
| ~ spl26_407 ),
inference(superposition,[],[f2816,f8246]) ).
tff(f8246,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl26_407 ),
inference(avatar_component_clause,[],[f8245]) ).
tff(f2816,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl26_217 ),
inference(avatar_component_clause,[],[f2815]) ).
tff(f11801,plain,
( spl26_469
| ~ spl26_142
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1779,f1754,f1498,f11799]) ).
tff(f11799,plain,
( spl26_469
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK24(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_469])]) ).
tff(f1779,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK24(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl26_142
| ~ spl26_170 ),
inference(superposition,[],[f1499,f1755]) ).
tff(f11797,plain,
( spl26_468
| ~ spl26_141
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1778,f1754,f1494,f11795]) ).
tff(f11795,plain,
( spl26_468
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK22(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_468])]) ).
tff(f1778,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( map(X1,X0,X2,X4) = map(X5,X0,X6,sK22(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl26_141
| ~ spl26_170 ),
inference(superposition,[],[f1495,f1755]) ).
tff(f11793,plain,
( spl26_467
| ~ spl26_119
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1609,f1600,f1246,f11791]) ).
tff(f11791,plain,
( spl26_467
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_467])]) ).
tff(f1609,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl26_119
| ~ spl26_151 ),
inference(resolution,[],[f1601,f1247]) ).
tff(f11789,plain,
( spl26_466
| ~ spl26_119
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1589,f1580,f1246,f11787]) ).
tff(f11787,plain,
( spl26_466
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_466])]) ).
tff(f1589,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,var(X2),X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK15(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,var(X2),X3),X0),X1),X3,X2,X0))) )
| ~ spl26_119
| ~ spl26_149 ),
inference(resolution,[],[f1581,f1247]) ).
tff(f11785,plain,
( spl26_465
| ~ spl26_105
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1331,f1327,f1151,f11783]) ).
tff(f11783,plain,
( spl26_465
<=> ! [X0: $tType,X3: type,X4: fun(nat,fun(list(type),X0)),X6: X0,X5: list(type),X2: type,X1: fun(type,fun(type,fun(list(type),X0)))] : ( list_case(X0,type,X6,aa(type,fun(type,fun(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(fun(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_465])]) ).
tff(f1331,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,fun(list(type),X0))),X6: X0,X4: fun(nat,fun(list(type),X0)),X5: list(type)] : ( list_case(X0,type,X6,aa(type,fun(type,fun(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(fun(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5) )
| ~ spl26_105
| ~ spl26_131 ),
inference(superposition,[],[f1328,f1152]) ).
tff(f11781,plain,
( spl26_464
| ~ spl26_95
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1161,f1151,f1083,f11779]) ).
tff(f11779,plain,
( spl26_464
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,X0),X2: type,X1: fun(type,fun(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,sK17(X0,type,aa(type,fun(type,X0),X1,X2),X3)),X2)) != aa(type,X0,X3,sK17(X0,type,aa(type,fun(type,X0),X1,X2),X3)) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_464])]) ).
tff(f1083,plain,
( spl26_95
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_95])]) ).
tff(f1161,plain,
( ! [X0: $tType,X2: type,X3: fun(type,X0),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,sK17(X0,type,aa(type,fun(type,X0),X1,X2),X3)),X2)) != aa(type,X0,X3,sK17(X0,type,aa(type,fun(type,X0),X1,X2),X3)) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) )
| ~ spl26_95
| ~ spl26_105 ),
inference(superposition,[],[f1084,f1152]) ).
tff(f1084,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl26_95 ),
inference(avatar_component_clause,[],[f1083]) ).
tff(f11777,plain,
( spl26_463
| ~ spl26_95
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1160,f1151,f1083,f11775]) ).
tff(f11775,plain,
( spl26_463
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,X0),X2: type,X1: fun(type,fun(type,X0))] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,sK17(X0,type,X3,aa(type,fun(type,X0),X1,X2))),X2)) != aa(type,X0,X3,sK17(X0,type,X3,aa(type,fun(type,X0),X1,X2))) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_463])]) ).
tff(f1160,plain,
( ! [X0: $tType,X2: type,X3: fun(type,X0),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] :
( ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,sK17(X0,type,X3,aa(type,fun(type,X0),X1,X2))),X2)) != aa(type,X0,X3,sK17(X0,type,X3,aa(type,fun(type,X0),X1,X2))) )
| ( aa(type,fun(type,X0),X1,X2) = X3 ) )
| ~ spl26_95
| ~ spl26_105 ),
inference(superposition,[],[f1084,f1152]) ).
tff(f11060,plain,
( spl26_462
| ~ spl26_82
| ~ spl26_352
| ~ spl26_461 ),
inference(avatar_split_clause,[],[f11056,f11053,f5723,f986,f11058]) ).
tff(f11058,plain,
( spl26_462
<=> ! [X4: nat,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_462])]) ).
tff(f11053,plain,
( spl26_461
<=> ! [X4: nat,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_461])]) ).
tff(f11056,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X2),X3),var(X4))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_461 ),
inference(forward_demodulation,[],[f11054,f5776]) ).
tff(f11054,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl26_461 ),
inference(avatar_component_clause,[],[f11053]) ).
tff(f11055,plain,
( spl26_461
| ~ spl26_65
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2007,f1998,f893,f11053]) ).
tff(f2007,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(nat,type,shift(type,X0,X3,X1),X4)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,var(X4)),X3),X2))) )
| ~ spl26_65
| ~ spl26_185 ),
inference(resolution,[],[f1999,f894]) ).
tff(f11051,plain,
( spl26_460
| ~ spl26_27
| ~ spl26_82
| ~ spl26_182 ),
inference(avatar_split_clause,[],[f1996,f1961,f986,f674,f11049]) ).
tff(f11049,plain,
( spl26_460
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK23(X0,X0,X1,combi(X0),X3,X2)),sK24(X0,X0,X1,combi(X0),X3,X2)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_460])]) ).
tff(f674,plain,
( spl26_27
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_27])]) ).
tff(f1996,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK23(X0,X0,X1,combi(X0),X3,X2)),sK24(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl26_27
| ~ spl26_82
| ~ spl26_182 ),
inference(forward_demodulation,[],[f1994,f987]) ).
tff(f1994,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK23(X0,X0,X1,combi(X0),X3,X2)),sK24(X0,X0,X1,combi(X0),X3,X2)) = X1 ) )
| ~ spl26_27
| ~ spl26_182 ),
inference(superposition,[],[f1962,f675]) ).
tff(f675,plain,
( ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 )
| ~ spl26_27 ),
inference(avatar_component_clause,[],[f674]) ).
tff(f11047,plain,
( spl26_459
| ~ spl26_27
| ~ spl26_82
| ~ spl26_181 ),
inference(avatar_split_clause,[],[f1988,f1957,f986,f674,f11045]) ).
tff(f11045,plain,
( spl26_459
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X3,X2,X1,combi(X0))),sK22(X0,X0,X3,X2,X1,combi(X0))) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_459])]) ).
tff(f1988,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X3,X2,X1,combi(X0))),sK22(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl26_27
| ~ spl26_82
| ~ spl26_181 ),
inference(forward_demodulation,[],[f1986,f987]) ).
tff(f1986,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X0,X3,X2,X1,combi(X0))),sK22(X0,X0,X3,X2,X1,combi(X0))) = X1 ) )
| ~ spl26_27
| ~ spl26_181 ),
inference(superposition,[],[f1958,f675]) ).
tff(f11041,plain,
( spl26_458
| ~ spl26_51
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1831,f1793,f804,f11039]) ).
tff(f11039,plain,
( spl26_458
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X4: X0,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_458])]) ).
tff(f804,plain,
( spl26_51
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_51])]) ).
tff(f1831,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3))) )
| ~ spl26_51
| ~ spl26_171 ),
inference(superposition,[],[f805,f1794]) ).
tff(f805,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl26_51 ),
inference(avatar_component_clause,[],[f804]) ).
tff(f11037,plain,
( spl26_457
| ~ spl26_137
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1775,f1754,f1372,f11035]) ).
tff(f11035,plain,
( spl26_457
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK23(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_457])]) ).
tff(f1372,plain,
( spl26_137
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK23(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_137])]) ).
tff(f1775,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK23(X0,X5,X7,X6,map(X1,X0,X2,X4),aa(X1,X0,X2,X3))) ) )
| ~ spl26_137
| ~ spl26_170 ),
inference(superposition,[],[f1373,f1755]) ).
tff(f1373,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl26_137 ),
inference(avatar_component_clause,[],[f1372]) ).
tff(f11033,plain,
( spl26_456
| ~ spl26_136
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1774,f1754,f1368,f11031]) ).
tff(f11031,plain,
( spl26_456
<=> ! [X0: $tType,X1: $tType,X5: $tType,X4: list(X1),X2: fun(X1,X0),X6: fun(X5,X0),X3: X1,X7: list(X5)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK21(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_456])]) ).
tff(f1368,plain,
( spl26_136
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK21(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_136])]) ).
tff(f1774,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: fun(X5,X0),X7: list(X5),X4: list(X1)] :
( ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) != map(X5,X0,X6,X7) )
| ( aa(X1,X0,X2,X3) = aa(X5,X0,X6,sK21(X5,X0,map(X1,X0,X2,X4),aa(X1,X0,X2,X3),X7,X6)) ) )
| ~ spl26_136
| ~ spl26_170 ),
inference(superposition,[],[f1369,f1755]) ).
tff(f1369,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(X0,X1,X5,sK21(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl26_136 ),
inference(avatar_component_clause,[],[f1368]) ).
tff(f11029,plain,
( spl26_455
| ~ spl26_138
| ~ spl26_146 ),
inference(avatar_split_clause,[],[f1549,f1541,f1376,f11027]) ).
tff(f11027,plain,
( spl26_455
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_455])]) ).
tff(f1541,plain,
( spl26_146
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_146])]) ).
tff(f1549,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( foldr(X0,list(X0),cons(X0),X2,X3) = X5 ) )
| ~ spl26_138
| ~ spl26_146 ),
inference(superposition,[],[f1542,f1377]) ).
tff(f1542,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 = X3 ) )
| ~ spl26_146 ),
inference(avatar_component_clause,[],[f1541]) ).
tff(f11025,plain,
( spl26_454
| ~ spl26_82
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1333,f1327,f986,f11023]) ).
tff(f11023,plain,
( spl26_454
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun(X2,fun(X0,fun(list(X0),X1)))] : ( list_case(X1,X0,X7,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_454])]) ).
tff(f1333,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,fun(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X6) )
| ~ spl26_82
| ~ spl26_131 ),
inference(superposition,[],[f1328,f987]) ).
tff(f11021,plain,
( spl26_453
| ~ spl26_82
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1332,f1327,f986,f11019]) ).
tff(f11019,plain,
( spl26_453
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: X2,X7: X1,X6: list(X0),X3: fun(X0,fun(X2,fun(list(X0),X1)))] : ( list_case(X1,X0,X7,combc(X0,X2,fun(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_453])]) ).
tff(f1332,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(list(X0),X1))),X6: list(X0),X7: X1,X4: X2,X5: X0] : ( list_case(X1,X0,X7,combc(X0,X2,fun(list(X0),X1),X3,X4),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X6),X5)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X6) )
| ~ spl26_82
| ~ spl26_131 ),
inference(superposition,[],[f1328,f987]) ).
tff(f10690,plain,
( spl26_452
| ~ spl26_4
| ~ spl26_217
| ~ spl26_402 ),
inference(avatar_split_clause,[],[f9935,f7739,f2815,f559,f10687]) ).
tff(f10687,plain,
( spl26_452
<=> sP1(abs(abs(abs(abs(ua))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_452])]) ).
tff(f7739,plain,
( spl26_402
<=> ( fTrue = aa(dB,bool,it,abs(abs(ua))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_402])]) ).
tff(f9935,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(ua)))))
| ~ spl26_217
| ~ spl26_402 ),
inference(superposition,[],[f2816,f7741]) ).
tff(f7741,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl26_402 ),
inference(avatar_component_clause,[],[f7739]) ).
tff(f9930,plain,
( spl26_451
| ~ spl26_107
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1898,f1895,f1172,f9928]) ).
tff(f9928,plain,
( spl26_451
<=> ! [X4: dB,X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,X3,X0))),X4))
| ~ beta(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_451])]) ).
tff(f1172,plain,
( spl26_107
<=> ! [X0: dB,X3: fun(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,[spl26_107])]) ).
tff(f1898,plain,
( ! [X2: dB,X3: dB,X0: fun(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,fun1,X1),sK16(X1,X2,X3,X0))),X4))
| ~ beta(X3,X4) )
| ~ spl26_107
| ~ spl26_175 ),
inference(resolution,[],[f1896,f1173]) ).
tff(f1173,plain,
( ! [X2: dB,X3: fun(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) )
| ~ spl26_107 ),
inference(avatar_component_clause,[],[f1172]) ).
tff(f9926,plain,
( spl26_450
| ~ spl26_101
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1861,f1793,f1122,f9924]) ).
tff(f9924,plain,
( spl26_450
<=> ! [X0: type,X3: type,X2: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_450])]) ).
tff(f1122,plain,
( spl26_101
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_101])]) ).
tff(f1861,plain,
( ! [X2: type,X3: type,X0: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( aa(type,type,X1,X0) = X3 ) )
| ~ spl26_101
| ~ spl26_171 ),
inference(superposition,[],[f1123,f1794]) ).
tff(f1123,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) )
| ( X0 = X2 ) )
| ~ spl26_101 ),
inference(avatar_component_clause,[],[f1122]) ).
tff(f9922,plain,
( spl26_449
| ~ spl26_103
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1845,f1793,f1130,f9920]) ).
tff(f9920,plain,
( spl26_449
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_449])]) ).
tff(f1845,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( aa(dB,dB,X1,X0) = X3 ) )
| ~ spl26_103
| ~ spl26_171 ),
inference(superposition,[],[f1131,f1794]) ).
tff(f9918,plain,
( spl26_448
| ~ spl26_13
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1828,f1793,f599,f9916]) ).
tff(f9916,plain,
( spl26_448
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: fun(X1,fun(X0,bool))] :
( ( fFalse = aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_448])]) ).
tff(f599,plain,
( spl26_13
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_13])]) ).
tff(f1828,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: fun(X1,X0)] :
( ( fFalse = aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),aa(X1,X0,X4,X3)) ) )
| ~ spl26_13
| ~ spl26_171 ),
inference(superposition,[],[f1794,f600]) ).
tff(f600,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl26_13 ),
inference(avatar_component_clause,[],[f599]) ).
tff(f9914,plain,
( spl26_447
| ~ spl26_105
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1823,f1793,f1151,f9912]) ).
tff(f9912,plain,
( spl26_447
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,type),X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,aa(type,type,X3,X2)),X2)) = aa(type,X0,aa(fun(type,type),fun(type,X0),aa(fun(type,fun(type,X0)),fun(fun(type,type),fun(type,X0)),combs(type,type,X0),X1),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_447])]) ).
tff(f1823,plain,
( ! [X0: $tType,X2: type,X3: fun(type,type),X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,aa(type,type,X3,X2)),X2)) = aa(type,X0,aa(fun(type,type),fun(type,X0),aa(fun(type,fun(type,X0)),fun(fun(type,type),fun(type,X0)),combs(type,type,X0),X1),X3),X2) )
| ~ spl26_105
| ~ spl26_171 ),
inference(superposition,[],[f1794,f1152]) ).
tff(f9910,plain,
( spl26_446
| ~ spl26_13
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1819,f1793,f599,f9908]) ).
tff(f9908,plain,
( spl26_446
<=> ! [X3: $tType,X0: $tType,X4: fun(X0,fun(bool,X3)),X2: X0,X1: fun(X0,bool)] :
( ( aa(X0,X3,aa(fun(X0,bool),fun(X0,X3),aa(fun(X0,fun(bool,X3)),fun(fun(X0,bool),fun(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_446])]) ).
tff(f1819,plain,
( ! [X0: $tType,X3: $tType,X2: X0,X1: fun(X0,bool),X4: fun(X0,fun(bool,X3))] :
( ( aa(X0,X3,aa(fun(X0,bool),fun(X0,X3),aa(fun(X0,fun(bool,X3)),fun(fun(X0,bool),fun(X0,X3)),combs(X0,bool,X3),X4),X1),X2) = aa(bool,X3,aa(X0,fun(bool,X3),X4,X2),fFalse) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl26_13
| ~ spl26_171 ),
inference(superposition,[],[f1794,f600]) ).
tff(f9906,plain,
( spl26_445
| ~ spl26_13
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1798,f1793,f599,f9904]) ).
tff(f9904,plain,
( spl26_445
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X4: X0,X3: fun(X0,X1)] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_445])]) ).
tff(f1798,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(fun(X0,X1),fun(X0,bool)),combs(X0,X1,bool),X2),X3),X4) ) )
| ~ spl26_13
| ~ spl26_171 ),
inference(superposition,[],[f1794,f600]) ).
tff(f9902,plain,
( spl26_444
| ~ spl26_164
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1730,f1722,f1707,f9900]) ).
tff(f9900,plain,
( spl26_444
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(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,[spl26_444])]) ).
tff(f1707,plain,
( spl26_164
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_164])]) ).
tff(f1730,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK15(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X4))) )
| ~ spl26_164
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1708]) ).
tff(f1708,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(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))) )
| ~ spl26_164 ),
inference(avatar_component_clause,[],[f1707]) ).
tff(f9898,plain,
( spl26_443
| ~ spl26_114
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1608,f1600,f1216,f9896]) ).
tff(f9896,plain,
( spl26_443
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK13(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_443])]) ).
tff(f1608,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK13(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl26_114
| ~ spl26_151 ),
inference(resolution,[],[f1601,f1217]) ).
tff(f9894,plain,
( spl26_442
| ~ spl26_116
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1607,f1600,f1228,f9892]) ).
tff(f9892,plain,
( spl26_442
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_442])]) ).
tff(f1607,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK14(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl26_116
| ~ spl26_151 ),
inference(resolution,[],[f1601,f1229]) ).
tff(f9888,plain,
( spl26_441
| ~ spl26_114
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1588,f1580,f1216,f9886]) ).
tff(f9886,plain,
( spl26_441
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK13(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_441])]) ).
tff(f1588,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK13(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl26_114
| ~ spl26_149 ),
inference(resolution,[],[f1581,f1217]) ).
tff(f9884,plain,
( spl26_440
| ~ spl26_116
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1587,f1580,f1228,f9882]) ).
tff(f9882,plain,
( spl26_440
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_440])]) ).
tff(f1587,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,foldl(dB,dB,app,X2,X3),X4)))
| pp(aa(list(type),bool,typings(X0,X3),sK14(foldr(type,type,fun1,sK13(X1,X4,foldl(dB,dB,app,X2,X3),X0),X1),X3,X2,X0))) )
| ~ spl26_116
| ~ spl26_149 ),
inference(resolution,[],[f1581,f1229]) ).
tff(f9880,plain,
( spl26_439
| ~ spl26_109
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1443,f1380,f1188,f9878]) ).
tff(f9878,plain,
( spl26_439
<=> ! [X0: dB,X3: list(nat),X2: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_439])]) ).
tff(f1188,plain,
( spl26_109
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_109])]) ).
tff(f1443,plain,
( ! [X2: dB,X3: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X3),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X2,X3) )
| ~ spl26_109
| ~ spl26_139 ),
inference(superposition,[],[f1381,f1189]) ).
tff(f1189,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl26_109 ),
inference(avatar_component_clause,[],[f1188]) ).
tff(f9876,plain,
( spl26_438
| ~ spl26_138
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1439,f1380,f1376,f9874]) ).
tff(f9874,plain,
( spl26_438
<=> ! [X0: $tType,X3: list(X0),X4: X0,X5: list(X0),X2: X0,X1: fun(X0,fun(X0,X0))] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_438])]) ).
tff(f1439,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(X0,X0)),X4: X0,X5: list(X0)] : ( foldl(X0,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),foldr(X0,X0,X1,X3,X4))) = foldl(X0,X0,X1,foldr(X0,X0,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4),X5) )
| ~ spl26_138
| ~ spl26_139 ),
inference(superposition,[],[f1381,f1377]) ).
tff(f9733,plain,
( spl26_437
| ~ spl26_4
| ~ spl26_217
| ~ spl26_396 ),
inference(avatar_split_clause,[],[f9526,f7511,f2815,f559,f9730]) ).
tff(f9730,plain,
( spl26_437
<=> sP1(abs(abs(abs(abs(u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_437])]) ).
tff(f7511,plain,
( spl26_396
<=> ( fTrue = aa(dB,bool,it,abs(abs(u))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_396])]) ).
tff(f9526,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(u)))))
| ~ spl26_217
| ~ spl26_396 ),
inference(superposition,[],[f2816,f7513]) ).
tff(f7513,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl26_396 ),
inference(avatar_component_clause,[],[f7511]) ).
tff(f9728,plain,
( spl26_436
| ~ spl26_82
| ~ spl26_352
| ~ spl26_435 ),
inference(avatar_split_clause,[],[f9724,f9721,f5723,f986,f9726]) ).
tff(f9726,plain,
( spl26_436
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_436])]) ).
tff(f9721,plain,
( spl26_435
<=> ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_435])]) ).
tff(f9724,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),zero_zero(nat)),X1),X2))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_435 ),
inference(forward_demodulation,[],[f9722,f5776]) ).
tff(f9722,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl26_435 ),
inference(avatar_component_clause,[],[f9721]) ).
tff(f9723,plain,
( spl26_435
| ~ spl26_18
| ~ spl26_184 ),
inference(avatar_split_clause,[],[f1975,f1971,f626,f9721]) ).
tff(f1971,plain,
( spl26_184
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_184])]) ).
tff(f1975,plain,
( ! [X2: list(dB),X0: dB,X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),X2))
| ~ pp(aa(dB,bool,it,X0))
| ~ sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0),X2)) )
| ~ spl26_18
| ~ spl26_184 ),
inference(resolution,[],[f1972,f627]) ).
tff(f1972,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_184 ),
inference(avatar_component_clause,[],[f1971]) ).
tff(f9719,plain,
( spl26_434
| ~ spl26_82
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1944,f1940,f986,f9717]) ).
tff(f9717,plain,
( spl26_434
<=> ! [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,[spl26_434])]) ).
tff(f1940,plain,
( spl26_180
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_180])]) ).
tff(f1944,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)) )
| ~ spl26_82
| ~ spl26_180 ),
inference(superposition,[],[f1941,f987]) ).
tff(f1941,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl26_180 ),
inference(avatar_component_clause,[],[f1940]) ).
tff(f9715,plain,
( spl26_433
| ~ spl26_67
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1852,f1793,f907,f9713]) ).
tff(f9713,plain,
( spl26_433
<=> ! [X0: $tType,X2: fun(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_433])]) ).
tff(f907,plain,
( spl26_67
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_67])]) ).
tff(f1852,plain,
( ! [X0: $tType,X2: fun(X0,list(X0)),X1: X0] : ( aa(X0,list(X0),X2,X1) != aa(X0,list(X0),aa(fun(X0,list(X0)),fun(X0,list(X0)),aa(fun(X0,fun(list(X0),list(X0))),fun(fun(X0,list(X0)),fun(X0,list(X0))),combs(X0,list(X0),list(X0)),cons(X0)),X2),X1) )
| ~ spl26_67
| ~ spl26_171 ),
inference(superposition,[],[f908,f1794]) ).
tff(f908,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 )
| ~ spl26_67 ),
inference(avatar_component_clause,[],[f907]) ).
tff(f9711,plain,
( spl26_432
| ~ spl26_29
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1759,f1754,f691,f9709]) ).
tff(f9709,plain,
( spl26_432
<=> ! [X0: $tType,X4: list(nat),X3: X0,X2: nat,X1: fun(nat,X0)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_432])]) ).
tff(f691,plain,
( spl26_29
<=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_29])]) ).
tff(f1759,plain,
( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X4: list(nat)] : ( map(nat,X0,shift(X0,X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),map(nat,X0,shift(X0,X1,X2,X3),X4)) )
| ~ spl26_29
| ~ spl26_170 ),
inference(superposition,[],[f1755,f692]) ).
tff(f692,plain,
( ! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 )
| ~ spl26_29 ),
inference(avatar_component_clause,[],[f691]) ).
tff(f9707,plain,
( spl26_431
| ~ spl26_136
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1403,f1376,f1368,f9705]) ).
tff(f9705,plain,
( spl26_431
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK21(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_431])]) ).
tff(f1403,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK21(X4,X0,foldr(X0,list(X0),cons(X0),X2,X3),X1,X6,X5)) = X1 ) )
| ~ spl26_136
| ~ spl26_138 ),
inference(superposition,[],[f1369,f1377]) ).
tff(f9703,plain,
( spl26_430
| ~ spl26_137
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1402,f1376,f1372,f9701]) ).
tff(f9701,plain,
( spl26_430
<=> ! [X0: $tType,X4: $tType,X5: fun(X4,X0),X6: list(X4),X3: list(X0),X2: list(X0),X1: X0] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK23(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_430])]) ).
tff(f1402,plain,
( ! [X4: $tType,X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X6: list(X4),X5: fun(X4,X0)] :
( ( map(X4,X0,X5,X6) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( aa(X4,X0,X5,sK23(X0,X4,X6,X5,foldr(X0,list(X0),cons(X0),X2,X3),X1)) = X1 ) )
| ~ spl26_137
| ~ spl26_138 ),
inference(superposition,[],[f1373,f1377]) ).
tff(f9111,plain,
( spl26_429
| ~ spl26_82
| ~ spl26_352
| ~ spl26_428 ),
inference(avatar_split_clause,[],[f9107,f9104,f5723,f986,f9109]) ).
tff(f9109,plain,
( spl26_429
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_429])]) ).
tff(f9104,plain,
( spl26_428
<=> ! [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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_428])]) ).
tff(f9107,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t_a),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),ia),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_428 ),
inference(forward_demodulation,[],[f9105,f5776]) ).
tff(f9105,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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl26_428 ),
inference(avatar_component_clause,[],[f9104]) ).
tff(f9106,plain,
( spl26_428
| ~ spl26_90
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2012,f1998,f1053,f9104]) ).
tff(f1053,plain,
( spl26_90
<=> 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,[spl26_90])]) ).
tff(f2012,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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),ia),X0))) )
| ~ spl26_90
| ~ spl26_185 ),
inference(resolution,[],[f1999,f1055]) ).
tff(f1055,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl26_90 ),
inference(avatar_component_clause,[],[f1053]) ).
tff(f9087,plain,
( spl26_427
| ~ spl26_82
| ~ spl26_352
| ~ spl26_426 ),
inference(avatar_split_clause,[],[f9083,f9080,f5723,f986,f9085]) ).
tff(f9085,plain,
( spl26_427
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_427])]) ).
tff(f9080,plain,
( spl26_426
<=> ! [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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_426])]) ).
tff(f9083,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),foldl(dB,dB,app,var(i),rs))))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl26_82
| ~ spl26_352
| ~ spl26_426 ),
inference(forward_demodulation,[],[f9081,f5776]) ).
tff(f9081,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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl26_426 ),
inference(avatar_component_clause,[],[f9080]) ).
tff(f9082,plain,
( spl26_426
| ~ spl26_92
| ~ spl26_185 ),
inference(avatar_split_clause,[],[f2010,f1998,f1066,f9080]) ).
tff(f1066,plain,
( spl26_92
<=> 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,[spl26_92])]) ).
