TSTP Solution File: COM099_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM099_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:22 EDT 2024
% Result : Theorem 61.57s 9.34s
% Output : Refutation 61.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 762
% Syntax : Number of formulae : 2366 ( 247 unt; 67 typ; 0 def)
% Number of atoms : 7448 (1123 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 8908 (3759 ~;4299 |; 79 &)
% ( 609 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 21 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 39 ( 27 >; 12 *; 0 +; 0 <<)
% Number of predicates : 580 ( 578 usr; 566 prp; 0-2 aty)
% Number of functors : 51 ( 51 usr; 14 con; 0-4 aty)
% Number of variables : 4821 (4706 !; 50 ?;4821 :)
% ( 65 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
atom: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
big_linorder_Max:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_1,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_2,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_5,type,
minus_minus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_6,type,
iprod:
!>[X0: $tType] : fun(list(X0),fun(list(X0),X0)) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_9,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_10,type,
ord_less_eq:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_11,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_12,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_13,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_14,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_15,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fNot: fun(bool,bool) ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_20,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_22,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_23,type,
a: atom ).
tff(func_def_24,type,
as: list(atom) ).
tff(func_def_25,type,
i: int ).
tff(func_def_26,type,
ks: list(int) ).
tff(func_def_27,type,
li: int ).
tff(func_def_28,type,
lks: list(int) ).
tff(func_def_29,type,
xs: list(int) ).
tff(func_def_30,type,
sK0: int ).
tff(func_def_31,type,
sK1: list(int) ).
tff(func_def_32,type,
sK2:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).
tff(func_def_33,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_34,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_35,type,
sK5:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_36,type,
sK6:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_37,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_38,type,
sK8:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_39,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_40,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_41,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_42,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(X1,bool) ) > X1 ) ).
tff(func_def_43,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_44,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * fun(X1,fun(X0,bool)) ) > X1 ) ).
tff(func_def_45,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * fun(X1,fun(X0,bool)) ) > X0 ) ).
tff(func_def_46,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).
tff(func_def_47,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
finite_finite:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
finite_finite1:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f34480,plain,
$false,
inference(avatar_sat_refutation,[],[f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f739,f743,f747,f751,f755,f759,f763,f767,f771,f778,f782,f786,f790,f794,f798,f802,f811,f816,f823,f827,f832,f839,f847,f851,f861,f865,f869,f873,f877,f889,f896,f900,f904,f908,f918,f933,f938,f942,f946,f950,f954,f959,f982,f986,f1010,f1017,f1022,f1029,f1033,f1049,f1055,f1063,f1068,f1082,f1086,f1091,f1096,f1112,f1116,f1121,f1126,f1130,f1134,f1158,f1178,f1182,f1189,f1193,f1198,f1214,f1218,f1222,f1234,f1239,f1245,f1249,f1253,f1544,f1565,f1570,f1587,f1601,f1618,f1622,f1626,f1630,f1682,f1686,f1692,f1733,f1751,f1755,f1793,f1866,f1870,f1874,f1913,f1917,f1921,f2007,f2012,f2016,f2020,f2046,f2050,f2126,f2130,f2135,f2176,f2200,f2205,f2229,f2233,f2301,f2305,f2309,f2313,f2324,f2328,f2335,f2339,f2377,f2382,f2386,f2439,f2443,f2516,f2556,f2567,f2575,f2581,f2587,f2591,f2651,f2657,f2662,f2669,f2675,f2681,f2690,f2695,f2700,f2706,f2712,f2738,f2745,f2769,f2777,f2793,f2794,f2795,f2796,f2809,f3116,f4213,f4231,f4243,f4247,f4251,f4255,f4321,f4333,f4337,f4341,f4378,f4383,f4398,f4402,f4406,f4410,f4577,f4584,f4611,f4612,f4613,f4630,f4655,f4681,f4952,f5931,f5988,f6002,f6006,f6025,f6034,f6038,f6042,f6055,f6059,f6063,f6067,f6176,f6180,f6231,f6235,f6236,f6240,f6244,f6293,f6297,f6301,f6380,f6384,f6397,f6400,f6433,f6461,f6465,f6517,f6522,f6533,f6543,f6547,f6551,f6606,f6610,f6614,f6624,f6628,f6632,f6636,f7045,f7109,f7131,f7135,f7139,f7143,f7147,f7151,f7321,f7348,f7352,f7356,f7360,f7429,f7433,f7437,f7473,f7490,f7526,f7551,f7555,f7559,f7563,f7567,f7576,f7580,f7684,f7689,f7694,f7699,f7751,f7755,f7759,f7763,f7915,f7919,f7923,f7985,f7989,f7994,f7998,f8002,f8006,f8101,f8105,f8114,f8118,f8122,f8126,f8312,f8316,f8320,f8503,f8507,f8511,f8685,f8780,f8784,f8788,f8966,f9023,f9137,f9141,f9145,f9237,f9242,f9268,f9272,f9276,f9280,f9284,f9556,f9560,f9564,f9568,f9572,f9577,f9581,f10382,f10401,f10439,f10443,f10447,f10451,f10727,f10785,f10789,f10793,f10797,f11027,f11039,f11043,f11047,f11051,f11055,f11059,f11063,f11625,f11655,f11659,f11663,f11667,f11672,f11720,f11920,f11924,f11930,f11937,f11992,f12044,f12049,f12104,f12263,f12267,f12271,f12275,f12513,f12517,f12528,f12532,f12550,f12555,f12563,f12674,f12700,f12704,f12875,f12879,f13324,f13408,f13457,f13462,f13467,f13471,f13476,f14348,f14352,f14356,f15123,f15127,f15131,f15412,f15416,f15501,f15505,f15509,f15631,f15635,f15639,f15643,f15647,f15779,f15783,f15829,f15833,f15837,f15948,f15952,f16045,f16049,f16053,f16057,f16061,f16065,f16069,f16073,f17221,f17224,f17246,f17946,f17950,f17954,f17958,f17979,f17983,f17987,f17991,f17995,f18299,f18465,f18469,f18501,f18586,f18590,f18594,f18598,f18606,f18612,f18636,f18640,f18669,f19829,f19860,f19864,f20262,f20266,f20270,f20274,f20503,f20507,f20511,f20515,f20519,f21259,f21263,f21374,f21378,f21382,f22003,f22007,f22027,f22031,f22499,f22503,f22507,f23029,f23137,f23141,f23631,f23635,f23639,f23980,f23984,f24172,f24176,f25098,f25103,f25108,f25356,f25360,f25364,f25546,f25635,f25639,f25751,f25812,f25816,f25820,f25824,f25828,f25832,f25836,f25840,f26352,f26402,f26406,f26410,f26582,f26667,f27456,f27460,f27464,f27726,f27730,f27954,f28099,f28103,f28107,f28180,f28246,f28252,f28258,f28425,f28451,f28455,f28581,f28585,f28589,f28593,f29229,f29318,f29384,f29441,f29445,f29449,f29453,f29637,f30171,f30242,f30320,f30324,f30542,f30561,f30580,f30599,f30603,f30607,f31370,f31374,f31560,f31564,f31868,f31872,f31878,f31897,f31916,f31920,f31924,f31985,f31989,f31993,f32073,f32261,f32266,f32289,f32448,f32508,f32512,f32636,f32719,f32776,f32948,f33148,f33152,f33156,f33205,f33223,f33265,f33269,f33498,f33550,f33606,f33635,f33724,f33791,f33795,f33943,f33947,f33951,f33955,f34462,f34479]) ).
tff(f34479,plain,
( ~ spl18_8
| ~ spl18_154
| spl18_1
| spl18_55
| ~ spl18_101
| ~ spl18_158
| ~ spl18_161
| ~ spl18_163
| ~ spl18_181 ),
inference(avatar_split_clause,[],[f4619,f4376,f2709,f2697,f2678,f1599,f930,f647,f2654,f682]) ).
tff(f682,plain,
( spl18_8
<=> linorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
tff(f2654,plain,
( spl18_154
<=> finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_154])]) ).
tff(f647,plain,
( spl18_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
tff(f930,plain,
( spl18_55
<=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).
tff(f1599,plain,
( spl18_101
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).
tff(f2678,plain,
( spl18_158
<=> ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_158])]) ).
tff(f2697,plain,
( spl18_161
<=> ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_161])]) ).
tff(f2709,plain,
( spl18_163
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_163])]) ).
tff(f4376,plain,
( spl18_181
<=> ! [X2: bool] :
( pp(X2)
| ( fFalse = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_181])]) ).
tff(f4619,plain,
( pp(fFalse)
| ~ finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))
| ~ linorder(int)
| spl18_55
| ~ spl18_101
| ~ spl18_158
| ~ spl18_161
| ~ spl18_163
| ~ spl18_181 ),
inference(forward_demodulation,[],[f2724,f4573]) ).
tff(f4573,plain,
( ( fFalse = aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))) )
| spl18_55
| ~ spl18_158
| ~ spl18_181 ),
inference(forward_demodulation,[],[f4548,f2680]) ).
tff(f2680,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
| ~ spl18_158 ),
inference(avatar_component_clause,[],[f2678]) ).
tff(f4548,plain,
( ( fFalse = aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))) )
| spl18_55
| ~ spl18_181 ),
inference(resolution,[],[f4377,f932]) ).
tff(f932,plain,
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))))
| spl18_55 ),
inference(avatar_component_clause,[],[f930]) ).
tff(f4377,plain,
( ! [X2: bool] :
( pp(X2)
| ( fFalse = X2 ) )
| ~ spl18_181 ),
inference(avatar_component_clause,[],[f4376]) ).
tff(f2724,plain,
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))))
| ~ finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))
| ~ linorder(int)
| ~ spl18_101
| ~ spl18_161
| ~ spl18_163 ),
inference(forward_demodulation,[],[f2714,f2699]) ).
tff(f2699,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) )
| ~ spl18_161 ),
inference(avatar_component_clause,[],[f2697]) ).
tff(f2714,plain,
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))))
| ~ finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))
| ~ linorder(int)
| ~ spl18_101
| ~ spl18_163 ),
inference(resolution,[],[f2711,f1600]) ).
tff(f1600,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) )
| ~ spl18_101 ),
inference(avatar_component_clause,[],[f1599]) ).
tff(f2711,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_163 ),
inference(avatar_component_clause,[],[f2709]) ).
tff(f34462,plain,
( spl18_565
| ~ spl18_112
| ~ spl18_148 ),
inference(avatar_split_clause,[],[f2570,f2565,f1791,f34460]) ).
tff(f34460,plain,
( spl18_565
<=> ! [X1: $tType,X0: $tType,X4: X1,X3: fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),X2: fun(X1,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)))),fun(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)))),combs(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0)),X3),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))))
| ~ finite_finite1(X1,X2)
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),X3,aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))),X4))
| ~ pp(aa(X1,bool,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_565])]) ).
tff(f1791,plain,
( spl18_112
<=> ! [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,[spl18_112])]) ).
tff(f2565,plain,
( spl18_148
<=> ! [X1: $tType,X0: $tType,X5: X1,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_148])]) ).
tff(f2570,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),X4: X1] :
( ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)))),fun(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)))),combs(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0)),X3),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))))
| ~ finite_finite1(X1,X2)
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),X3,aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))),X4))
| ~ pp(aa(X1,bool,X2,X4)) )
| ~ spl18_112
| ~ spl18_148 ),
inference(superposition,[],[f2566,f1792]) ).
tff(f1792,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)) )
| ~ spl18_112 ),
inference(avatar_component_clause,[],[f1791]) ).
tff(f2566,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5)) )
| ~ spl18_148 ),
inference(avatar_component_clause,[],[f2565]) ).
tff(f33955,plain,
( spl18_564
| ~ spl18_131
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2457,f2437,f2227,f33953]) ).
tff(f33953,plain,
( spl18_564
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X4))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3) = X4 )
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_564])]) ).
tff(f2227,plain,
( spl18_131
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_131])]) ).
tff(f2437,plain,
( spl18_144
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X1,X0),bool),X2: fun(product_prod(X1,X0),bool)] :
( ( X2 = X3 )
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_144])]) ).
tff(f2457,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X4))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3) = X4 )
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X3)) )
| ~ spl18_131
| ~ spl18_144 ),
inference(resolution,[],[f2438,f2228]) ).
tff(f2228,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) )
| ~ spl18_131 ),
inference(avatar_component_clause,[],[f2227]) ).
tff(f2438,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ( X2 = X3 ) )
| ~ spl18_144 ),
inference(avatar_component_clause,[],[f2437]) ).
tff(f33951,plain,
( spl18_563
| ~ spl18_132
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2456,f2437,f2231,f33949]) ).
tff(f33949,plain,
( spl18_563
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X4))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3) = X4 )
| pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_563])]) ).
tff(f2231,plain,
( spl18_132
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_132])]) ).
tff(f2456,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X4))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3) = X4 )
| pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4)),sK17(X1,X0,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X2),X3),X4))),X2)) )
| ~ spl18_132
| ~ spl18_144 ),
inference(resolution,[],[f2438,f2232]) ).
tff(f2232,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ~ spl18_132 ),
inference(avatar_component_clause,[],[f2231]) ).
tff(f33947,plain,
( spl18_562
| ~ spl18_131
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2449,f2437,f2227,f33945]) ).
tff(f33945,plain,
( spl18_562
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X2))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4) = X2 )
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_562])]) ).
tff(f2449,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X2))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4) = X2 )
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X4)) )
| ~ spl18_131
| ~ spl18_144 ),
inference(resolution,[],[f2438,f2228]) ).
tff(f33943,plain,
( spl18_561
| ~ spl18_132
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2448,f2437,f2231,f33941]) ).
tff(f33941,plain,
( spl18_561
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X2))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4) = X2 )
| pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_561])]) ).
tff(f2448,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X2))
| ( aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4) = X2 )
| pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4))),sK17(X1,X0,X2,aa(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),fun(product_prod(X0,X1),bool)),minus_minus(fun(product_prod(X0,X1),bool)),X3),X4)))),X3)) )
| ~ spl18_132
| ~ spl18_144 ),
inference(resolution,[],[f2438,f2232]) ).
tff(f33795,plain,
( spl18_560
| ~ spl18_112
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2537,f2514,f1791,f33793]) ).
tff(f33793,plain,
( spl18_560
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),X2: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)))),fun(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)))),combs(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0)),X3),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))))
| pp(aa(X1,bool,X2,sK12(X0,X1,aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),X3,aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2))),X2)))
| ~ finite_finite1(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_560])]) ).
tff(f2514,plain,
( spl18_146
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_146])]) ).
tff(f2537,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)))] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),aa(fun(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)))),fun(fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)))),combs(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0)),X3),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)))))
| pp(aa(X1,bool,X2,sK12(X0,X1,aa(fun(fun(X1,bool),fun(X1,bool)),fun(X0,fun(X1,bool)),X3,aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2))),X2)))
| ~ finite_finite1(X1,X2) )
| ~ spl18_112
| ~ spl18_146 ),
inference(superposition,[],[f2515,f1792]) ).