tff(f2010,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,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,var(i),rs)),i),X0))) )
| ~ spl26_92
| ~ spl26_185 ),
inference(resolution,[],[f1999,f1068]) ).
tff(f1068,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs)))
| ~ spl26_92 ),
inference(avatar_component_clause,[],[f1066]) ).
tff(f9078,plain,
( spl26_425
| ~ spl26_13
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1765,f1754,f599,f9076]) ).
tff(f9076,plain,
( spl26_425
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: fun(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_425])]) ).
tff(f1765,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,bool)] :
( ( map(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2)) = aa(list(bool),list(bool),aa(bool,fun(list(bool),list(bool)),cons(bool),fFalse),map(X0,bool,X1,X3)) )
| ( fTrue = aa(X0,bool,X1,X2) ) )
| ~ spl26_13
| ~ spl26_170 ),
inference(superposition,[],[f1755,f600]) ).
tff(f9072,plain,
( spl26_424
| ~ spl26_151
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1729,f1722,f1600,f9070]) ).
tff(f9070,plain,
( spl26_424
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK14(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_424])]) ).
tff(f1729,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK14(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl26_151
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1601]) ).
tff(f9068,plain,
( spl26_423
| ~ spl26_149
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1728,f1722,f1580,f9066]) ).
tff(f9066,plain,
( spl26_423
<=> ! [X4: list(dB),X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK13(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,[spl26_423])]) ).
tff(f1728,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type,X4: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| ~ pp(aa(list(type),bool,typings(X0,X3),sK13(X1,X4,X2,X0)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X4))) )
| ~ spl26_149
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1581]) ).
tff(f9064,plain,
( spl26_422
| ~ spl26_82
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1341,f1327,f986,f9062]) ).
tff(f9062,plain,
( spl26_422
<=> ! [X0: $tType,X1: $tType,X2: $tType,X6: fun(X1,X2),X4: X0,X5: list(X0),X3: fun(X0,fun(list(X0),fun(X1,X2))),X7: X1] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_422])]) ).
tff(f1341,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(list(X0),fun(X1,X2))),X6: fun(X1,X2),X7: X1,X4: X0,X5: list(X0)] : ( aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)),X7) )
| ~ spl26_82
| ~ spl26_131 ),
inference(superposition,[],[f987,f1328]) ).
tff(f9060,plain,
( spl26_421
| ~ spl26_82
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1093,f1083,f986,f9058]) ).
tff(f9058,plain,
( spl26_421
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK17(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK17(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_421])]) ).
tff(f1093,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK17(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)),X4) != aa(X0,X1,X5,sK17(X1,X0,aa(X2,fun(X0,X1),X3,X4),X5)) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) )
| ~ spl26_82
| ~ spl26_95 ),
inference(superposition,[],[f1084,f987]) ).
tff(f9056,plain,
( spl26_420
| ~ spl26_82
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1088,f1083,f986,f9054]) ).
tff(f9054,plain,
( spl26_420
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X3: fun(X2,fun(X0,X1)),X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK17(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK17(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_420])]) ).
tff(f1088,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,combc(X2,X0,X1,X3,sK17(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))),X4) != aa(X0,X1,X5,sK17(X1,X0,X5,aa(X2,fun(X0,X1),X3,X4))) )
| ( aa(X2,fun(X0,X1),X3,X4) = X5 ) )
| ~ spl26_82
| ~ spl26_95 ),
inference(superposition,[],[f1084,f987]) ).
tff(f8969,plain,
( spl26_419
| ~ spl26_51
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1844,f1793,f804,f8967]) ).
tff(f8967,plain,
( spl26_419
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_419])]) ).
tff(f1844,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: fun(X1,X0)] :
( ~ pp(aa(X1,bool,aa(fun(X1,X0),fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(fun(X1,X0),fun(X1,bool)),combs(X1,X0,bool),X2),X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) )
| ~ spl26_51
| ~ spl26_171 ),
inference(superposition,[],[f805,f1794]) ).
tff(f8965,plain,
( spl26_418
| ~ spl26_29
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1801,f1793,f691,f8963]) ).
tff(f8963,plain,
( spl26_418
<=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X4: fun(X0,X1),X5: fun(nat,X0),X3: nat] : ( aa(nat,X1,aa(fun(nat,X0),fun(nat,X1),aa(fun(nat,fun(X0,X1)),fun(fun(nat,X0),fun(nat,X1)),combs(nat,X0,X1),shift(fun(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_418])]) ).
tff(f1801,plain,
( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,X0)] : ( aa(nat,X1,aa(fun(nat,X0),fun(nat,X1),aa(fun(nat,fun(X0,X1)),fun(fun(nat,X0),fun(nat,X1)),combs(nat,X0,X1),shift(fun(X0,X1),X2,X3,X4)),X5),X3) = aa(X0,X1,X4,aa(nat,X0,X5,X3)) )
| ~ spl26_29
| ~ spl26_171 ),
inference(superposition,[],[f1794,f692]) ).
tff(f8898,plain,
( spl26_417
| ~ spl26_4
| ~ spl26_217
| ~ spl26_389 ),
inference(avatar_split_clause,[],[f8364,f7207,f2815,f559,f8895]) ).
tff(f8895,plain,
( spl26_417
<=> sP1(abs(abs(abs(abs(t2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_417])]) ).
tff(f7207,plain,
( spl26_389
<=> ( fTrue = aa(dB,bool,it,abs(abs(t2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_389])]) ).
tff(f8364,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(abs(t2)))))
| ~ spl26_217
| ~ spl26_389 ),
inference(superposition,[],[f2816,f7209]) ).
tff(f7209,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t2))) )
| ~ spl26_389 ),
inference(avatar_component_clause,[],[f7207]) ).
tff(f8396,plain,
( spl26_416
| ~ spl26_29
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1873,f1793,f986,f691,f8394]) ).
tff(f8394,plain,
( spl26_416
<=> ! [X0: $tType,X4: $tType,X3: X0,X5: fun(nat,fun(X0,X4)),X2: nat,X1: fun(nat,X0)] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_416])]) ).
tff(f1873,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X5: fun(nat,fun(X0,X4))] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(nat,X4,combc(nat,X0,X4,X5,X3),X2) )
| ~ spl26_29
| ~ spl26_82
| ~ spl26_171 ),
inference(forward_demodulation,[],[f1811,f987]) ).
tff(f1811,plain,
( ! [X4: $tType,X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0),X5: fun(nat,fun(X0,X4))] : ( aa(nat,X4,aa(fun(nat,X0),fun(nat,X4),aa(fun(nat,fun(X0,X4)),fun(fun(nat,X0),fun(nat,X4)),combs(nat,X0,X4),X5),shift(X0,X1,X2,X3)),X2) = aa(X0,X4,aa(nat,fun(X0,X4),X5,X2),X3) )
| ~ spl26_29
| ~ spl26_171 ),
inference(superposition,[],[f1794,f692]) ).
tff(f8392,plain,
( spl26_415
| ~ spl26_100
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1863,f1793,f1117,f8390]) ).
tff(f8390,plain,
( spl26_415
<=> ! [X0: type,X3: type,X2: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_415])]) ).
tff(f1117,plain,
( spl26_100
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_100])]) ).
tff(f1863,plain,
( ! [X2: type,X3: type,X0: type,X1: fun(type,type)] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_100
| ~ spl26_171 ),
inference(superposition,[],[f1118,f1794]) ).
tff(f1118,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) )
| ( X1 = X3 ) )
| ~ spl26_100 ),
inference(avatar_component_clause,[],[f1117]) ).
tff(f8388,plain,
( spl26_414
| ~ spl26_102
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1847,f1793,f1126,f8386]) ).
tff(f8386,plain,
( spl26_414
<=> ! [X0: dB,X3: dB,X2: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_414])]) ).
tff(f1847,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: fun(dB,dB)] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_102
| ~ spl26_171 ),
inference(superposition,[],[f1127,f1794]) ).
tff(f8384,plain,
( spl26_413
| ~ spl26_82
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1824,f1793,f986,f8382]) ).
tff(f8382,plain,
( spl26_413
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(fun(X2,X0),fun(X2,X1),aa(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_413])]) ).
tff(f1824,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(fun(X2,X0),fun(X2,X1),aa(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1)),combs(X2,X0,X1),X3),X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) )
| ~ spl26_82
| ~ spl26_171 ),
inference(superposition,[],[f1794,f987]) ).
tff(f8380,plain,
( spl26_412
| ~ spl26_82
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1092,f1083,f986,f8378]) ).
tff(f8378,plain,
( spl26_412
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK17(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK17(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_412])]) ).
tff(f1092,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK17(X1,X0,combc(X0,X2,X1,X3,X4),X5)),X4) != aa(X0,X1,X5,sK17(X1,X0,combc(X0,X2,X1,X3,X4),X5)) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl26_82
| ~ spl26_95 ),
inference(superposition,[],[f1084,f987]) ).
tff(f8359,plain,
( spl26_411
| ~ spl26_82
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1087,f1083,f986,f8357]) ).
tff(f8357,plain,
( spl26_411
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,X1),X4: X2,X3: fun(X0,fun(X2,X1))] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK17(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK17(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_411])]) ).
tff(f1087,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ( aa(X2,X1,aa(X0,fun(X2,X1),X3,sK17(X1,X0,X5,combc(X0,X2,X1,X3,X4))),X4) != aa(X0,X1,X5,sK17(X1,X0,X5,combc(X0,X2,X1,X3,X4))) )
| ( combc(X0,X2,X1,X3,X4) = X5 ) )
| ~ spl26_82
| ~ spl26_95 ),
inference(superposition,[],[f1084,f987]) ).
tff(f8300,plain,
( spl26_410
| ~ spl26_146
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1780,f1754,f1541,f8298]) ).
tff(f8298,plain,
( spl26_410
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_410])]) ).
tff(f1780,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( map(X1,X0,X2,X4) = X6 ) )
| ~ spl26_146
| ~ spl26_170 ),
inference(superposition,[],[f1542,f1755]) ).
tff(f8296,plain,
( spl26_409
| ~ spl26_130
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1727,f1722,f1319,f8294]) ).
tff(f8294,plain,
( spl26_409
<=> ! [X0: list(dB)] :
( 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)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),X0),sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_409])]) ).
tff(f1727,plain,
( ! [X0: list(dB)] :
( 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)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),X0),sK2)) )
| ~ spl26_130
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1321]) ).
tff(f8292,plain,
( spl26_408
| ~ spl26_126
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1726,f1722,f1286,f8290]) ).
tff(f8290,plain,
( spl26_408
<=> ! [X0: list(dB)] :
( 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)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),X0),ts)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_408])]) ).
tff(f1726,plain,
( ! [X0: list(dB)] :
( 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)))
| ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),X0),ts)) )
| ~ spl26_126
| ~ spl26_166 ),
inference(resolution,[],[f1723,f1288]) ).
tff(f8247,plain,
( spl26_407
| ~ spl26_113
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5028,f4969,f1212,f8245]) ).
tff(f1212,plain,
( spl26_113
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_113])]) ).
tff(f5028,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,abs(var(X0))) )
| ~ spl26_113
| ~ spl26_313 ),
inference(resolution,[],[f4970,f1213]) ).
tff(f1213,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl26_113 ),
inference(avatar_component_clause,[],[f1212]) ).
tff(f7758,plain,
( spl26_406
| ~ spl26_102
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1947,f1940,f1126,f7756]) ).
tff(f7756,plain,
( spl26_406
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_406])]) ).
tff(f1947,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl26_102
| ~ spl26_180 ),
inference(superposition,[],[f1127,f1941]) ).
tff(f7754,plain,
( spl26_405
| ~ spl26_103
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1945,f1940,f1130,f7752]) ).
tff(f7752,plain,
( spl26_405
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_405])]) ).
tff(f1945,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB,X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X2) = X4 ) )
| ~ spl26_103
| ~ spl26_180 ),
inference(superposition,[],[f1131,f1941]) ).
tff(f7750,plain,
( spl26_404
| ~ spl26_75
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1901,f1895,f949,f7748]) ).
tff(f7748,plain,
( spl26_404
<=> ! [X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,var(X3),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_404])]) ).
tff(f949,plain,
( spl26_75
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_75])]) ).
tff(f1901,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),var(X3))))
| ( aa(nat,type,X0,X3) = aa(type,type,combc(type,type,type,fun1,X1),sK16(X1,X2,var(X3),X0)) ) )
| ~ spl26_75
| ~ spl26_175 ),
inference(resolution,[],[f1896,f950]) ).
tff(f950,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl26_75 ),
inference(avatar_component_clause,[],[f949]) ).
tff(f7746,plain,
( spl26_403
| ~ spl26_135
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1899,f1895,f1363,f7744]) ).
tff(f7744,plain,
( spl26_403
<=> ! [X0: fun(nat,type),X3: dB,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X3,X0))),sK10(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_403])]) ).
tff(f1363,plain,
( spl26_135
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),sK10(X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_135])]) ).
tff(f1899,plain,
( ! [X2: dB,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X3))))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X3,X0))),sK10(X3,X0)),X3)) )
| ~ spl26_135
| ~ spl26_175 ),
inference(resolution,[],[f1896,f1364]) ).
tff(f1364,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),sK10(X1,X2)),X1)) )
| ~ spl26_135 ),
inference(avatar_component_clause,[],[f1363]) ).
tff(f7742,plain,
( spl26_402
| ~ spl26_235
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5026,f4969,f2946,f7739]) ).
tff(f2946,plain,
( spl26_235
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_235])]) ).
tff(f5026,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(ua))) )
| ~ spl26_235
| ~ spl26_313 ),
inference(resolution,[],[f4970,f2948]) ).
tff(f2948,plain,
( sP1(abs(abs(ua)))
| ~ spl26_235 ),
inference(avatar_component_clause,[],[f2946]) ).
tff(f7737,plain,
( spl26_401
| ~ spl26_20
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1809,f1793,f634,f7735]) ).
tff(f7735,plain,
( spl26_401
<=> ! [X2: $tType,X0: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun(X0,X0),fun(X0,X2),aa(fun(X0,fun(X0,X2)),fun(fun(X0,X0),fun(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_401])]) ).
tff(f1809,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,aa(fun(X0,X0),fun(X0,X2),aa(fun(X0,fun(X0,X2)),fun(fun(X0,X0),fun(X0,X2)),combs(X0,X0,X2),X3),combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) )
| ~ spl26_20
| ~ spl26_171 ),
inference(superposition,[],[f1794,f635]) ).
tff(f7733,plain,
( spl26_400
| ~ spl26_140
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1776,f1754,f1490,f7731]) ).
tff(f7731,plain,
( spl26_400
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: list(X0),X4: list(X1),X3: X1,X2: fun(X1,X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_400])]) ).
tff(f1776,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ( aa(X1,X0,X2,X3) = X5 ) )
| ~ spl26_140
| ~ spl26_170 ),
inference(superposition,[],[f1491,f1755]) ).
tff(f7729,plain,
( spl26_399
| ~ spl26_59
| ~ spl26_160 ),
inference(avatar_split_clause,[],[f1681,f1676,f859,f7727]) ).
tff(f7727,plain,
( spl26_399
<=> ! [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,[spl26_399])]) ).
tff(f859,plain,
( spl26_59
<=> ! [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,[spl26_59])]) ).
tff(f1676,plain,
( spl26_160
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_160])]) ).
tff(f1681,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X1,X2)) != foldl(dB,dB,app,X3,map(dB,dB,combc(dB,nat,dB,lift,X0),X2)) )
| ( aa(dB,dB,combc(dB,nat,dB,lift,X0),X1) = X3 ) )
| ~ spl26_59
| ~ spl26_160 ),
inference(superposition,[],[f860,f1677]) ).
tff(f1677,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl26_160 ),
inference(avatar_component_clause,[],[f1676]) ).
tff(f860,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) )
| ( X0 = X2 ) )
| ~ spl26_59 ),
inference(avatar_component_clause,[],[f859]) ).
tff(f7725,plain,
( spl26_398
| ~ spl26_65
| ~ spl26_82
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1572,f1545,f986,f893,f7723]) ).
tff(f7723,plain,
( spl26_398
<=> ! [X0: $tType,X3: nat,X2: fun(nat,X0),X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_398])]) ).
tff(f1572,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl26_65
| ~ spl26_82
| ~ spl26_147 ),
inference(forward_demodulation,[],[f1564,f987]) ).
tff(f1564,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: fun(X0,type)] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(X0,type),fun(fun(nat,X0),fun(nat,type)),combb(X0,type,nat),X1),X2)),aa(X0,type,X1,aa(nat,X0,X2,X3))),var(X3)))
| ~ spl26_65
| ~ spl26_147 ),
inference(superposition,[],[f894,f1546]) ).
tff(f7721,plain,
( spl26_397
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1154,f1151,f7719]) ).
tff(f7719,plain,
( spl26_397
<=> ! [X0: $tType,X3: type,X4: fun(nat,fun(type,X0)),X6: fun(nat,X0),X5: type,X2: type,X1: fun(type,fun(type,fun(type,X0)))] : ( type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_397])]) ).
tff(f1154,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,fun(type,X0))),X6: fun(nat,X0),X4: fun(nat,fun(type,X0)),X5: type] : ( type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5) )
| ~ spl26_105 ),
inference(superposition,[],[f1152,f1152]) ).
tff(f7514,plain,
( spl26_396
| ~ spl26_228
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5025,f4969,f2904,f7511]) ).
tff(f2904,plain,
( spl26_228
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_228])]) ).
tff(f5025,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(u))) )
| ~ spl26_228
| ~ spl26_313 ),
inference(resolution,[],[f4970,f2906]) ).
tff(f2906,plain,
( sP1(abs(abs(u)))
| ~ spl26_228 ),
inference(avatar_component_clause,[],[f2904]) ).
tff(f7298,plain,
( spl26_395
| ~ spl26_82
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1772,f1754,f986,f7296]) ).
tff(f7296,plain,
( spl26_395
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_395])]) ).
tff(f1772,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) = aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),map(X1,X0,X2,X4)),aa(X1,X0,X2,X3)) )
| ~ spl26_82
| ~ spl26_170 ),
inference(superposition,[],[f1755,f987]) ).
tff(f7294,plain,
( spl26_394
| ~ spl26_51
| ~ spl26_164 ),
inference(avatar_split_clause,[],[f1712,f1707,f804,f7292]) ).
tff(f7292,plain,
( spl26_394
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_394])]) ).
tff(f1712,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1)))) )
| ~ spl26_51
| ~ spl26_164 ),
inference(resolution,[],[f1708,f805]) ).
tff(f7290,plain,
( spl26_393
| ~ spl26_107
| ~ spl26_162 ),
inference(avatar_split_clause,[],[f1696,f1691,f1172,f7288]) ).
tff(f7288,plain,
( spl26_393
<=> ! [X4: dB,X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X2),X1)),X4))
| ~ beta(abs(X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_393])]) ).
tff(f1696,plain,
( ! [X2: type,X3: dB,X0: fun(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,fun1,X2),X1)),X4))
| ~ beta(abs(X3),X4) )
| ~ spl26_107
| ~ spl26_162 ),
inference(resolution,[],[f1692,f1173]) ).
tff(f7286,plain,
( spl26_392
| ~ spl26_138
| ~ spl26_140 ),
inference(avatar_split_clause,[],[f1502,f1490,f1376,f7284]) ).
tff(f7284,plain,
( spl26_392
<=> ! [X0: $tType,X5: list(X0),X4: X0,X3: list(X0),X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_392])]) ).
tff(f1502,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0,X4: X0,X5: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ( X1 = X4 ) )
| ~ spl26_138
| ~ spl26_140 ),
inference(superposition,[],[f1491,f1377]) ).
tff(f7282,plain,
( spl26_391
| ~ spl26_29
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1434,f1380,f691,f7280]) ).
tff(f7280,plain,
( spl26_391
<=> ! [X0: $tType,X2: nat,X4: X0,X5: list(X0),X3: fun(X0,nat),X1: fun(nat,fun(X0,nat))] : ( foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_391])]) ).
tff(f1434,plain,
( ! [X0: $tType,X2: nat,X3: fun(X0,nat),X1: fun(nat,fun(X0,nat)),X4: X0,X5: list(X0)] : ( foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5) )
| ~ spl26_29
| ~ spl26_139 ),
inference(superposition,[],[f1381,f692]) ).
tff(f7278,plain,
( spl26_390
| ~ spl26_29
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1390,f1376,f691,f7276]) ).
tff(f7276,plain,
( spl26_390
<=> ! [X0: $tType,X3: fun(X0,X0),X4: list(nat),X5: X0,X2: nat,X1: fun(nat,fun(X0,X0))] : ( foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_390])]) ).
tff(f1390,plain,
( ! [X0: $tType,X2: nat,X3: fun(X0,X0),X1: fun(nat,fun(X0,X0)),X4: list(nat),X5: X0] : ( foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5)) )
| ~ spl26_29
| ~ spl26_138 ),
inference(superposition,[],[f1377,f692]) ).
tff(f7210,plain,
( spl26_389
| ~ spl26_221
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5024,f4969,f2865,f7207]) ).
tff(f2865,plain,
( spl26_221
<=> sP1(abs(abs(t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_221])]) ).
tff(f5024,plain,
( ( fTrue = aa(dB,bool,it,abs(abs(t2))) )
| ~ spl26_221
| ~ spl26_313 ),
inference(resolution,[],[f4970,f2867]) ).
tff(f2867,plain,
( sP1(abs(abs(t2)))
| ~ spl26_221 ),
inference(avatar_component_clause,[],[f2865]) ).
tff(f6899,plain,
( spl26_388
| ~ spl26_51
| ~ spl26_162 ),
inference(avatar_split_clause,[],[f1697,f1691,f804,f6897]) ).
tff(f6897,plain,
( spl26_388
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X2),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_388])]) ).
tff(f1697,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(type,type,combc(type,type,type,fun1,X2),X1)))) )
| ~ spl26_51
| ~ spl26_162 ),
inference(resolution,[],[f1692,f805]) ).
tff(f6895,plain,
( spl26_387
| ~ spl26_51
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1610,f1600,f804,f6893]) ).
tff(f6893,plain,
( spl26_387
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK14(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_387])]) ).
tff(f1610,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK14(X1,X3,X2,X0),X1)))) )
| ~ spl26_51
| ~ spl26_151 ),
inference(resolution,[],[f1601,f805]) ).
tff(f6891,plain,
( spl26_386
| ~ spl26_107
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1603,f1600,f1172,f6889]) ).
tff(f6889,plain,
( spl26_386
<=> ! [X4: dB,X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK14(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_386])]) ).
tff(f1603,plain,
( ! [X2: dB,X3: list(dB),X0: fun(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,fun1,sK14(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) )
| ~ spl26_107
| ~ spl26_151 ),
inference(resolution,[],[f1601,f1173]) ).
tff(f6885,plain,
( spl26_385
| ~ spl26_51
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1590,f1580,f804,f6883]) ).
tff(f6883,plain,
( spl26_385
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK13(X1,X3,X2,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_385])]) ).
tff(f1590,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK13(X1,X3,X2,X0),X1)))) )
| ~ spl26_51
| ~ spl26_149 ),
inference(resolution,[],[f1581,f805]) ).
tff(f6881,plain,
( spl26_384
| ~ spl26_107
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1583,f1580,f1172,f6879]) ).
tff(f6879,plain,
( spl26_384
<=> ! [X4: dB,X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,X2,X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X0),foldr(type,type,fun1,sK13(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_384])]) ).
tff(f1583,plain,
( ! [X2: dB,X3: list(dB),X0: fun(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,fun1,sK13(X1,X3,X2,X0),X1)),X4))
| ~ beta(X2,X4) )
| ~ spl26_107
| ~ spl26_149 ),
inference(resolution,[],[f1581,f1173]) ).
tff(f6877,plain,
( spl26_383
| ~ spl26_51
| ~ spl26_82
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1571,f1545,f986,f804,f6875]) ).
tff(f6875,plain,
( spl26_383
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,X1),X2: fun(X1,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_383])]) ).
tff(f1571,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)))
| ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) )
| ~ spl26_51
| ~ spl26_82
| ~ spl26_147 ),
inference(forward_demodulation,[],[f1563,f987]) ).
tff(f1563,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))) )
| ~ spl26_51
| ~ spl26_147 ),
inference(superposition,[],[f805,f1546]) ).
tff(f6873,plain,
( spl26_382
| ~ spl26_69
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1480,f1380,f986,f916,f6871]) ).
tff(f6871,plain,
( spl26_382
<=> ! [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,[spl26_382])]) ).
tff(f916,plain,
( spl26_69
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_69])]) ).
tff(f1480,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 ) )
| ~ spl26_69
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1457,f987]) ).
tff(f1457,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl26_69
| ~ spl26_139 ),
inference(superposition,[],[f917,f1381]) ).
tff(f917,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 ) )
| ~ spl26_69 ),
inference(avatar_component_clause,[],[f916]) ).
tff(f6869,plain,
( spl26_381
| ~ spl26_70
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1476,f1380,f986,f920,f6867]) ).
tff(f6867,plain,
( spl26_381
<=> ! [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,[spl26_381])]) ).
tff(f920,plain,
( spl26_70
<=> ! [X2: list(dB),X0: list(dB),X1: nat,X3: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_70])]) ).
tff(f1476,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 ) )
| ~ spl26_70
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1453,f987]) ).
tff(f1453,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) )
| ( aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2) = X4 ) )
| ~ spl26_70
| ~ spl26_139 ),
inference(superposition,[],[f921,f1381]) ).
tff(f921,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 ) )
| ~ spl26_70 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f6865,plain,
( spl26_380
| ~ spl26_78
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1442,f1380,f964,f6863]) ).
tff(f6863,plain,
( spl26_380
<=> ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_380])]) ).
tff(f1442,plain,
( ! [X2: list(nat),X0: dB,X1: nat] : ( foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),var(X1),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X2),X1)) = foldl(dB,nat,combc(dB,dB,fun(nat,dB),subst,X0),X0,X2) )
| ~ spl26_78
| ~ spl26_139 ),
inference(superposition,[],[f1381,f965]) ).
tff(f6861,plain,
( spl26_379
| ~ spl26_82
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1155,f1151,f986,f6859]) ).
tff(f6859,plain,
( spl26_379
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: type,X6: fun(nat,X0),X5: type,X2: fun(X1,fun(type,fun(type,X0)))] : ( type_case(X0,X6,aa(X1,fun(type,fun(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),combc(X1,type,fun(type,X0),X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_379])]) ).
tff(f1155,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(type,fun(type,X0))),X3: X1,X6: fun(nat,X0),X4: type,X5: type] : ( type_case(X0,X6,aa(X1,fun(type,fun(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),combc(X1,type,fun(type,X0),X2,X4),X3),X5) )
| ~ spl26_82
| ~ spl26_105 ),
inference(superposition,[],[f1152,f987]) ).
tff(f6789,plain,
( spl26_378
| ~ spl26_4
| ~ spl26_217
| ~ spl26_338 ),
inference(avatar_split_clause,[],[f6615,f5276,f2815,f559,f6786]) ).
tff(f6786,plain,
( spl26_378
<=> sP1(abs(abs(abs(ua)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_378])]) ).
tff(f5276,plain,
( spl26_338
<=> ( fTrue = aa(dB,bool,it,abs(ua)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_338])]) ).
tff(f6615,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(ua))))
| ~ spl26_217
| ~ spl26_338 ),
inference(superposition,[],[f2816,f5278]) ).
tff(f5278,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl26_338 ),
inference(avatar_component_clause,[],[f5276]) ).
tff(f6784,plain,
( spl26_377
| ~ spl26_38
| ~ spl26_168 ),
inference(avatar_split_clause,[],[f1744,f1741,f739,f6781]) ).
tff(f6781,plain,
( spl26_377
<=> listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t))),fEx(type)),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_377])]) ).
tff(f739,plain,
( spl26_38
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_38])]) ).
tff(f1744,plain,
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t))),fEx(type)),as)
| ~ spl26_38
| ~ spl26_168 ),
inference(resolution,[],[f1742,f741]) ).
tff(f741,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts))
| ~ spl26_38 ),
inference(avatar_component_clause,[],[f739]) ).
tff(f6779,plain,
( spl26_376
| ~ spl26_107
| ~ spl26_156 ),
inference(avatar_split_clause,[],[f1645,f1642,f1172,f6777]) ).
tff(f6777,plain,
( spl26_376
<=> ! [X3: nat,X4: type,X0: fun(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,[spl26_376])]) ).
tff(f1645,plain,
( ! [X2: dB,X3: nat,X0: fun(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) )
| ~ spl26_107
| ~ spl26_156 ),
inference(resolution,[],[f1643,f1173]) ).
tff(f6775,plain,
( spl26_375
| ~ spl26_13
| ~ spl26_82
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1570,f1545,f986,f599,f6773]) ).
tff(f6773,plain,
( spl26_375
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,X1),X2: fun(X1,bool)] :
( ( fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_375])]) ).
tff(f1570,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ( fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) )
| ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_147 ),
inference(forward_demodulation,[],[f1558,f987]) ).
tff(f1558,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X4: X0] :
( ( fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) )
| ( fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3),X4) ) )
| ~ spl26_13
| ~ spl26_147 ),
inference(superposition,[],[f1546,f600]) ).
tff(f6351,plain,
( spl26_374
| ~ spl26_66
| ~ spl26_182 ),
inference(avatar_split_clause,[],[f1989,f1961,f902,f6349]) ).
tff(f6349,plain,
( spl26_374
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK23(dB,X0,X2,X1,as,a)),sK24(dB,X0,X2,X1,as,a)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_374])]) ).
tff(f902,plain,
( spl26_66
<=> ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_66])]) ).
tff(f1989,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK23(dB,X0,X2,X1,as,a)),sK24(dB,X0,X2,X1,as,a)) = X2 ) )
| ~ spl26_66
| ~ spl26_182 ),
inference(superposition,[],[f1962,f904]) ).
tff(f904,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl26_66 ),
inference(avatar_component_clause,[],[f902]) ).
tff(f6347,plain,
( spl26_373
| ~ spl26_66
| ~ spl26_181 ),
inference(avatar_split_clause,[],[f1981,f1957,f902,f6345]) ).
tff(f6345,plain,
( spl26_373
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,dB,as,a,X2,X1)),sK22(X0,dB,as,a,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_373])]) ).
tff(f1981,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,dB,as,a,X2,X1)),sK22(X0,dB,as,a,X2,X1)) = X2 ) )
| ~ spl26_66
| ~ spl26_181 ),
inference(superposition,[],[f1958,f904]) ).
tff(f6343,plain,
( spl26_372
| ~ spl26_72
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1851,f1793,f931,f6341]) ).
tff(f6341,plain,
( spl26_372
<=> ! [X2: nat,X0: dB,X1: fun(dB,dB),X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_372])]) ).
tff(f931,plain,
( spl26_72
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_72])]) ).
tff(f1851,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: fun(dB,dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),abs(X0)) )
| ~ spl26_72
| ~ spl26_171 ),
inference(superposition,[],[f932,f1794]) ).
tff(f932,plain,
( ! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) )
| ~ spl26_72 ),
inference(avatar_component_clause,[],[f931]) ).
tff(f6339,plain,
( spl26_371
| ~ spl26_135
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1584,f1580,f1363,f6337]) ).
tff(f6337,plain,
( spl26_371
<=> ! [X0: fun(nat,type),X3: list(dB),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X2,X0))),sK10(X2,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_371])]) ).
tff(f1584,plain,
( ! [X2: dB,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,abs(X2),X3)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X2,X0))),sK10(X2,X0)),X2)) )
| ~ spl26_135
| ~ spl26_149 ),
inference(resolution,[],[f1581,f1364]) ).
tff(f6335,plain,
( spl26_370
| ~ spl26_51
| ~ spl26_144 ),
inference(avatar_split_clause,[],[f1533,f1523,f804,f6333]) ).
tff(f6333,plain,
( spl26_370
<=> ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X1,X2,X0))),sK12(X1,X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_370])]) ).
tff(f1523,plain,
( spl26_144
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),sK12(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_144])]) ).
tff(f1533,plain,
( ! [X2: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(X2)))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK11(X1,X2,X0))),sK12(X1,X2,X0)))) )
| ~ spl26_51
| ~ spl26_144 ),
inference(resolution,[],[f1524,f805]) ).
tff(f1524,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),sK12(X0,X1,X2)),X1))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1))) )
| ~ spl26_144 ),
inference(avatar_component_clause,[],[f1523]) ).
tff(f6331,plain,
( spl26_369
| ~ spl26_107
| ~ spl26_144 ),
inference(avatar_split_clause,[],[f1526,f1523,f1172,f6329]) ).
tff(f6329,plain,
( spl26_369
<=> ! [X0: fun(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),sK11(X1,X2,X0))),sK12(X1,X2,X0)),X3))
| ~ beta(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_369])]) ).
tff(f1526,plain,
( ! [X2: dB,X3: dB,X0: fun(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),sK11(X1,X2,X0))),sK12(X1,X2,X0)),X3))
| ~ beta(X2,X3) )
| ~ spl26_107
| ~ spl26_144 ),
inference(resolution,[],[f1524,f1173]) ).
tff(f6325,plain,
( spl26_368
| ~ spl26_13
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1399,f1376,f599,f6323]) ).
tff(f6323,plain,
( spl26_368
<=> ! [X0: $tType,X4: bool,X3: X0,X2: list(X0),X1: fun(X0,fun(bool,bool))] :
( ( fFalse = aa(bool,bool,aa(X0,fun(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_368])]) ).
tff(f1399,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: fun(X0,fun(bool,bool)),X4: bool] :
( ( fFalse = aa(bool,bool,aa(X0,fun(bool,bool),X1,X3),foldr(X0,bool,X1,X2,X4)) )
| ( fTrue = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X3),X4) ) )
| ~ spl26_13
| ~ spl26_138 ),
inference(superposition,[],[f1377,f600]) ).
tff(f6321,plain,
( spl26_367
| ~ spl26_13
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1398,f1376,f599,f6319]) ).
tff(f6319,plain,
( spl26_367
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun(X0,fun(bool,bool))] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_367])]) ).
tff(f1398,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(bool,bool)),X4: bool] :
( ( fFalse = foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4) )
| ( fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)) ) )
| ~ spl26_13
| ~ spl26_138 ),
inference(superposition,[],[f1377,f600]) ).
tff(f6317,plain,
( spl26_366
| ~ spl26_13
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1396,f1376,f599,f6315]) ).
tff(f6315,plain,
( spl26_366
<=> ! [X0: $tType,X2: list(X0),X4: X0,X3: bool,X1: fun(X0,fun(bool,bool))] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_366])]) ).
tff(f1396,plain,
( ! [X0: $tType,X2: list(X0),X3: bool,X1: fun(X0,fun(bool,bool)),X4: X0] :
( ( foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X4),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) )
| ( fTrue = foldr(X0,bool,X1,X2,X3) ) )
| ~ spl26_13
| ~ spl26_138 ),
inference(superposition,[],[f1377,f600]) ).
tff(f6313,plain,
( spl26_365
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1335,f1327,f6311]) ).
tff(f6311,plain,
( spl26_365
<=> ! [X1: $tType,X0: $tType,X5: X1,X6: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_365])]) ).
tff(f1335,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = list_case(X1,X0,X6,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ~ spl26_131 ),
inference(superposition,[],[f1328,f1328]) ).
tff(f6309,plain,
( spl26_364
| ~ spl26_82
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1162,f1151,f986,f6307]) ).
tff(f6307,plain,
( spl26_364
<=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(X0,X1)),X3: type,X4: type,X6: X0,X2: fun(type,fun(type,fun(X0,X1)))] : ( aa(type,X1,combc(type,X0,X1,aa(type,fun(type,fun(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun1,X4),X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_364])]) ).
tff(f1162,plain,
( ! [X1: $tType,X0: $tType,X2: fun(type,fun(type,fun(X0,X1))),X3: type,X6: X0,X4: type,X5: fun(nat,fun(X0,X1))] : ( aa(type,X1,combc(type,X0,X1,aa(type,fun(type,fun(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun1,X4),X3)),X6) )
| ~ spl26_82
| ~ spl26_105 ),
inference(superposition,[],[f987,f1152]) ).
tff(f6143,plain,
( spl26_363
| ~ spl26_4
| ~ spl26_217
| ~ spl26_329 ),
inference(avatar_split_clause,[],[f5994,f5213,f2815,f559,f6140]) ).
tff(f6140,plain,
( spl26_363
<=> sP1(abs(abs(abs(u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_363])]) ).
tff(f5213,plain,
( spl26_329
<=> ( fTrue = aa(dB,bool,it,abs(u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_329])]) ).
tff(f5994,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(u))))
| ~ spl26_217
| ~ spl26_329 ),
inference(superposition,[],[f2816,f5215]) ).
tff(f5215,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl26_329 ),
inference(avatar_component_clause,[],[f5213]) ).
tff(f6114,plain,
( spl26_362
| ~ spl26_135
| ~ spl26_162 ),
inference(avatar_split_clause,[],[f1694,f1691,f1363,f6112]) ).
tff(f6112,plain,
( spl26_362
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X3,X0))),sK10(X3,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_362])]) ).
tff(f1694,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),X1)),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,zero_zero(nat),sK9(X3,X0))),sK10(X3,X0)),X3)) )
| ~ spl26_135
| ~ spl26_162 ),
inference(resolution,[],[f1692,f1364]) ).
tff(f6110,plain,
( spl26_361
| ~ spl26_59
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1487,f1380,f986,f859,f6108]) ).
tff(f6108,plain,
( spl26_361
<=> ! [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,[spl26_361])]) ).
tff(f1487,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 ) )
| ~ spl26_59
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1464,f987]) ).
tff(f1464,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),X1) != foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ( X0 = X3 ) )
| ~ spl26_59
| ~ spl26_139 ),
inference(superposition,[],[f860,f1381]) ).
tff(f6106,plain,
( spl26_360
| ~ spl26_56
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1473,f1380,f986,f844,f6104]) ).
tff(f6104,plain,
( spl26_360
<=> ! [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,[spl26_360])]) ).
tff(f844,plain,
( spl26_56
<=> ! [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,[spl26_56])]) ).
tff(f1473,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)) )
| ~ spl26_56
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1450,f987]) ).
tff(f1450,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl26_56
| ~ spl26_139 ),
inference(superposition,[],[f845,f1381]) ).
tff(f845,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl26_56 ),
inference(avatar_component_clause,[],[f844]) ).
tff(f6102,plain,
( spl26_359
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1470,f1380,f986,f599,f6100]) ).
tff(f6100,plain,
( spl26_359
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_359])]) ).
tff(f1470,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1447,f987]) ).
tff(f1447,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X4),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl26_13
| ~ spl26_139 ),
inference(superposition,[],[f1381,f600]) ).
tff(f6098,plain,
( spl26_358
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1469,f1380,f986,f599,f6096]) ).
tff(f6096,plain,
( spl26_358
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_358])]) ).
tff(f1469,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1445,f987]) ).
tff(f1445,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ( fTrue = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3),X4) ) )
| ~ spl26_13
| ~ spl26_139 ),
inference(superposition,[],[f1381,f600]) ).
tff(f6094,plain,
( spl26_357
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1468,f1380,f986,f599,f6092]) ).
tff(f6092,plain,
( spl26_357
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_357])]) ).
tff(f1468,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1441,f987]) ).
tff(f1441,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) )
| ( fTrue = aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) ) )
| ~ spl26_13
| ~ spl26_139 ),
inference(superposition,[],[f1381,f600]) ).
tff(f5741,plain,
( spl26_356
| ~ spl26_39
| ~ spl26_176 ),
inference(avatar_split_clause,[],[f1915,f1911,f744,f5739]) ).
tff(f5739,plain,
( spl26_356
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_356])]) ).
tff(f744,plain,
( spl26_39
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_39])]) ).
tff(f1915,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl26_39
| ~ spl26_176 ),
inference(resolution,[],[f1912,f746]) ).
tff(f746,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK2))
| ~ spl26_39 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f5737,plain,
( spl26_355
| ~ spl26_38
| ~ spl26_176 ),
inference(avatar_split_clause,[],[f1914,f1911,f739,f5735]) ).
tff(f5735,plain,
( spl26_355
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_355])]) ).
tff(f1914,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl26_38
| ~ spl26_176 ),
inference(resolution,[],[f1912,f741]) ).
tff(f5733,plain,
( spl26_354
| ~ spl26_82
| ~ spl26_147 ),
inference(avatar_split_clause,[],[f1556,f1545,f986,f5731]) ).
tff(f5731,plain,
( spl26_354
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X1),X5: X0,X3: fun(X1,X2)] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_354])]) ).
tff(f1556,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: fun(X0,X1),X5: X0] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) )
| ~ spl26_82
| ~ spl26_147 ),
inference(superposition,[],[f1546,f987]) ).
tff(f5729,plain,
( spl26_353
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f996,f986,f5727]) ).
tff(f5727,plain,
( spl26_353
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_353])]) ).
tff(f996,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) )
| ~ spl26_82 ),
inference(superposition,[],[f987,f987]) ).
tff(f5725,plain,
( spl26_352
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f995,f986,f5723]) ).
tff(f995,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) )
| ~ spl26_82 ),
inference(superposition,[],[f987,f987]) ).
tff(f5714,plain,
( spl26_351
| ~ spl26_82
| ~ spl26_146 ),
inference(avatar_split_clause,[],[f1550,f1541,f986,f5712]) ).
tff(f5712,plain,
( spl26_351
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_351])]) ).
tff(f1550,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) )
| ~ spl26_82
| ~ spl26_146 ),
inference(superposition,[],[f1542,f987]) ).
tff(f5451,plain,
( spl26_350
| ~ spl26_4
| ~ spl26_217
| ~ spl26_323 ),
inference(avatar_split_clause,[],[f5397,f5158,f2815,f559,f5448]) ).
tff(f5448,plain,
( spl26_350
<=> sP1(abs(abs(abs(t2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_350])]) ).
tff(f5158,plain,
( spl26_323
<=> ( fTrue = aa(dB,bool,it,abs(t2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_323])]) ).
tff(f5397,plain,
( ~ pp(fTrue)
| sP1(abs(abs(abs(t2))))
| ~ spl26_217
| ~ spl26_323 ),
inference(superposition,[],[f2816,f5160]) ).
tff(f5160,plain,
( ( fTrue = aa(dB,bool,it,abs(t2)) )
| ~ spl26_323 ),
inference(avatar_component_clause,[],[f5158]) ).
tff(f5446,plain,
( spl26_349
| ~ spl26_75
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1606,f1600,f949,f5444]) ).
tff(f5444,plain,
( spl26_349
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_349])]) ).
tff(f1606,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) )
| ~ spl26_75
| ~ spl26_151 ),
inference(resolution,[],[f1601,f950]) ).
tff(f5442,plain,
( spl26_348
| ~ spl26_75
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1586,f1580,f949,f5440]) ).
tff(f5440,plain,
( spl26_348
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK13(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_348])]) ).
tff(f1586,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK13(X1,X3,var(X2),X0),X1) ) )
| ~ spl26_75
| ~ spl26_149 ),
inference(resolution,[],[f1581,f950]) ).
tff(f5438,plain,
( spl26_347
| ~ spl26_27
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1515,f1498,f674,f5436]) ).
tff(f5436,plain,
( spl26_347
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK24(X0,X0,X1,combi(X0),X3,X2)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_347])]) ).
tff(f1515,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK24(X0,X0,X1,combi(X0),X3,X2)) = X3 ) )
| ~ spl26_27
| ~ spl26_142 ),
inference(superposition,[],[f1499,f675]) ).
tff(f5434,plain,
( spl26_346
| ~ spl26_82
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1514,f1498,f986,f5432]) ).
tff(f5432,plain,
( spl26_346
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK24(X0,X3,X5,X4,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_346])]) ).
tff(f1514,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK24(X0,X3,X5,X4,X2,X1)) = X2 ) )
| ~ spl26_82
| ~ spl26_142 ),
inference(superposition,[],[f1499,f987]) ).
tff(f5430,plain,
( spl26_345
| ~ spl26_27
| ~ spl26_141 ),
inference(avatar_split_clause,[],[f1511,f1494,f674,f5428]) ).
tff(f5428,plain,
( spl26_345
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X3,X2,X1,combi(X0))) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_345])]) ).
tff(f1511,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X3,X2,X1,combi(X0))) = X3 ) )
| ~ spl26_27
| ~ spl26_141 ),
inference(superposition,[],[f1495,f675]) ).
tff(f5426,plain,
( spl26_344
| ~ spl26_82
| ~ spl26_141 ),
inference(avatar_split_clause,[],[f1510,f1494,f986,f5424]) ).
tff(f5424,plain,
( spl26_344
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X3,X0,X2,X1,X5,X4)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_344])]) ).
tff(f1510,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X3,X0,X2,X1,X5,X4)) = X2 ) )
| ~ spl26_82
| ~ spl26_141 ),
inference(superposition,[],[f1495,f987]) ).
tff(f5422,plain,
( spl26_343
| ~ spl26_82
| ~ spl26_140 ),
inference(avatar_split_clause,[],[f1503,f1490,f986,f5420]) ).
tff(f5420,plain,
( spl26_343
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_343])]) ).
tff(f1503,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) )
| ~ spl26_82
| ~ spl26_140 ),
inference(superposition,[],[f1491,f987]) ).
tff(f5418,plain,
( spl26_342
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1440,f1380,f986,f5416]) ).
tff(f5416,plain,
( spl26_342
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: list(X0),X2: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_342])]) ).
tff(f1440,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X1)),X3: X1,X4: X0,X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) )
| ~ spl26_82
| ~ spl26_139 ),
inference(superposition,[],[f1381,f987]) ).
tff(f5414,plain,
( spl26_341
| ~ spl26_51
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1401,f1376,f804,f5412]) ).
tff(f5412,plain,
( spl26_341
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun(X0,fun(bool,bool))] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_341])]) ).
tff(f1401,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(bool,bool)),X4: bool] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) )
| ~ spl26_51
| ~ spl26_138 ),
inference(superposition,[],[f805,f1377]) ).
tff(f5410,plain,
( spl26_340
| ~ spl26_82
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1397,f1376,f986,f5408]) ).
tff(f5408,plain,
( spl26_340
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X1),X5: X0,X2: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_340])]) ).
tff(f1397,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X0)),X3: X1,X4: list(X1),X5: X0] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) )
| ~ spl26_82
| ~ spl26_138 ),
inference(superposition,[],[f1377,f987]) ).
tff(f5392,plain,
( spl26_339
| ~ spl26_51
| ~ spl26_117 ),
inference(avatar_split_clause,[],[f1238,f1235,f804,f5390]) ).
tff(f5390,plain,
( spl26_339
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_339])]) ).
tff(f1238,plain,
( ! [X2: list(type),X3: nat,X0: fun(nat,type),X1: list(dB),X4: type] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) )
| ~ spl26_51
| ~ spl26_117 ),
inference(resolution,[],[f1236,f805]) ).
tff(f5279,plain,
( spl26_338
| ~ spl26_81
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5035,f4969,f981,f5276]) ).
tff(f981,plain,
( spl26_81
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_81])]) ).
tff(f5035,plain,
( ( fTrue = aa(dB,bool,it,abs(ua)) )
| ~ spl26_81
| ~ spl26_313 ),
inference(resolution,[],[f4970,f983]) ).
tff(f983,plain,
( sP1(abs(ua))
| ~ spl26_81 ),
inference(avatar_component_clause,[],[f981]) ).
tff(f5248,plain,
( spl26_337
| ~ spl26_75
| ~ spl26_164 ),
inference(avatar_split_clause,[],[f1710,f1707,f949,f5246]) ).
tff(f5246,plain,
( spl26_337
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_337])]) ).
tff(f1710,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,X2,X0),X1) ) )
| ~ spl26_75
| ~ spl26_164 ),
inference(resolution,[],[f1708,f950]) ).
tff(f5244,plain,
( spl26_336
| ~ spl26_75
| ~ spl26_144 ),
inference(avatar_split_clause,[],[f1529,f1523,f949,f5242]) ).
tff(f5242,plain,
( spl26_336
<=> ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK11(X1,var(X2),X0)),X2) = sK12(X1,var(X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_336])]) ).
tff(f1529,plain,
( ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK11(X1,var(X2),X0)),X2) = sK12(X1,var(X2),X0) ) )
| ~ spl26_75
| ~ spl26_144 ),
inference(resolution,[],[f1524,f950]) ).
tff(f5240,plain,
( spl26_335
| ~ spl26_32
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1471,f1380,f986,f705,f5238]) ).
tff(f5238,plain,
( spl26_335
<=> ! [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,[spl26_335])]) ).
tff(f1471,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)) )
| ~ spl26_32
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1448,f987]) ).
tff(f1448,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl26_32
| ~ spl26_139 ),
inference(superposition,[],[f706,f1381]) ).
tff(f5236,plain,
( spl26_334
| ~ spl26_27
| ~ spl26_137 ),
inference(avatar_split_clause,[],[f1388,f1372,f674,f5234]) ).
tff(f5234,plain,
( spl26_334
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK23(X0,X0,X1,combi(X0),X3,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_334])]) ).
tff(f1388,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK23(X0,X0,X1,combi(X0),X3,X2)) = X2 ) )
| ~ spl26_27
| ~ spl26_137 ),
inference(superposition,[],[f1373,f675]) ).
tff(f5232,plain,
( spl26_333
| ~ spl26_82
| ~ spl26_137 ),
inference(avatar_split_clause,[],[f1387,f1372,f986,f5230]) ).
tff(f5230,plain,
( spl26_333
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK23(X0,X3,X5,X4,X2,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_333])]) ).
tff(f1387,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK23(X0,X3,X5,X4,X2,X1)) = X1 ) )
| ~ spl26_82
| ~ spl26_137 ),
inference(superposition,[],[f1373,f987]) ).
tff(f5228,plain,
( spl26_332
| ~ spl26_27
| ~ spl26_136 ),
inference(avatar_split_clause,[],[f1385,f1368,f674,f5226]) ).
tff(f5226,plain,
( spl26_332
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X3,X2,X1,combi(X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_332])]) ).
tff(f1385,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X3,X2,X1,combi(X0))) = X2 ) )
| ~ spl26_27
| ~ spl26_136 ),
inference(superposition,[],[f1369,f675]) ).
tff(f5224,plain,
( spl26_331
| ~ spl26_82
| ~ spl26_136 ),
inference(avatar_split_clause,[],[f1384,f1368,f986,f5222]) ).
tff(f5222,plain,
( spl26_331
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X3,X0,X2,X1,X5,X4)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_331])]) ).
tff(f1384,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X3,X0,X2,X1,X5,X4)) = X1 ) )
| ~ spl26_82
| ~ spl26_136 ),
inference(superposition,[],[f1369,f987]) ).
tff(f5220,plain,
( spl26_330
| ~ spl26_13
| ~ spl26_82
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1342,f1327,f986,f599,f5218]) ).
tff(f5218,plain,
( spl26_330
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: fun(X0,fun(list(X0),bool)),X1: bool] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_330])]) ).
tff(f1342,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_131 ),
inference(forward_demodulation,[],[f1337,f987]) ).
tff(f1337,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X2,X4),X3) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl26_13
| ~ spl26_131 ),
inference(superposition,[],[f1328,f600]) ).
tff(f5216,plain,
( spl26_329
| ~ spl26_73
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5034,f4969,f939,f5213]) ).
tff(f939,plain,
( spl26_73
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_73])]) ).
tff(f5034,plain,
( ( fTrue = aa(dB,bool,it,abs(u)) )
| ~ spl26_73
| ~ spl26_313 ),
inference(resolution,[],[f4970,f941]) ).
tff(f941,plain,
( sP1(abs(u))
| ~ spl26_73 ),
inference(avatar_component_clause,[],[f939]) ).
tff(f5211,plain,
( spl26_328
| ~ spl26_107
| ~ spl26_130 ),
inference(avatar_split_clause,[],[f1323,f1319,f1172,f5209]) ).
tff(f5209,plain,
( spl26_328
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),X0))
| ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_328])]) ).
tff(f1323,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),X0))
| ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0) )
| ~ spl26_107
| ~ spl26_130 ),
inference(resolution,[],[f1321,f1173]) ).
tff(f5207,plain,
( spl26_327
| ~ spl26_107
| ~ spl26_128 ),
inference(avatar_split_clause,[],[f1308,f1302,f1172,f5205]) ).
tff(f5205,plain,
( spl26_327
<=> ! [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,[spl26_327])]) ).
tff(f1308,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) )
| ~ spl26_107
| ~ spl26_128 ),
inference(resolution,[],[f1304,f1173]) ).
tff(f5203,plain,
( spl26_326
| ~ spl26_107
| ~ spl26_126 ),
inference(avatar_split_clause,[],[f1290,f1286,f1172,f5201]) ).
tff(f5201,plain,
( spl26_326
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),X0))
| ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_326])]) ).
tff(f1290,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),X0))
| ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),X0) )
| ~ spl26_107
| ~ spl26_126 ),
inference(resolution,[],[f1288,f1173]) ).
tff(f5169,plain,
( spl26_325
| ~ spl26_133
| ~ spl26_188 ),
inference(avatar_split_clause,[],[f2029,f2026,f1349,f5167]) ).
tff(f5167,plain,
( spl26_325
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0))))
| ~ pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_325])]) ).
tff(f1349,plain,
( spl26_133
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_133])]) ).
tff(f2029,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0))))
| ~ pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) )
| ~ spl26_133
| ~ spl26_188 ),
inference(resolution,[],[f2027,f1350]) ).
tff(f1350,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0))))
| ~ sP0(X0) )
| ~ spl26_133 ),
inference(avatar_component_clause,[],[f1349]) ).
tff(f5165,plain,
( spl26_324
| ~ spl26_48
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1865,f1793,f792,f5163]) ).
tff(f5163,plain,
( spl26_324
<=> ! [X2: nat,X0: type,X1: fun(type,type)] : ( atom(X2) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_324])]) ).
tff(f792,plain,
( spl26_48
<=> ! [X2: type,X0: nat,X1: type] : ( atom(X0) != aa(type,type,aa(type,fun(type,type),fun1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_48])]) ).
tff(f1865,plain,
( ! [X2: nat,X0: type,X1: fun(type,type)] : ( atom(X2) != aa(type,type,aa(fun(type,type),fun(type,type),aa(fun(type,fun(type,type)),fun(fun(type,type),fun(type,type)),combs(type,type,type),fun1),X1),X0) )
| ~ spl26_48
| ~ spl26_171 ),
inference(superposition,[],[f793,f1794]) ).
tff(f793,plain,
( ! [X2: type,X0: nat,X1: type] : ( atom(X0) != aa(type,type,aa(type,fun(type,type),fun1,X2),X1) )
| ~ spl26_48 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f5161,plain,
( spl26_323
| ~ spl26_68
| ~ spl26_313 ),
inference(avatar_split_clause,[],[f5033,f4969,f911,f5158]) ).