tff(f2515,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3)))
| ~ finite_finite1(X1,X3) )
| ~ spl18_146 ),
inference(avatar_component_clause,[],[f2514]) ).
tff(f33791,plain,
( spl18_463
| ~ spl18_30
| ~ spl18_527 ),
inference(avatar_split_clause,[],[f32623,f31865,f784,f25100]) ).
tff(f25100,plain,
( spl18_463
<=> ( fTrue = sK13(fun(bool,bool),bool,fconj,fconj) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_463])]) ).
tff(f784,plain,
( spl18_30
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
tff(f31865,plain,
( spl18_527
<=> pp(sK13(fun(bool,bool),bool,fconj,fconj)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_527])]) ).
tff(f32623,plain,
( ( fTrue = sK13(fun(bool,bool),bool,fconj,fconj) )
| ~ spl18_30
| ~ spl18_527 ),
inference(resolution,[],[f31866,f785]) ).
tff(f785,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f784]) ).
tff(f31866,plain,
( pp(sK13(fun(bool,bool),bool,fconj,fconj))
| ~ spl18_527 ),
inference(avatar_component_clause,[],[f31865]) ).
tff(f33724,plain,
( spl18_559
| ~ spl18_122
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2530,f2514,f2018,f33722]) ).
tff(f33722,plain,
( spl18_559
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_559])]) ).
tff(f2018,plain,
( spl18_122
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X2 )
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_122])]) ).
tff(f2530,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0) )
| ~ spl18_122
| ~ spl18_146 ),
inference(resolution,[],[f2515,f2019]) ).
tff(f2019,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( combk(bool,X0,fFalse) = X2 )
| ~ linorder(X0) )
| ~ spl18_122 ),
inference(avatar_component_clause,[],[f2018]) ).
tff(f33635,plain,
( spl18_558
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(avatar_split_clause,[],[f2637,f2589,f1749,f1628,f1624,f33633]) ).
tff(f33633,plain,
( spl18_558
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X2)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_558])]) ).
tff(f1624,plain,
( spl18_104
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).
tff(f1628,plain,
( spl18_105
<=> ! [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,[spl18_105])]) ).
tff(f1749,plain,
( spl18_110
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X5: X1,X2: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X5)),aa(X1,X0,X2,X5)))
| ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_110])]) ).
tff(f2589,plain,
( spl18_152
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X1,X0),bool),X2: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2)))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_152])]) ).
tff(f2637,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X2)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2636,f1629]) ).
tff(f1629,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)) )
| ~ spl18_105 ),
inference(avatar_component_clause,[],[f1628]) ).
tff(f2636,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)),X4)),X2)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2635,f1629]) ).
tff(f2635,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1))),X4),X2)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2634,f1625]) ).
tff(f1625,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl18_104 ),
inference(avatar_component_clause,[],[f1624]) ).
tff(f2634,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X2),X4)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1))),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4))),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2633,f1629]) ).
tff(f2633,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X2),X4)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),combc(X1,fun(product_prod(X0,X1),bool),bool),aa(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)),X4)),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_105
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2632,f1629]) ).
tff(f2632,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X2),X4)),aa(fun(product_prod(X0,X1),bool),fun(X1,bool),aa(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1))),X4),X3)))
| ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| ~ ord(fun(X1,bool)) )
| ~ spl18_104
| ~ spl18_110
| ~ spl18_152 ),
inference(forward_demodulation,[],[f2608,f1625]) ).
tff(f2608,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool),X4: X0] :
( ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X2),X3))
| pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X2),X4)),aa(X0,fun(X1,bool),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X3),X4)))
| ~ ord(fun(X1,bool)) )
| ~ spl18_110
| ~ spl18_152 ),
inference(resolution,[],[f2590,f1750]) ).
tff(f1750,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: X1] :
( ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X5)),aa(X1,X0,X2,X5)))
| ~ ord(X0) )
| ~ spl18_110 ),
inference(avatar_component_clause,[],[f1749]) ).
tff(f2590,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2)))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2)) )
| ~ spl18_152 ),
inference(avatar_component_clause,[],[f2589]) ).
tff(f33606,plain,
( spl18_557
| ~ spl18_115
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2531,f2514,f1872,f33604]) ).
tff(f33604,plain,
( spl18_557
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_557])]) ).
tff(f1872,plain,
( spl18_115
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( X1 = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_115])]) ).
tff(f2531,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 ) )
| ~ spl18_115
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1873]) ).
tff(f1873,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ( X1 = X2 ) )
| ~ spl18_115 ),
inference(avatar_component_clause,[],[f1872]) ).
tff(f33550,plain,
( spl18_556
| ~ spl18_109
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2526,f2514,f1731,f33548]) ).
tff(f33548,plain,
( spl18_556
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| ( big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_556])]) ).
tff(f1731,plain,
( spl18_109
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),X1))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_109])]) ).
tff(f2526,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| ( big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0) )
| ~ spl18_109
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1732]) ).
tff(f1732,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),X1))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) )
| ~ spl18_109 ),
inference(avatar_component_clause,[],[f1731]) ).
tff(f33498,plain,
( spl18_555
| ~ spl18_128
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2529,f2514,f2174,f33496]) ).
tff(f33496,plain,
( spl18_555
<=> ! [X2: $tType,X0: $tType,X4: X0,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_555])]) ).
tff(f2174,plain,
( spl18_128
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_128])]) ).
tff(f2529,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool),X4: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))) )
| ~ spl18_128
| ~ spl18_146 ),
inference(resolution,[],[f2515,f2175]) ).
tff(f2175,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) )
| ~ spl18_128 ),
inference(avatar_component_clause,[],[f2174]) ).
tff(f33269,plain,
( spl18_554
| ~ spl18_110
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2534,f2514,f1749,f33267]) ).
tff(f33267,plain,
( spl18_554
<=> ! [X1: $tType,X3: $tType,X0: $tType,X5: X0,X4: fun(X3,fun(fun(X0,X1),bool)),X2: fun(X0,X1)] :
( finite_finite1(X3,aa(fun(X3,fun(fun(X0,X1),bool)),fun(X3,bool),aa(fun(fun(fun(X0,X1),bool),bool),fun(fun(X3,fun(fun(X0,X1),bool)),fun(X3,bool)),combb(fun(fun(X0,X1),bool),bool,X3),fEx(fun(X0,X1))),aa(fun(X3,fun(fun(X0,X1),bool)),fun(X3,fun(fun(X0,X1),bool)),aa(fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool)),fun(fun(X3,fun(fun(X0,X1),bool)),fun(X3,fun(fun(X0,X1),bool))),combb(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool),X3),aa(fun(fun(X0,X1),fun(bool,bool)),fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool)),combs(fun(X0,X1),bool,bool),aa(fun(fun(X0,X1),bool),fun(fun(X0,X1),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,X1)),fconj),aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2)))),X4)))
| ~ finite_finite1(fun(X0,X1),aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X2,X5)),aa(X0,X1,sK12(X3,fun(X0,X1),X4,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2)),X5)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_554])]) ).
tff(f2534,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: fun(X0,X1),X4: fun(X3,fun(fun(X0,X1),bool)),X5: X0] :
( finite_finite1(X3,aa(fun(X3,fun(fun(X0,X1),bool)),fun(X3,bool),aa(fun(fun(fun(X0,X1),bool),bool),fun(fun(X3,fun(fun(X0,X1),bool)),fun(X3,bool)),combb(fun(fun(X0,X1),bool),bool,X3),fEx(fun(X0,X1))),aa(fun(X3,fun(fun(X0,X1),bool)),fun(X3,fun(fun(X0,X1),bool)),aa(fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool)),fun(fun(X3,fun(fun(X0,X1),bool)),fun(X3,fun(fun(X0,X1),bool))),combb(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool),X3),aa(fun(fun(X0,X1),fun(bool,bool)),fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),bool)),combs(fun(X0,X1),bool,bool),aa(fun(fun(X0,X1),bool),fun(fun(X0,X1),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,X1),bool),fun(fun(X0,X1),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,X1)),fconj),aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2)))),X4)))
| ~ finite_finite1(fun(X0,X1),aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X2,X5)),aa(X0,X1,sK12(X3,fun(X0,X1),X4,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2)),X5)))
| ~ ord(X1) )
| ~ spl18_110
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1750]) ).
tff(f33265,plain,
( spl18_553
| ~ spl18_101
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2527,f2514,f1599,f33263]) ).
tff(f33263,plain,
( spl18_553
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_553])]) ).
tff(f2527,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0) )
| ~ spl18_101
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1600]) ).
tff(f33223,plain,
( spl18_552
| ~ spl18_97
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2532,f2514,f1542,f33221]) ).
tff(f33221,plain,
( spl18_552
<=> ! [X2: $tType,X0: $tType,X4: X0,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| pp(aa(X0,bool,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X4))
| ~ pp(aa(X0,bool,X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_552])]) ).
tff(f1542,plain,
( spl18_97
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).
tff(f2532,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool),X4: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| pp(aa(X0,bool,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X4))
| ~ pp(aa(X0,bool,X1,X4)) )
| ~ spl18_97
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1543]) ).
tff(f1543,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2)) )
| ~ spl18_97 ),
inference(avatar_component_clause,[],[f1542]) ).
tff(f33205,plain,
( spl18_551
| ~ spl18_80
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2533,f2514,f1124,f33203]) ).
tff(f33203,plain,
( spl18_551
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_551])]) ).
tff(f1124,plain,
( spl18_80
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).
tff(f2533,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK12(X2,fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))) )
| ~ spl18_80
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1125]) ).
tff(f1125,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,X2) )
| ~ spl18_80 ),
inference(avatar_component_clause,[],[f1124]) ).
tff(f33156,plain,
( spl18_550
| ~ spl18_475
| ~ spl18_527 ),
inference(avatar_split_clause,[],[f32624,f31865,f25822,f33154]) ).
tff(f33154,plain,
( spl18_550
<=> ! [X0: bool] :
( pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_550])]) ).
tff(f25822,plain,
( spl18_475
<=> ! [X0: bool] :
( ( sK13(fun(bool,bool),bool,fconj,fconj) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_475])]) ).
tff(f32624,plain,
( ! [X0: bool] :
( pp(X0)
| ( fTrue = X0 ) )
| ~ spl18_475
| ~ spl18_527 ),
inference(superposition,[],[f31866,f25823]) ).
tff(f25823,plain,
( ! [X0: bool] :
( ( sK13(fun(bool,bool),bool,fconj,fconj) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_475 ),
inference(avatar_component_clause,[],[f25822]) ).
tff(f33152,plain,
( spl18_549
| ~ spl18_116
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f2558,f2554,f1911,f33150]) ).
tff(f33150,plain,
( spl18_549
<=> ! [X0: $tType,X1: fun(fun(X0,bool),bool)] :
( ~ finite_finite1(fun(X0,bool),X1)
| finite_finite1(fun(X0,bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),bool)),combb(fun(fun(X0,bool),bool),bool,fun(X0,bool)),fEx(fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),X1))),ord_less_eq(fun(X0,bool)))))
| ~ finite_finite1(X0,sK12(fun(X0,bool),fun(X0,bool),ord_less_eq(fun(X0,bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_549])]) ).
tff(f1911,plain,
( spl18_116
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))
| ~ finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_116])]) ).
tff(f2554,plain,
( spl18_147
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_147])]) ).
tff(f2558,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),bool)] :
( ~ finite_finite1(fun(X0,bool),X1)
| finite_finite1(fun(X0,bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),bool)),combb(fun(fun(X0,bool),bool),bool,fun(X0,bool)),fEx(fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),X1))),ord_less_eq(fun(X0,bool)))))
| ~ finite_finite1(X0,sK12(fun(X0,bool),fun(X0,bool),ord_less_eq(fun(X0,bool)),X1)) )
| ~ spl18_116
| ~ spl18_147 ),
inference(resolution,[],[f2555,f1912]) ).
tff(f1912,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))
| ~ finite_finite1(X0,X1) )
| ~ spl18_116 ),
inference(avatar_component_clause,[],[f1911]) ).
tff(f2555,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3)))
| ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))) )
| ~ spl18_147 ),
inference(avatar_component_clause,[],[f2554]) ).
tff(f33148,plain,
( spl18_548
| ~ spl18_71
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2528,f2514,f1061,f33146]) ).
tff(f33146,plain,
( spl18_548
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| pp(aa(X0,bool,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_548])]) ).
tff(f1061,plain,
( spl18_71
<=> ! [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,[spl18_71])]) ).
tff(f2528,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(fun(X0,bool),bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool),aa(fun(fun(fun(X0,bool),bool),bool),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,bool)),combb(fun(fun(X0,bool),bool),bool,X2),fEx(fun(X0,bool))),aa(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool)),aa(fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),fun(fun(X2,fun(fun(X0,bool),bool)),fun(X2,fun(fun(X0,bool),bool))),combb(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),X2),aa(fun(fun(X0,bool),fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool)),combs(fun(X0,bool),bool,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(fun(X0,bool),bool),fun(fun(X0,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X0,bool)),fconj),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X3)))
| ~ finite_finite1(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))
| pp(aa(X0,bool,sK12(X2,fun(X0,bool),X3,aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1)) )
| ~ spl18_71
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1062]) ).
tff(f1062,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)) )
| ~ spl18_71 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f32948,plain,
( spl18_547
| ~ spl18_105
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2550,f2514,f1628,f32946]) ).
tff(f32946,plain,
( spl18_547
<=> ! [X1: $tType,X0: $tType,X4: $tType,X5: fun(X4,fun(X0,bool)),X3: fun(X0,X1),X2: fun(X1,bool)] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK12(X4,X0,X5,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3)))))
| finite_finite1(X4,aa(fun(X4,fun(X0,bool)),fun(X4,bool),aa(fun(fun(X0,bool),bool),fun(fun(X4,fun(X0,bool)),fun(X4,bool)),combb(fun(X0,bool),bool,X4),fEx(X0)),aa(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X4),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),aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3)))),X5)))
| ~ finite_finite1(X0,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_547])]) ).
tff(f2550,plain,
( ! [X4: $tType,X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1),X5: fun(X4,fun(X0,bool))] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK12(X4,X0,X5,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3)))))
| finite_finite1(X4,aa(fun(X4,fun(X0,bool)),fun(X4,bool),aa(fun(fun(X0,bool),bool),fun(fun(X4,fun(X0,bool)),fun(X4,bool)),combb(fun(X0,bool),bool,X4),fEx(X0)),aa(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X4),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),aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3)))),X5)))
| ~ finite_finite1(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)) )
| ~ spl18_105
| ~ spl18_146 ),
inference(superposition,[],[f2515,f1629]) ).