tff(f911,plain,
( spl26_68
<=> sP1(abs(t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_68])]) ).
tff(f5033,plain,
( ( fTrue = aa(dB,bool,it,abs(t2)) )
| ~ spl26_68
| ~ spl26_313 ),
inference(resolution,[],[f4970,f913]) ).
tff(f913,plain,
( sP1(abs(t2))
| ~ spl26_68 ),
inference(avatar_component_clause,[],[f911]) ).
tff(f5156,plain,
( spl26_322
| ~ spl26_49
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1850,f1793,f796,f5154]) ).
tff(f5154,plain,
( spl26_322
<=> ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_322])]) ).
tff(f796,plain,
( spl26_49
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_49])]) ).
tff(f1850,plain,
( ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl26_49
| ~ spl26_171 ),
inference(superposition,[],[f797,f1794]) ).
tff(f797,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) )
| ~ spl26_49 ),
inference(avatar_component_clause,[],[f796]) ).
tff(f5152,plain,
( spl26_321
| ~ spl26_50
| ~ spl26_171 ),
inference(avatar_split_clause,[],[f1849,f1793,f800,f5150]) ).
tff(f5150,plain,
( spl26_321
<=> ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_321])]) ).
tff(f800,plain,
( spl26_50
<=> ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_50])]) ).
tff(f1849,plain,
( ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl26_50
| ~ spl26_171 ),
inference(superposition,[],[f801,f1794]) ).
tff(f801,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) )
| ~ spl26_50 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f5148,plain,
( spl26_320
| ~ spl26_29
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1330,f1327,f691,f5146]) ).
tff(f5146,plain,
( spl26_320
<=> ! [X0: $tType,X5: X0,X4: list(nat),X3: fun(list(nat),X0),X2: nat,X1: fun(nat,fun(list(nat),X0))] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_320])]) ).
tff(f1330,plain,
( ! [X0: $tType,X2: nat,X3: fun(list(nat),X0),X1: fun(nat,fun(list(nat),X0)),X4: list(nat),X5: X0] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) )
| ~ spl26_29
| ~ spl26_131 ),
inference(superposition,[],[f1328,f692]) ).
tff(f5052,plain,
( spl26_319
| ~ spl26_51
| ~ spl26_156 ),
inference(avatar_split_clause,[],[f1646,f1642,f804,f5050]) ).
tff(f5050,plain,
( spl26_319
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_319])]) ).
tff(f1646,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) )
| ~ spl26_51
| ~ spl26_156 ),
inference(resolution,[],[f1643,f805]) ).
tff(f5020,plain,
( spl26_318
| ~ spl26_67
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1404,f1376,f907,f5018]) ).
tff(f5018,plain,
( spl26_318
<=> ! [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,[spl26_318])]) ).
tff(f1404,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) )
| ~ spl26_67
| ~ spl26_138 ),
inference(superposition,[],[f908,f1377]) ).
tff(f5016,plain,
( spl26_317
| ~ spl26_28
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1352,f1349,f678,f5014]) ).
tff(f5014,plain,
( spl26_317
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_317])]) ).
tff(f678,plain,
( spl26_28
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_28])]) ).
tff(f1352,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0)))) )
| ~ spl26_28
| ~ spl26_133 ),
inference(resolution,[],[f1350,f679]) ).
tff(f679,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl26_28 ),
inference(avatar_component_clause,[],[f678]) ).
tff(f5012,plain,
( spl26_316
| ~ spl26_82
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1336,f1327,f986,f5010]) ).
tff(f5010,plain,
( spl26_316
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_316])]) ).
tff(f1336,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) )
| ~ spl26_82
| ~ spl26_131 ),
inference(superposition,[],[f1328,f987]) ).
tff(f5008,plain,
( spl26_315
| ~ spl26_114
| ~ spl26_128 ),
inference(avatar_split_clause,[],[f1307,f1302,f1216,f5005]) ).
tff(f5005,plain,
( spl26_315
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK13(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_315])]) ).
tff(f1307,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK13(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl26_114
| ~ spl26_128 ),
inference(resolution,[],[f1304,f1217]) ).
tff(f5003,plain,
( spl26_314
| ~ spl26_116
| ~ spl26_128 ),
inference(avatar_split_clause,[],[f1306,f1302,f1228,f5000]) ).
tff(f5000,plain,
( spl26_314
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK14(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_314])]) ).
tff(f1306,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK14(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl26_116
| ~ spl26_128 ),
inference(resolution,[],[f1304,f1229]) ).
tff(f4971,plain,
( spl26_313
| ~ spl26_18
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f1409,f630,f626,f4969]) ).
tff(f1409,plain,
( ! [X0: dB] :
( ( fTrue = aa(dB,bool,it,X0) )
| ~ sP1(X0) )
| ~ spl26_18
| ~ spl26_19 ),
inference(resolution,[],[f631,f627]) ).
tff(f4967,plain,
( spl26_312
| ~ spl26_49
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f2169,f2160,f796,f4965]) ).
tff(f4965,plain,
( spl26_312
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_312])]) ).
tff(f2169,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl26_49
| ~ spl26_204 ),
inference(superposition,[],[f797,f2161]) ).
tff(f4963,plain,
( spl26_311
| ~ spl26_50
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f2168,f2160,f800,f4961]) ).
tff(f4961,plain,
( spl26_311
<=> ! [X4: nat,X0: dB,X3: dB,X2: dB,X1: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_311])]) ).
tff(f2168,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl26_50
| ~ spl26_204 ),
inference(superposition,[],[f801,f2161]) ).
tff(f4959,plain,
( spl26_310
| ~ spl26_130
| ~ spl26_154 ),
inference(avatar_split_clause,[],[f1629,f1625,f1319,f4956]) ).
tff(f4956,plain,
( spl26_310
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,sK2,t1),a,var(i),shift(type,e,i,t))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_310])]) ).
tff(f1629,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,sK2,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl26_130
| ~ spl26_154 ),
inference(resolution,[],[f1626,f1321]) ).
tff(f4954,plain,
( spl26_309
| ~ spl26_126
| ~ spl26_154 ),
inference(avatar_split_clause,[],[f1628,f1625,f1286,f4951]) ).
tff(f1628,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK16(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl26_126
| ~ spl26_154 ),
inference(resolution,[],[f1626,f1288]) ).
tff(f4949,plain,
( spl26_308
| ~ spl26_17
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1353,f1349,f622,f4947]) ).
tff(f4947,plain,
( spl26_308
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_308])]) ).
tff(f622,plain,
( spl26_17
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_17])]) ).
tff(f1353,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0))) )
| ~ spl26_17
| ~ spl26_133 ),
inference(resolution,[],[f1350,f623]) ).
tff(f623,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl26_17 ),
inference(avatar_component_clause,[],[f622]) ).
tff(f4913,plain,
( spl26_307
| ~ spl26_133
| ~ spl26_184 ),
inference(avatar_split_clause,[],[f1974,f1971,f1349,f4911]) ).
tff(f4911,plain,
( spl26_307
<=> ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0)))
| ~ pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_307])]) ).
tff(f1974,plain,
( ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0)))
| ~ pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) )
| ~ spl26_133
| ~ spl26_184 ),
inference(resolution,[],[f1972,f1350]) ).
tff(f4909,plain,
( spl26_306
| ~ spl26_72
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1478,f1380,f986,f931,f4907]) ).
tff(f4907,plain,
( spl26_306
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_306])]) ).
tff(f1478,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl26_72
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1455,f987]) ).
tff(f1455,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) )
| ~ spl26_72
| ~ spl26_139 ),
inference(superposition,[],[f932,f1381]) ).
tff(f4870,plain,
( spl26_305
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1156,f1151,f4868]) ).
tff(f4868,plain,
( spl26_305
<=> ! [X0: $tType,X3: type,X4: fun(nat,X0),X5: fun(nat,X0),X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_305])]) ).
tff(f1156,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,X0)),X4: fun(nat,X0),X5: fun(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) )
| ~ spl26_105 ),
inference(superposition,[],[f1152,f1152]) ).
tff(f4823,plain,
( spl26_304
| ~ spl26_82
| ~ spl26_109 ),
inference(avatar_split_clause,[],[f1191,f1188,f986,f4821]) ).
tff(f4821,plain,
( spl26_304
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_304])]) ).
tff(f1191,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 )
| ~ spl26_82
| ~ spl26_109 ),
inference(superposition,[],[f1189,f987]) ).
tff(f4819,plain,
( spl26_303
| ~ spl26_13
| ~ spl26_82
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1163,f1151,f986,f599,f4817]) ).
tff(f4817,plain,
( spl26_303
<=> ! [X2: type,X0: fun(nat,bool),X1: fun(type,fun(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,fun1,X2),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_303])]) ).
tff(f1163,plain,
( ! [X2: type,X3: type,X0: fun(nat,bool),X1: fun(type,fun(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,fun1,X2),X3)) ) )
| ~ spl26_13
| ~ spl26_82
| ~ spl26_105 ),
inference(forward_demodulation,[],[f1158,f987]) ).
tff(f1158,plain,
( ! [X2: type,X3: type,X0: fun(nat,bool),X1: fun(type,fun(type,bool))] :
( ( fFalse = aa(type,bool,aa(type,fun(type,bool),X1,X3),X2) )
| ( fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun1,X2),X3)) ) )
| ~ spl26_13
| ~ spl26_105 ),
inference(superposition,[],[f1152,f600]) ).
tff(f4815,plain,
( spl26_302
| ~ spl26_65
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1009,f986,f893,f4813]) ).
tff(f4813,plain,
( spl26_302
<=> ! [X0: $tType,X3: nat,X2: X0,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_302])]) ).
tff(f1009,plain,
( ! [X0: $tType,X2: X0,X3: nat,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3)))
| ~ spl26_65
| ~ spl26_82 ),
inference(superposition,[],[f894,f987]) ).
tff(f4734,plain,
( spl26_301
| ~ spl26_62
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1482,f1380,f986,f880,f4732]) ).
tff(f4732,plain,
( spl26_301
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_301])]) ).
tff(f880,plain,
( spl26_62
<=> ! [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,[spl26_62])]) ).
tff(f1482,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 ) )
| ~ spl26_62
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1459,f987]) ).
tff(f1459,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl26_62
| ~ spl26_139 ),
inference(superposition,[],[f881,f1381]) ).
tff(f881,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 ) )
| ~ spl26_62 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f4730,plain,
( spl26_300
| ~ spl26_63
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1474,f1380,f986,f884,f4728]) ).
tff(f4728,plain,
( spl26_300
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_300])]) ).
tff(f884,plain,
( spl26_63
<=> ! [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,[spl26_63])]) ).
tff(f1474,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 ) )
| ~ spl26_63
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1451,f987]) ).
tff(f1451,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl26_63
| ~ spl26_139 ),
inference(superposition,[],[f885,f1381]) ).
tff(f885,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 ) )
| ~ spl26_63 ),
inference(avatar_component_clause,[],[f884]) ).
tff(f4726,plain,
( spl26_299
| ~ spl26_28
| ~ spl26_111 ),
inference(avatar_split_clause,[],[f1202,f1199,f678,f4724]) ).
tff(f4724,plain,
( spl26_299
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_299])]) ).
tff(f1199,plain,
( spl26_111
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_111])]) ).
tff(f1202,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) )
| ~ spl26_28
| ~ spl26_111 ),
inference(resolution,[],[f1200,f679]) ).
tff(f1200,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_111 ),
inference(avatar_component_clause,[],[f1199]) ).
tff(f4722,plain,
( spl26_298
| ~ spl26_13
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1094,f1083,f599,f4720]) ).
tff(f4720,plain,
( spl26_298
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK17(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK17(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_298])]) ).
tff(f1094,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK17(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK17(bool,X0,X1,X2)) ) )
| ~ spl26_13
| ~ spl26_95 ),
inference(superposition,[],[f1084,f600]) ).
tff(f4718,plain,
( spl26_297
| ~ spl26_13
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1089,f1083,f599,f4716]) ).
tff(f4716,plain,
( spl26_297
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK17(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK17(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_297])]) ).
tff(f1089,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK17(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK17(bool,X0,X2,X1)) ) )
| ~ spl26_13
| ~ spl26_95 ),
inference(superposition,[],[f1084,f600]) ).
tff(f4653,plain,
( spl26_296
| ~ spl26_4
| ~ spl26_215 ),
inference(avatar_split_clause,[],[f2523,f2315,f559,f4651]) ).
tff(f4651,plain,
( spl26_296
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_296])]) ).
tff(f2315,plain,
( spl26_215
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_215])]) ).
tff(f2523,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl26_4
| ~ spl26_215 ),
inference(superposition,[],[f561,f2316]) ).
tff(f2316,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl26_215 ),
inference(avatar_component_clause,[],[f2315]) ).
tff(f561,plain,
( pp(fTrue)
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f4649,plain,
( spl26_295
| ~ spl26_17
| ~ spl26_111 ),
inference(avatar_split_clause,[],[f1203,f1199,f622,f4647]) ).
tff(f4647,plain,
( spl26_295
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_295])]) ).
tff(f1203,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) )
| ~ spl26_17
| ~ spl26_111 ),
inference(resolution,[],[f1200,f623]) ).
tff(f4645,plain,
( spl26_294
| ~ spl26_51
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1001,f986,f804,f4643]) ).
tff(f4643,plain,
( spl26_294
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_294])]) ).
tff(f1001,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) )
| ~ spl26_51
| ~ spl26_82 ),
inference(superposition,[],[f805,f987]) ).
tff(f4641,plain,
( spl26_293
| ~ spl26_51
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1000,f986,f804,f4639]) ).
tff(f4639,plain,
( spl26_293
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_293])]) ).
tff(f1000,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) )
| ~ spl26_51
| ~ spl26_82 ),
inference(superposition,[],[f805,f987]) ).
tff(f4528,plain,
( spl26_292
| ~ spl26_15
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f1411,f630,f613,f4526]) ).
tff(f4526,plain,
( spl26_292
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_292])]) ).
tff(f613,plain,
( spl26_15
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_15])]) ).
tff(f1411,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) )
| ~ spl26_15
| ~ spl26_19 ),
inference(resolution,[],[f631,f614]) ).
tff(f614,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl26_15 ),
inference(avatar_component_clause,[],[f613]) ).
tff(f4298,plain,
( spl26_291
| ~ spl26_67
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1773,f1754,f907,f4296]) ).
tff(f4296,plain,
( spl26_291
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_291])]) ).
tff(f1773,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ~ spl26_67
| ~ spl26_170 ),
inference(superposition,[],[f908,f1755]) ).
tff(f4294,plain,
( spl26_290
| ~ spl26_90
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1662,f1656,f1053,f4292]) ).
tff(f4292,plain,
( spl26_290
<=> ! [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,[spl26_290])]) ).
tff(f1662,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 ) )
| ~ spl26_90
| ~ spl26_158 ),
inference(resolution,[],[f1657,f1055]) ).
tff(f4290,plain,
( spl26_289
| ~ spl26_92
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1661,f1656,f1066,f4288]) ).
tff(f4288,plain,
( spl26_289
<=> ! [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,[spl26_289])]) ).
tff(f1661,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 ) )
| ~ spl26_92
| ~ spl26_158 ),
inference(resolution,[],[f1657,f1068]) ).
tff(f4286,plain,
( spl26_288
| ~ spl26_90
| ~ spl26_107 ),
inference(avatar_split_clause,[],[f1177,f1172,f1053,f4284]) ).
tff(f4284,plain,
( spl26_288
<=> ! [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,[spl26_288])]) ).
tff(f1177,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) )
| ~ spl26_90
| ~ spl26_107 ),
inference(resolution,[],[f1173,f1055]) ).
tff(f4282,plain,
( spl26_287
| ~ spl26_92
| ~ spl26_107 ),
inference(avatar_split_clause,[],[f1176,f1172,f1066,f4280]) ).
tff(f4280,plain,
( spl26_287
<=> ! [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,[spl26_287])]) ).
tff(f1176,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) )
| ~ spl26_92
| ~ spl26_107 ),
inference(resolution,[],[f1173,f1068]) ).
tff(f4277,plain,
( spl26_286
| ~ spl26_82
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1157,f1151,f986,f4275]) ).
tff(f4275,plain,
( spl26_286
<=> ! [X0: $tType,X4: fun(nat,X0),X3: type,X2: type,X1: fun(type,fun(type,X0))] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_286])]) ).
tff(f1157,plain,
( ! [X0: $tType,X2: type,X3: type,X1: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2) )
| ~ spl26_82
| ~ spl26_105 ),
inference(superposition,[],[f1152,f987]) ).
tff(f4273,plain,
( spl26_285
| ~ spl26_82
| ~ spl26_103 ),
inference(avatar_split_clause,[],[f1142,f1130,f986,f4271]) ).
tff(f4271,plain,
( spl26_285
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_285])]) ).
tff(f1142,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) )
| ~ spl26_82
| ~ spl26_103 ),
inference(superposition,[],[f1131,f987]) ).
tff(f4269,plain,
( spl26_284
| ~ spl26_82
| ~ spl26_102 ),
inference(avatar_split_clause,[],[f1139,f1126,f986,f4267]) ).
tff(f4267,plain,
( spl26_284
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_284])]) ).
tff(f1139,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_82
| ~ spl26_102 ),
inference(superposition,[],[f1127,f987]) ).
tff(f4265,plain,
( spl26_283
| ~ spl26_82
| ~ spl26_101 ),
inference(avatar_split_clause,[],[f1136,f1122,f986,f4263]) ).
tff(f4263,plain,
( spl26_283
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_283])]) ).
tff(f1136,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl26_82
| ~ spl26_101 ),
inference(superposition,[],[f1123,f987]) ).
tff(f4261,plain,
( spl26_282
| ~ spl26_82
| ~ spl26_100 ),
inference(avatar_split_clause,[],[f1133,f1117,f986,f4259]) ).
tff(f4259,plain,
( spl26_282
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_282])]) ).
tff(f1133,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_82
| ~ spl26_100 ),
inference(superposition,[],[f1118,f987]) ).
tff(f4257,plain,
( spl26_281
| ~ spl26_13
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f997,f986,f599,f4255]) ).
tff(f4255,plain,
( spl26_281
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_281])]) ).
tff(f997,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) )
| ~ spl26_13
| ~ spl26_82 ),
inference(superposition,[],[f987,f600]) ).
tff(f4253,plain,
( spl26_280
| ~ spl26_13
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f993,f986,f599,f4251]) ).
tff(f4251,plain,
( spl26_280
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_280])]) ).
tff(f993,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) )
| ~ spl26_13
| ~ spl26_82 ),
inference(superposition,[],[f987,f600]) ).
tff(f4233,plain,
( spl26_279
| ~ spl26_26
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2831,f2815,f670,f4231]) ).
tff(f4231,plain,
( spl26_279
<=> ! [X0: dB] :
( sP1(abs(abs(sK7(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_279])]) ).
tff(f2831,plain,
( ! [X0: dB] :
( sP1(abs(abs(sK7(X0))))
| ~ sP0(X0) )
| ~ spl26_26
| ~ spl26_217 ),
inference(resolution,[],[f2816,f671]) ).
tff(f4221,plain,
( spl26_278
| ~ spl26_52
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1484,f1380,f986,f808,f4219]) ).
tff(f4219,plain,
( spl26_278
<=> ! [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,[spl26_278])]) ).
tff(f808,plain,
( spl26_52
<=> ! [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,[spl26_52])]) ).
tff(f1484,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) )
| ~ spl26_52
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1461,f987]) ).
tff(f1461,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ~ spl26_52
| ~ spl26_139 ),
inference(superposition,[],[f809,f1381]) ).
tff(f809,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) )
| ~ spl26_52 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f4217,plain,
( spl26_277
| ~ spl26_52
| ~ spl26_82
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1472,f1380,f986,f808,f4215]) ).
tff(f4215,plain,
( spl26_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,[spl26_277])]) ).
tff(f1472,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) )
| ~ spl26_52
| ~ spl26_82
| ~ spl26_139 ),
inference(forward_demodulation,[],[f1449,f987]) ).
tff(f1449,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != foldl(dB,dB,app,abs(X3),X4) )
| ~ spl26_52
| ~ spl26_139 ),
inference(superposition,[],[f809,f1381]) ).
tff(f4213,plain,
( spl26_276
| ~ spl26_51
| ~ spl26_130 ),
inference(avatar_split_clause,[],[f1324,f1319,f804,f4210]) ).
tff(f4210,plain,
( spl26_276
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_276])]) ).
tff(f1324,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1))))
| ~ spl26_51
| ~ spl26_130 ),
inference(resolution,[],[f1321,f805]) ).
tff(f4208,plain,
( spl26_275
| ~ spl26_51
| ~ spl26_126 ),
inference(avatar_split_clause,[],[f1291,f1286,f804,f4205]) ).
tff(f4205,plain,
( spl26_275
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_275])]) ).
tff(f1291,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1))))
| ~ spl26_51
| ~ spl26_126 ),
inference(resolution,[],[f1288,f805]) ).
tff(f4040,plain,
( spl26_274
| ~ spl26_66
| ~ spl26_146 ),
inference(avatar_split_clause,[],[f1548,f1541,f902,f4038]) ).
tff(f4038,plain,
( spl26_274
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_274])]) ).
tff(f1548,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) )
| ~ spl26_66
| ~ spl26_146 ),
inference(superposition,[],[f1542,f904]) ).
tff(f4036,plain,
( spl26_273
| ~ spl26_20
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1091,f1083,f634,f4034]) ).
tff(f4034,plain,
( spl26_273
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK17(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK17(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_273])]) ).
tff(f1091,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK17(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK17(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl26_20
| ~ spl26_95 ),
inference(superposition,[],[f1084,f635]) ).
tff(f4032,plain,
( spl26_272
| ~ spl26_13
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1090,f1083,f599,f4030]) ).
tff(f4030,plain,
( spl26_272
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK17(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_272])]) ).
tff(f1090,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK17(X0,bool,X1,X2) ) )
| ~ spl26_13
| ~ spl26_95 ),
inference(superposition,[],[f1084,f600]) ).
tff(f4028,plain,
( spl26_271
| ~ spl26_20
| ~ spl26_95 ),
inference(avatar_split_clause,[],[f1086,f1083,f634,f4026]) ).
tff(f4026,plain,
( spl26_271
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK17(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK17(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_271])]) ).
tff(f1086,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK17(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK17(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl26_20
| ~ spl26_95 ),
inference(superposition,[],[f1084,f635]) ).
tff(f4024,plain,
( spl26_270
| ~ spl26_51
| ~ spl26_88 ),
inference(avatar_split_clause,[],[f1044,f1040,f804,f4022]) ).
tff(f4022,plain,
( spl26_270
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_270])]) ).
tff(f1040,plain,
( spl26_88
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_88])]) ).
tff(f1044,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) )
| ~ spl26_51
| ~ spl26_88 ),
inference(resolution,[],[f1041,f805]) ).
tff(f1041,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl26_88 ),
inference(avatar_component_clause,[],[f1040]) ).
tff(f3946,plain,
( spl26_269
| ~ spl26_49
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1950,f1940,f796,f3944]) ).
tff(f3944,plain,
( spl26_269
<=> ! [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,[spl26_269])]) ).
tff(f1950,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)) )
| ~ spl26_49
| ~ spl26_180 ),
inference(superposition,[],[f797,f1941]) ).
tff(f3942,plain,
( spl26_268
| ~ spl26_50
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1949,f1940,f800,f3940]) ).
tff(f3940,plain,
( spl26_268
<=> ! [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,[spl26_268])]) ).
tff(f1949,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)) )
| ~ spl26_50
| ~ spl26_180 ),
inference(superposition,[],[f801,f1941]) ).
tff(f3938,plain,
( spl26_267
| ~ spl26_66
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1512,f1498,f902,f3936]) ).
tff(f3936,plain,
( spl26_267
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK24(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_267])]) ).
tff(f1512,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK24(dB,X0,X2,X1,as,a)) ) )
| ~ spl26_66
| ~ spl26_142 ),
inference(superposition,[],[f1499,f904]) ).
tff(f3934,plain,
( spl26_266
| ~ spl26_66
| ~ spl26_141 ),
inference(avatar_split_clause,[],[f1508,f1494,f902,f3932]) ).
tff(f3932,plain,
( spl26_266
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_266])]) ).
tff(f1508,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(X0,dB,as,a,X2,X1)) ) )
| ~ spl26_66
| ~ spl26_141 ),
inference(superposition,[],[f1495,f904]) ).
tff(f3930,plain,
( spl26_265
| ~ spl26_66
| ~ spl26_140 ),
inference(avatar_split_clause,[],[f1501,f1490,f902,f3928]) ).
tff(f3928,plain,
( spl26_265
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_265])]) ).
tff(f1501,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) )
| ~ spl26_66
| ~ spl26_140 ),
inference(superposition,[],[f1491,f904]) ).
tff(f3914,plain,
( spl26_264
| ~ spl26_90
| ~ spl26_116 ),
inference(avatar_split_clause,[],[f1232,f1228,f1053,f3911]) ).
tff(f3911,plain,
( spl26_264
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_264])]) ).
tff(f1232,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl26_90
| ~ spl26_116 ),
inference(resolution,[],[f1229,f1055]) ).
tff(f3909,plain,
( spl26_263
| ~ spl26_92
| ~ spl26_116 ),
inference(avatar_split_clause,[],[f1231,f1228,f1066,f3906]) ).
tff(f3906,plain,
( spl26_263
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK14(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_263])]) ).
tff(f1231,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK14(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl26_92
| ~ spl26_116 ),
inference(resolution,[],[f1229,f1068]) ).
tff(f3904,plain,
( spl26_262
| ~ spl26_90
| ~ spl26_114 ),
inference(avatar_split_clause,[],[f1220,f1216,f1053,f3901]) ).
tff(f3901,plain,
( spl26_262
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK13(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_262])]) ).
tff(f1220,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK13(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl26_90
| ~ spl26_114 ),
inference(resolution,[],[f1217,f1055]) ).
tff(f3899,plain,
( spl26_261
| ~ spl26_92
| ~ spl26_114 ),
inference(avatar_split_clause,[],[f1219,f1216,f1066,f3896]) ).
tff(f3896,plain,
( spl26_261
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK13(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_261])]) ).
tff(f1219,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK13(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl26_92
| ~ spl26_114 ),
inference(resolution,[],[f1217,f1068]) ).
tff(f3894,plain,
( spl26_260
| ~ spl26_29
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f994,f986,f691,f3892]) ).
tff(f3892,plain,
( spl26_260
<=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_260])]) ).
tff(f994,plain,
( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) )
| ~ spl26_29
| ~ spl26_82 ),
inference(superposition,[],[f987,f692]) ).
tff(f3868,plain,
( spl26_259
| ~ spl26_66
| ~ spl26_137 ),
inference(avatar_split_clause,[],[f1386,f1372,f902,f3866]) ).
tff(f3866,plain,
( spl26_259
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK23(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_259])]) ).
tff(f1386,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK23(dB,X0,X2,X1,as,a)) ) )
| ~ spl26_66
| ~ spl26_137 ),
inference(superposition,[],[f1373,f904]) ).
tff(f3863,plain,
( spl26_258
| ~ spl26_66
| ~ spl26_136 ),
inference(avatar_split_clause,[],[f1383,f1368,f902,f3861]) ).
tff(f3861,plain,
( spl26_258
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_258])]) ).
tff(f1383,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(X0,dB,as,a,X2,X1)) ) )
| ~ spl26_66
| ~ spl26_136 ),
inference(superposition,[],[f1369,f904]) ).