tff(f32776,plain,
( spl18_546
| ~ spl18_104
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2549,f2514,f1624,f32774]) ).
tff(f32774,plain,
( spl18_546
<=> ! [X1: $tType,X0: $tType,X4: $tType,X5: fun(X4,fun(X0,bool)),X3: X1,X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK12(X4,X0,X5,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| finite_finite1(X4,aa(fun(X4,fun(X0,bool)),fun(X4,bool),aa(fun(fun(X0,bool),bool),fun(fun(X4,fun(X0,bool)),fun(X4,bool)),combb(fun(X0,bool),bool,X4),fEx(X0)),aa(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X4),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),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)))),X5)))
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_546])]) ).
tff(f2549,plain,
( ! [X4: $tType,X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X5: fun(X4,fun(X0,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK12(X4,X0,X5,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| finite_finite1(X4,aa(fun(X4,fun(X0,bool)),fun(X4,bool),aa(fun(fun(X0,bool),bool),fun(fun(X4,fun(X0,bool)),fun(X4,bool)),combb(fun(X0,bool),bool,X4),fEx(X0)),aa(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X4,fun(X0,bool)),fun(X4,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X4),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),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)))),X5)))
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)) )
| ~ spl18_104
| ~ spl18_146 ),
inference(superposition,[],[f2515,f1625]) ).
tff(f32719,plain,
( spl18_545
| ~ spl18_86
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2520,f2514,f1187,f32717]) ).
tff(f32717,plain,
( spl18_545
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(X0,bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_545])]) ).
tff(f1187,plain,
( spl18_86
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).
tff(f2520,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0) )
| ~ spl18_86
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1188]) ).
tff(f1188,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ( X1 = X2 )
| ~ order(X0) )
| ~ spl18_86 ),
inference(avatar_component_clause,[],[f1187]) ).
tff(f32636,plain,
( spl18_544
| ~ spl18_108
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2519,f2514,f1690,f32634]) ).
tff(f32634,plain,
( spl18_544
<=> ! [X2: $tType,X0: $tType,X4: X0,X3: fun(X2,fun(X0,bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X4))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X4))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_544])]) ).
tff(f1690,plain,
( spl18_108
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_108])]) ).
tff(f2519,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: X0,X4: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK12(X2,X0,X3,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X4))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X4))
| ~ preorder(X0) )
| ~ spl18_108
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1691]) ).
tff(f1691,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ preorder(X0) )
| ~ spl18_108 ),
inference(avatar_component_clause,[],[f1690]) ).
tff(f32512,plain,
( spl18_543
| ~ spl18_109
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2453,f2437,f1731,f32510]) ).
tff(f32510,plain,
( spl18_543
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)) = big_linorder_Max(product_prod(X0,X1),X2) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),sK2(product_prod(X0,X1),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)),X2)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))
| ~ finite_finite1(product_prod(X0,X1),X2)
| ~ linorder(product_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_543])]) ).
tff(f2453,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)) = big_linorder_Max(product_prod(X0,X1),X2) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),sK2(product_prod(X0,X1),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)),X2)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))
| ~ finite_finite1(product_prod(X0,X1),X2)
| ~ linorder(product_prod(X0,X1)) )
| ~ spl18_109
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1732]) ).
tff(f32508,plain,
( spl18_542
| ~ spl18_109
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2445,f2437,f1731,f32506]) ).
tff(f32506,plain,
( spl18_542
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)) = big_linorder_Max(product_prod(X0,X1),X3) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),sK2(product_prod(X0,X1),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)),X3)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))
| ~ finite_finite1(product_prod(X0,X1),X3)
| ~ linorder(product_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_542])]) ).
tff(f2445,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)) = big_linorder_Max(product_prod(X0,X1),X3) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),sK2(product_prod(X0,X1),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)),X3)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))
| ~ finite_finite1(product_prod(X0,X1),X3)
| ~ linorder(product_prod(X0,X1)) )
| ~ spl18_109
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1732]) ).
tff(f32448,plain,
( spl18_541
| ~ spl18_122
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2415,f2384,f2018,f32446]) ).
tff(f32446,plain,
( spl18_541
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1) )
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_541])]) ).
tff(f2384,plain,
( spl18_143
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_143])]) ).
tff(f2415,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1) )
| ~ linorder(X0) )
| ~ spl18_122
| ~ spl18_143 ),
inference(resolution,[],[f2385,f2019]) ).
tff(f2385,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) )
| ~ spl18_143 ),
inference(avatar_component_clause,[],[f2384]) ).
tff(f32289,plain,
( spl18_540
| ~ spl18_29
| ~ spl18_149 ),
inference(avatar_split_clause,[],[f2576,f2573,f780,f32287]) ).
tff(f32287,plain,
( spl18_540
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = 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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_540])]) ).
tff(f780,plain,
( spl18_29
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).
tff(f2573,plain,
( spl18_149
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = collect(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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_149])]) ).
tff(f2576,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = 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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))) )
| ~ spl18_29
| ~ spl18_149 ),
inference(superposition,[],[f2574,f781]) ).
tff(f781,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f780]) ).
tff(f2574,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = collect(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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) )
| ~ spl18_149 ),
inference(avatar_component_clause,[],[f2573]) ).
tff(f32266,plain,
( spl18_539
| ~ spl18_181
| spl18_527 ),
inference(avatar_split_clause,[],[f31954,f31865,f4376,f32263]) ).
tff(f32263,plain,
( spl18_539
<=> ( fFalse = sK13(fun(bool,bool),bool,fconj,fconj) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_539])]) ).
tff(f31954,plain,
( ( fFalse = sK13(fun(bool,bool),bool,fconj,fconj) )
| ~ spl18_181
| spl18_527 ),
inference(resolution,[],[f31867,f4377]) ).
tff(f31867,plain,
( ~ pp(sK13(fun(bool,bool),bool,fconj,fconj))
| spl18_527 ),
inference(avatar_component_clause,[],[f31865]) ).
tff(f32261,plain,
( spl18_538
| ~ spl18_115
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2416,f2384,f1872,f32259]) ).
tff(f32259,plain,
( spl18_538
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_538])]) ).
tff(f2416,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1) ) )
| ~ spl18_115
| ~ spl18_143 ),
inference(resolution,[],[f2385,f1873]) ).
tff(f32073,plain,
( spl18_537
| ~ spl18_112
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f2344,f2333,f1791,f32071]) ).
tff(f32071,plain,
( spl18_537
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)),aa(fun(X0,bool),fun(X0,bool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_537])]) ).
tff(f2333,plain,
( spl18_139
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_139])]) ).
tff(f2344,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)),aa(fun(X0,bool),fun(X0,bool),X2,X1)) )
| ~ spl18_112
| ~ spl18_139 ),
inference(superposition,[],[f2334,f1792]) ).
tff(f2334,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X1) )
| ~ spl18_139 ),
inference(avatar_component_clause,[],[f2333]) ).
tff(f31993,plain,
( spl18_536
| ~ spl18_112
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2431,f2384,f1791,f31991]) ).
tff(f31991,plain,
( spl18_536
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_536])]) ).
tff(f2431,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) )
| ~ spl18_112
| ~ spl18_143 ),
inference(superposition,[],[f2385,f1792]) ).
tff(f31989,plain,
( spl18_535
| ~ spl18_112
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f2412,f2380,f1791,f31987]) ).
tff(f31987,plain,
( spl18_535
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_535])]) ).
tff(f2380,plain,
( spl18_142
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_142])]) ).
tff(f2412,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) )
| ~ spl18_112
| ~ spl18_142 ),
inference(superposition,[],[f2381,f1792]) ).
tff(f2381,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) )
| ~ spl18_142 ),
inference(avatar_component_clause,[],[f2380]) ).
tff(f31985,plain,
( spl18_534
| ~ spl18_112
| ~ spl18_138 ),
inference(avatar_split_clause,[],[f2331,f2326,f1791,f31983]) ).
tff(f31983,plain,
( spl18_534
<=> ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),fdisj),X1)))
| ~ finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_534])]) ).
tff(f2326,plain,
( spl18_138
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| ~ finite_finite1(X0,X1)
| finite_finite1(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),fdisj),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_138])]) ).
tff(f2331,plain,
( ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),fdisj),X1)))
| ~ finite_finite1(X0,X1) )
| ~ spl18_112
| ~ spl18_138 ),
inference(superposition,[],[f2327,f1792]) ).
tff(f2327,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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),fdisj),X2)),X1))
| ~ finite_finite1(X0,X1)
| ~ finite_finite1(X0,X2) )
| ~ spl18_138 ),
inference(avatar_component_clause,[],[f2326]) ).
tff(f31924,plain,
( spl18_533
| ~ spl18_22
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f2563,f2554,f749,f31922]) ).
tff(f31922,plain,
( spl18_533
<=> ! [X0: $tType,X2: fun(bool,bool),X1: fun(X0,fun(bool,bool))] :
( ~ finite_finite1(X0,aa(bool,fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(bool,fun(X0,bool)),combc(X0,bool,bool),X1),fFalse))
| ~ finite_finite1(bool,X2)
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(bool,bool),bool),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),combb(fun(bool,bool),bool,X0),fEx(bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X0),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),X2))),X1)))
| ( fTrue = sK12(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_533])]) ).
tff(f749,plain,
( spl18_22
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
tff(f2563,plain,
( ! [X0: $tType,X2: fun(bool,bool),X1: fun(X0,fun(bool,bool))] :
( ~ finite_finite1(X0,aa(bool,fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(bool,fun(X0,bool)),combc(X0,bool,bool),X1),fFalse))
| ~ finite_finite1(bool,X2)
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(bool,bool),bool),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),combb(fun(bool,bool),bool,X0),fEx(bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X0),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),X2))),X1)))
| ( fTrue = sK12(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_147 ),
inference(superposition,[],[f2555,f750]) ).
tff(f750,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl18_22 ),
inference(avatar_component_clause,[],[f749]) ).
tff(f31920,plain,
( spl18_532
| ~ spl18_112
| ~ spl18_135 ),
inference(avatar_split_clause,[],[f2317,f2307,f1791,f31918]) ).
tff(f31918,plain,
( spl18_532
<=> ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),fdisj),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_532])]) ).
tff(f2307,plain,
( spl18_135
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_135])]) ).
tff(f2317,plain,
( ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),fdisj),X1))) )
| ~ spl18_112
| ~ spl18_135 ),
inference(superposition,[],[f2308,f1792]) ).
tff(f2308,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X1) )
| ~ spl18_135 ),
inference(avatar_component_clause,[],[f2307]) ).
tff(f31916,plain,
( spl18_531
| ~ spl18_112
| ~ spl18_133 ),
inference(avatar_split_clause,[],[f2314,f2299,f1791,f31914]) ).
tff(f31914,plain,
( spl18_531
<=> ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),X1)))
| ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_531])]) ).
tff(f2299,plain,
( spl18_133
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_133])]) ).
tff(f2314,plain,
( ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),X1)))
| ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),X2,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),X1))) )
| ~ spl18_112
| ~ spl18_133 ),
inference(superposition,[],[f2300,f1792]) ).
tff(f2300,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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))
| ~ finite_finite1(X0,X1) )
| ~ spl18_133 ),
inference(avatar_component_clause,[],[f2299]) ).
tff(f31897,plain,
( spl18_530
| ~ spl18_59
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2518,f2514,f948,f31895]) ).
tff(f31895,plain,
( spl18_530
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(X0,bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),fequal(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1))
| ( sK12(X2,X0,X3,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_530])]) ).
tff(f948,plain,
( spl18_59
<=> ! [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,[spl18_59])]) ).
tff(f2518,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: X0] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),aa(X0,fun(X0,bool),fequal(X0),X1)))),X3)))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),fequal(X0),X1))
| ( sK12(X2,X0,X3,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) )
| ~ spl18_59
| ~ spl18_146 ),
inference(resolution,[],[f2515,f949]) ).
tff(f949,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 = X2 ) )
| ~ spl18_59 ),
inference(avatar_component_clause,[],[f948]) ).
tff(f31878,plain,
( spl18_529
| ~ spl18_58
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2525,f2514,f944,f31876]) ).
tff(f31876,plain,
( spl18_529
<=> ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fdisj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fdisj,X0))
| pp(X0)
| pp(sK12(X1,bool,X2,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_529])]) ).
tff(f944,plain,
( spl18_58
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).
tff(f2525,plain,
( ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fdisj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fdisj,X0))
| pp(X0)
| pp(sK12(X1,bool,X2,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl18_58
| ~ spl18_146 ),
inference(resolution,[],[f2515,f945]) ).
tff(f945,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| pp(X1)
| pp(X0) )
| ~ spl18_58 ),
inference(avatar_component_clause,[],[f944]) ).
tff(f31872,plain,
( spl18_528
| ~ spl18_46
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2524,f2514,f867,f31870]) ).
tff(f31870,plain,
( spl18_528
<=> ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fconj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fconj,X0))
| pp(sK12(X1,bool,X2,aa(bool,fun(bool,bool),fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_528])]) ).
tff(f867,plain,
( spl18_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,[spl18_46])]) ).
tff(f2524,plain,
( ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fconj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fconj,X0))
| pp(sK12(X1,bool,X2,aa(bool,fun(bool,bool),fconj,X0))) )
| ~ spl18_46
| ~ spl18_146 ),
inference(resolution,[],[f2515,f868]) ).
tff(f868,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X0) )
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f867]) ).
tff(f31868,plain,
( ~ spl18_527
| spl18_42
| ~ spl18_181
| spl18_216
| ~ spl18_475 ),
inference(avatar_split_clause,[],[f31231,f25822,f6394,f4376,f844,f31865]) ).
tff(f844,plain,
( spl18_42
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).
tff(f6394,plain,
( spl18_216
<=> pp(aa(atom,bool,aa(atom,fun(atom,bool),ord_less_eq(atom),a),big_linorder_Max(atom,set(atom,as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_216])]) ).
tff(f31231,plain,
( ( fFalse = fTrue )
| ~ pp(sK13(fun(bool,bool),bool,fconj,fconj))
| ~ spl18_181
| spl18_216
| ~ spl18_475 ),
inference(forward_demodulation,[],[f30778,f6405]) ).
tff(f6405,plain,
( ( fFalse = aa(atom,bool,aa(atom,fun(atom,bool),ord_less_eq(atom),a),big_linorder_Max(atom,set(atom,as))) )
| ~ spl18_181
| spl18_216 ),
inference(resolution,[],[f6395,f4377]) ).
tff(f6395,plain,
( ~ pp(aa(atom,bool,aa(atom,fun(atom,bool),ord_less_eq(atom),a),big_linorder_Max(atom,set(atom,as))))
| spl18_216 ),
inference(avatar_component_clause,[],[f6394]) ).