tff(f3859,plain,
( spl26_257
| ~ spl26_90
| ~ spl26_119 ),
inference(avatar_split_clause,[],[f1250,f1246,f1053,f3856]) ).
tff(f3856,plain,
( spl26_257
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,i,shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_257])]) ).
tff(f1250,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,i,shift(type,ea,ia,t))))
| ~ spl26_90
| ~ spl26_119 ),
inference(resolution,[],[f1247,f1055]) ).
tff(f3854,plain,
( spl26_256
| ~ spl26_92
| ~ spl26_119 ),
inference(avatar_split_clause,[],[f1249,f1246,f1066,f3851]) ).
tff(f3851,plain,
( spl26_256
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,i,shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_256])]) ).
tff(f1249,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,i,shift(type,e,i,t))))
| ~ spl26_92
| ~ spl26_119 ),
inference(resolution,[],[f1247,f1068]) ).
tff(f3846,plain,
( spl26_255
| ~ spl26_78
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f998,f986,f964,f3844]) ).
tff(f3844,plain,
( spl26_255
<=> ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_255])]) ).
tff(f998,plain,
( ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 )
| ~ spl26_78
| ~ spl26_82 ),
inference(superposition,[],[f987,f965]) ).
tff(f3824,plain,
( spl26_254
| ~ spl26_18
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2818,f2815,f626,f3822]) ).
tff(f3822,plain,
( spl26_254
<=> ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_254])]) ).
tff(f2818,plain,
( ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) )
| ~ spl26_18
| ~ spl26_217 ),
inference(resolution,[],[f2816,f627]) ).
tff(f3806,plain,
( spl26_253
| ~ spl26_51
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f1070,f1066,f804,f3803]) ).
tff(f3803,plain,
( spl26_253
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_253])]) ).
tff(f1070,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1)))
| ~ spl26_51
| ~ spl26_92 ),
inference(resolution,[],[f1068,f805]) ).
tff(f3801,plain,
( spl26_252
| ~ spl26_51
| ~ spl26_90 ),
inference(avatar_split_clause,[],[f1057,f1053,f804,f3798]) ).
tff(f3798,plain,
( spl26_252
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_252])]) ).
tff(f1057,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a)))
| ~ spl26_51
| ~ spl26_90 ),
inference(resolution,[],[f1055,f805]) ).
tff(f3796,plain,
( spl26_251
| ~ spl26_28
| ~ spl26_84 ),
inference(avatar_split_clause,[],[f1019,f1016,f678,f3794]) ).
tff(f3794,plain,
( spl26_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,[spl26_251])]) ).
tff(f1016,plain,
( spl26_84
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_84])]) ).
tff(f1019,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) )
| ~ spl26_28
| ~ spl26_84 ),
inference(resolution,[],[f1017,f679]) ).
tff(f1017,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)) )
| ~ spl26_84 ),
inference(avatar_component_clause,[],[f1016]) ).
tff(f3792,plain,
( spl26_250
| ~ spl26_72
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1004,f986,f931,f3790]) ).
tff(f3790,plain,
( spl26_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,[spl26_250])]) ).
tff(f1004,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)) )
| ~ spl26_72
| ~ spl26_82 ),
inference(superposition,[],[f932,f987]) ).
tff(f3788,plain,
( spl26_249
| ~ spl26_28
| ~ spl26_76 ),
inference(avatar_split_clause,[],[f989,f955,f678,f3786]) ).
tff(f3786,plain,
( spl26_249
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK3(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_249])]) ).
tff(f955,plain,
( spl26_76
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK3(X0)))
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_76])]) ).
tff(f989,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK3(X0))) )
| ~ spl26_28
| ~ spl26_76 ),
inference(resolution,[],[f956,f679]) ).
tff(f956,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK3(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl26_76 ),
inference(avatar_component_clause,[],[f955]) ).
tff(f3784,plain,
( spl26_248
| ~ spl26_51
| ~ spl26_65 ),
inference(avatar_split_clause,[],[f896,f893,f804,f3782]) ).
tff(f3782,plain,
( spl26_248
<=> ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_248])]) ).
tff(f896,plain,
( ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1))))
| ~ spl26_51
| ~ spl26_65 ),
inference(resolution,[],[f894,f805]) ).
tff(f3776,plain,
( spl26_247
| ~ spl26_17
| ~ spl26_84 ),
inference(avatar_split_clause,[],[f1020,f1016,f622,f3774]) ).
tff(f3774,plain,
( spl26_247
<=> ! [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,[spl26_247])]) ).
tff(f1020,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) )
| ~ spl26_17
| ~ spl26_84 ),
inference(resolution,[],[f1017,f623]) ).
tff(f3772,plain,
( spl26_246
| ~ spl26_17
| ~ spl26_76 ),
inference(avatar_split_clause,[],[f990,f955,f622,f3770]) ).
tff(f3770,plain,
( spl26_246
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_246])]) ).
tff(f990,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK3(X0)) )
| ~ spl26_17
| ~ spl26_76 ),
inference(resolution,[],[f956,f623]) ).
tff(f3768,plain,
( spl26_245
| ~ spl26_28
| ~ spl26_80 ),
inference(avatar_split_clause,[],[f976,f973,f678,f3766]) ).
tff(f3766,plain,
( spl26_245
<=> ! [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,[spl26_245])]) ).
tff(f973,plain,
( spl26_80
<=> ! [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,[spl26_80])]) ).
tff(f976,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) )
| ~ spl26_28
| ~ spl26_80 ),
inference(resolution,[],[f974,f679]) ).
tff(f974,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)) )
| ~ spl26_80 ),
inference(avatar_component_clause,[],[f973]) ).
tff(f3710,plain,
( spl26_244
| ~ spl26_15
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2820,f2815,f613,f3708]) ).
tff(f2820,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl26_15
| ~ spl26_217 ),
inference(resolution,[],[f2816,f614]) ).
tff(f3135,plain,
( ~ spl26_4
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3082]) ).
tff(f3082,plain,
( $false
| ~ spl26_4
| ~ spl26_220 ),
inference(resolution,[],[f2862,f561]) ).
tff(f2862,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl26_220 ),
inference(avatar_component_clause,[],[f2861]) ).
tff(f2861,plain,
( spl26_220
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_220])]) ).
tff(f3134,plain,
( ~ spl26_42
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3083]) ).
tff(f3083,plain,
( $false
| ~ spl26_42
| ~ spl26_220 ),
inference(resolution,[],[f2862,f759]) ).
tff(f759,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl26_42 ),
inference(avatar_component_clause,[],[f758]) ).
tff(f758,plain,
( spl26_42
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_42])]) ).
tff(f3133,plain,
( ~ spl26_15
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3085]) ).
tff(f3085,plain,
( $false
| ~ spl26_15
| ~ spl26_220 ),
inference(resolution,[],[f2862,f614]) ).
tff(f3132,plain,
( ~ spl26_8
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3088]) ).
tff(f3088,plain,
( $false
| ~ spl26_8
| ~ spl26_220 ),
inference(resolution,[],[f2862,f578]) ).
tff(f578,plain,
( pp(aa(dB,bool,it,t2))
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f576]) ).
tff(f576,plain,
( spl26_8
<=> pp(aa(dB,bool,it,t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
tff(f3131,plain,
( ~ spl26_10
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3089]) ).
tff(f3089,plain,
( $false
| ~ spl26_10
| ~ spl26_220 ),
inference(resolution,[],[f2862,f588]) ).
tff(f588,plain,
( pp(aa(dB,bool,it,u))
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f586]) ).
tff(f586,plain,
( spl26_10
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
tff(f3130,plain,
( ~ spl26_9
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3090]) ).
tff(f3090,plain,
( $false
| ~ spl26_9
| ~ spl26_220 ),
inference(resolution,[],[f2862,f583]) ).
tff(f583,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f581]) ).
tff(f581,plain,
( spl26_9
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
tff(f3129,plain,
( ~ spl26_220
| ~ spl26_239 ),
inference(avatar_contradiction_clause,[],[f3094]) ).
tff(f3094,plain,
( $false
| ~ spl26_220
| ~ spl26_239 ),
inference(resolution,[],[f2862,f3037]) ).
tff(f3037,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl26_239 ),
inference(avatar_component_clause,[],[f3036]) ).
tff(f3036,plain,
( spl26_239
<=> ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_239])]) ).
tff(f3128,plain,
( ~ spl26_126
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3095]) ).
tff(f3095,plain,
( $false
| ~ spl26_126
| ~ spl26_220 ),
inference(resolution,[],[f2862,f1288]) ).
tff(f3127,plain,
( ~ spl26_130
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3096]) ).
tff(f3096,plain,
( $false
| ~ spl26_130
| ~ spl26_220 ),
inference(resolution,[],[f2862,f1321]) ).
tff(f3126,plain,
( ~ spl26_65
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3097]) ).
tff(f3097,plain,
( $false
| ~ spl26_65
| ~ spl26_220 ),
inference(resolution,[],[f2862,f894]) ).
tff(f3125,plain,
( ~ spl26_92
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3098]) ).
tff(f3098,plain,
( $false
| ~ spl26_92
| ~ spl26_220 ),
inference(resolution,[],[f2862,f1068]) ).
tff(f3124,plain,
( ~ spl26_128
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3099]) ).
tff(f3099,plain,
( $false
| ~ spl26_128
| ~ spl26_220 ),
inference(resolution,[],[f2862,f1304]) ).
tff(f3123,plain,
( ~ spl26_90
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3100]) ).
tff(f3100,plain,
( $false
| ~ spl26_90
| ~ spl26_220 ),
inference(resolution,[],[f2862,f1055]) ).
tff(f3122,plain,
( ~ spl26_34
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3101]) ).
tff(f3101,plain,
( $false
| ~ spl26_34
| ~ spl26_220 ),
inference(resolution,[],[f2862,f718]) ).
tff(f718,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl26_34 ),
inference(avatar_component_clause,[],[f716]) ).
tff(f716,plain,
( spl26_34
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_34])]) ).
tff(f3121,plain,
( ~ spl26_36
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3102]) ).
tff(f3102,plain,
( $false
| ~ spl26_36
| ~ spl26_220 ),
inference(resolution,[],[f2862,f730]) ).
tff(f730,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl26_36 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f728,plain,
( spl26_36
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_36])]) ).
tff(f3120,plain,
( ~ spl26_38
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3105]) ).
tff(f3105,plain,
( $false
| ~ spl26_38
| ~ spl26_220 ),
inference(resolution,[],[f2862,f741]) ).
tff(f3119,plain,
( ~ spl26_39
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3106]) ).
tff(f3106,plain,
( $false
| ~ spl26_39
| ~ spl26_220 ),
inference(resolution,[],[f2862,f746]) ).
tff(f3118,plain,
( ~ spl26_220
| ~ spl26_231 ),
inference(avatar_contradiction_clause,[],[f3107]) ).
tff(f3107,plain,
( $false
| ~ spl26_220
| ~ spl26_231 ),
inference(resolution,[],[f2862,f2930]) ).
tff(f2930,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl26_231 ),
inference(avatar_component_clause,[],[f2928]) ).
tff(f2928,plain,
( spl26_231
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_231])]) ).
tff(f3117,plain,
( ~ spl26_220
| ~ spl26_232 ),
inference(avatar_contradiction_clause,[],[f3108]) ).
tff(f3108,plain,
( $false
| ~ spl26_220
| ~ spl26_232 ),
inference(resolution,[],[f2862,f2935]) ).
tff(f2935,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl26_232 ),
inference(avatar_component_clause,[],[f2933]) ).
tff(f2933,plain,
( spl26_232
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_232])]) ).
tff(f3116,plain,
( ~ spl26_220
| ~ spl26_233 ),
inference(avatar_contradiction_clause,[],[f3109]) ).
tff(f3109,plain,
( $false
| ~ spl26_220
| ~ spl26_233 ),
inference(resolution,[],[f2862,f2939]) ).
tff(f2939,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl26_233 ),
inference(avatar_component_clause,[],[f2938]) ).
tff(f2938,plain,
( spl26_233
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_233])]) ).
tff(f3115,plain,
( ~ spl26_219
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3110]) ).
tff(f3110,plain,
( $false
| ~ spl26_219
| ~ spl26_220 ),
inference(resolution,[],[f2862,f2859]) ).
tff(f2859,plain,
( pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool)))
| ~ spl26_219 ),
inference(avatar_component_clause,[],[f2857]) ).
tff(f2857,plain,
( spl26_219
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_219])]) ).
tff(f3114,plain,
( ~ spl26_216
| ~ spl26_220 ),
inference(avatar_contradiction_clause,[],[f3111]) ).
tff(f3111,plain,
( $false
| ~ spl26_216
| ~ spl26_220 ),
inference(resolution,[],[f2862,f2321]) ).
tff(f3113,plain,
( ~ spl26_220
| ~ spl26_238 ),
inference(avatar_contradiction_clause,[],[f3112]) ).
tff(f3112,plain,
( $false
| ~ spl26_220
| ~ spl26_238 ),
inference(resolution,[],[f2862,f3032]) ).
tff(f3032,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as)))
| ~ spl26_238 ),
inference(avatar_component_clause,[],[f3030]) ).
tff(f3030,plain,
( spl26_238
<=> pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_238])]) ).
tff(f3081,plain,
( spl26_220
| spl26_243
| ~ spl26_51
| ~ spl26_55 ),
inference(avatar_split_clause,[],[f841,f836,f804,f3079,f2861]) ).
tff(f3079,plain,
( spl26_243
<=> ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_243])]) ).
tff(f836,plain,
( spl26_55
<=> ! [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,[spl26_55])]) ).
tff(f841,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) )
| ~ spl26_51
| ~ spl26_55 ),
inference(resolution,[],[f837,f805]) ).
tff(f837,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl26_55 ),
inference(avatar_component_clause,[],[f836]) ).
tff(f3051,plain,
( spl26_242
| ~ spl26_67
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1007,f986,f907,f3049]) ).
tff(f3049,plain,
( spl26_242
<=> ! [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,[spl26_242])]) ).
tff(f1007,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 )
| ~ spl26_67
| ~ spl26_82 ),
inference(superposition,[],[f908,f987]) ).
tff(f3047,plain,
( spl26_241
| ~ spl26_66
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f999,f986,f902,f3044]) ).
tff(f3044,plain,
( spl26_241
<=> ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_241])]) ).
tff(f999,plain,
( ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) )
| ~ spl26_66
| ~ spl26_82 ),
inference(superposition,[],[f987,f904]) ).
tff(f3042,plain,
( spl26_240
| ~ spl26_17
| ~ spl26_80 ),
inference(avatar_split_clause,[],[f977,f973,f622,f3040]) ).
tff(f3040,plain,
( spl26_240
<=> ! [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,[spl26_240])]) ).
tff(f977,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl26_17
| ~ spl26_80 ),
inference(resolution,[],[f974,f623]) ).
tff(f3038,plain,
( spl26_239
| ~ spl26_29
| ~ spl26_65 ),
inference(avatar_split_clause,[],[f897,f893,f691,f3036]) ).
tff(f897,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl26_29
| ~ spl26_65 ),
inference(superposition,[],[f894,f692]) ).
tff(f3033,plain,
( spl26_238
| ~ spl26_38
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f821,f804,f739,f3030]) ).
tff(f821,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as)))
| ~ spl26_38
| ~ spl26_51 ),
inference(resolution,[],[f805,f741]) ).
tff(f2957,plain,
( spl26_237
| ~ spl26_36
| ~ spl26_107 ),
inference(avatar_split_clause,[],[f1179,f1172,f728,f2955]) ).
tff(f2955,plain,
( spl26_237
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| ~ beta(u,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_237])]) ).
tff(f1179,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0))
| ~ beta(u,X0) )
| ~ spl26_36
| ~ spl26_107 ),
inference(resolution,[],[f1173,f730]) ).
tff(f2953,plain,
( spl26_236
| ~ spl26_34
| ~ spl26_107 ),
inference(avatar_split_clause,[],[f1178,f1172,f716,f2951]) ).
tff(f2951,plain,
( spl26_236
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| ~ beta(ua,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_236])]) ).
tff(f1178,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),X0))
| ~ beta(ua,X0) )
| ~ spl26_34
| ~ spl26_107 ),
inference(resolution,[],[f1173,f718]) ).
tff(f2949,plain,
( spl26_235
| ~ spl26_9
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2828,f2815,f581,f2946]) ).
tff(f2828,plain,
( sP1(abs(abs(ua)))
| ~ spl26_9
| ~ spl26_217 ),
inference(resolution,[],[f2816,f583]) ).
tff(f2944,plain,
( spl26_234
| ~ spl26_29
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f825,f804,f691,f2942]) ).
tff(f2942,plain,
( spl26_234
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_234])]) ).
tff(f825,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) )
| ~ spl26_29
| ~ spl26_51 ),
inference(superposition,[],[f805,f692]) ).
tff(f2940,plain,
( spl26_233
| ~ spl26_42
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f820,f804,f758,f2938]) ).
tff(f820,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl26_42
| ~ spl26_51 ),
inference(resolution,[],[f805,f759]) ).
tff(f2936,plain,
( spl26_232
| ~ spl26_36
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f819,f804,f728,f2933]) ).
tff(f819,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl26_36
| ~ spl26_51 ),
inference(resolution,[],[f805,f730]) ).
tff(f2931,plain,
( spl26_231
| ~ spl26_34
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f818,f804,f716,f2928]) ).
tff(f818,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl26_34
| ~ spl26_51 ),
inference(resolution,[],[f805,f718]) ).
tff(f2926,plain,
( spl26_230
| ~ spl26_13
| ~ spl26_31 ),
inference(avatar_split_clause,[],[f708,f701,f599,f2924]) ).
tff(f2924,plain,
( spl26_230
<=> ! [X2: nat,X0: fun(nat,bool),X1: fun(type,fun(type,bool))] :
( ( fFalse = aa(nat,bool,X0,X2) )
| ( fTrue = type_case(bool,X0,X1,atom(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_230])]) ).
tff(f701,plain,
( spl26_31
<=> ! [X0: $tType,X3: fun(nat,X0),X2: fun(type,fun(type,X0)),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_31])]) ).
tff(f708,plain,
( ! [X2: nat,X0: fun(nat,bool),X1: fun(type,fun(type,bool))] :
( ( fFalse = aa(nat,bool,X0,X2) )
| ( fTrue = type_case(bool,X0,X1,atom(X2)) ) )
| ~ spl26_13
| ~ spl26_31 ),
inference(superposition,[],[f702,f600]) ).
tff(f702,plain,
( ! [X0: $tType,X2: fun(type,fun(type,X0)),X3: fun(nat,X0),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) )
| ~ spl26_31 ),
inference(avatar_component_clause,[],[f701]) ).
tff(f2911,plain,
( spl26_229
| ~ spl26_13
| ~ spl26_29 ),
inference(avatar_split_clause,[],[f694,f691,f599,f2909]) ).
tff(f2909,plain,
( spl26_229
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_229])]) ).
tff(f694,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) )
| ~ spl26_13
| ~ spl26_29 ),
inference(superposition,[],[f692,f600]) ).
tff(f2907,plain,
( spl26_228
| ~ spl26_10
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2827,f2815,f586,f2904]) ).
tff(f2827,plain,
( sP1(abs(abs(u)))
| ~ spl26_10
| ~ spl26_217 ),
inference(resolution,[],[f2816,f588]) ).
tff(f2899,plain,
( spl26_227
| ~ spl26_48
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1008,f986,f792,f2897]) ).
tff(f2897,plain,
( spl26_227
<=> ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,combc(type,type,type,fun1,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_227])]) ).
tff(f1008,plain,
( ! [X2: nat,X0: type,X1: type] : ( atom(X2) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ~ spl26_48
| ~ spl26_82 ),
inference(superposition,[],[f793,f987]) ).
tff(f2895,plain,
( spl26_226
| ~ spl26_49
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1003,f986,f796,f2893]) ).
tff(f2893,plain,
( spl26_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,[spl26_226])]) ).
tff(f1003,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl26_49
| ~ spl26_82 ),
inference(superposition,[],[f797,f987]) ).
tff(f2891,plain,
( spl26_225
| ~ spl26_50
| ~ spl26_82 ),
inference(avatar_split_clause,[],[f1002,f986,f800,f2889]) ).
tff(f2889,plain,
( spl26_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,[spl26_225])]) ).
tff(f1002,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl26_50
| ~ spl26_82 ),
inference(superposition,[],[f801,f987]) ).
tff(f2887,plain,
( spl26_224
| ~ spl26_28
| ~ spl26_56 ),
inference(avatar_split_clause,[],[f866,f844,f678,f2885]) ).
tff(f2885,plain,
( spl26_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,[spl26_224])]) ).
tff(f866,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl26_28
| ~ spl26_56 ),
inference(resolution,[],[f845,f679]) ).
tff(f2883,plain,
( spl26_223
| ~ spl26_28
| ~ spl26_53 ),
inference(avatar_split_clause,[],[f862,f827,f678,f2881]) ).
tff(f2881,plain,
( spl26_223
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK4(X0))
| ~ sP1(X0)
| sP1(abs(sK3(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_223])]) ).
tff(f827,plain,
( spl26_53
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK3(X0)))
| listsp(dB,it,sK4(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_53])]) ).
tff(f862,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK4(X0))
| ~ sP1(X0)
| sP1(abs(sK3(X0))) )
| ~ spl26_28
| ~ spl26_53 ),
inference(resolution,[],[f828,f679]) ).
tff(f828,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK3(X0)))
| sP0(X0)
| listsp(dB,it,sK4(X0))
| ~ sP1(X0) )
| ~ spl26_53 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f2879,plain,
( spl26_222
| ~ spl26_17
| ~ spl26_53 ),
inference(avatar_split_clause,[],[f863,f827,f622,f2877]) ).
tff(f2877,plain,
( spl26_222
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK4(X0))
| ~ sP1(X0)
| sP1(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_222])]) ).
tff(f863,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK4(X0))
| ~ sP1(X0)
| sP1(sK3(X0)) )
| ~ spl26_17
| ~ spl26_53 ),
inference(resolution,[],[f828,f623]) ).
tff(f2868,plain,
( spl26_221
| ~ spl26_8
| ~ spl26_217 ),
inference(avatar_split_clause,[],[f2826,f2815,f576,f2865]) ).
tff(f2826,plain,
( sP1(abs(abs(t2)))
| ~ spl26_8
| ~ spl26_217 ),
inference(resolution,[],[f2816,f578]) ).
tff(f2863,plain,
( spl26_219
| spl26_220
| ~ spl26_20
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f824,f804,f634,f2861,f2857]) ).
tff(f824,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl26_20
| ~ spl26_51 ),
inference(superposition,[],[f805,f635]) ).
tff(f2840,plain,
( spl26_218
| ~ spl26_13
| ~ spl26_20 ),
inference(avatar_split_clause,[],[f660,f634,f599,f2838]) ).
tff(f2838,plain,
( spl26_218
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_218])]) ).
tff(f660,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl26_13
| ~ spl26_20 ),
inference(superposition,[],[f635,f600]) ).
tff(f2817,plain,
( spl26_217
| ~ spl26_28
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f764,f749,f678,f2815]) ).
tff(f749,plain,
( spl26_40
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_40])]) ).
tff(f764,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl26_28
| ~ spl26_40 ),
inference(resolution,[],[f750,f679]) ).
tff(f750,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl26_40 ),
inference(avatar_component_clause,[],[f749]) ).
tff(f2322,plain,
( spl26_216
| ~ spl26_15
| ~ spl26_51 ),
inference(avatar_split_clause,[],[f813,f804,f613,f2319]) ).
tff(f813,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl26_15
| ~ spl26_51 ),
inference(resolution,[],[f805,f614]) ).
tff(f2317,plain,
( spl26_215
| ~ spl26_13 ),
inference(avatar_split_clause,[],[f602,f599,f2315]) ).
tff(f602,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl26_13 ),
inference(superposition,[],[f600,f600]) ).
tff(f2310,plain,
( spl26_214
| ~ spl26_9
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f1419,f630,f581,f2307]) ).
tff(f2307,plain,
( spl26_214
<=> ( aa(dB,bool,it,ua) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_214])]) ).
tff(f1419,plain,
( ( aa(dB,bool,it,ua) = fTrue )
| ~ spl26_9
| ~ spl26_19 ),
inference(resolution,[],[f631,f583]) ).
tff(f2305,plain,
( spl26_213
| ~ spl26_82
| ~ spl26_212 ),
inference(avatar_split_clause,[],[f2301,f2297,f986,f2303]) ).
tff(f2303,plain,
( spl26_213
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_213])]) ).
tff(f2297,plain,
( spl26_212
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_212])]) ).
tff(f2301,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) )
| ~ spl26_82
| ~ spl26_212 ),
inference(forward_demodulation,[],[f2300,f987]) ).
tff(f2300,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) )
| ~ spl26_82
| ~ spl26_212 ),
inference(forward_demodulation,[],[f2298,f987]) ).
tff(f2298,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) )
| ~ spl26_212 ),
inference(avatar_component_clause,[],[f2297]) ).
tff(f2299,plain,
spl26_212,
inference(avatar_split_clause,[],[f493,f2297]) ).
tff(f493,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ),
inference(definition_unfolding,[],[f399,f402]) ).
tff(f402,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: fun(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType,X87: fun(list(X0),bool),X66: fun(X0,bool)] : ( set_Cons(X0,X66,X87) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X66))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X87)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_set__Cons__def) ).
tff(f399,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: list(fun(X0,bool)),X2: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType,X88: list(fun(X0,bool)),X66: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X66),X88)) = set_Cons(X0,X66,listset(X0,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_listset_Osimps_I2_J) ).
tff(f2290,plain,
( spl26_211
| ~ spl26_82
| ~ spl26_210 ),
inference(avatar_split_clause,[],[f2286,f2283,f986,f2288]) ).
tff(f2288,plain,
( spl26_211
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_211])]) ).
tff(f2283,plain,
( spl26_210
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_210])]) ).
tff(f2286,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl26_82
| ~ spl26_210 ),
inference(forward_demodulation,[],[f2284,f987]) ).
tff(f2284,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl26_210 ),
inference(avatar_component_clause,[],[f2283]) ).
tff(f2285,plain,
spl26_210,
inference(avatar_split_clause,[],[f449,f2283]) ).
tff(f449,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X34: list(type),X33: list(dB),X16: dB,X8: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X8,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X16),X33)),X34))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X8),X16))),typings(X8,X33)),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_typings_Osimps_I2_J) ).
tff(f2276,plain,
( spl26_209
| ~ spl26_82
| ~ spl26_208 ),
inference(avatar_split_clause,[],[f2272,f2269,f986,f2274]) ).
tff(f2274,plain,
( spl26_209
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_209])]) ).
tff(f2269,plain,
( spl26_208
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_208])]) ).
tff(f2272,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl26_82
| ~ spl26_208 ),
inference(forward_demodulation,[],[f2270,f987]) ).
tff(f2270,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) )
| ~ spl26_208 ),
inference(avatar_component_clause,[],[f2269]) ).
tff(f2271,plain,
spl26_208,
inference(avatar_split_clause,[],[f448,f2269]) ).
tff(f448,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
inference(cnf_transformation,[],[f310]) ).
tff(f2192,plain,
spl26_207,
inference(avatar_split_clause,[],[f472,f2190]) ).
tff(f2190,plain,
( spl26_207
<=> ! [X1: $tType,X0: $tType,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0)),X2: X1] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK18(X0,X1,X5))),sK19(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK19(X0,X1,X5))),sK18(X0,X1,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_207])]) ).