tff(f30778,plain,
( ~ pp(sK13(fun(bool,bool),bool,fconj,fconj))
| ( fTrue = aa(atom,bool,aa(atom,fun(atom,bool),ord_less_eq(atom),a),big_linorder_Max(atom,set(atom,as))) )
| spl18_216
| ~ spl18_475 ),
inference(superposition,[],[f6395,f25823]) ).
tff(f31564,plain,
( spl18_526
| ~ spl18_105
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1989,f1919,f1628,f31562]) ).
tff(f31562,plain,
( spl18_526
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X5: fun(X0,fun(X1,bool)),X3: fun(X2,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X2,fun(X1,bool),X3,aa(X0,X2,X4,sK14(X1,X0,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4),X5))),sK15(X1,X0,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4),X5)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_526])]) ).
tff(f1919,plain,
( spl18_118
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,fun(X0,bool)),X2: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_118])]) ).
tff(f1989,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,bool)),X4: fun(X0,X2),X5: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X2,fun(X1,bool),X3,aa(X0,X2,X4,sK14(X1,X0,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4),X5))),sK15(X1,X0,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4),X5)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4))) )
| ~ spl18_105
| ~ spl18_118 ),
inference(superposition,[],[f1920,f1629]) ).
tff(f1920,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3)))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2)) )
| ~ spl18_118 ),
inference(avatar_component_clause,[],[f1919]) ).
tff(f31560,plain,
( spl18_525
| ~ spl18_105
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1958,f1915,f1628,f31558]) ).
tff(f31558,plain,
( spl18_525
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X3: fun(X2,fun(X1,bool)),X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X2,fun(X1,bool),X3,aa(X0,X2,X4,sK14(X1,X0,X5,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4)))),sK15(X1,X0,X5,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_525])]) ).
tff(f1915,plain,
( spl18_117
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,fun(X0,bool)),X2: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_117])]) ).
tff(f1958,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,bool)),X4: fun(X0,X2),X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X2,fun(X1,bool),X3,aa(X0,X2,X4,sK14(X1,X0,X5,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4)))),sK15(X1,X0,X5,aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),aa(fun(X0,X2),fun(X0,fun(X1,bool)),aa(fun(X2,fun(X1,bool)),fun(fun(X0,X2),fun(X0,fun(X1,bool))),combb(X2,fun(X1,bool),X0),X3),X4)),X5)) )
| ~ spl18_105
| ~ spl18_117 ),
inference(superposition,[],[f1916,f1629]) ).
tff(f1916,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) )
| ~ spl18_117 ),
inference(avatar_component_clause,[],[f1915]) ).
tff(f31374,plain,
( spl18_524
| ~ spl18_104
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1988,f1919,f1624,f31372]) ).
tff(f31372,plain,
( spl18_524
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,bool))),X4: X2,X5: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X3,sK14(X1,X0,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4),X5)),X4),sK15(X1,X0,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4),X5)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_524])]) ).
tff(f1988,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,bool))),X4: X2,X5: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X3,sK14(X1,X0,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4),X5)),X4),sK15(X1,X0,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4),X5)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))) )
| ~ spl18_104
| ~ spl18_118 ),
inference(superposition,[],[f1920,f1625]) ).
tff(f31370,plain,
( spl18_523
| ~ spl18_104
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1957,f1915,f1624,f31368]) ).
tff(f31368,plain,
( spl18_523
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,fun(X1,bool)),X4: X2,X3: fun(X0,fun(X2,fun(X1,bool)))] :
( pp(aa(X1,bool,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X3,sK14(X1,X0,X5,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))),X4),sK15(X1,X0,X5,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_523])]) ).
tff(f1957,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,fun(X1,bool))),X4: X2,X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X3,sK14(X1,X0,X5,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))),X4),sK15(X1,X0,X5,aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),aa(X2,fun(X0,fun(X1,bool)),aa(fun(X0,fun(X2,fun(X1,bool))),fun(X2,fun(X0,fun(X1,bool))),combc(X0,X2,fun(X1,bool)),X3),X4)),X5)) )
| ~ spl18_104
| ~ spl18_117 ),
inference(superposition,[],[f1916,f1625]) ).
tff(f30607,plain,
( spl18_522
| ~ spl18_47
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2523,f2514,f871,f30605]) ).
tff(f30605,plain,
( spl18_522
<=> ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fconj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fconj,X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_522])]) ).
tff(f871,plain,
( spl18_47
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).
tff(f2523,plain,
( ! [X1: $tType,X2: fun(X1,fun(bool,bool)),X0: bool] :
( finite_finite1(X1,aa(fun(X1,fun(bool,bool)),fun(X1,bool),aa(fun(fun(bool,bool),bool),fun(fun(X1,fun(bool,bool)),fun(X1,bool)),combb(fun(bool,bool),bool,X1),fEx(bool)),aa(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X1,fun(bool,bool)),fun(X1,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X1),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),aa(bool,fun(bool,bool),fconj,X0)))),X2)))
| ~ finite_finite1(bool,aa(bool,fun(bool,bool),fconj,X0))
| pp(X0) )
| ~ spl18_47
| ~ spl18_146 ),
inference(resolution,[],[f2515,f872]) ).
tff(f872,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X1) )
| ~ spl18_47 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f30603,plain,
( spl18_521
| ~ spl18_113
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2286,f2231,f1864,f30601]) ).
tff(f30601,plain,
( spl18_521
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)) = X1 )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_521])]) ).
tff(f1864,plain,
( spl18_113
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),X2))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_113])]) ).
tff(f2286,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)) = X1 )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))
| ~ linorder(X0) )
| ~ spl18_113
| ~ spl18_132 ),
inference(resolution,[],[f2232,f1865]) ).
tff(f1865,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) )
| ~ spl18_113 ),
inference(avatar_component_clause,[],[f1864]) ).
tff(f30599,plain,
( spl18_520
| ~ spl18_113
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2270,f2227,f1864,f30597]) ).
tff(f30597,plain,
( spl18_520
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)) = X1 )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_520])]) ).
tff(f2270,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)) = X1 )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))
| ~ linorder(X0) )
| ~ spl18_113
| ~ spl18_131 ),
inference(resolution,[],[f2228,f1865]) ).
tff(f30580,plain,
( spl18_519
| ~ spl18_22
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2542,f2514,f749,f30578]) ).
tff(f30578,plain,
( spl18_519
<=> ! [X0: $tType,X2: fun(bool,bool),X1: fun(X0,fun(bool,bool))] :
( pp(aa(bool,bool,X2,fFalse))
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(bool,bool),bool),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),combb(fun(bool,bool),bool,X0),fEx(bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X0),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),X2))),X1)))
| ~ finite_finite1(bool,X2)
| ( fTrue = sK12(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_519])]) ).
tff(f2542,plain,
( ! [X0: $tType,X2: fun(bool,bool),X1: fun(X0,fun(bool,bool))] :
( pp(aa(bool,bool,X2,fFalse))
| finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(bool,bool),bool),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),combb(fun(bool,bool),bool,X0),fEx(bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool)),aa(fun(fun(bool,bool),fun(bool,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,fun(bool,bool))),combb(fun(bool,bool),fun(bool,bool),X0),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),aa(fun(bool,bool),fun(bool,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,fun(bool,bool))),combb(bool,fun(bool,bool),bool),fconj),X2))),X1)))
| ~ finite_finite1(bool,X2)
| ( fTrue = sK12(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_146 ),
inference(superposition,[],[f2515,f750]) ).
tff(f30561,plain,
( spl18_518
| ~ spl18_52
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2517,f2514,f902,f30559]) ).
tff(f30559,plain,
( spl18_518
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),X1))),X3)))
| ~ finite_finite1(X0,X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_518])]) ).
tff(f902,plain,
( spl18_52
<=> ! [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,[spl18_52])]) ).
tff(f2517,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),X1))),X3)))
| ~ finite_finite1(X0,X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) )
| ~ spl18_52
| ~ spl18_146 ),
inference(resolution,[],[f2515,f903]) ).
tff(f903,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl18_52 ),
inference(avatar_component_clause,[],[f902]) ).
tff(f30542,plain,
( spl18_517
| ~ spl18_35
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2548,f2514,f809,f30540]) ).
tff(f30540,plain,
( spl18_517
<=> ! [X2: $tType,X0: $tType,X3: fun(X2,fun(X0,bool)),X1: bool] :
( pp(X1)
| finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),combk(bool,X0,X1)))),X3)))
| ~ finite_finite1(X0,combk(bool,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_517])]) ).
tff(f809,plain,
( spl18_35
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).
tff(f2548,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: bool] :
( pp(X1)
| finite_finite1(X2,aa(fun(X2,fun(X0,bool)),fun(X2,bool),aa(fun(fun(X0,bool),bool),fun(fun(X2,fun(X0,bool)),fun(X2,bool)),combb(fun(X0,bool),bool,X2),fEx(X0)),aa(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X2,fun(X0,bool)),fun(X2,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X2),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),combk(bool,X0,X1)))),X3)))
| ~ finite_finite1(X0,combk(bool,X0,X1)) )
| ~ spl18_35
| ~ spl18_146 ),
inference(superposition,[],[f2515,f810]) ).
tff(f810,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f809]) ).
tff(f30324,plain,
( spl18_516
| ~ spl18_62
| ~ spl18_64
| ~ spl18_146 ),
inference(avatar_split_clause,[],[f2552,f2514,f1008,f980,f30322]) ).
tff(f30322,plain,
( spl18_516
<=> ! [X3: $tType,X0: $tType,X4: fun(X3,fun(X0,bool))] :
( ~ finite_finite1(X0,combk(bool,X0,fFalse))
| finite_finite1(X3,aa(fun(X3,fun(X0,bool)),fun(X3,bool),aa(fun(fun(X0,bool),bool),fun(fun(X3,fun(X0,bool)),fun(X3,bool)),combb(fun(X0,bool),bool,X3),fEx(X0)),aa(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X3),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),combk(bool,X0,fFalse)))),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_516])]) ).
tff(f980,plain,
( spl18_62
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK5(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).
tff(f1008,plain,
( spl18_64
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: X1] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),bot_bot(fun(X0,fun(X1,bool))),X3),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).
tff(f2552,plain,
( ! [X0: $tType,X3: $tType,X4: fun(X3,fun(X0,bool))] :
( ~ finite_finite1(X0,combk(bool,X0,fFalse))
| finite_finite1(X3,aa(fun(X3,fun(X0,bool)),fun(X3,bool),aa(fun(fun(X0,bool),bool),fun(fun(X3,fun(X0,bool)),fun(X3,bool)),combb(fun(X0,bool),bool,X3),fEx(X0)),aa(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X3),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),combk(bool,X0,fFalse)))),X4))) )
| ~ spl18_62
| ~ spl18_64
| ~ spl18_146 ),
inference(forward_demodulation,[],[f2551,f1011]) ).
tff(f1011,plain,
( ! [X1: $tType,X0: $tType,X2: X1] : ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2) )
| ~ spl18_62
| ~ spl18_64 ),
inference(resolution,[],[f1009,f981]) ).
tff(f981,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,sK5(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_62 ),
inference(avatar_component_clause,[],[f980]) ).
tff(f1009,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),bot_bot(fun(X0,fun(X1,bool))),X3),X2))
| ~ spl18_64 ),
inference(avatar_component_clause,[],[f1008]) ).
tff(f2551,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: X1,X4: fun(X3,fun(X0,bool))] :
( finite_finite1(X3,aa(fun(X3,fun(X0,bool)),fun(X3,bool),aa(fun(fun(X0,bool),bool),fun(fun(X3,fun(X0,bool)),fun(X3,bool)),combb(fun(X0,bool),bool,X3),fEx(X0)),aa(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X3),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),combk(bool,X0,fFalse)))),X4)))
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2)) )
| ~ spl18_62
| ~ spl18_64
| ~ spl18_146 ),
inference(forward_demodulation,[],[f2521,f1011]) ).
tff(f2521,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: X1,X4: fun(X3,fun(X0,bool))] :
( finite_finite1(X3,aa(fun(X3,fun(X0,bool)),fun(X3,bool),aa(fun(fun(X0,bool),bool),fun(fun(X3,fun(X0,bool)),fun(X3,bool)),combb(fun(X0,bool),bool,X3),fEx(X0)),aa(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X3,fun(X0,bool)),fun(X3,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X3),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),aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2)))),X4)))
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2)) )
| ~ spl18_64
| ~ spl18_146 ),
inference(resolution,[],[f2515,f1009]) ).
tff(f30320,plain,
( spl18_515
| ~ spl18_112
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f2354,f2333,f1791,f30318]) ).
tff(f30318,plain,
( spl18_515
<=> ! [X3: $tType,X0: $tType,X4: fun(fun(X0,bool),fun(fun(X0,bool),X3)),X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),X3,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X3),aa(fun(fun(X0,bool),fun(fun(X0,bool),X3)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X3)),combs(fun(X0,bool),fun(X0,bool),X3),X4),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2) = aa(fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),X3),X4,X2),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_515])]) ).
tff(f2354,plain,
( ! [X0: $tType,X3: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X4: fun(fun(X0,bool),fun(fun(X0,bool),X3))] : ( aa(fun(X0,bool),X3,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X3),aa(fun(fun(X0,bool),fun(fun(X0,bool),X3)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X3)),combs(fun(X0,bool),fun(X0,bool),X3),X4),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2) = aa(fun(X0,bool),X3,aa(fun(X0,bool),fun(fun(X0,bool),X3),X4,X2),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) )
| ~ spl18_112
| ~ spl18_139 ),
inference(superposition,[],[f1792,f2334]) ).
tff(f30242,plain,
( spl18_514
| ~ spl18_109
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f2359,f2337,f1731,f30240]) ).
tff(f30240,plain,
( spl18_514
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))),X1))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_514])]) ).
tff(f2337,plain,
( spl18_140
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_140])]) ).
tff(f2359,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ( big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))),X1))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))
| ~ linorder(X0) )
| ~ spl18_109
| ~ spl18_140 ),
inference(resolution,[],[f2338,f1732]) ).
tff(f2338,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ~ spl18_140 ),
inference(avatar_component_clause,[],[f2337]) ).
tff(f30171,plain,
( spl18_513
| ~ spl18_108
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2422,f2384,f1690,f30169]) ).
tff(f30169,plain,
( spl18_513
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)),X3))
| ~ preorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_513])]) ).
tff(f2422,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)),X3))
| ~ preorder(fun(X0,bool)) )
| ~ spl18_108
| ~ spl18_143 ),
inference(resolution,[],[f2385,f1691]) ).
tff(f29637,plain,
( spl18_512
| ~ spl18_22
| ~ spl18_434 ),
inference(avatar_split_clause,[],[f22008,f20496,f749,f29635]) ).
tff(f29635,plain,
( spl18_512
<=> ! [X0: bool] :
( ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,X0)),fconj) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_512])]) ).