tff(f472,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK18(X0,X1,X5))),sK19(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK19(X0,X1,X5))),sK18(X0,X1,X5)) ) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK18(X0,X1,X5))),sK19(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK19(X0,X1,X5))),sK18(X0,X1,X5)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f257,f315]) ).
tff(f315,plain,
! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X0))] :
( ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK18(X0,X1,X5))),sK19(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK20(X0,X1,X5)),sK19(X0,X1,X5))),sK18(X0,X1,X5)) ) ),
introduced(choice_axiom,[]) ).
tff(f257,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) )
| ? [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) ) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X1),X4: X0,X5: fun(X0,fun(X1,X0))] :
( ! [X6: X1,X7: X1,X8: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X6)),X7) = aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X8),X7)),X6) )
=> ( aa(X1,X0,aa(X0,fun(X1,X0),X5,foldl(X0,X1,X5,X4,X3)),X2) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X2),X3) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X1: $tType,X0: $tType,X5: X0,X53: list(X0),X18: X1,X54: fun(X1,fun(X0,X1))] :
( ! [X59: X0,X60: X0,X61: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),X54,aa(X0,X1,aa(X1,fun(X0,X1),X54,X61),X59)),X60) = aa(X0,X1,aa(X1,fun(X0,X1),X54,aa(X0,X1,aa(X1,fun(X0,X1),X54,X61),X60)),X59) )
=> ( aa(X0,X1,aa(X1,fun(X0,X1),X54,foldl(X1,X0,X54,X18,X53)),X5) = foldl(X1,X0,X54,aa(X0,X1,aa(X1,fun(X0,X1),X54,X18),X5),X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_foldl__fun__comm) ).
tff(f2188,plain,
( spl26_206
| ~ spl26_10
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f1418,f630,f586,f2185]) ).
tff(f2185,plain,
( spl26_206
<=> ( aa(dB,bool,it,u) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_206])]) ).
tff(f1418,plain,
( ( aa(dB,bool,it,u) = fTrue )
| ~ spl26_10
| ~ spl26_19 ),
inference(resolution,[],[f631,f588]) ).
tff(f2176,plain,
spl26_205,
inference(avatar_split_clause,[],[f481,f2174]) ).
tff(f2174,plain,
( spl26_205
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_205])]) ).
tff(f481,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X53: list(X2),X54: fun(X2,X1),X52: X0,X67: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X67,X52,map(X2,X1,X54,X53)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X67),X54),X52,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_foldl__map) ).
tff(f2162,plain,
( spl26_204
| ~ spl26_82
| ~ spl26_203 ),
inference(avatar_split_clause,[],[f2158,f2152,f986,f2160]) ).
tff(f2152,plain,
( spl26_203
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_203])]) ).
tff(f2158,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl26_82
| ~ spl26_203 ),
inference(forward_demodulation,[],[f2157,f987]) ).
tff(f2157,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl26_82
| ~ spl26_203 ),
inference(forward_demodulation,[],[f2156,f987]) ).
tff(f2156,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl26_82
| ~ spl26_203 ),
inference(forward_demodulation,[],[f2155,f987]) ).
tff(f2155,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl26_82
| ~ spl26_203 ),
inference(forward_demodulation,[],[f2153,f987]) ).
tff(f2153,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) )
| ~ spl26_203 ),
inference(avatar_component_clause,[],[f2152]) ).
tff(f2154,plain,
spl26_203,
inference(avatar_split_clause,[],[f424,f2152]) ).
tff(f424,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X26: nat,X27: dB,X28: dB,X29: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X29),X28)),X27),X26) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X29),X27),X26)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X28),X27),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_subst__App) ).
tff(f2150,plain,
spl26_202,
inference(avatar_split_clause,[],[f534,f2148]) ).
tff(f2148,plain,
( spl26_202
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_202])]) ).
tff(f534,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f533,f465]) ).
tff(f465,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X91: X0,X92: X1,X90: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X90,X92),X91) = aa(X1,X2,aa(X0,fun(X1,X2),X90,X91),X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f533,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f532,f465]) ).
tff(f532,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f531,f465]) ).
tff(f531,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f483,f465]) ).
tff(f483,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f260]) ).
tff(f260,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X19: dB,X4: type,X7: nat,X8: fun(nat,type),X16: dB,X20: type,X21: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X21),X20) )
=> ( pp(aa(dB,bool,it,X16))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,X7,X20)),X16),X4))
=> ( pp(aa(dB,bool,it,X19))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X19),X20))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X16),X19),X7))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_MI2) ).
tff(f2146,plain,
spl26_201,
inference(avatar_split_clause,[],[f530,f2144]) ).
tff(f2144,plain,
( spl26_201
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_201])]) ).
tff(f530,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f529,f465]) ).
tff(f529,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f528,f465]) ).
tff(f528,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f527,f465]) ).
tff(f527,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f482,f465]) ).
tff(f482,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f258]) ).
tff(f258,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X19: dB,X4: type,X7: nat,X8: fun(nat,type),X16: dB,X20: type,X21: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X21),X20) )
=> ( pp(aa(dB,bool,it,X16))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,X7,X21)),X16),X4))
=> ( pp(aa(dB,bool,it,X19))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X19),X21))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X16),X19),X7))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_MI1) ).
tff(f2134,plain,
( spl26_200
| ~ spl26_8
| ~ spl26_19 ),
inference(avatar_split_clause,[],[f1417,f630,f576,f2131]) ).
tff(f2131,plain,
( spl26_200
<=> ( aa(dB,bool,it,t2) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_200])]) ).
tff(f1417,plain,
( ( aa(dB,bool,it,t2) = fTrue )
| ~ spl26_8
| ~ spl26_19 ),
inference(resolution,[],[f631,f578]) ).
tff(f2129,plain,
( spl26_199
| ~ spl26_82
| ~ spl26_198 ),
inference(avatar_split_clause,[],[f2125,f2119,f986,f2127]) ).
tff(f2127,plain,
( spl26_199
<=> ! [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,[spl26_199])]) ).
tff(f2119,plain,
( spl26_198
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_198])]) ).
tff(f2125,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)) )
| ~ spl26_82
| ~ spl26_198 ),
inference(forward_demodulation,[],[f2124,f987]) ).
tff(f2124,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,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X1),X2)) )
| ~ spl26_82
| ~ spl26_198 ),
inference(forward_demodulation,[],[f2123,f987]) ).
tff(f2123,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(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) )
| ~ spl26_82
| ~ spl26_198 ),
inference(forward_demodulation,[],[f2122,f987]) ).
tff(f2122,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(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,fun(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))),X4) )
| ~ spl26_82
| ~ spl26_198 ),
inference(forward_demodulation,[],[f2120,f987]) ).
tff(f2120,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) )
| ~ spl26_198 ),
inference(avatar_component_clause,[],[f2119]) ).
tff(f2121,plain,
spl26_198,
inference(avatar_split_clause,[],[f455,f2119]) ).
tff(f455,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),splice(X0,X3,X1))) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType,X62: list(X0),X63: X0,X58: list(X0),X57: X0] : ( splice(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X57),X58),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X63),X62)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X57),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X63),splice(X0,X58,X62))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_splice_Osimps_I3_J) ).
tff(f2113,plain,
spl26_197,
inference(avatar_split_clause,[],[f452,f2111]) ).
tff(f2111,plain,
( spl26_197
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_197])]) ).
tff(f452,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(flattening,[],[f311]) ).
tff(f311,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(nnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType,X65: fun(X0,bool),X66: fun(X0,bool),X64: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X66)),X65),X64)
<=> ( listsp(X0,X65,X64)
& listsp(X0,X66,X64) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_listsp__conj__eq) ).
tff(f2103,plain,
( spl26_196
| ~ spl26_82
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f2099,f2095,f986,f2101]) ).
tff(f2101,plain,
( spl26_196
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_196])]) ).
tff(f2095,plain,
( spl26_195
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_195])]) ).
tff(f2099,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl26_82
| ~ spl26_195 ),
inference(forward_demodulation,[],[f2098,f987]) ).
tff(f2098,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl26_82
| ~ spl26_195 ),
inference(forward_demodulation,[],[f2096,f987]) ).
tff(f2096,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl26_195 ),
inference(avatar_component_clause,[],[f2095]) ).
tff(f2097,plain,
spl26_195,
inference(avatar_split_clause,[],[f423,f2095]) ).
tff(f423,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X7: nat,X19: dB,X33: list(dB),X16: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X16,X33)),X19),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X16),X19),X7),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X19),X7),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_subst__map) ).
tff(f2089,plain,
spl26_194,
inference(avatar_split_clause,[],[f451,f2087]) ).
tff(f2087,plain,
( spl26_194
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_194])]) ).
tff(f451,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f312]) ).
tff(f2084,plain,
spl26_193,
inference(avatar_split_clause,[],[f450,f2082]) ).
tff(f2082,plain,
( spl26_193
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_193])]) ).
tff(f450,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f312]) ).
tff(f2070,plain,
spl26_192,
inference(avatar_split_clause,[],[f540,f2068]) ).
tff(f2068,plain,
( spl26_192
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_192])]) ).
tff(f540,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f539,f465]) ).
tff(f539,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f486,f465]) ).
tff(f486,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f265,f325]) ).
tff(f325,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
=> ( pp(aa(list(type),bool,typings(X6,X3),sK25(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f265,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f264]) ).
tff(f264,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( pp(aa(list(type),bool,typings(X6,X4),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X17: type,X34: list(type),X4: type,X42: list(dB),X33: list(dB),X7: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,foldl(dB,dB,app,var(X7),X33),X42)),X4))
=> ( pp(aa(list(type),bool,typings(X8,X33),X34))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X33)),X17))
=> ? [X43: list(type)] :
( pp(aa(list(type),bool,typings(X8,X42),X43))
& ( foldr(type,type,fun1,X43,X4) = X17 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_var__app__types) ).
tff(f2056,plain,
spl26_191,
inference(avatar_split_clause,[],[f542,f2054]) ).
tff(f2054,plain,
( spl26_191
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_191])]) ).
tff(f542,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f541,f465]) ).
tff(f541,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f485,f465]) ).
tff(f485,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f2048,plain,
( spl26_190
| ~ spl26_82
| ~ spl26_189 ),
inference(avatar_split_clause,[],[f2044,f2037,f986,f2046]) ).
tff(f2037,plain,
( spl26_189
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_189])]) ).
tff(f2044,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl26_82
| ~ spl26_189 ),
inference(forward_demodulation,[],[f2043,f987]) ).
tff(f2043,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl26_82
| ~ spl26_189 ),
inference(forward_demodulation,[],[f2042,f987]) ).
tff(f2042,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl26_82
| ~ spl26_189 ),
inference(forward_demodulation,[],[f2041,f987]) ).
tff(f2041,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl26_82
| ~ spl26_189 ),
inference(forward_demodulation,[],[f2040,f987]) ).
tff(f2040,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl26_82
| ~ spl26_189 ),
inference(forward_demodulation,[],[f2038,f987]) ).
tff(f2038,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl26_189 ),
inference(avatar_component_clause,[],[f2037]) ).
tff(f2039,plain,
spl26_189,
inference(avatar_split_clause,[],[f461,f2037]) ).
tff(f461,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X16: dB,X17: type,X4: type,X18: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X18),aa(type,type,aa(type,fun(type,type),fun1,X4),X17)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X16),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),aa(dB,dB,aa(dB,fun(dB,dB),app,X18),X16)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_App) ).
tff(f2028,plain,
( spl26_188
| ~ spl26_82
| ~ spl26_186 ),
inference(avatar_split_clause,[],[f2020,f2016,f986,f2026]) ).
tff(f2016,plain,
( spl26_186
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_186])]) ).
tff(f2020,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_82
| ~ spl26_186 ),
inference(forward_demodulation,[],[f2019,f987]) ).
tff(f2019,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl26_82
| ~ spl26_186 ),
inference(forward_demodulation,[],[f2017,f987]) ).
tff(f2017,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl26_186 ),
inference(avatar_component_clause,[],[f2016]) ).
tff(f2024,plain,
( spl26_187
| ~ spl26_26
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f688,f678,f670,f2022]) ).
tff(f2022,plain,
( spl26_187
<=> ! [X0: dB] :
( sP1(abs(sK7(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_187])]) ).
tff(f688,plain,
( ! [X0: dB] :
( sP1(abs(sK7(X0)))
| ~ sP0(X0) )
| ~ spl26_26
| ~ spl26_28 ),
inference(resolution,[],[f679,f671]) ).
tff(f2018,plain,
spl26_186,
inference(avatar_split_clause,[],[f415,f2016]) ).
tff(f415,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f236]) ).
tff(f236,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0)))
=> ( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X44: list(dB),X18: dB,X48: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X48),X18),zero_zero(nat)),X44)))
=> ( pp(aa(dB,bool,it,X18))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X48)),X18),X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Beta) ).
tff(f2000,plain,
spl26_185,
inference(avatar_split_clause,[],[f538,f1998]) ).
tff(f538,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ),
inference(forward_demodulation,[],[f537,f465]) ).
tff(f537,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f536,f465]) ).
tff(f536,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f535,f465]) ).
tff(f535,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f522,f465]) ).
tff(f522,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f484]) ).
tff(f484,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f262]) ).
tff(f262,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
=> ( ( shift(type,X3,X0,X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X7: nat,X17: type,X19: dB,X36: fun(nat,type),X4: type,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X36),X19),X17))
=> ( ( shift(type,X36,X7,X17) = X8 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X36),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X16),X19),X7)),X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_subst__lemma) ).
tff(f1973,plain,
( spl26_184
| ~ spl26_82
| ~ spl26_183 ),
inference(avatar_split_clause,[],[f1969,f1965,f986,f1971]) ).
tff(f1965,plain,
( spl26_183
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_183])]) ).
tff(f1969,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_82
| ~ spl26_183 ),
inference(forward_demodulation,[],[f1968,f987]) ).
tff(f1968,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl26_82
| ~ spl26_183 ),
inference(forward_demodulation,[],[f1966,f987]) ).
tff(f1966,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl26_183 ),
inference(avatar_component_clause,[],[f1965]) ).
tff(f1967,plain,
spl26_183,
inference(avatar_split_clause,[],[f498,f1965]) ).
tff(f498,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f366]) ).
tff(f366,plain,
! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK7(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),sK7(X0)),zero_zero(nat)),sK8(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK6(X0))),sK7(X0)),sK8(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f279,f280]) ).
tff(f280,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK7(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),sK7(X0)),zero_zero(nat)),sK8(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK6(X0))),sK7(X0)),sK8(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f279,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f278]) ).
tff(f278,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1963,plain,
spl26_182,
inference(avatar_split_clause,[],[f477,f1961]) ).
tff(f477,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ( ( map(X1,X0,X3,sK24(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK23(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f322,f323]) ).
tff(f323,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
=> ( ( map(X1,X0,X3,sK24(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK23(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK23(X0,X1,X2,X3,X4,X5)),sK24(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f322,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(rectify,[],[f321]) ).
tff(f321,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
<=> ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X1: $tType,X68: list(X1),X54: fun(X1,X0),X53: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X53) = map(X1,X0,X54,X68) )
<=> ? [X70: X1,X71: list(X1)] :
( ( map(X1,X0,X54,X71) = X53 )
& ( aa(X1,X0,X54,X70) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X70),X71) = X68 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Cons__eq__map__conv) ).
tff(f1959,plain,
spl26_181,
inference(avatar_split_clause,[],[f473,f1957]) ).
tff(f473,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ( ( map(X0,X1,X5,sK22(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK21(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f318,f319]) ).
tff(f319,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
=> ( ( map(X0,X1,X5,sK22(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK21(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f318,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(rectify,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X1: $tType,X0: $tType,X68: list(X0),X69: X0,X53: list(X1),X54: fun(X1,X0)] :
( ( map(X1,X0,X54,X53) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X69),X68) )
<=> ? [X70: X1,X71: list(X1)] :
( ( map(X1,X0,X54,X71) = X68 )
& ( aa(X1,X0,X54,X70) = X69 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X70),X71) = X53 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_map__eq__Cons__conv) ).
tff(f1942,plain,
( spl26_180
| ~ spl26_82
| ~ spl26_179 ),
inference(avatar_split_clause,[],[f1938,f1932,f986,f1940]) ).
tff(f1932,plain,
( spl26_179
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_179])]) ).
tff(f1938,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl26_82
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1937,f987]) ).
tff(f1937,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )
| ~ spl26_82
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1936,f987]) ).
tff(f1936,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl26_82
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1935,f987]) ).
tff(f1935,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl26_82
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1933,f987]) ).
tff(f1933,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) )
| ~ spl26_179 ),
inference(avatar_component_clause,[],[f1932]) ).
tff(f1934,plain,
spl26_179,
inference(avatar_split_clause,[],[f401,f1932]) ).
tff(f401,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X26: nat,X29: dB,X27: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X27),X29)),X26) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X27),X26)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X29),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lift_Osimps_I2_J) ).
tff(f1928,plain,
( spl26_178
| ~ spl26_82
| ~ spl26_177 ),
inference(avatar_split_clause,[],[f1924,f1919,f986,f1926]) ).
tff(f1919,plain,
( spl26_177
<=> ! [X0: type] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_177])]) ).
tff(f1924,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),X0)),var(i)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),a)) )
| ~ spl26_82
| ~ spl26_177 ),
inference(forward_demodulation,[],[f1923,f987]) ).
tff(f1923,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1))),var(i)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),a)) )
| ~ spl26_82
| ~ spl26_177 ),
inference(forward_demodulation,[],[f1922,f987]) ).
tff(f1922,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),a))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) )
| ~ spl26_82
| ~ spl26_177 ),
inference(forward_demodulation,[],[f1920,f987]) ).
tff(f1920,plain,
( ! [X0: type] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) )
| ~ spl26_177 ),
inference(avatar_component_clause,[],[f1919]) ).
tff(f1921,plain,
( spl26_177
| spl26_1 ),
inference(avatar_split_clause,[],[f487,f544,f1919]) ).
tff(f544,plain,
( spl26_1
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
tff(f487,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(definition_unfolding,[],[f328,f333]) ).
tff(f333,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True) ).
tff(f328,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(flattening,[],[f218]) ).
tff(f218,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1))))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
=> thesis ) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X93: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X93),foldr(type,type,fun1,ts,t1))))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X93))
=> thesis ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f1913,plain,
spl26_176,
inference(avatar_split_clause,[],[f526,f1911]) ).
tff(f526,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ),
inference(forward_demodulation,[],[f471,f465]) ).
tff(f471,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(flattening,[],[f255]) ).
tff(f255,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0)) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X34: list(type),X33: list(dB),X7: nat,X4: type,X19: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X19),X4))
=> ( pp(aa(list(type),bool,typings(shift(type,X8,X7,X4),X33),X34))
=> pp(aa(list(type),bool,typings(X8,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X19),X7),X33)),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_substs__lemma) ).
tff(f1897,plain,
( spl26_175
| ~ spl26_82
| ~ spl26_172 ),
inference(avatar_split_clause,[],[f1885,f1879,f986,f1895]) ).
tff(f1879,plain,
( spl26_172
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_172])]) ).
tff(f1885,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK16(X0,X1,X2,X3))),X2)) )
| ~ spl26_82
| ~ spl26_172 ),
inference(forward_demodulation,[],[f1884,f987]) ).
tff(f1884,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK16(X0,X1,X2,X3))),X2)) )
| ~ spl26_82
| ~ spl26_172 ),
inference(forward_demodulation,[],[f1883,f987]) ).
tff(f1883,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK16(X0,X1,X2,X3))),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl26_82
| ~ spl26_172 ),
inference(forward_demodulation,[],[f1882,f987]) ).
tff(f1882,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl26_82
| ~ spl26_172 ),
inference(forward_demodulation,[],[f1880,f987]) ).
tff(f1880,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl26_172 ),
inference(avatar_component_clause,[],[f1879]) ).
tff(f1893,plain,
( spl26_173
| ~ spl26_174
| ~ spl26_13 ),
inference(avatar_split_clause,[],[f607,f599,f1890,f1887]) ).
tff(f1887,plain,
( spl26_173
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_173])]) ).
tff(f1890,plain,
( spl26_174
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_174])]) ).
tff(f607,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl26_13 ),
inference(equality_factoring,[],[f600]) ).
tff(f1881,plain,
spl26_172,
inference(avatar_split_clause,[],[f433,f1879]) ).
tff(f433,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f244,f298]) ).
tff(f298,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK16(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f244,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))
=> ~ ! [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4)) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X4: type,X19: dB,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),aa(dB,dB,aa(dB,fun(dB,dB),app,X16),X19)),X4))
=> ~ ! [X41: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),aa(type,type,aa(type,fun(type,type),fun1,X41),X4)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X19),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_typing__elims_I2_J) ).
tff(f1795,plain,
spl26_171,
inference(avatar_split_clause,[],[f470,f1793]) ).
tff(f470,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X91: X0,X92: fun(X0,X1),X90: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X90),X92),X91) = aa(X1,X2,aa(X0,fun(X1,X2),X90,X91),aa(X0,X1,X92,X91)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1756,plain,
( spl26_170
| ~ spl26_82
| ~ spl26_169 ),
inference(avatar_split_clause,[],[f1752,f1749,f986,f1754]) ).
tff(f1749,plain,
( spl26_169
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_169])]) ).
tff(f1752,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl26_82
| ~ spl26_169 ),
inference(forward_demodulation,[],[f1750,f987]) ).
tff(f1750,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) )
| ~ spl26_169 ),
inference(avatar_component_clause,[],[f1749]) ).
tff(f1751,plain,
spl26_169,
inference(avatar_split_clause,[],[f454,f1749]) ).
tff(f454,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X1: $tType,X53: list(X1),X5: X1,X54: fun(X1,X0)] : ( map(X1,X0,X54,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X53)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X54,X5)),map(X1,X0,X54,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_map_Osimps_I2_J) ).
tff(f1743,plain,
( spl26_168
| ~ spl26_82
| ~ spl26_167 ),
inference(avatar_split_clause,[],[f1739,f1736,f986,f1741]) ).
tff(f1736,plain,
( spl26_167
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_167])]) ).
tff(f1739,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl26_82
| ~ spl26_167 ),
inference(forward_demodulation,[],[f1737,f987]) ).
tff(f1737,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl26_167 ),
inference(avatar_component_clause,[],[f1736]) ).
tff(f1738,plain,
spl26_167,
inference(avatar_split_clause,[],[f410,f1736]) ).
tff(f410,plain,
! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X2,X1),X0))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X34: list(type),X33: list(dB),X8: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X33),X34))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X8)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lists__typings) ).
tff(f1724,plain,
( spl26_166
| ~ spl26_82
| ~ spl26_165 ),
inference(avatar_split_clause,[],[f1720,f1716,f986,f1722]) ).
tff(f1716,plain,
( spl26_165
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_165])]) ).
tff(f1720,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl26_82
| ~ spl26_165 ),
inference(forward_demodulation,[],[f1719,f987]) ).
tff(f1719,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl26_82
| ~ spl26_165 ),
inference(forward_demodulation,[],[f1717,f987]) ).
tff(f1717,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl26_165 ),
inference(avatar_component_clause,[],[f1716]) ).
tff(f1718,plain,
spl26_165,
inference(avatar_split_clause,[],[f459,f1716]) ).
tff(f459,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1)))
=> ( pp(aa(list(type),bool,typings(X4,X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X33: list(dB),X4: type,X34: list(type),X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),foldr(type,type,fun1,X34,X4)))
=> ( pp(aa(list(type),bool,typings(X8,X33),X34))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X16,X33)),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_list__app__typeI) ).
tff(f1709,plain,
( spl26_164
| ~ spl26_82
| ~ spl26_163 ),
inference(avatar_split_clause,[],[f1705,f1701,f986,f1707]) ).
tff(f1701,plain,
( spl26_163
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_163])]) ).
tff(f1705,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),var(X2))) )
| ~ spl26_82
| ~ spl26_163 ),
inference(forward_demodulation,[],[f1704,f987]) ).
tff(f1704,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl26_82
| ~ spl26_163 ),
inference(forward_demodulation,[],[f1702,f987]) ).
tff(f1702,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl26_163 ),
inference(avatar_component_clause,[],[f1701]) ).
tff(f1703,plain,
spl26_163,
inference(avatar_split_clause,[],[f431,f1701]) ).
tff(f431,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f243,f296]) ).
tff(f296,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f243,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X4: type,X33: list(dB),X7: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X33)),X4))
=> ~ ! [X9: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),var(X7)),foldr(type,type,fun1,X9,X4)))
=> ~ pp(aa(list(type),bool,typings(X8,X33),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_var__app__typesE) ).
tff(f1693,plain,
( spl26_162
| ~ spl26_82
| ~ spl26_161 ),
inference(avatar_split_clause,[],[f1689,f1684,f986,f1691]) ).
tff(f1684,plain,
( spl26_161
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_161])]) ).
tff(f1689,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) )
| ~ spl26_82
| ~ spl26_161 ),
inference(forward_demodulation,[],[f1688,f987]) ).
tff(f1688,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl26_82
| ~ spl26_161 ),
inference(forward_demodulation,[],[f1687,f987]) ).
tff(f1687,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl26_82
| ~ spl26_161 ),
inference(forward_demodulation,[],[f1685,f987]) ).
tff(f1685,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl26_161 ),
inference(avatar_component_clause,[],[f1684]) ).
tff(f1686,plain,
spl26_161,
inference(avatar_split_clause,[],[f430,f1684]) ).
tff(f430,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X17: type,X16: dB,X4: type,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X6,zero_zero(nat),X4)),X16),X17))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),abs(X16)),aa(type,type,aa(type,fun(type,type),fun1,X4),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Abs) ).
tff(f1678,plain,
( spl26_160
| ~ spl26_82
| ~ spl26_159 ),
inference(avatar_split_clause,[],[f1673,f1669,f986,f1676]) ).
tff(f1669,plain,
( spl26_159
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_159])]) ).
tff(f1673,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)) )
| ~ spl26_82
| ~ spl26_159 ),
inference(forward_demodulation,[],[f1672,f987]) ).
tff(f1672,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl26_82
| ~ spl26_159 ),
inference(forward_demodulation,[],[f1670,f987]) ).
tff(f1670,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl26_159 ),
inference(avatar_component_clause,[],[f1669]) ).
tff(f1671,plain,
spl26_159,
inference(avatar_split_clause,[],[f400,f1669]) ).
tff(f400,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X7: nat,X33: list(dB),X16: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X16,X33)),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X16),X7),map(dB,dB,combc(dB,nat,dB,lift,X7),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lift__map) ).
tff(f1658,plain,
( spl26_158
| ~ spl26_82
| ~ spl26_157 ),
inference(avatar_split_clause,[],[f1654,f1650,f986,f1656]) ).
tff(f1650,plain,
( spl26_157
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_157])]) ).
tff(f1654,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),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 ) )
| ~ spl26_82
| ~ spl26_157 ),
inference(forward_demodulation,[],[f1653,f987]) ).
tff(f1653,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl26_82
| ~ spl26_157 ),
inference(forward_demodulation,[],[f1651,f987]) ).
tff(f1651,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl26_157 ),
inference(avatar_component_clause,[],[f1650]) ).
tff(f1652,plain,
spl26_157,
inference(avatar_split_clause,[],[f460,f1650]) ).
tff(f460,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X17: type,X4: type,X33: list(dB),X7: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X33)),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X33)),X17))
=> ( X4 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_var__app__type__eq) ).
tff(f1644,plain,
( spl26_156
| ~ spl26_82
| ~ spl26_155 ),
inference(avatar_split_clause,[],[f1640,f1635,f986,f1642]) ).
tff(f1635,plain,
( spl26_155
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_155])]) ).
tff(f1640,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) )
| ~ spl26_82
| ~ spl26_155 ),
inference(forward_demodulation,[],[f1639,f987]) ).
tff(f1639,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl26_82
| ~ spl26_155 ),
inference(forward_demodulation,[],[f1638,f987]) ).
tff(f1638,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl26_82
| ~ spl26_155 ),
inference(forward_demodulation,[],[f1636,f987]) ).
tff(f1636,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl26_155 ),
inference(avatar_component_clause,[],[f1635]) ).
tff(f1637,plain,
spl26_155,
inference(avatar_split_clause,[],[f458,f1635]) ).
tff(f458,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X17: type,X7: nat,X4: type,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,X7,X17)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X16),X7)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_lift__type) ).
tff(f1627,plain,
( spl26_154
| ~ spl26_82
| ~ spl26_153 ),
inference(avatar_split_clause,[],[f1623,f1618,f986,f1625]) ).
tff(f1618,plain,
( spl26_153
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_153])]) ).
tff(f1623,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK16(X0,X1,X2,X3)),X1)) )
| ~ spl26_82
| ~ spl26_153 ),
inference(forward_demodulation,[],[f1622,f987]) ).
tff(f1622,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK16(X0,X1,X2,X3)),X1)) )
| ~ spl26_82
| ~ spl26_153 ),
inference(forward_demodulation,[],[f1621,f987]) ).
tff(f1621,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK16(X0,X1,X2,X3)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl26_82
| ~ spl26_153 ),
inference(forward_demodulation,[],[f1619,f987]) ).
tff(f1619,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl26_153 ),
inference(avatar_component_clause,[],[f1618]) ).
tff(f1620,plain,
spl26_153,
inference(avatar_split_clause,[],[f434,f1618]) ).
tff(f434,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f299]) ).
tff(f1616,plain,
( spl26_152
| ~ spl26_18
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f683,f678,f626,f1614]) ).
tff(f683,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl26_18
| ~ spl26_28 ),
inference(resolution,[],[f679,f627]) ).
tff(f1602,plain,
( spl26_151
| ~ spl26_82
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1598,f1594,f986,f1600]) ).
tff(f1594,plain,
( spl26_150
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_150])]) ).
tff(f1598,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) )
| ~ spl26_82
| ~ spl26_150 ),
inference(forward_demodulation,[],[f1597,f987]) ).
tff(f1597,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_82
| ~ spl26_150 ),
inference(forward_demodulation,[],[f1595,f987]) ).
tff(f1595,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_150 ),
inference(avatar_component_clause,[],[f1594]) ).
tff(f1596,plain,
spl26_150,
inference(avatar_split_clause,[],[f428,f1594]) ).
tff(f428,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f241,f294]) ).
tff(f294,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f241,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X4: type,X33: list(dB),X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X16,X33)),X4))
=> ? [X9: list(type)] :
( pp(aa(list(type),bool,typings(X8,X33),X9))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),foldr(type,type,fun1,X9,X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_list__app__typeD) ).
tff(f1582,plain,
( spl26_149
| ~ spl26_82
| ~ spl26_148 ),
inference(avatar_split_clause,[],[f1578,f1574,f986,f1580]) ).
tff(f1574,plain,
( spl26_148
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_148])]) ).
tff(f1578,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)),X2)) )
| ~ spl26_82
| ~ spl26_148 ),
inference(forward_demodulation,[],[f1577,f987]) ).
tff(f1577,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_82
| ~ spl26_148 ),
inference(forward_demodulation,[],[f1575,f987]) ).
tff(f1575,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_148 ),
inference(avatar_component_clause,[],[f1574]) ).
tff(f1576,plain,
spl26_148,
inference(avatar_split_clause,[],[f426,f1574]) ).
tff(f426,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f240,f292]) ).
tff(f292,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK13(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f240,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X4: type,X33: list(dB),X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X16,X33)),X4))
=> ~ ! [X9: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),foldr(type,type,fun1,X9,X4)))
=> ~ pp(aa(list(type),bool,typings(X8,X33),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_list__app__typeE) ).
tff(f1547,plain,
spl26_147,
inference(avatar_split_clause,[],[f469,f1545]) ).
tff(f469,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X91: X0,X92: fun(X0,X1),X90: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X90),X92),X91) = aa(X1,X2,X90,aa(X0,X1,X92,X91)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1543,plain,
spl26_146,
inference(avatar_split_clause,[],[f463,f1541]) ).
tff(f463,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(flattening,[],[f313]) ).
tff(f313,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X49: list(X0),X50: X0,X51: list(X0),X52: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X52),X51) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X50),X49) )
<=> ( ( X49 = X51 )
& ( X50 = X52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list_Oinject) ).
tff(f1539,plain,
( spl26_145
| ~ spl26_17
| ~ spl26_26 ),
inference(avatar_split_clause,[],[f681,f670,f622,f1537]) ).
tff(f1537,plain,
( spl26_145
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_145])]) ).
tff(f681,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK7(X0)) )
| ~ spl26_17
| ~ spl26_26 ),
inference(resolution,[],[f671,f623]) ).
tff(f1525,plain,
( spl26_144
| ~ spl26_82
| ~ spl26_143 ),
inference(avatar_split_clause,[],[f1521,f1517,f986,f1523]) ).
tff(f1517,plain,
( spl26_143
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),X1),sK12(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_143])]) ).
tff(f1521,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),sK12(X0,X1,X2)),X1)) )
| ~ spl26_82
| ~ spl26_143 ),
inference(forward_demodulation,[],[f1520,f987]) ).
tff(f1520,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),sK12(X0,X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_82
| ~ spl26_143 ),
inference(forward_demodulation,[],[f1518,f987]) ).
tff(f1518,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),X1),sK12(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_143 ),
inference(avatar_component_clause,[],[f1517]) ).
tff(f1519,plain,
spl26_143,
inference(avatar_split_clause,[],[f413,f1517]) ).
tff(f413,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),X1),sK12(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),X1),sK12(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK11(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f234,f288]) ).
tff(f288,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK11(X0,X1,X2))),X1),sK12(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK11(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f234,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X4: type,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),abs(X16)),X4))
=> ~ ! [X41: type,X80: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X41),X80) = X4 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,zero_zero(nat),X41)),X16),X80)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_typing__elims_I3_J) ).
tff(f1500,plain,
spl26_142,
inference(avatar_split_clause,[],[f479,f1498]) ).
tff(f479,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK24(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f324]) ).
tff(f1496,plain,
spl26_141,
inference(avatar_split_clause,[],[f475,f1494]) ).
tff(f475,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( map(X0,X1,X5,sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f1492,plain,
spl26_140,
inference(avatar_split_clause,[],[f462,f1490]) ).
tff(f462,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1382,plain,
spl26_139,
inference(avatar_split_clause,[],[f525,f1380]) ).
tff(f525,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f468,f465]) ).
tff(f468,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X1: $tType,X53: list(X1),X5: X1,X52: X0,X54: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X54,X52,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X53)) = foldl(X0,X1,X54,aa(X1,X0,aa(X0,fun(X1,X0),X54,X52),X5),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_foldl__Cons) ).
tff(f1378,plain,
spl26_138,
inference(avatar_split_clause,[],[f524,f1376]) ).
tff(f524,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ),
inference(forward_demodulation,[],[f467,f465]) ).
tff(f467,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X1: $tType,X0: $tType,X52: X0,X53: list(X1),X5: X1,X54: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X54,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X53),X52) = aa(X0,X0,aa(X1,fun(X0,X0),X54,X5),foldr(X1,X0,X54,X53,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_foldr_Osimps_I2_J) ).
tff(f1374,plain,
spl26_137,
inference(avatar_split_clause,[],[f478,f1372]) ).
tff(f478,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK23(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f324]) ).
tff(f1370,plain,
spl26_136,
inference(avatar_split_clause,[],[f474,f1368]) ).
tff(f474,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK21(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f1365,plain,
( spl26_135
| ~ spl26_82
| ~ spl26_134 ),
inference(avatar_split_clause,[],[f1361,f1357,f986,f1363]) ).
tff(f1357,plain,
( spl26_134
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),X1),sK10(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_134])]) ).
tff(f1361,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),sK10(X1,X2)),X1)) )
| ~ spl26_82
| ~ spl26_134 ),
inference(forward_demodulation,[],[f1360,f987]) ).
tff(f1360,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),sK10(X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_82
| ~ spl26_134 ),
inference(forward_demodulation,[],[f1358,f987]) ).
tff(f1358,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),X1),sK10(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_134 ),
inference(avatar_component_clause,[],[f1357]) ).
tff(f1359,plain,
spl26_134,
inference(avatar_split_clause,[],[f411,f1357]) ).
tff(f411,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),X1),sK10(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),X1),sK10(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f233,f286]) ).
tff(f286,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK9(X1,X2))),X1),sK10(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f233,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X4: type,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),abs(X16)),X4))
=> ~ ! [X80: type,X81: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,zero_zero(nat),X80)),X16),X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_abs__typeE) ).
tff(f1351,plain,
( spl26_133
| ~ spl26_82
| ~ spl26_132 ),
inference(avatar_split_clause,[],[f1347,f1344,f986,f1349]) ).
tff(f1344,plain,
( spl26_132
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),sK7(X0)),zero_zero(nat)),sK8(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_132])]) ).
tff(f1347,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),zero_zero(nat)),sK7(X0)),sK8(X0))))
| ~ sP0(X0) )
| ~ spl26_82
| ~ spl26_132 ),
inference(forward_demodulation,[],[f1345,f987]) ).
tff(f1345,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),sK7(X0)),zero_zero(nat)),sK8(X0))))
| ~ sP0(X0) )
| ~ spl26_132 ),
inference(avatar_component_clause,[],[f1344]) ).
tff(f1346,plain,
spl26_132,
inference(avatar_split_clause,[],[f364,f1344]) ).
tff(f364,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK6(X0)),sK7(X0)),zero_zero(nat)),sK8(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1329,plain,
spl26_131,
inference(avatar_split_clause,[],[f523,f1327]) ).
tff(f523,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f466,f465]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X1: $tType,X51: list(X1),X52: X1,X55: fun(X1,fun(list(X1),X0)),X56: X0] : ( list_case(X0,X1,X56,X55,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X52),X51)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X55,X52),X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_list_Osimps_I5_J) ).
tff(f1322,plain,
( spl26_130
| ~ spl26_82
| ~ spl26_129 ),
inference(avatar_split_clause,[],[f1317,f1312,f986,f1319]) ).
tff(f1312,plain,
( spl26_129
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK2,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_129])]) ).
tff(f1317,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl26_82
| ~ spl26_129 ),
inference(forward_demodulation,[],[f1316,f987]) ).
tff(f1316,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK2,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl26_82
| ~ spl26_129 ),
inference(forward_demodulation,[],[f1314,f987]) ).
tff(f1314,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK2,t1)))
| ~ spl26_129 ),
inference(avatar_component_clause,[],[f1312]) ).
tff(f1315,plain,
spl26_129,
inference(avatar_split_clause,[],[f492,f1312]) ).
tff(f492,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK2,t1))),
inference(definition_unfolding,[],[f345,f333]) ).
tff(f345,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK2,t1))),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK2,t1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f220,f269]) ).
tff(f269,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) )
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK2,t1))) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) ),
inference(ennf_transformation,[],[f120]) ).
tff(f120,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
~ ! [X9: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X9,t1)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1305,plain,
( spl26_128
| ~ spl26_82
| ~ spl26_127 ),
inference(avatar_split_clause,[],[f1299,f1294,f986,f1302]) ).
tff(f1294,plain,
( spl26_127
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_127])]) ).
tff(f1299,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)))
| ~ spl26_82
| ~ spl26_127 ),
inference(forward_demodulation,[],[f1298,f987]) ).
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,aa(dB,fun(dB,dB),app,var(i)),a),as)))
| ~ spl26_82
| ~ spl26_127 ),
inference(forward_demodulation,[],[f1296,f987]) ).
tff(f1296,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1))
| ~ spl26_127 ),
inference(avatar_component_clause,[],[f1294]) ).
tff(f1297,plain,
spl26_127,
inference(avatar_split_clause,[],[f491,f1294]) ).
tff(f491,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)),
inference(definition_unfolding,[],[f344,f333]) ).
tff(f344,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__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(f1289,plain,
( spl26_126
| ~ spl26_82
| ~ spl26_125 ),
inference(avatar_split_clause,[],[f1284,f1279,f986,f1286]) ).
tff(f1279,plain,
( spl26_125
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_125])]) ).
tff(f1284,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl26_82
| ~ spl26_125 ),
inference(forward_demodulation,[],[f1283,f987]) ).
tff(f1283,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl26_82
| ~ spl26_125 ),
inference(forward_demodulation,[],[f1281,f987]) ).
tff(f1281,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1)))
| ~ spl26_125 ),
inference(avatar_component_clause,[],[f1279]) ).
tff(f1282,plain,
spl26_125,
inference(avatar_split_clause,[],[f490,f1279]) ).
tff(f490,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))),
inference(definition_unfolding,[],[f343,f333]) ).
tff(f343,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_headT) ).
tff(f1276,plain,
( spl26_124
| ~ spl26_82
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1272,f1268,f986,f1274]) ).
tff(f1274,plain,
( spl26_124
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK12(X0,X1,X2)),sK11(X0,X1,X2)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_124])]) ).
tff(f1268,plain,
( spl26_123
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK11(X0,X1,X2)),sK12(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_123])]) ).
tff(f1272,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK12(X0,X1,X2)),sK11(X0,X1,X2)) = X0 ) )
| ~ spl26_82
| ~ spl26_123 ),
inference(forward_demodulation,[],[f1271,f987]) ).
tff(f1271,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun1,sK12(X0,X1,X2)),sK11(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_82
| ~ spl26_123 ),
inference(forward_demodulation,[],[f1269,f987]) ).
tff(f1269,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK11(X0,X1,X2)),sK12(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl26_123 ),
inference(avatar_component_clause,[],[f1268]) ).
tff(f1270,plain,
spl26_123,
inference(avatar_split_clause,[],[f412,f1268]) ).
tff(f412,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK11(X0,X1,X2)),sK12(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1266,plain,
( spl26_122
| ~ spl26_82
| ~ spl26_121 ),
inference(avatar_split_clause,[],[f1262,f1258,f986,f1264]) ).
tff(f1264,plain,
( spl26_122
<=> ! [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,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_122])]) ).
tff(f1258,plain,
( spl26_121
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_121])]) ).
tff(f1262,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,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl26_82
| ~ spl26_121 ),
inference(forward_demodulation,[],[f1261,f987]) ).
tff(f1261,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl26_82
| ~ spl26_121 ),
inference(forward_demodulation,[],[f1259,f987]) ).
tff(f1259,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))
| ~ spl26_121 ),
inference(avatar_component_clause,[],[f1258]) ).
tff(f1260,plain,
spl26_121,
inference(avatar_split_clause,[],[f376,f1258]) ).
tff(f376,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X29: dB,X27: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X27)),X29),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X27),X29),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_beta) ).
tff(f1256,plain,
( ~ spl26_120
| ~ spl26_66
| ~ spl26_67 ),
inference(avatar_split_clause,[],[f923,f907,f902,f1253]) ).
tff(f1253,plain,
( spl26_120
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_120])]) ).
tff(f923,plain,
( ( as != rs )
| ~ spl26_66
| ~ spl26_67 ),
inference(superposition,[],[f908,f904]) ).
tff(f1248,plain,
( spl26_119
| ~ spl26_82
| ~ spl26_118 ),
inference(avatar_split_clause,[],[f1244,f1241,f986,f1246]) ).
tff(f1241,plain,
( spl26_118
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_118])]) ).
tff(f1244,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl26_82
| ~ spl26_118 ),
inference(forward_demodulation,[],[f1242,f987]) ).
tff(f1242,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl26_118 ),
inference(avatar_component_clause,[],[f1241]) ).
tff(f1243,plain,
spl26_118,
inference(avatar_split_clause,[],[f432,f1241]) ).
tff(f432,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1237,plain,
spl26_117,
inference(avatar_split_clause,[],[f457,f1235]) ).
tff(f457,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X4,X3),X2))
=> pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X17: type,X7: nat,X34: list(type),X33: list(dB),X8: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X33),X34))
=> pp(aa(list(type),bool,typings(shift(type,X8,X7,X17),map(dB,dB,combc(dB,nat,dB,lift,X7),X33)),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_lift__types) ).
tff(f1230,plain,
( spl26_116
| ~ spl26_82
| ~ spl26_115 ),
inference(avatar_split_clause,[],[f1226,f1223,f986,f1228]) ).
tff(f1223,plain,
( spl26_115
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_115])]) ).
tff(f1226,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl26_82
| ~ spl26_115 ),
inference(forward_demodulation,[],[f1224,f987]) ).
tff(f1224,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_115 ),
inference(avatar_component_clause,[],[f1223]) ).
tff(f1225,plain,
spl26_115,
inference(avatar_split_clause,[],[f429,f1223]) ).
tff(f429,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1218,plain,
( spl26_114
| ~ spl26_82
| ~ spl26_112 ),
inference(avatar_split_clause,[],[f1210,f1207,f986,f1216]) ).
tff(f1207,plain,
( spl26_112
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_112])]) ).
tff(f1210,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3))) )
| ~ spl26_82
| ~ spl26_112 ),
inference(forward_demodulation,[],[f1208,f987]) ).
tff(f1208,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl26_112 ),
inference(avatar_component_clause,[],[f1207]) ).
tff(f1214,plain,
( spl26_113
| ~ spl26_15
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f684,f678,f613,f1212]) ).
tff(f684,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl26_15
| ~ spl26_28 ),
inference(resolution,[],[f679,f614]) ).
tff(f1209,plain,
spl26_112,
inference(avatar_split_clause,[],[f427,f1207]) ).
tff(f427,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK13(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f1201,plain,
( spl26_111
| ~ spl26_82
| ~ spl26_110 ),
inference(avatar_split_clause,[],[f1197,f1194,f986,f1199]) ).
tff(f1194,plain,
( spl26_110
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_110])]) ).
tff(f1197,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_82
| ~ spl26_110 ),
inference(forward_demodulation,[],[f1195,f987]) ).
tff(f1195,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_110 ),
inference(avatar_component_clause,[],[f1194]) ).
tff(f1196,plain,
spl26_110,
inference(avatar_split_clause,[],[f408,f1194]) ).
tff(f408,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X30: nat,X31: nat,X32: dB] :
( pp(aa(dB,bool,it,X32))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X32),var(X31)),X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_subst__Var__IT) ).
tff(f1190,plain,
( spl26_109
| ~ spl26_82
| ~ spl26_108 ),
inference(avatar_split_clause,[],[f1186,f1182,f986,f1188]) ).
tff(f1182,plain,
( spl26_108
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_108])]) ).
tff(f1186,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl26_82
| ~ spl26_108 ),
inference(forward_demodulation,[],[f1185,f987]) ).
tff(f1185,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl26_82
| ~ spl26_108 ),
inference(forward_demodulation,[],[f1183,f987]) ).
tff(f1183,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl26_108 ),
inference(avatar_component_clause,[],[f1182]) ).
tff(f1184,plain,
spl26_108,
inference(avatar_split_clause,[],[f398,f1182]) ).
tff(f398,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X27: dB,X26: nat,X29: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X29),X26)),X27),X26) = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_subst__lift) ).
tff(f1174,plain,
( spl26_107
| ~ spl26_82
| ~ spl26_106 ),
inference(avatar_split_clause,[],[f1170,f1166,f986,f1172]) ).
tff(f1166,plain,
( spl26_106
<=> ! [X0: dB,X3: fun(nat,type),X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_106])]) ).
tff(f1170,plain,
( ! [X2: dB,X3: fun(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) )
| ~ spl26_82
| ~ spl26_106 ),
inference(forward_demodulation,[],[f1169,f987]) ).
tff(f1169,plain,
( ! [X2: dB,X3: fun(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,fun(type,bool),typing(X3),X2),X1)) )
| ~ spl26_82
| ~ spl26_106 ),
inference(forward_demodulation,[],[f1167,f987]) ).
tff(f1167,plain,
( ! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1)) )
| ~ spl26_106 ),
inference(avatar_component_clause,[],[f1166]) ).
tff(f1168,plain,
spl26_106,
inference(avatar_split_clause,[],[f425,f1166]) ).
tff(f425,plain,
! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1)) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1)) ),
inference(flattening,[],[f238]) ).
tff(f238,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1)) ),
inference(ennf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
=> ( beta(X2,X0)
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X1)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X89: dB,X4: type,X16: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X16),X4))
=> ( beta(X16,X89)
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X89),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subject__reduction) ).
tff(f1153,plain,
( spl26_105
| ~ spl26_82
| ~ spl26_104 ),
inference(avatar_split_clause,[],[f1149,f1146,f986,f1151]) ).
tff(f1146,plain,
( spl26_104
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(type,fun(type,X0)),X2: type,X1: type] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_104])]) ).
tff(f1149,plain,
( ! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) = type_case(X0,X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2)) )
| ~ spl26_82
| ~ spl26_104 ),
inference(forward_demodulation,[],[f1147,f987]) ).
tff(f1147,plain,
( ! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) )
| ~ spl26_104 ),
inference(avatar_component_clause,[],[f1146]) ).
tff(f1148,plain,
spl26_104,
inference(avatar_split_clause,[],[f453,f1146]) ).
tff(f453,plain,
! [X0: $tType,X2: type,X3: fun(type,fun(type,X0)),X1: type,X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: type,X2: type,X3: fun(type,fun(type,X0)),X4: fun(nat,X0)] : ( type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType,X12: type,X13: type,X55: fun(type,fun(type,X0)),X56: fun(nat,X0)] : ( type_case(X0,X56,X55,aa(type,type,aa(type,fun(type,type),fun1,X13),X12)) = aa(type,X0,aa(type,fun(type,X0),X55,X13),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_type_Osimps_I6_J) ).
tff(f1132,plain,
spl26_103,
inference(avatar_split_clause,[],[f446,f1130]) ).
tff(f446,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f308]) ).
tff(f308,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X22: dB,X23: dB,X24: dB,X25: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X25),X24) = aa(dB,dB,aa(dB,fun(dB,dB),app,X23),X22) )
<=> ( ( X22 = X24 )
& ( X23 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dB_Osimps_I2_J) ).
tff(f1128,plain,
spl26_102,
inference(avatar_split_clause,[],[f445,f1126]) ).
tff(f445,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1124,plain,
spl26_101,
inference(avatar_split_clause,[],[f443,f1122]) ).
tff(f443,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) = aa(type,type,aa(type,fun(type,type),fun1,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ) ),
inference(flattening,[],[f306]) ).
tff(f306,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) = aa(type,type,aa(type,fun(type,type),fun1,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) = aa(type,type,aa(type,fun(type,type),fun1,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X10: type,X11: type,X12: type,X13: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X13),X12) = aa(type,type,aa(type,fun(type,type),fun1,X11),X10) )
<=> ( ( X10 = X12 )
& ( X11 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_type_Osimps_I2_J) ).
tff(f1119,plain,
spl26_100,
inference(avatar_split_clause,[],[f442,f1117]) ).
tff(f442,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X1),X0) != aa(type,type,aa(type,fun(type,type),fun1,X3),X2) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f1115,plain,
( spl26_99
| ~ spl26_82
| ~ spl26_98 ),
inference(avatar_split_clause,[],[f1111,f1107,f986,f1113]) ).
tff(f1113,plain,
( spl26_99
<=> ! [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,[spl26_99])]) ).
tff(f1107,plain,
( spl26_98
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_98])]) ).
tff(f1111,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) )
| ~ spl26_82
| ~ spl26_98 ),
inference(forward_demodulation,[],[f1110,f987]) ).
tff(f1110,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_82
| ~ spl26_98 ),
inference(forward_demodulation,[],[f1108,f987]) ).
tff(f1108,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_98 ),
inference(avatar_component_clause,[],[f1107]) ).
tff(f1109,plain,
spl26_98,
inference(avatar_split_clause,[],[f407,f1107]) ).
tff(f407,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ 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,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X28: dB,X29: dB,X27: dB] :
( beta(X27,X29)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X27),aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_appR) ).
tff(f1105,plain,
( spl26_97
| ~ spl26_82
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f1101,f1097,f986,f1103]) ).
tff(f1103,plain,
( spl26_97
<=> ! [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,[spl26_97])]) ).
tff(f1097,plain,
( spl26_96
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_96])]) ).
tff(f1101,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) )
| ~ spl26_82
| ~ spl26_96 ),
inference(forward_demodulation,[],[f1100,f987]) ).
tff(f1100,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_82
| ~ spl26_96 ),
inference(forward_demodulation,[],[f1098,f987]) ).
tff(f1098,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_96 ),
inference(avatar_component_clause,[],[f1097]) ).
tff(f1099,plain,
spl26_96,
inference(avatar_split_clause,[],[f406,f1097]) ).
tff(f406,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X28: dB,X29: dB,X27: dB] :
( beta(X27,X29)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X27),X28),aa(dB,dB,aa(dB,fun(dB,dB),app,X29),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_appL) ).
tff(f1085,plain,
spl26_95,
inference(avatar_split_clause,[],[f435,f1083]) ).
tff(f435,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f245,f300]) ).
tff(f300,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f245,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X67: fun(X0,X1),X54: fun(X0,X1)] :
( ! [X59: X0] : ( aa(X0,X1,X54,X59) = aa(X0,X1,X67,X59) )
=> ( X54 = X67 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1080,plain,
( spl26_94
| ~ spl26_82
| ~ spl26_93 ),
inference(avatar_split_clause,[],[f1076,f1073,f986,f1078]) ).
tff(f1078,plain,
( spl26_94
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_94])]) ).
tff(f1073,plain,
( spl26_93
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK6(X0))),sK7(X0)),sK8(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_93])]) ).
tff(f1076,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK7(X0)),abs(sK6(X0))),sK8(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl26_82
| ~ spl26_93 ),
inference(forward_demodulation,[],[f1074,f987]) ).
tff(f1074,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK6(X0))),sK7(X0)),sK8(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl26_93 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f1075,plain,
spl26_93,
inference(avatar_split_clause,[],[f363,f1073]) ).
tff(f363,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK6(X0))),sK7(X0)),sK8(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1069,plain,
( spl26_92
| ~ spl26_82
| ~ spl26_91 ),
inference(avatar_split_clause,[],[f1064,f1060,f986,f1066]) ).
tff(f1060,plain,
( spl26_91
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_91])]) ).
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)))
| ~ spl26_82
| ~ spl26_91 ),
inference(forward_demodulation,[],[f1062,f987]) ).
tff(f1062,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1))
| ~ spl26_91 ),
inference(avatar_component_clause,[],[f1060]) ).
tff(f1063,plain,
spl26_91,
inference(avatar_split_clause,[],[f489,f1060]) ).
tff(f489,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)),
inference(definition_unfolding,[],[f342,f333]) ).
tff(f342,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_nT) ).
tff(f1056,plain,
( spl26_90
| ~ spl26_82
| ~ spl26_89 ),
inference(avatar_split_clause,[],[f1051,f1047,f986,f1053]) ).
tff(f1047,plain,
( spl26_89
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_89])]) ).