tff(f20496,plain,
( spl18_434
<=> ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,fFalse)),fconj) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_434])]) ).
tff(f22008,plain,
( ! [X0: bool] :
( ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,X0)),fconj) )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_434 ),
inference(superposition,[],[f20498,f750]) ).
tff(f20498,plain,
( ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,fFalse)),fconj) )
| ~ spl18_434 ),
inference(avatar_component_clause,[],[f20496]) ).
tff(f29453,plain,
( spl18_511
| ~ spl18_105
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2116,f2048,f1628,f29451]) ).
tff(f29451,plain,
( spl18_511
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X5: fun(X0,X1),X3: fun(X2,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK4(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))),aa(X2,X1,X3,aa(X0,X2,X4,sK4(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_511])]) ).
tff(f2048,plain,
( spl18_124
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK4(X0,X1,X2,X3))),aa(X1,X0,X2,sK4(X0,X1,X2,X3))))
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_124])]) ).
tff(f2116,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK4(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))),aa(X2,X1,X3,aa(X0,X2,X4,sK4(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))
| ~ ord(X1) )
| ~ spl18_105
| ~ spl18_124 ),
inference(superposition,[],[f2049,f1629]) ).
tff(f2049,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK4(X0,X1,X2,X3))),aa(X1,X0,X2,sK4(X0,X1,X2,X3))))
| pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ ord(X0) )
| ~ spl18_124 ),
inference(avatar_component_clause,[],[f2048]) ).
tff(f29449,plain,
( spl18_510
| ~ spl18_105
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2102,f2048,f1628,f29447]) ).
tff(f29447,plain,
( spl18_510
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X3: fun(X2,X1),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,X3,aa(X0,X2,X4,sK4(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))))),aa(X0,X1,X5,sK4(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_510])]) ).
tff(f2102,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,X3,aa(X0,X2,X4,sK4(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))))),aa(X0,X1,X5,sK4(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5))
| ~ ord(X1) )
| ~ spl18_105
| ~ spl18_124 ),
inference(superposition,[],[f2049,f1629]) ).
tff(f29445,plain,
( spl18_509
| ~ spl18_105
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2080,f2044,f1628,f29443]) ).
tff(f29443,plain,
( spl18_509
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X5: fun(X0,X1),X3: fun(X2,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK3(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))),aa(X2,X1,X3,aa(X0,X2,X4,sK3(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_509])]) ).
tff(f2044,plain,
( spl18_123
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK3(X0,X1,X2,X3))),aa(X1,X0,X2,sK3(X0,X1,X2,X3))))
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_123])]) ).
tff(f2080,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK3(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))),aa(X2,X1,X3,aa(X0,X2,X4,sK3(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))
| ~ ord(X1) )
| ~ spl18_105
| ~ spl18_123 ),
inference(superposition,[],[f2045,f1629]) ).
tff(f2045,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK3(X0,X1,X2,X3))),aa(X1,X0,X2,sK3(X0,X1,X2,X3))))
| pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ ord(X0) )
| ~ spl18_123 ),
inference(avatar_component_clause,[],[f2044]) ).
tff(f29441,plain,
( spl18_508
| ~ spl18_105
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2066,f2044,f1628,f29439]) ).
tff(f29439,plain,
( spl18_508
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X3: fun(X2,X1),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,X3,aa(X0,X2,X4,sK3(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))))),aa(X0,X1,X5,sK3(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_508])]) ).
tff(f2066,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,X3,aa(X0,X2,X4,sK3(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))))),aa(X0,X1,X5,sK3(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5))
| ~ ord(X1) )
| ~ spl18_105
| ~ spl18_123 ),
inference(superposition,[],[f2045,f1629]) ).
tff(f29384,plain,
( spl18_507
| ~ spl18_117
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2163,f2128,f1915,f29382]) ).
tff(f29382,plain,
( spl18_507
<=> ! [X1: $tType,X0: $tType,X2: fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),X4: X0,X3: X1] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK15(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),X2,ord_less_eq(fun(X1,fun(X0,bool)))),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),sK14(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),X2,ord_less_eq(fun(X1,fun(X0,bool)))),X3),X4))
| pp(aa(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),bool,aa(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),fun(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),bool),ord_less_eq(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool))),ord_less_eq(fun(X1,fun(X0,bool)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_507])]) ).
tff(f2128,plain,
( spl18_126
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,bool)),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,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_126])]) ).
tff(f2163,plain,
( ! [X1: $tType,X0: $tType,X2: fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),X3: X1,X4: X0] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK15(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),X2,ord_less_eq(fun(X1,fun(X0,bool)))),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),sK14(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),X2,ord_less_eq(fun(X1,fun(X0,bool)))),X3),X4))
| pp(aa(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),bool,aa(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),fun(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool)),bool),ord_less_eq(fun(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool))),ord_less_eq(fun(X1,fun(X0,bool)))),X2)) )
| ~ spl18_117
| ~ spl18_126 ),
inference(resolution,[],[f2129,f1916]) ).
tff(f2129,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0,X5: fun(X0,fun(X1,bool))] :
( ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3)) )
| ~ spl18_126 ),
inference(avatar_component_clause,[],[f2128]) ).
tff(f29318,plain,
( spl18_506
| ~ spl18_112
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f2368,f2337,f1791,f29316]) ).
tff(f29316,plain,
( spl18_506
<=> ! [X0: $tType,X3: X0,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_506])]) ).
tff(f2368,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X3: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) )
| ~ spl18_112
| ~ spl18_140 ),
inference(superposition,[],[f2338,f1792]) ).
tff(f29229,plain,
( spl18_505
| ~ spl18_117
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2033,f2018,f1915,f29227]) ).
tff(f29227,plain,
( spl18_505
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))),big_linorder_Max(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))
| ( combk(bool,X0,fFalse) = sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) )
| ~ linorder(X0)
| pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_505])]) ).
tff(f2033,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))),big_linorder_Max(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))
| ( combk(bool,X0,fFalse) = sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) )
| ~ linorder(X0)
| pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1)) )
| ~ spl18_117
| ~ spl18_122 ),
inference(resolution,[],[f2019,f1916]) ).
tff(f28593,plain,
( spl18_504
| ~ spl18_104
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2115,f2048,f1624,f28591]) ).
tff(f28591,plain,
( spl18_504
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK4(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5))),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK4(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4)))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_504])]) ).
tff(f2115,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK4(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5))),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK4(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4)))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))
| ~ ord(X1) )
| ~ spl18_104
| ~ spl18_124 ),
inference(superposition,[],[f2049,f1625]) ).
tff(f28589,plain,
( spl18_503
| ~ spl18_104
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2101,f2048,f1624,f28587]) ).
tff(f28587,plain,
( spl18_503
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,X1),X4: X2,X3: fun(X0,fun(X2,X1))] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK4(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4)),aa(X0,X1,X5,sK4(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)),X5))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_503])]) ).
tff(f2101,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK4(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4)),aa(X0,X1,X5,sK4(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)),X5))
| ~ ord(X1) )
| ~ spl18_104
| ~ spl18_124 ),
inference(superposition,[],[f2049,f1625]) ).
tff(f28585,plain,
( spl18_502
| ~ spl18_104
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2079,f2044,f1624,f28583]) ).
tff(f28583,plain,
( spl18_502
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK3(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5))),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK3(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4)))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_502])]) ).
tff(f2079,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X5,sK3(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5))),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK3(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4)))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X5),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))
| ~ ord(X1) )
| ~ spl18_104
| ~ spl18_123 ),
inference(superposition,[],[f2045,f1625]) ).
tff(f28581,plain,
( spl18_501
| ~ spl18_104
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2065,f2044,f1624,f28579]) ).
tff(f28579,plain,
( spl18_501
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,X1),X4: X2,X3: fun(X0,fun(X2,X1))] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK3(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4)),aa(X0,X1,X5,sK3(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)),X5))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_501])]) ).
tff(f2065,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X2,X1,aa(X0,fun(X2,X1),X3,sK3(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4)),aa(X0,X1,X5,sK3(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4)),X5))
| ~ ord(X1) )
| ~ spl18_104
| ~ spl18_123 ),
inference(superposition,[],[f2045,f1625]) ).
tff(f28455,plain,
( spl18_500
| ~ spl18_125
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f2352,f2333,f2124,f28453]) ).
tff(f28453,plain,
( spl18_500
<=> ! [X0: $tType,X4: fun(X0,bool),X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X4) )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2))
| ~ ordered_ab_group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_500])]) ).
tff(f2124,plain,
( spl18_125
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_125])]) ).
tff(f2352,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool),X4: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X4) )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_125
| ~ spl18_139 ),
inference(superposition,[],[f2125,f2334]) ).
tff(f2125,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
| ~ ordered_ab_group_add(X0) )
| ~ spl18_125 ),
inference(avatar_component_clause,[],[f2124]) ).
tff(f28451,plain,
( spl18_499
| ~ spl18_125
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f2351,f2333,f2124,f28449]) ).
tff(f28449,plain,
( spl18_499
<=> ! [X0: $tType,X4: fun(X0,bool),X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X4) )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4))
| ~ ordered_ab_group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_499])]) ).
tff(f2351,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool),X4: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X4) )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_125
| ~ spl18_139 ),
inference(superposition,[],[f2125,f2334]) ).
tff(f28425,plain,
( spl18_498
| ~ spl18_115
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1939,f1915,f1872,f28423]) ).
tff(f28423,plain,
( spl18_498
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))),sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))))
| ( sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) = sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_498])]) ).
tff(f1939,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))),sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))))
| ( sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) = sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))) ) )
| ~ spl18_115
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1873]) ).
tff(f28258,plain,
( spl18_497
| ~ spl18_112
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f2350,f2333,f1791,f28256]) ).
tff(f28256,plain,
( spl18_497
<=> ! [X0: $tType,X3: fun(fun(X0,bool),X0),X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X3),X2) = aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),aa(fun(X0,bool),X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_497])]) ).
tff(f2350,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X3),X2) = aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),aa(fun(X0,bool),X0,X3,X2)) )
| ~ spl18_112
| ~ spl18_139 ),
inference(superposition,[],[f1792,f2334]) ).
tff(f28252,plain,
( spl18_496
| ~ spl18_99
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2113,f2048,f1568,f28250]) ).
tff(f28250,plain,
( spl18_496
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X1,sK4(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1))),combk(bool,X0,fFalse)))
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),X1),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))))
| ~ ord(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_496])]) ).
tff(f1568,plain,
( spl18_99
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).
tff(f2113,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X1,sK4(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1))),combk(bool,X0,fFalse)))
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),X1),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))))
| ~ ord(fun(X0,bool)) )
| ~ spl18_99
| ~ spl18_124 ),
inference(superposition,[],[f2049,f1569]) ).
tff(f1569,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1) )
| ~ spl18_99 ),
inference(avatar_component_clause,[],[f1568]) ).
tff(f28246,plain,
( spl18_495
| ~ spl18_99
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2077,f2044,f1568,f28244]) ).
tff(f28244,plain,
( spl18_495
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X1,sK3(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1))),combk(bool,X0,fFalse)))
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),X1),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))))
| ~ ord(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_495])]) ).
tff(f2077,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X1,sK3(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1))),combk(bool,X0,fFalse)))
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),X1),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))))
| ~ ord(fun(X0,bool)) )
| ~ spl18_99
| ~ spl18_123 ),
inference(superposition,[],[f2045,f1569]) ).
tff(f28180,plain,
( spl18_494
| ~ spl18_112
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2172,f2128,f1791,f28178]) ).
tff(f28178,plain,
( spl18_494
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: X0,X3: fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(X0,fun(X1,bool)),bool),aa(fun(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool)),fun(fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(X0,fun(X1,bool)),bool)),combs(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool)))),X3),X2))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),X3,X2),X4),X5))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_494])]) ).
tff(f2172,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),X4: X0,X5: X1] :
( ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(X0,fun(X1,bool)),bool),aa(fun(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool)),fun(fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),fun(fun(X0,fun(X1,bool)),bool)),combs(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool)))),X3),X2))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),X3,X2),X4),X5))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X5)) )
| ~ spl18_112
| ~ spl18_126 ),
inference(superposition,[],[f2129,f1792]) ).
tff(f28107,plain,
( spl18_493
| ~ spl18_128
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2414,f2384,f2174,f28105]) ).
tff(f28105,plain,
( spl18_493
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_493])]) ).
tff(f2414,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))) )
| ~ spl18_128
| ~ spl18_143 ),
inference(resolution,[],[f2385,f2175]) ).
tff(f28103,plain,
( spl18_492
| ~ spl18_112
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f2319,f2311,f1791,f28101]) ).
tff(f28101,plain,
( spl18_492
<=> ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_492])]) ).
tff(f2311,plain,
( spl18_136
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_136])]) ).
tff(f2319,plain,
( ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),fdisj),X1)))
| finite_finite1(X0,X1) )
| ~ spl18_112
| ~ spl18_136 ),
inference(superposition,[],[f2312,f1792]) ).
tff(f2312,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X2) )
| ~ spl18_136 ),
inference(avatar_component_clause,[],[f2311]) ).
tff(f28099,plain,
( spl18_491
| ~ spl18_112
| ~ spl18_134 ),
inference(avatar_split_clause,[],[f2315,f2303,f1791,f28097]) ).
tff(f28097,plain,
( spl18_491
<=> ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),X1)))
| ~ finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_491])]) ).
tff(f2303,plain,
( spl18_134
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| finite_finite1(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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_134])]) ).
tff(f2315,plain,
( ! [X0: $tType,X2: fun(fun(X0,fun(bool,bool)),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(bool,bool)),fun(X0,bool),aa(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool)),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,fun(bool,bool)),fun(X0,bool)),fun(fun(X0,fun(bool,bool)),fun(X0,bool))),combs(fun(X0,fun(bool,bool)),fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool)),X2),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),X1)))
| ~ finite_finite1(X0,X1) )
| ~ spl18_112
| ~ spl18_134 ),
inference(superposition,[],[f2304,f1792]) ).
tff(f2304,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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))
| ~ finite_finite1(X0,X2) )
| ~ spl18_134 ),
inference(avatar_component_clause,[],[f2303]) ).
tff(f27954,plain,
( spl18_490
| ~ spl18_35
| ~ spl18_435 ),
inference(avatar_split_clause,[],[f23862,f20500,f809,f27952]) ).
tff(f27952,plain,
( spl18_490
<=> ! [X0: bool] : ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_490])]) ).
tff(f20500,plain,
( spl18_435
<=> ( fconj = combk(fun(bool,bool),bool,combk(bool,bool,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_435])]) ).
tff(f23862,plain,
( ! [X0: bool] : ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| ~ spl18_35
| ~ spl18_435 ),
inference(superposition,[],[f810,f20502]) ).