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)))
| ~ spl26_82
| ~ spl26_89 ),
inference(forward_demodulation,[],[f1049,f987]) ).
tff(f1049,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a))
| ~ spl26_89 ),
inference(avatar_component_clause,[],[f1047]) ).
tff(f1050,plain,
spl26_89,
inference(avatar_split_clause,[],[f488,f1047]) ).
tff(f488,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f341,f333]) ).
tff(f341,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f38]) ).
tff(f38,axiom,
pp(aa(type,bool,aa(dB,fun(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_37_Var_I2_J) ).
tff(f1042,plain,
( spl26_88
| ~ spl26_82
| ~ spl26_87 ),
inference(avatar_split_clause,[],[f1037,f1034,f986,f1040]) ).
tff(f1034,plain,
( spl26_87
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_87])]) ).
tff(f1037,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl26_82
| ~ spl26_87 ),
inference(forward_demodulation,[],[f1035,f987]) ).
tff(f1035,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl26_87 ),
inference(avatar_component_clause,[],[f1034]) ).
tff(f1036,plain,
spl26_87,
inference(avatar_split_clause,[],[f419,f1034]) ).
tff(f419,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X66: fun(X0,bool),X5: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X66))
<=> pp(aa(X0,bool,X66,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f1031,plain,
( spl26_86
| ~ spl26_82
| ~ spl26_85 ),
inference(avatar_split_clause,[],[f1027,f1024,f986,f1029]) ).
tff(f1029,plain,
( spl26_86
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_86])]) ).
tff(f1024,plain,
( spl26_85
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_85])]) ).
tff(f1027,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl26_82
| ~ spl26_85 ),
inference(forward_demodulation,[],[f1025,f987]) ).
tff(f1025,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl26_85 ),
inference(avatar_component_clause,[],[f1024]) ).
tff(f1026,plain,
spl26_85,
inference(avatar_split_clause,[],[f418,f1024]) ).
tff(f418,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f1018,plain,
( spl26_84
| ~ spl26_82
| ~ spl26_83 ),
inference(avatar_split_clause,[],[f1014,f1011,f986,f1016]) ).
tff(f1011,plain,
( spl26_83
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_83])]) ).
tff(f1014,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)) )
| ~ spl26_82
| ~ spl26_83 ),
inference(forward_demodulation,[],[f1012,f987]) ).
tff(f1012,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_83 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f1013,plain,
spl26_83,
inference(avatar_split_clause,[],[f383,f1011]) ).
tff(f383,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X31: nat,X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X29),var(X31)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_app__Var__IT) ).
tff(f988,plain,
spl26_82,
inference(avatar_split_clause,[],[f465,f986]) ).
tff(f984,plain,
( spl26_81
| ~ spl26_9
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f687,f678,f581,f981]) ).
tff(f687,plain,
( sP1(abs(ua))
| ~ spl26_9
| ~ spl26_28 ),
inference(resolution,[],[f679,f583]) ).
tff(f975,plain,
( spl26_80
| ~ spl26_79 ),
inference(avatar_split_clause,[],[f971,f968,f973]) ).
tff(f968,plain,
( spl26_79
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_79])]) ).
tff(f971,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)) )
| ~ spl26_79 ),
inference(forward_demodulation,[],[f969,f465]) ).
tff(f969,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_79 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f970,plain,
spl26_79,
inference(avatar_split_clause,[],[f382,f968]) ).
tff(f382,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X31: nat,X29: dB] :
( pp(aa(dB,bool,it,X29))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X29),X31))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_lift__IT) ).
tff(f966,plain,
( spl26_78
| ~ spl26_77 ),
inference(avatar_split_clause,[],[f962,f959,f964]) ).
tff(f959,plain,
( spl26_77
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_77])]) ).
tff(f962,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl26_77 ),
inference(forward_demodulation,[],[f960,f465]) ).
tff(f960,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl26_77 ),
inference(avatar_component_clause,[],[f959]) ).
tff(f961,plain,
spl26_77,
inference(avatar_split_clause,[],[f375,f959]) ).
tff(f375,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X28: dB,X26: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X26)),X28),X26) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_subst__eq) ).
tff(f957,plain,
spl26_76,
inference(avatar_split_clause,[],[f358,f955]) ).
tff(f358,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK3(X0)))
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,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,sK3(X0)))
& ( abs(sK3(X0)) = X0 ) )
| ( listsp(dB,it,sK4(X0))
& ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f274,f276,f275]) ).
tff(f275,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK3(X0)))
& ( abs(sK3(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f276,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK4(X0))
& ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f274,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,[],[f273]) ).
tff(f273,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,[],[f272]) ).
tff(f272,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,[],[f267]) ).
tff(f267,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f951,plain,
( spl26_75
| ~ spl26_74 ),
inference(avatar_split_clause,[],[f947,f944,f949]) ).
tff(f944,plain,
( spl26_74
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_74])]) ).
tff(f947,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl26_74 ),
inference(forward_demodulation,[],[f945,f465]) ).
tff(f945,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) )
| ~ spl26_74 ),
inference(avatar_component_clause,[],[f944]) ).
tff(f946,plain,
spl26_74,
inference(avatar_split_clause,[],[f414,f944]) ).
tff(f414,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X4: type,X7: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),var(X7)),X4))
=> ( aa(nat,type,X8,X7) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_typing__elims_I1_J) ).
tff(f942,plain,
( spl26_73
| ~ spl26_10
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f686,f678,f586,f939]) ).
tff(f686,plain,
( sP1(abs(u))
| ~ spl26_10
| ~ spl26_28 ),
inference(resolution,[],[f679,f588]) ).
tff(f933,plain,
spl26_72,
inference(avatar_split_clause,[],[f422,f931]) ).
tff(f422,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X44: list(dB),X45: nat,X16: dB,X18: dB] : ( foldl(dB,dB,app,var(X45),X44) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X18)),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Abs__App__neq__Var__apps) ).
tff(f929,plain,
spl26_71,
inference(avatar_split_clause,[],[f356,f927]) ).
tff(f356,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK3(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK5(X0)),sK4(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f922,plain,
spl26_70,
inference(avatar_split_clause,[],[f440,f920]) ).
tff(f440,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,[],[f305]) ).
tff(f305,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,[],[f304]) ).
tff(f304,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,[],[f188]) ).
tff(f188,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,[],[f34]) ).
tff(f34,axiom,
! [X44: list(dB),X45: nat,X46: list(dB),X47: nat] :
( ( foldl(dB,dB,app,var(X47),X46) = foldl(dB,dB,app,var(X45),X44) )
<=> ( ( X44 = X46 )
& ( X45 = X47 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Var__apps__eq__Var__apps__conv) ).
tff(f918,plain,
spl26_69,
inference(avatar_split_clause,[],[f437,f916]) ).
tff(f437,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,[],[f303]) ).
tff(f303,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,[],[f302]) ).
tff(f302,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,[],[f187]) ).
tff(f187,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,
! [X44: list(dB),X18: dB,X46: list(dB),X48: dB] :
( ( foldl(dB,dB,app,abs(X48),X46) = foldl(dB,dB,app,abs(X18),X44) )
<=> ( ( X44 = X46 )
& ( X18 = X48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Abs__apps__eq__Abs__apps__conv) ).
tff(f914,plain,
( spl26_68
| ~ spl26_8
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f685,f678,f576,f911]) ).
tff(f685,plain,
( sP1(abs(t2))
| ~ spl26_8
| ~ spl26_28 ),
inference(resolution,[],[f679,f578]) ).
tff(f909,plain,
spl26_67,
inference(avatar_split_clause,[],[f396,f907]) ).
tff(f396,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(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,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X57: X0,X58: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X57),X58) != X58 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_not__Cons__self) ).
tff(f905,plain,
spl26_66,
inference(avatar_split_clause,[],[f340,f902]) ).
tff(f340,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Cons) ).
tff(f895,plain,
( spl26_65
| ~ spl26_64 ),
inference(avatar_split_clause,[],[f891,f888,f893]) ).
tff(f888,plain,
( spl26_64
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_64])]) ).
tff(f891,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl26_64 ),
inference(forward_demodulation,[],[f889,f465]) ).
tff(f889,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl26_64 ),
inference(avatar_component_clause,[],[f888]) ).
tff(f890,plain,
spl26_64,
inference(avatar_split_clause,[],[f503,f888]) ).
tff(f503,plain,
! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f409]) ).
tff(f409,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X4: type,X5: nat,X6: fun(nat,type)] :
( ( aa(nat,type,X6,X5) = X4 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),var(X5)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_typing_OVar) ).
tff(f886,plain,
spl26_63,
inference(avatar_split_clause,[],[f439,f884]) ).
tff(f439,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,[],[f305]) ).
tff(f882,plain,
spl26_62,
inference(avatar_split_clause,[],[f436,f880]) ).
tff(f436,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,[],[f303]) ).
tff(f878,plain,
( spl26_61
| ~ spl26_15
| ~ spl26_17 ),
inference(avatar_split_clause,[],[f653,f622,f613,f876]) ).
tff(f876,plain,
( spl26_61
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_61])]) ).
tff(f653,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl26_15
| ~ spl26_17 ),
inference(resolution,[],[f623,f614]) ).
tff(f874,plain,
spl26_60,
inference(avatar_split_clause,[],[f354,f872]) ).
tff(f872,plain,
( spl26_60
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_60])]) ).
tff(f354,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,[],[f222]) ).
tff(f222,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,[],[f127]) ).
tff(f127,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,[],[f65]) ).
tff(f65,axiom,
! [X33: list(dB)] :
( listsp(dB,it,X33)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lifts__IT) ).
tff(f861,plain,
spl26_59,
inference(avatar_split_clause,[],[f416,f859]) ).
tff(f416,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,[],[f290]) ).
tff(f290,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,[],[f173]) ).
tff(f173,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X18: dB,X33: list(dB),X48: dB] :
( ( foldl(dB,dB,app,X48,X33) = foldl(dB,dB,app,X18,X33) )
<=> ( X18 = X48 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_apps__eq__tail__conv) ).
tff(f855,plain,
( spl26_58
| ~ spl26_57 ),
inference(avatar_split_clause,[],[f851,f848,f853]) ).
tff(f853,plain,
( spl26_58
<=> ! [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,[spl26_58])]) ).
tff(f848,plain,
( spl26_57
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_57])]) ).
tff(f851,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl26_57 ),
inference(forward_demodulation,[],[f849,f465]) ).
tff(f849,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) )
| ~ spl26_57 ),
inference(avatar_component_clause,[],[f848]) ).
tff(f850,plain,
spl26_57,
inference(avatar_split_clause,[],[f405,f848]) ).
tff(f405,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X0: $tType,X63: X0,X57: X0] :
( ( X57 = X63 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X57),X63)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f846,plain,
spl26_56,
inference(avatar_split_clause,[],[f381,f844]) ).
tff(f381,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,[],[f225]) ).
tff(f225,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,[],[f50]) ).
tff(f50,axiom,
! [X45: nat,X46: list(dB)] :
( listsp(dB,it,X46)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X45),X46))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_IT_OVar) ).
tff(f838,plain,
( spl26_55
| ~ spl26_54 ),
inference(avatar_split_clause,[],[f834,f831,f836]) ).
tff(f831,plain,
( spl26_54
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_54])]) ).
tff(f834,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl26_54 ),
inference(forward_demodulation,[],[f832,f465]) ).
tff(f832,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl26_54 ),
inference(avatar_component_clause,[],[f831]) ).
tff(f833,plain,
spl26_54,
inference(avatar_split_clause,[],[f377,f831]) ).
tff(f377,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(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,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X92: bool,X90: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X90),X92))
| ~ pp(X92)
| ~ pp(X90) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f829,plain,
spl26_53,
inference(avatar_split_clause,[],[f359,f827]) ).
tff(f359,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK3(X0)))
| listsp(dB,it,sK4(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f810,plain,
spl26_52,
inference(avatar_split_clause,[],[f421,f808]) ).
tff(f421,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X44: list(dB),X48: dB,X33: list(dB),X45: nat] : ( foldl(dB,dB,app,var(X45),X33) != foldl(dB,dB,app,abs(X48),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Var__apps__neq__Abs__apps) ).
tff(f806,plain,
spl26_51,
inference(avatar_split_clause,[],[f404,f804]) ).
tff(f404,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X57: X0,X90: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X90))
| ~ pp(aa(X0,bool,X90,X57)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f802,plain,
spl26_50,
inference(avatar_split_clause,[],[f394,f800]) ).
tff(f394,plain,
! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(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,fun(dB,dB),app,X1),X0) != var(X2) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X38: dB,X39: dB,X37: nat] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X39),X38) != var(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_dB_Osimps_I4_J) ).
tff(f798,plain,
spl26_49,
inference(avatar_split_clause,[],[f392,f796]) ).
tff(f392,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X78: dB,X79: dB,X77: dB] : ( abs(X77) != aa(dB,dB,aa(dB,fun(dB,dB),app,X79),X78) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_dB_Osimps_I9_J) ).
tff(f794,plain,
spl26_48,
inference(avatar_split_clause,[],[f390,f792]) ).
tff(f390,plain,
! [X2: type,X0: nat,X1: type] : ( atom(X0) != aa(type,type,aa(type,fun(type,type),fun1,X2),X1) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: nat,X1: type,X2: type] : ( atom(X0) != aa(type,type,aa(type,fun(type,type),fun1,X2),X1) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X37: nat,X72: type,X73: type] : ( atom(X37) != aa(type,type,aa(type,fun(type,type),fun1,X73),X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_type_Osimps_I4_J) ).
tff(f789,plain,
( spl26_47
| ~ spl26_46 ),
inference(avatar_split_clause,[],[f785,f782,f787]) ).
tff(f787,plain,
( spl26_47
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_47])]) ).
tff(f782,plain,
( spl26_46
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_46])]) ).
tff(f785,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl26_46 ),
inference(forward_demodulation,[],[f783,f465]) ).
tff(f783,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl26_46 ),
inference(avatar_component_clause,[],[f782]) ).
tff(f784,plain,
spl26_46,
inference(avatar_split_clause,[],[f379,f782]) ).
tff(f379,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X92: bool,X90: bool] :
( pp(X92)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X90),X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f779,plain,
( spl26_45
| ~ spl26_44 ),
inference(avatar_split_clause,[],[f775,f772,f777]) ).
tff(f777,plain,
( spl26_45
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_45])]) ).
tff(f772,plain,
( spl26_44
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_44])]) ).
tff(f775,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl26_44 ),
inference(forward_demodulation,[],[f773,f465]) ).
tff(f773,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl26_44 ),
inference(avatar_component_clause,[],[f772]) ).
tff(f774,plain,
spl26_44,
inference(avatar_split_clause,[],[f378,f772]) ).
tff(f378,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X92: bool,X90: bool] :
( pp(X90)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X90),X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f770,plain,
spl26_43,
inference(avatar_split_clause,[],[f357,f768]) ).
tff(f768,plain,
( spl26_43
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK3(X0)) = X0 )
| listsp(dB,it,sK4(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_43])]) ).
tff(f357,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK3(X0)) = X0 )
| listsp(dB,it,sK4(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f760,plain,
( spl26_42
| ~ spl26_41 ),
inference(avatar_split_clause,[],[f756,f753,f758]) ).
tff(f753,plain,
( spl26_41
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_41])]) ).
tff(f756,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl26_41 ),
inference(forward_demodulation,[],[f754,f465]) ).
tff(f754,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl26_41 ),
inference(avatar_component_clause,[],[f753]) ).
tff(f755,plain,
spl26_41,
inference(avatar_split_clause,[],[f502,f753]) ).
tff(f502,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f403]) ).
tff(f403,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X63: X0,X57: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X57),X63))
| ( X57 != X63 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f751,plain,
spl26_40,
inference(avatar_split_clause,[],[f355,f749]) ).
tff(f355,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X32: dB] :
( pp(aa(dB,bool,it,X32))
=> pp(aa(dB,bool,it,abs(X32))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Lambda) ).
tff(f747,plain,
spl26_39,
inference(avatar_split_clause,[],[f346,f744]) ).
tff(f346,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK2)),
inference(cnf_transformation,[],[f270]) ).
tff(f742,plain,
spl26_38,
inference(avatar_split_clause,[],[f339,f739]) ).
tff(f339,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_argsT) ).
tff(f737,plain,
( spl26_37
| ~ spl26_9
| ~ spl26_17 ),
inference(avatar_split_clause,[],[f656,f622,f581,f734]) ).
tff(f734,plain,
( spl26_37
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_37])]) ).
tff(f656,plain,
( sP1(ua)
| ~ spl26_9
| ~ spl26_17 ),
inference(resolution,[],[f623,f583]) ).
tff(f731,plain,
( spl26_36
| ~ spl26_35 ),
inference(avatar_split_clause,[],[f726,f722,f728]) ).
tff(f722,plain,
( spl26_35
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_35])]) ).
tff(f726,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl26_35 ),
inference(forward_demodulation,[],[f724,f465]) ).
tff(f724,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t))
| ~ spl26_35 ),
inference(avatar_component_clause,[],[f722]) ).
tff(f725,plain,
spl26_35,
inference(avatar_split_clause,[],[f338,f722]) ).
tff(f338,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uT) ).
tff(f719,plain,
( spl26_34
| ~ spl26_33 ),
inference(avatar_split_clause,[],[f714,f710,f716]) ).
tff(f710,plain,
( spl26_33
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_33])]) ).
tff(f714,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl26_33 ),
inference(forward_demodulation,[],[f712,f465]) ).
tff(f712,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t))
| ~ spl26_33 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f713,plain,
spl26_33,
inference(avatar_split_clause,[],[f337,f710]) ).
tff(f337,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)),
inference(cnf_transformation,[],[f39]) ).
tff(f39,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Var_I4_J) ).
tff(f707,plain,
spl26_32,
inference(avatar_split_clause,[],[f497,f705]) ).
tff(f497,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f360]) ).
tff(f360,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,[],[f277]) ).
tff(f703,plain,
spl26_31,
inference(avatar_split_clause,[],[f420,f701]) ).
tff(f420,plain,
! [X0: $tType,X2: fun(type,fun(type,X0)),X3: fun(nat,X0),X1: nat] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: nat,X2: fun(type,fun(type,X0)),X3: fun(nat,X0)] : ( type_case(X0,X3,X2,atom(X1)) = aa(nat,X0,X3,X1) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X15: nat,X55: fun(type,fun(type,X0)),X56: fun(nat,X0)] : ( type_case(X0,X56,X55,atom(X15)) = aa(nat,X0,X56,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_type_Osimps_I5_J) ).
tff(f699,plain,
( spl26_30
| ~ spl26_10
| ~ spl26_17 ),
inference(avatar_split_clause,[],[f655,f622,f586,f696]) ).
tff(f696,plain,
( spl26_30
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_30])]) ).
tff(f655,plain,
( sP1(u)
| ~ spl26_10
| ~ spl26_17 ),
inference(resolution,[],[f623,f588]) ).
tff(f693,plain,
spl26_29,
inference(avatar_split_clause,[],[f513,f691]) ).
tff(f513,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f456]) ).
tff(f456,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X4: X0,X8: fun(nat,X0),X40: nat,X7: nat] :
( ( X7 = X40 )
=> ( aa(nat,X0,shift(X0,X8,X7,X4),X40) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_shift__eq) ).
tff(f680,plain,
spl26_28,
inference(avatar_split_clause,[],[f496,f678]) ).
tff(f496,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f361]) ).
tff(f361,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f676,plain,
spl26_27,
inference(avatar_split_clause,[],[f374,f674]) ).
tff(f374,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(f672,plain,
spl26_26,
inference(avatar_split_clause,[],[f365,f670]) ).
tff(f365,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f666,plain,
( spl26_25
| ~ spl26_8
| ~ spl26_17 ),
inference(avatar_split_clause,[],[f654,f622,f576,f663]) ).
tff(f663,plain,
( spl26_25
<=> sP1(t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_25])]) ).
tff(f654,plain,
( sP1(t2)
| ~ spl26_8
| ~ spl26_17 ),
inference(resolution,[],[f623,f578]) ).
tff(f652,plain,
spl26_24,
inference(avatar_split_clause,[],[f388,f650]) ).
tff(f650,plain,
( spl26_24
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_24])]) ).
tff(f388,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,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,
! [X14: nat,X15: nat] :
( ( var(X15) = var(X14) )
<=> ( X14 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dB_Osimps_I1_J) ).
tff(f648,plain,
spl26_23,
inference(avatar_split_clause,[],[f386,f646]) ).
tff(f646,plain,
( spl26_23
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_23])]) ).
tff(f386,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,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,
! [X75: dB,X76: dB] :
( ( abs(X76) = abs(X75) )
<=> ( X75 = X76 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_dB_Osimps_I3_J) ).
tff(f644,plain,
spl26_22,
inference(avatar_split_clause,[],[f384,f642]) ).
tff(f642,plain,
( spl26_22
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( atom(X0) != atom(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_22])]) ).
tff(f384,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( atom(X0) != atom(X1) ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,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,[],[f68]) ).
tff(f68,axiom,
! [X14: nat,X15: nat] :
( ( atom(X15) = atom(X14) )
<=> ( X14 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_type_Osimps_I1_J) ).
tff(f640,plain,
spl26_21,
inference(avatar_split_clause,[],[f380,f638]) ).
tff(f638,plain,
( spl26_21
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_21])]) ).
tff(f380,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,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,[],[f98]) ).
tff(f98,axiom,
! [X29: dB,X27: dB] :
( beta(X27,X29)
=> beta(abs(X27),abs(X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_abs) ).
tff(f636,plain,
spl26_20,
inference(avatar_split_clause,[],[f373,f634]) ).
tff(f373,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,X90: X0] : ( aa(X0,X0,combi(X0),X90) = X90 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f632,plain,
( spl26_19
| spl26_2
| ~ spl26_13 ),
inference(avatar_split_clause,[],[f603,f599,f549,f630]) ).
tff(f549,plain,
( spl26_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
tff(f603,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl26_2
| ~ spl26_13 ),
inference(superposition,[],[f551,f600]) ).
tff(f551,plain,
( ~ pp(fFalse)
| spl26_2 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f628,plain,
spl26_18,
inference(avatar_split_clause,[],[f368,f626]) ).
tff(f368,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f129,f267,f266]) ).
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,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X52: dB] :
( pp(aa(dB,bool,it,X52))
<=> ( ? [X84: dB,X85: dB,X86: list(dB)] :
( pp(aa(dB,bool,it,X85))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X84),X85),zero_zero(nat)),X86)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X84)),X85),X86) = X52 ) )
| ? [X84: dB] :
( pp(aa(dB,bool,it,X84))
& ( abs(X84) = X52 ) )
| ? [X82: list(dB),X83: nat] :
( listsp(dB,it,X82)
& ( foldl(dB,dB,app,var(X83),X82) = X52 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_IT_Osimps) ).
tff(f624,plain,
spl26_17,
inference(avatar_split_clause,[],[f367,f622]) ).
tff(f367,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f282]) ).
tff(f619,plain,
spl26_16,
inference(avatar_split_clause,[],[f372,f617]) ).
tff(f617,plain,
( spl26_16
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_16])]) ).
tff(f372,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X74: fun(X0,bool)] : ( collect(X0,X74) = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f615,plain,
spl26_15,
inference(avatar_split_clause,[],[f350,f613]) ).
tff(f350,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X35: nat] : pp(aa(dB,bool,it,var(X35))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Var__IT) ).
tff(f611,plain,
spl26_14,
inference(avatar_split_clause,[],[f349,f609]) ).
tff(f609,plain,
( spl26_14
<=> ! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_14])]) ).
tff(f349,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(type,atom(X0)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X37: nat] : ( zero_zero(nat) = size_size(type,atom(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_type_Osize_I3_J) ).
tff(f601,plain,
spl26_13,
inference(avatar_split_clause,[],[f351,f599]) ).
tff(f351,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X90: bool] :
( ( fFalse = X90 )
| ( fTrue = X90 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f597,plain,
spl26_12,
inference(avatar_split_clause,[],[f348,f595]) ).
tff(f595,plain,
( spl26_12
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
tff(f348,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X37: nat] : ( zero_zero(nat) = dB_size(var(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dB_Osize_I1_J) ).
tff(f593,plain,
spl26_11,
inference(avatar_split_clause,[],[f347,f591]) ).
tff(f591,plain,
( spl26_11
<=> ! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
tff(f347,plain,
! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : ( zero_zero(nat) = type_size(atom(X0)) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X37: nat] : ( zero_zero(nat) = type_size(atom(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_type_Osize_I1_J) ).
tff(f589,plain,
spl26_10,
inference(avatar_split_clause,[],[f336,f586]) ).
tff(f336,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(f584,plain,
spl26_9,
inference(avatar_split_clause,[],[f335,f581]) ).
tff(f335,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(f579,plain,
spl26_8,
inference(avatar_split_clause,[],[f334,f576]) ).
tff(f334,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(f574,plain,
spl26_7,
inference(avatar_split_clause,[],[f370,f572]) ).
tff(f572,plain,
( spl26_7
<=> ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
tff(f370,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X37: nat,X77: dB] : ( var(X37) != abs(X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_dB_Osimps_I7_J) ).
tff(f570,plain,
spl26_6,
inference(avatar_split_clause,[],[f369,f568]) ).
tff(f568,plain,
( spl26_6
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
tff(f369,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,[],[f97]) ).
tff(f97,axiom,
! [X29: dB,X31: nat] : ~ beta(var(X31),X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_beta__cases_I1_J) ).
tff(f566,plain,
spl26_5,
inference(avatar_split_clause,[],[f362,f564]) ).
tff(f564,plain,
( spl26_5
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
tff(f362,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f562,plain,
spl26_4,
inference(avatar_split_clause,[],[f332,f559]) ).
tff(f332,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(f557,plain,
spl26_3,
inference(avatar_split_clause,[],[f331,f554]) ).
tff(f554,plain,
( spl26_3
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
tff(f331,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(f552,plain,
~ spl26_2,
inference(avatar_split_clause,[],[f329,f549]) ).
tff(f329,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(f547,plain,
~ spl26_1,
inference(avatar_split_clause,[],[f327,f544]) ).
tff(f327,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
% 0.03/0.10 % Problem : LCL787_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 13:52:22 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (2956)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (2959)WARNING: value z3 for option sas not known
% 0.11/0.35 % (2957)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (2960)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (2962)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (2958)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (2959)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (2963)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.35 % (2961)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.36 % (2963)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.36 % Exception at run slice level% Exception at run slice level
% 0.11/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.36
% 0.11/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.36 % Exception at run slice level
% 0.11/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.37 % (2965)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)
% 0.17/0.37 % (2966)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)
% 0.17/0.37 % (2964)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.38 % (2965)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.38 % (2964)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.38 % Exception at run slice level
% 0.17/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.39 % (2967)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)
% 17.66/2.94 % (2961)First to succeed.
% 18.74/3.01 % (2961)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2956"
% 18.74/3.01 % (2961)Refutation found. Thanks to Tanya!
% 18.74/3.01 % SZS status Theorem for theBenchmark
% 18.74/3.01 % SZS output start Proof for theBenchmark
% See solution above
% 18.74/3.03 % (2961)------------------------------
% 18.74/3.03 % (2961)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 18.74/3.03 % (2961)Termination reason: Refutation
% 18.74/3.03
% 18.74/3.03 % (2961)Memory used [KB]: 25812
% 18.74/3.03 % (2961)Time elapsed: 2.660 s
% 18.74/3.03 % (2961)Instructions burned: 5272 (million)
% 18.74/3.03 % (2956)Success in time 2.68 s
%------------------------------------------------------------------------------