tff(f20502,plain,
( ( fconj = combk(fun(bool,bool),bool,combk(bool,bool,fFalse)) )
| ~ spl18_435 ),
inference(avatar_component_clause,[],[f20500]) ).
tff(f27730,plain,
( spl18_489
| ~ spl18_101
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2454,f2437,f1599,f27728]) ).
tff(f27728,plain,
( spl18_489
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),big_linorder_Max(product_prod(X0,X1),X2)))
| ~ finite_finite1(product_prod(X0,X1),X2)
| ~ linorder(product_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_489])]) ).
tff(f2454,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),big_linorder_Max(product_prod(X0,X1),X2)))
| ~ finite_finite1(product_prod(X0,X1),X2)
| ~ linorder(product_prod(X0,X1)) )
| ~ spl18_101
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1600]) ).
tff(f27726,plain,
( spl18_488
| ~ spl18_101
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2446,f2437,f1599,f27724]) ).
tff(f27724,plain,
( spl18_488
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),big_linorder_Max(product_prod(X0,X1),X3)))
| ~ finite_finite1(product_prod(X0,X1),X3)
| ~ linorder(product_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_488])]) ).
tff(f2446,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,aa(product_prod(X0,X1),fun(product_prod(X0,X1),bool),ord_less_eq(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),big_linorder_Max(product_prod(X0,X1),X3)))
| ~ finite_finite1(product_prod(X0,X1),X3)
| ~ linorder(product_prod(X0,X1)) )
| ~ spl18_101
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1600]) ).
tff(f27464,plain,
( spl18_487
| ~ spl18_52
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2458,f2437,f902,f27462]) ).
tff(f27462,plain,
( spl18_487
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(fun(fun(product_prod(X0,X1),bool),bool),bool,fEx(fun(product_prod(X0,X1),bool)),aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_487])]) ).
tff(f2458,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(fun(fun(product_prod(X0,X1),bool),bool),bool,fEx(fun(product_prod(X0,X1),bool)),aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))) )
| ~ spl18_52
| ~ spl18_144 ),
inference(resolution,[],[f2438,f903]) ).
tff(f27460,plain,
( spl18_486
| ~ spl18_52
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2450,f2437,f902,f27458]) ).
tff(f27458,plain,
( spl18_486
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(fun(fun(product_prod(X0,X1),bool),bool),bool,fEx(fun(product_prod(X0,X1),bool)),aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_486])]) ).
tff(f2450,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(fun(fun(product_prod(X0,X1),bool),bool),bool,fEx(fun(product_prod(X0,X1),bool)),aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))))) )
| ~ spl18_52
| ~ spl18_144 ),
inference(resolution,[],[f2438,f903]) ).
tff(f27456,plain,
( spl18_485
| ~ spl18_102
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1678,f1628,f1616,f27454]) ).
tff(f27454,plain,
( spl18_485
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X2,bool),X4: fun(product_prod(X0,X1),X2),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,X5)))
| ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))),sK10(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_485])]) ).
tff(f1616,plain,
( spl18_102
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).
tff(f1678,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,bool),X4: fun(product_prod(X0,X1),X2),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,X5)))
| ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))),sK10(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4)))))) )
| ~ spl18_102
| ~ spl18_105 ),
inference(forward_demodulation,[],[f1676,f1629]) ).
tff(f1676,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,bool),X4: fun(product_prod(X0,X1),X2),X5: product_prod(X0,X1)] :
( ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))),sK10(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))))))
| pp(aa(product_prod(X0,X1),bool,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4),X5)) )
| ~ spl18_102
| ~ spl18_105 ),
inference(superposition,[],[f1617,f1629]) ).
tff(f1617,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2))))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) )
| ~ spl18_102 ),
inference(avatar_component_clause,[],[f1616]) ).
tff(f26667,plain,
( spl18_484
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1794,f1791,f26665]) ).
tff(f26665,plain,
( spl18_484
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X0,fun(X1,X2)),X4: fun(fun(X0,fun(X1,X2)),fun(X0,X1)),X5: X0] : ( aa(X1,X2,aa(X0,fun(X1,X2),X3,X5),aa(X0,X1,aa(fun(X0,fun(X1,X2)),fun(X0,X1),X4,X3),X5)) = aa(X0,X2,aa(fun(X0,fun(X1,X2)),fun(X0,X2),aa(fun(fun(X0,fun(X1,X2)),fun(X0,X1)),fun(fun(X0,fun(X1,X2)),fun(X0,X2)),aa(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),fun(fun(fun(X0,fun(X1,X2)),fun(X0,X1)),fun(fun(X0,fun(X1,X2)),fun(X0,X2))),combs(fun(X0,fun(X1,X2)),fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2)),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_484])]) ).
tff(f1794,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X1,X2)),X4: fun(fun(X0,fun(X1,X2)),fun(X0,X1)),X5: X0] : ( aa(X1,X2,aa(X0,fun(X1,X2),X3,X5),aa(X0,X1,aa(fun(X0,fun(X1,X2)),fun(X0,X1),X4,X3),X5)) = aa(X0,X2,aa(fun(X0,fun(X1,X2)),fun(X0,X2),aa(fun(fun(X0,fun(X1,X2)),fun(X0,X1)),fun(fun(X0,fun(X1,X2)),fun(X0,X2)),aa(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),fun(fun(fun(X0,fun(X1,X2)),fun(X0,X1)),fun(fun(X0,fun(X1,X2)),fun(X0,X2))),combs(fun(X0,fun(X1,X2)),fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2)),X4),X3),X5) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f26582,plain,
( spl18_483
| ~ spl18_102
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1664,f1624,f1616,f26580]) ).
tff(f26580,plain,
( spl18_483
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(product_prod(X0,X1),fun(X2,bool)),X4: X2,X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,X5),X4))
| ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),sK10(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4)))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_483])]) ).
tff(f1664,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(product_prod(X0,X1),fun(X2,bool)),X4: X2,X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,X5),X4))
| ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),sK10(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4)))),X4)) )
| ~ spl18_102
| ~ spl18_104 ),
inference(forward_demodulation,[],[f1662,f1625]) ).
tff(f1662,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(product_prod(X0,X1),fun(X2,bool)),X4: X2,X5: product_prod(X0,X1)] :
( ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),sK10(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4)))),X4))
| pp(aa(product_prod(X0,X1),bool,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4),X5)) )
| ~ spl18_102
| ~ spl18_104 ),
inference(superposition,[],[f1617,f1625]) ).
tff(f26410,plain,
( spl18_482
| ~ spl18_83
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f2403,f2380,f1156,f26408]) ).
tff(f26408,plain,
( spl18_482
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ linorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_482])]) ).
tff(f1156,plain,
( spl18_83
<=> ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).
tff(f2403,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ linorder(fun(X0,bool)) )
| ~ spl18_83
| ~ spl18_142 ),
inference(resolution,[],[f2381,f1157]) ).
tff(f1157,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) )
| ~ spl18_83 ),
inference(avatar_component_clause,[],[f1156]) ).
tff(f26406,plain,
( spl18_481
| ~ spl18_112
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2276,f2227,f1791,f26404]) ).
tff(f26404,plain,
( spl18_481
<=> ! [X0: $tType,X3: X0,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_481])]) ).
tff(f2276,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1))) )
| ~ spl18_112
| ~ spl18_131 ),
inference(superposition,[],[f2228,f1792]) ).
tff(f26402,plain,
( spl18_480
| ~ spl18_109
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1936,f1915,f1731,f26400]) ).
tff(f26400,plain,
( spl18_480
<=> ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| ( sK14(fun(X0,bool),X0,X1,member(X0)) = big_linorder_Max(X0,sK15(fun(X0,bool),X0,X1,member(X0))) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK14(fun(X0,bool),X0,X1,member(X0)),sK15(fun(X0,bool),X0,X1,member(X0)))),sK14(fun(X0,bool),X0,X1,member(X0))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),X0,X1,member(X0)))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_480])]) ).
tff(f1936,plain,
( ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| ( sK14(fun(X0,bool),X0,X1,member(X0)) = big_linorder_Max(X0,sK15(fun(X0,bool),X0,X1,member(X0))) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK14(fun(X0,bool),X0,X1,member(X0)),sK15(fun(X0,bool),X0,X1,member(X0)))),sK14(fun(X0,bool),X0,X1,member(X0))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),X0,X1,member(X0)))
| ~ linorder(X0) )
| ~ spl18_109
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1732]) ).
tff(f26352,plain,
( ~ spl18_463
| spl18_434
| ~ spl18_435 ),
inference(avatar_split_clause,[],[f25104,f20500,f20496,f25100]) ).
tff(f25104,plain,
( ( fTrue != sK13(fun(bool,bool),bool,fconj,fconj) )
| spl18_434
| ~ spl18_435 ),
inference(forward_demodulation,[],[f20497,f20502]) ).
tff(f20497,plain,
( ( fTrue != sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,fFalse)),fconj) )
| spl18_434 ),
inference(avatar_component_clause,[],[f20496]) ).
tff(f25840,plain,
( spl18_479
| ~ spl18_22
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f2506,f2441,f749,f25838]) ).
tff(f25838,plain,
( spl18_479
<=> ! [X0: $tType,X2: fun(product_prod(X0,bool),bool),X1: fun(product_prod(X0,bool),bool)] :
( ~ pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X2))
| ~ pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X1))
| ( X1 = X2 )
| ( fTrue = sK17(bool,X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_479])]) ).
tff(f2441,plain,
( spl18_145
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X1,X0),bool),X2: fun(product_prod(X1,X0),bool)] :
( ( X2 = X3 )
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_145])]) ).
tff(f2506,plain,
( ! [X0: $tType,X2: fun(product_prod(X0,bool),bool),X1: fun(product_prod(X0,bool),bool)] :
( ~ pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X2))
| ~ pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X1))
| ( X1 = X2 )
| ( fTrue = sK17(bool,X0,X1,X2) ) )
| ~ spl18_22
| ~ spl18_145 ),
inference(superposition,[],[f2442,f750]) ).
tff(f2442,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ( X2 = X3 ) )
| ~ spl18_145 ),
inference(avatar_component_clause,[],[f2441]) ).
tff(f25836,plain,
( spl18_478
| ~ spl18_22
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f2501,f2441,f749,f25834]) ).
tff(f25834,plain,
( spl18_478
<=> ! [X0: $tType,X2: fun(product_prod(bool,X0),bool),X1: fun(product_prod(bool,X0),bool)] :
( ~ pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X2))
| ~ pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X1))
| ( X1 = X2 )
| ( fTrue = sK16(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_478])]) ).
tff(f2501,plain,
( ! [X0: $tType,X2: fun(product_prod(bool,X0),bool),X1: fun(product_prod(bool,X0),bool)] :
( ~ pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X2))
| ~ pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X1))
| ( X1 = X2 )
| ( fTrue = sK16(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_145 ),
inference(superposition,[],[f2442,f750]) ).
tff(f25832,plain,
( spl18_477
| ~ spl18_22
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2470,f2437,f749,f25830]) ).
tff(f25830,plain,
( spl18_477
<=> ! [X0: $tType,X2: fun(product_prod(X0,bool),bool),X1: fun(product_prod(X0,bool),bool)] :
( pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X2))
| pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X1))
| ( X1 = X2 )
| ( fTrue = sK17(bool,X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_477])]) ).
tff(f2470,plain,
( ! [X0: $tType,X2: fun(product_prod(X0,bool),bool),X1: fun(product_prod(X0,bool),bool)] :
( pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X2))
| pp(aa(fun(product_prod(X0,bool),bool),bool,aa(product_prod(X0,bool),fun(fun(product_prod(X0,bool),bool),bool),member(product_prod(X0,bool)),aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK16(bool,X0,X1,X2)),fFalse)),X1))
| ( X1 = X2 )
| ( fTrue = sK17(bool,X0,X1,X2) ) )
| ~ spl18_22
| ~ spl18_144 ),
inference(superposition,[],[f2438,f750]) ).
tff(f25828,plain,
( spl18_476
| ~ spl18_22
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2465,f2437,f749,f25826]) ).
tff(f25826,plain,
( spl18_476
<=> ! [X0: $tType,X2: fun(product_prod(bool,X0),bool),X1: fun(product_prod(bool,X0),bool)] :
( pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X2))
| pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X1))
| ( X1 = X2 )
| ( fTrue = sK16(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_476])]) ).
tff(f2465,plain,
( ! [X0: $tType,X2: fun(product_prod(bool,X0),bool),X1: fun(product_prod(bool,X0),bool)] :
( pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X2))
| pp(aa(fun(product_prod(bool,X0),bool),bool,aa(product_prod(bool,X0),fun(fun(product_prod(bool,X0),bool),bool),member(product_prod(bool,X0)),aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK17(X0,bool,X1,X2))),X1))
| ( X1 = X2 )
| ( fTrue = sK16(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_144 ),
inference(superposition,[],[f2438,f750]) ).
tff(f25824,plain,
( spl18_475
| ~ spl18_91
| spl18_463 ),
inference(avatar_split_clause,[],[f25556,f25100,f1220,f25822]) ).
tff(f1220,plain,
( spl18_91
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).
tff(f25556,plain,
( ! [X0: bool] :
( ( sK13(fun(bool,bool),bool,fconj,fconj) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_91
| spl18_463 ),
inference(trivial_inequality_removal,[],[f25548]) ).
tff(f25548,plain,
( ! [X0: bool] :
( ( fTrue != fTrue )
| ( sK13(fun(bool,bool),bool,fconj,fconj) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_91
| spl18_463 ),
inference(superposition,[],[f25101,f1221]) ).
tff(f1221,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl18_91 ),
inference(avatar_component_clause,[],[f1220]) ).
tff(f25101,plain,
( ( fTrue != sK13(fun(bool,bool),bool,fconj,fconj) )
| spl18_463 ),
inference(avatar_component_clause,[],[f25100]) ).
tff(f25820,plain,
( spl18_474
| ~ spl18_117
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f2185,f2174,f1915,f25818]) ).
tff(f25818,plain,
( spl18_474
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(fun(X0,bool),bool)),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK14(fun(X0,bool),fun(X0,bool),X2,ord_less_eq(fun(X0,bool)))))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK15(fun(X0,bool),fun(X0,bool),X2,ord_less_eq(fun(X0,bool)))))
| pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_474])]) ).
tff(f2185,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(fun(X0,bool),bool)),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK14(fun(X0,bool),fun(X0,bool),X2,ord_less_eq(fun(X0,bool)))))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK15(fun(X0,bool),fun(X0,bool),X2,ord_less_eq(fun(X0,bool)))))
| pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X2)) )
| ~ spl18_117
| ~ spl18_128 ),
inference(resolution,[],[f2175,f1916]) ).
tff(f25816,plain,
( spl18_473
| ~ spl18_105
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f2001,f1919,f1628,f25814]) ).
tff(f25814,plain,
( spl18_473
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(X0,X1),fun(X0,bool)),X2: fun(X1,bool)] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,sK14(X0,fun(X0,X1),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3),sK15(X0,fun(X0,X1),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))))
| pp(aa(fun(fun(X0,X1),fun(X0,bool)),bool,aa(fun(fun(X0,X1),fun(X0,bool)),fun(fun(fun(X0,X1),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(X0,bool))),X3),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_473])]) ).
tff(f2001,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(fun(X0,X1),fun(X0,bool))] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,sK14(X0,fun(X0,X1),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3),sK15(X0,fun(X0,X1),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))))
| pp(aa(fun(fun(X0,X1),fun(X0,bool)),bool,aa(fun(fun(X0,X1),fun(X0,bool)),fun(fun(fun(X0,X1),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(X0,bool))),X3),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2))) )
| ~ spl18_105
| ~ spl18_118 ),
inference(superposition,[],[f1920,f1629]) ).
tff(f25812,plain,
( spl18_472
| ~ spl18_105
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1970,f1915,f1628,f25810]) ).
tff(f25810,plain,
( spl18_472
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(X0,X1),fun(X0,bool)),X2: fun(X1,bool)] :
( pp(aa(X1,bool,X2,aa(X0,X1,sK14(X0,fun(X0,X1),X3,aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)),sK15(X0,fun(X0,X1),X3,aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)))))
| pp(aa(fun(fun(X0,X1),fun(X0,bool)),bool,aa(fun(fun(X0,X1),fun(X0,bool)),fun(fun(fun(X0,X1),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(X0,bool))),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_472])]) ).
tff(f1970,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(fun(X0,X1),fun(X0,bool))] :
( pp(aa(X1,bool,X2,aa(X0,X1,sK14(X0,fun(X0,X1),X3,aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)),sK15(X0,fun(X0,X1),X3,aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)))))
| pp(aa(fun(fun(X0,X1),fun(X0,bool)),bool,aa(fun(fun(X0,X1),fun(X0,bool)),fun(fun(fun(X0,X1),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(X0,bool))),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2)),X3)) )
| ~ spl18_105
| ~ spl18_117 ),
inference(superposition,[],[f1916,f1629]) ).
tff(f25751,plain,
( spl18_471
| ~ spl18_112
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2042,f2018,f1791,f25749]) ).
tff(f25749,plain,
( spl18_471
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_471])]) ).
tff(f2042,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0) )
| ~ spl18_112
| ~ spl18_122 ),
inference(superposition,[],[f2019,f1792]) ).
tff(f25639,plain,
( spl18_470
| ~ spl18_95
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2284,f2231,f1247,f25637]) ).
tff(f25637,plain,
( spl18_470
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_470])]) ).
tff(f1247,plain,
( spl18_95
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).
tff(f2284,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ linorder(X0) )
| ~ spl18_95
| ~ spl18_132 ),
inference(resolution,[],[f2232,f1248]) ).
tff(f1248,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( combk(bool,X0,fFalse) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) )
| ~ spl18_95 ),
inference(avatar_component_clause,[],[f1247]) ).
tff(f25635,plain,
( spl18_469
| ~ spl18_95
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2268,f2227,f1247,f25633]) ).
tff(f25633,plain,
( spl18_469
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_469])]) ).
tff(f2268,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ linorder(X0) )
| ~ spl18_95
| ~ spl18_131 ),
inference(resolution,[],[f2228,f1248]) ).
tff(f25546,plain,
( spl18_468
| ~ spl18_101
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f2360,f2337,f1599,f25544]) ).
tff(f25544,plain,
( spl18_468
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_468])]) ).
tff(f2360,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2))
| ~ linorder(X0) )
| ~ spl18_101
| ~ spl18_140 ),
inference(resolution,[],[f2338,f1600]) ).
tff(f25364,plain,
( spl18_467
| ~ spl18_112
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2292,f2231,f1791,f25362]) ).
tff(f25362,plain,
( spl18_467
<=> ! [X0: $tType,X3: X0,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_467])]) ).
tff(f2292,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) )
| ~ spl18_112
| ~ spl18_132 ),
inference(superposition,[],[f2232,f1792]) ).
tff(f25360,plain,
( spl18_466
| ~ spl18_112
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f2194,f2174,f1791,f25358]) ).
tff(f25358,plain,
( spl18_466
<=> ! [X0: $tType,X3: X0,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_466])]) ).
tff(f2194,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),X2,X1))) )
| ~ spl18_112
| ~ spl18_128 ),
inference(superposition,[],[f2175,f1792]) ).
tff(f25356,plain,
( spl18_465
| ~ spl18_112
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1909,f1872,f1791,f25354]) ).
tff(f25354,plain,
( spl18_465
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X2,X1)),X1))
| ( aa(fun(X0,bool),fun(X0,bool),X2,X1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_465])]) ).
tff(f1909,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),X2,X1)),X1))
| ( aa(fun(X0,bool),fun(X0,bool),X2,X1) = X1 ) )
| ~ spl18_112
| ~ spl18_115 ),
inference(superposition,[],[f1873,f1792]) ).
tff(f25108,plain,
( spl18_464
| ~ spl18_75
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1671,f1628,f1089,f25106]) ).
tff(f25106,plain,
( spl18_464
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X5: fun(X0,X1),X3: fun(X2,X1)] :
( ( aa(X2,X1,X3,aa(X0,X2,X4,sK13(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))) != aa(X0,X1,X5,sK13(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)) )
| ( aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_464])]) ).
tff(f1089,plain,
( spl18_75
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK13(X0,X1,X2,X3)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).
tff(f1671,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ( aa(X2,X1,X3,aa(X0,X2,X4,sK13(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5))) != aa(X0,X1,X5,sK13(X1,X0,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5)) )
| ( aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4) = X5 ) )
| ~ spl18_75
| ~ spl18_105 ),
inference(superposition,[],[f1090,f1629]) ).
tff(f1090,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK13(X0,X1,X2,X3)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl18_75 ),
inference(avatar_component_clause,[],[f1089]) ).
tff(f25103,plain,
( spl18_463
| ~ spl18_434
| ~ spl18_435 ),
inference(avatar_split_clause,[],[f23857,f20500,f20496,f25100]) ).
tff(f23857,plain,
( ( fTrue = sK13(fun(bool,bool),bool,fconj,fconj) )
| ~ spl18_434
| ~ spl18_435 ),
inference(superposition,[],[f20498,f20502]) ).
tff(f25098,plain,
( spl18_462
| ~ spl18_75
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1670,f1628,f1089,f25096]) ).
tff(f25096,plain,
( spl18_462
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X3: fun(X2,X1),X5: fun(X0,X1)] :
( ( aa(X2,X1,X3,aa(X0,X2,X4,sK13(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))) != aa(X0,X1,X5,sK13(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))) )
| ( aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_462])]) ).
tff(f1670,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(X0,X1)] :
( ( aa(X2,X1,X3,aa(X0,X2,X4,sK13(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)))) != aa(X0,X1,X5,sK13(X1,X0,X5,aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4))) )
| ( aa(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4) = X5 ) )
| ~ spl18_75
| ~ spl18_105 ),
inference(superposition,[],[f1090,f1629]) ).
tff(f24176,plain,
( spl18_461
| ~ spl18_104
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1852,f1791,f1624,f24174]) ).
tff(f24174,plain,
( spl18_461
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X1,fun(X0,X2)),X4: fun(fun(X1,fun(X0,X2)),X0),X5: X1] : ( aa(X0,X2,aa(X1,fun(X0,X2),X3,X5),aa(fun(X1,fun(X0,X2)),X0,X4,X3)) = aa(X1,X2,aa(fun(X1,fun(X0,X2)),fun(X1,X2),aa(fun(fun(X1,fun(X0,X2)),X0),fun(fun(X1,fun(X0,X2)),fun(X1,X2)),aa(fun(fun(X1,fun(X0,X2)),fun(X0,fun(X1,X2))),fun(fun(fun(X1,fun(X0,X2)),X0),fun(fun(X1,fun(X0,X2)),fun(X1,X2))),combs(fun(X1,fun(X0,X2)),X0,fun(X1,X2)),combc(X1,X0,X2)),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_461])]) ).
tff(f1852,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,fun(X0,X2)),X4: fun(fun(X1,fun(X0,X2)),X0),X5: X1] : ( aa(X0,X2,aa(X1,fun(X0,X2),X3,X5),aa(fun(X1,fun(X0,X2)),X0,X4,X3)) = aa(X1,X2,aa(fun(X1,fun(X0,X2)),fun(X1,X2),aa(fun(fun(X1,fun(X0,X2)),X0),fun(fun(X1,fun(X0,X2)),fun(X1,X2)),aa(fun(fun(X1,fun(X0,X2)),fun(X0,fun(X1,X2))),fun(fun(fun(X1,fun(X0,X2)),X0),fun(fun(X1,fun(X0,X2)),fun(X1,X2))),combs(fun(X1,fun(X0,X2)),X0,fun(X1,X2)),combc(X1,X0,X2)),X4),X3),X5) )
| ~ spl18_104
| ~ spl18_112 ),
inference(superposition,[],[f1625,f1792]) ).
tff(f24172,plain,
( spl18_460
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1807,f1791,f24170]) ).
tff(f24170,plain,
( spl18_460
<=> ! [X3: $tType,X0: $tType,X2: $tType,X1: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X6: fun(X3,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),aa(X3,X0,X6,X5)) = aa(X1,X2,aa(X3,fun(X1,X2),aa(fun(X3,X0),fun(X3,fun(X1,X2)),aa(fun(X3,fun(X0,fun(X1,X2))),fun(fun(X3,X0),fun(X3,fun(X1,X2))),combs(X3,X0,fun(X1,X2)),X4),X6),X5),aa(X0,X1,X7,aa(X3,X0,X6,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_460])]) ).
tff(f1807,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(X3,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),aa(X3,X0,X6,X5)) = aa(X1,X2,aa(X3,fun(X1,X2),aa(fun(X3,X0),fun(X3,fun(X1,X2)),aa(fun(X3,fun(X0,fun(X1,X2))),fun(fun(X3,X0),fun(X3,fun(X1,X2))),combs(X3,X0,fun(X1,X2)),X4),X6),X5),aa(X0,X1,X7,aa(X3,X0,X6,X5))) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f23984,plain,
( spl18_459
| ~ spl18_104
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f2000,f1919,f1624,f23982]) ).
tff(f23982,plain,
( spl18_459
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,fun(X0,bool)),X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK15(X0,X1,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)),sK14(X0,X1,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_459])]) ).
tff(f2000,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK15(X0,X1,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)),sK14(X0,X1,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3)))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))) )
| ~ spl18_104
| ~ spl18_118 ),
inference(superposition,[],[f1920,f1625]) ).
tff(f23980,plain,
( spl18_458
| ~ spl18_104
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1969,f1915,f1624,f23978]) ).
tff(f23978,plain,
( spl18_458
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,fun(X0,bool)),X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK15(X0,X1,X3,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))),sK14(X0,X1,X3,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_458])]) ).
tff(f1969,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK15(X0,X1,X3,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))),sK14(X0,X1,X3,aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2))))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2)),X3)) )
| ~ spl18_104
| ~ spl18_117 ),
inference(superposition,[],[f1916,f1625]) ).
tff(f23639,plain,
( spl18_457
| ~ spl18_110
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1942,f1915,f1749,f23637]) ).
tff(f23637,plain,
( spl18_457
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: fun(fun(X0,X1),fun(fun(X0,X1),bool))] :
( pp(aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),bool,aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),fun(fun(fun(X0,X1),fun(fun(X0,X1),bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(fun(X0,X1),bool))),ord_less_eq(fun(X0,X1))),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,sK14(fun(X0,X1),fun(X0,X1),X2,ord_less_eq(fun(X0,X1))),X3)),aa(X0,X1,sK15(fun(X0,X1),fun(X0,X1),X2,ord_less_eq(fun(X0,X1))),X3)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_457])]) ).
tff(f1942,plain,
( ! [X1: $tType,X0: $tType,X2: fun(fun(X0,X1),fun(fun(X0,X1),bool)),X3: X0] :
( pp(aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),bool,aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),fun(fun(fun(X0,X1),fun(fun(X0,X1),bool)),bool),ord_less_eq(fun(fun(X0,X1),fun(fun(X0,X1),bool))),ord_less_eq(fun(X0,X1))),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,sK14(fun(X0,X1),fun(X0,X1),X2,ord_less_eq(fun(X0,X1))),X3)),aa(X0,X1,sK15(fun(X0,X1),fun(X0,X1),X2,ord_less_eq(fun(X0,X1))),X3)))
| ~ ord(X1) )
| ~ spl18_110
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1750]) ).
tff(f23635,plain,
( spl18_456
| ~ spl18_75
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1657,f1624,f1089,f23633]) ).
tff(f23633,plain,
( spl18_456
<=> ! [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,sK13(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4) != aa(X0,X1,X5,sK13(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)) )
| ( aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_456])]) ).
tff(f1657,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,sK13(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)),X4) != aa(X0,X1,X5,sK13(X1,X0,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5)) )
| ( aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4) = X5 ) )
| ~ spl18_75
| ~ spl18_104 ),
inference(superposition,[],[f1090,f1625]) ).
tff(f23631,plain,
( spl18_455
| ~ spl18_75
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1656,f1624,f1089,f23629]) ).
tff(f23629,plain,
( spl18_455
<=> ! [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,sK13(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4) != aa(X0,X1,X5,sK13(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))) )
| ( aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_455])]) ).
tff(f1656,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,sK13(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))),X4) != aa(X0,X1,X5,sK13(X1,X0,X5,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4))) )
| ( aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4) = X5 ) )
| ~ spl18_75
| ~ spl18_104 ),
inference(superposition,[],[f1090,f1625]) ).
tff(f23141,plain,
( spl18_454
| ~ spl18_99
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1814,f1791,f1568,f23139]) ).
tff(f23139,plain,
( spl18_454
<=> ! [X2: $tType,X0: $tType,X3: fun(fun(X0,bool),fun(fun(X0,bool),X2)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),X2,aa(fun(X0,bool),fun(fun(X0,bool),X2),X3,X1),combk(bool,X0,fFalse)) = aa(fun(X0,bool),X2,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2),aa(fun(fun(X0,bool),fun(fun(X0,bool),X2)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2)),combs(fun(X0,bool),fun(X0,bool),X2),X3),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_454])]) ).
tff(f1814,plain,
( ! [X0: $tType,X2: $tType,X3: fun(fun(X0,bool),fun(fun(X0,bool),X2)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),X2,aa(fun(X0,bool),fun(fun(X0,bool),X2),X3,X1),combk(bool,X0,fFalse)) = aa(fun(X0,bool),X2,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2),aa(fun(fun(X0,bool),fun(fun(X0,bool),X2)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2)),combs(fun(X0,bool),fun(X0,bool),X2),X3),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X1) )
| ~ spl18_99
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1569]) ).
tff(f23137,plain,
( spl18_453
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1806,f1791,f23135]) ).
tff(f23135,plain,
( spl18_453
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: fun(X0,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),aa(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X0,fun(X3,fun(X1,X2))),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combs(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),aa(X0,X3,X5,X6)),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_453])]) ).
tff(f1806,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X0,fun(X3,fun(X1,X2))),X5: fun(X0,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(fun(X0,X3),fun(X0,fun(X1,X2)),aa(fun(X0,fun(X3,fun(X1,X2))),fun(fun(X0,X3),fun(X0,fun(X1,X2))),combs(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),aa(X0,X3,X5,X6)),aa(X0,X1,X7,X6)) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f23029,plain,
( spl18_452
| ~ spl18_22
| spl18_435 ),
inference(avatar_split_clause,[],[f21264,f20500,f749,f23027]) ).
tff(f23027,plain,
( spl18_452
<=> ! [X0: bool] :
( ( fconj != combk(fun(bool,bool),bool,combk(bool,bool,X0)) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_452])]) ).
tff(f21264,plain,
( ! [X0: bool] :
( ( fconj != combk(fun(bool,bool),bool,combk(bool,bool,X0)) )
| ( fTrue = X0 ) )
| ~ spl18_22
| spl18_435 ),
inference(superposition,[],[f20501,f750]) ).
tff(f20501,plain,
( ( fconj != combk(fun(bool,bool),bool,combk(bool,bool,fFalse)) )
| spl18_435 ),
inference(avatar_component_clause,[],[f20500]) ).
tff(f22507,plain,
( spl18_451
| ~ spl18_63
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2035,f2018,f984,f22505]) ).
tff(f22505,plain,
( spl18_451
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_451])]) ).
tff(f984,plain,
( spl18_63
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK6(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).
tff(f2035,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_122 ),
inference(resolution,[],[f2019,f985]) ).
tff(f985,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,sK6(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_63 ),
inference(avatar_component_clause,[],[f984]) ).
tff(f22503,plain,
( spl18_450
| ~ spl18_62
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2034,f2018,f980,f22501]) ).
tff(f22501,plain,
( spl18_450
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_450])]) ).
tff(f2034,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_122 ),
inference(resolution,[],[f2019,f981]) ).
tff(f22499,plain,
( spl18_449
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1800,f1791,f22497]) ).
tff(f22497,plain,
( spl18_449
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X0,fun(X2,X1)),X4: fun(X0,X2),X5: fun(fun(X0,X2),X0)] : ( aa(fun(X0,X2),X1,aa(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1),aa(fun(fun(X0,X2),fun(X0,X1)),fun(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1)),combs(fun(X0,X2),X0,X1),aa(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(X0,X2,X1),X3)),X5),X4) = aa(X2,X1,aa(X0,fun(X2,X1),X3,aa(fun(X0,X2),X0,X5,X4)),aa(X0,X2,X4,aa(fun(X0,X2),X0,X5,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_449])]) ).
tff(f1800,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: fun(X0,X2),X5: fun(fun(X0,X2),X0)] : ( aa(fun(X0,X2),X1,aa(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1),aa(fun(fun(X0,X2),fun(X0,X1)),fun(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1)),combs(fun(X0,X2),X0,X1),aa(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(X0,X2,X1),X3)),X5),X4) = aa(X2,X1,aa(X0,fun(X2,X1),X3,aa(fun(X0,X2),X0,X5,X4)),aa(X0,X2,X4,aa(fun(X0,X2),X0,X5,X4))) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f22031,plain,
( spl18_448
| ~ spl18_72
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f2492,f2441,f1066,f22029]) ).
tff(f22029,plain,
( spl18_448
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| ~ pp(aa(product_prod(X0,X1),bool,X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_448])]) ).
tff(f1066,plain,
( spl18_72
<=> ! [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,[spl18_72])]) ).
tff(f2492,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( ~ pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| ~ pp(aa(product_prod(X0,X1),bool,X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) )
| ~ spl18_72
| ~ spl18_145 ),
inference(resolution,[],[f2442,f1067]) ).
tff(f1067,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)) )
| ~ spl18_72 ),
inference(avatar_component_clause,[],[f1066]) ).
tff(f22027,plain,
( spl18_447
| ~ spl18_71
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2455,f2437,f1061,f22025]) ).
tff(f22025,plain,
( spl18_447
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_447])]) ).
tff(f2455,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X3))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) )
| ~ spl18_71
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1062]) ).
tff(f22007,plain,
( spl18_446
| ~ spl18_71
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2447,f2437,f1061,f22005]) ).
tff(f22005,plain,
( spl18_446
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_446])]) ).
tff(f2447,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3))),X2))
| ( X2 = X3 )
| pp(aa(product_prod(X0,X1),bool,X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,X3)),sK17(X1,X0,X2,X3)))) )
| ~ spl18_71
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1062]) ).
tff(f22003,plain,
( spl18_445
| ~ spl18_89
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1813,f1791,f1212,f22001]) ).
tff(f22001,plain,
( spl18_445
<=> ! [X2: $tType,X0: $tType,X3: fun(fun(X0,bool),fun(fun(X0,bool),X2)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),X2,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2),aa(fun(fun(X0,bool),fun(fun(X0,bool),X2)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2)),combs(fun(X0,bool),fun(X0,bool),X2),X3),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1)),X1) = aa(fun(X0,bool),X2,aa(fun(X0,bool),fun(fun(X0,bool),X2),X3,X1),combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_445])]) ).
tff(f1212,plain,
( spl18_89
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).
tff(f1813,plain,
( ! [X0: $tType,X2: $tType,X3: fun(fun(X0,bool),fun(fun(X0,bool),X2)),X1: fun(X0,bool)] : ( aa(fun(X0,bool),X2,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2),aa(fun(fun(X0,bool),fun(fun(X0,bool),X2)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),X2)),combs(fun(X0,bool),fun(X0,bool),X2),X3),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1)),X1) = aa(fun(X0,bool),X2,aa(fun(X0,bool),fun(fun(X0,bool),X2),X3,X1),combk(bool,X0,fFalse)) )
| ~ spl18_89
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1213]) ).
tff(f1213,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) )
| ~ spl18_89 ),
inference(avatar_component_clause,[],[f1212]) ).
tff(f21382,plain,
( spl18_444
| ~ spl18_80
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2418,f2384,f1124,f21380]) ).
tff(f21380,plain,
( spl18_444
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_444])]) ).
tff(f2418,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)) )
| ~ spl18_80
| ~ spl18_143 ),
inference(resolution,[],[f2385,f1125]) ).
tff(f21378,plain,
( spl18_443
| ~ spl18_105
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1853,f1791,f1628,f21376]) ).
tff(f21376,plain,
( spl18_443
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(fun(X1,X2),fun(X0,X1)),X5: X0,X3: fun(X1,X2)] : ( aa(X1,X2,X3,aa(X0,X1,aa(fun(X1,X2),fun(X0,X1),X4,X3),X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),aa(fun(fun(X1,X2),fun(X0,X1)),fun(fun(X1,X2),fun(X0,X2)),aa(fun(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2))),fun(fun(fun(X1,X2),fun(X0,X1)),fun(fun(X1,X2),fun(X0,X2))),combs(fun(X1,X2),fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0)),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_443])]) ).
tff(f1853,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: fun(fun(X1,X2),fun(X0,X1)),X5: X0] : ( aa(X1,X2,X3,aa(X0,X1,aa(fun(X1,X2),fun(X0,X1),X4,X3),X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),aa(fun(fun(X1,X2),fun(X0,X1)),fun(fun(X1,X2),fun(X0,X2)),aa(fun(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2))),fun(fun(fun(X1,X2),fun(X0,X1)),fun(fun(X1,X2),fun(X0,X2))),combs(fun(X1,X2),fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0)),X4),X3),X5) )
| ~ spl18_105
| ~ spl18_112 ),
inference(superposition,[],[f1629,f1792]) ).
tff(f21374,plain,
( spl18_442
| ~ spl18_110
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1851,f1791,f1749,f21372]) ).
tff(f21372,plain,
( spl18_442
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(fun(X0,X1),fun(X0,X1)),X2: fun(X0,X1)] :
( ~ pp(aa(fun(X0,X1),bool,aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(X0,X1),bool),aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),fun(fun(fun(X0,X1),fun(X0,X1)),fun(fun(X0,X1),bool)),combs(fun(X0,X1),fun(X0,X1),bool),ord_less_eq(fun(X0,X1))),X3),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X2,X4)),aa(X0,X1,aa(fun(X0,X1),fun(X0,X1),X3,X2),X4)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_442])]) ).
tff(f1851,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(fun(X0,X1),fun(X0,X1)),X4: X0] :
( ~ pp(aa(fun(X0,X1),bool,aa(fun(fun(X0,X1),fun(X0,X1)),fun(fun(X0,X1),bool),aa(fun(fun(X0,X1),fun(fun(X0,X1),bool)),fun(fun(fun(X0,X1),fun(X0,X1)),fun(fun(X0,X1),bool)),combs(fun(X0,X1),fun(X0,X1),bool),ord_less_eq(fun(X0,X1))),X3),X2))
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X2,X4)),aa(X0,X1,aa(fun(X0,X1),fun(X0,X1),X3,X2),X4)))
| ~ ord(X1) )
| ~ spl18_110
| ~ spl18_112 ),
inference(superposition,[],[f1750,f1792]) ).
tff(f21263,plain,
( spl18_441
| ~ spl18_63
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f1740,f1731,f984,f21261]) ).
tff(f21261,plain,
( spl18_441
<=> ! [X0: $tType,X1: X0] :
( ( big_linorder_Max(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_441])]) ).
tff(f1740,plain,
( ! [X0: $tType,X1: X0] :
( ( big_linorder_Max(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_109 ),
inference(resolution,[],[f1732,f985]) ).
tff(f21259,plain,
( spl18_440
| ~ spl18_62
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f1739,f1731,f980,f21257]) ).
tff(f21257,plain,
( spl18_440
<=> ! [X0: $tType,X1: X0] :
( ( big_linorder_Max(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_440])]) ).
tff(f1739,plain,
( ! [X0: $tType,X1: X0] :
( ( big_linorder_Max(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1))) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))),X1))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_109 ),
inference(resolution,[],[f1732,f981]) ).
tff(f20519,plain,
( spl18_439
| ~ spl18_63
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1902,f1872,f984,f20517]) ).
tff(f20517,plain,
( spl18_439
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 )
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_439])]) ).
tff(f1902,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 )
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_115 ),
inference(resolution,[],[f1873,f985]) ).
tff(f20515,plain,
( spl18_438
| ~ spl18_62
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1901,f1872,f980,f20513]) ).
tff(f20513,plain,
( spl18_438
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 )
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_438])]) ).
tff(f1901,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))),X1))
| ( sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)) = X1 )
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_115 ),
inference(resolution,[],[f1873,f981]) ).
tff(f20511,plain,
( spl18_437
| ~ spl18_111
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1854,f1791,f1753,f20509]) ).
tff(f20509,plain,
( spl18_437
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_437])]) ).
tff(f1753,plain,
( spl18_111
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_111])]) ).
tff(f1854,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1)),X1))
| ~ spl18_111
| ~ spl18_112 ),
inference(superposition,[],[f1754,f1792]) ).
tff(f1754,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X2))
| ~ spl18_111 ),
inference(avatar_component_clause,[],[f1753]) ).
tff(f20507,plain,
( spl18_436
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1819,f1791,f20505]) ).
tff(f20505,plain,
( spl18_436
<=> ! [X1: $tType,X6: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,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)),aa(X2,X0,X5,X4)) = aa(X1,X6,aa(X0,fun(X1,X6),X7,aa(X2,X0,X5,X4)),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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_436])]) ).
tff(f1819,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X7: fun(X0,fun(X1,X6)),X4: X2,X5: fun(X2,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)),aa(X2,X0,X5,X4)) = aa(X1,X6,aa(X0,fun(X1,X6),X7,aa(X2,X0,X5,X4)),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)) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f20503,plain,
( spl18_434
| spl18_435
| ~ spl18_415 ),
inference(avatar_split_clause,[],[f19870,f18297,f20500,f20496]) ).
tff(f18297,plain,
( spl18_415
<=> ! [X0: fun(bool,bool)] :
( ( combk(bool,bool,fFalse) != X0 )
| ( fconj = combk(fun(bool,bool),bool,X0) )
| ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,X0),fconj) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_415])]) ).
tff(f19870,plain,
( ( fconj = combk(fun(bool,bool),bool,combk(bool,bool,fFalse)) )
| ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,combk(bool,bool,fFalse)),fconj) )
| ~ spl18_415 ),
inference(equality_resolution,[],[f18298]) ).
tff(f18298,plain,
( ! [X0: fun(bool,bool)] :
( ( combk(bool,bool,fFalse) != X0 )
| ( fconj = combk(fun(bool,bool),bool,X0) )
| ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,X0),fconj) ) )
| ~ spl18_415 ),
inference(avatar_component_clause,[],[f18297]) ).
tff(f20274,plain,
( spl18_433
| ~ spl18_63
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2165,f2128,f984,f20272]) ).
tff(f20272,plain,
( spl18_433
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK6(fun(X1,fun(X0,bool)),aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2)),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ( aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2) = combk(bool,fun(X1,fun(X0,bool)),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_433])]) ).
tff(f2165,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK6(fun(X1,fun(X0,bool)),aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2)),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ( aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2) = combk(bool,fun(X1,fun(X0,bool)),fFalse) ) )
| ~ spl18_63
| ~ spl18_126 ),
inference(resolution,[],[f2129,f985]) ).
tff(f20270,plain,
( spl18_432
| ~ spl18_62
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2164,f2128,f980,f20268]) ).
tff(f20268,plain,
( spl18_432
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK5(fun(X1,fun(X0,bool)),aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2)),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ( aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2) = combk(bool,fun(X1,fun(X0,bool)),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_432])]) ).
tff(f2164,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),sK5(fun(X1,fun(X0,bool)),aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2)),X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ( aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2) = combk(bool,fun(X1,fun(X0,bool)),fFalse) ) )
| ~ spl18_62
| ~ spl18_126 ),
inference(resolution,[],[f2129,f981]) ).
tff(f20266,plain,
( spl18_431
| ~ spl18_108
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1923,f1915,f1690,f20264]) ).
tff(f20264,plain,
( spl18_431
<=> ! [X1: $tType,X0: $tType,X4: fun(X0,fun(X1,bool)),X3: fun(X0,fun(X1,bool)),X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),X4))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X4))
| ~ preorder(fun(X0,fun(X1,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_431])]) ).
tff(f1923,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,fun(X1,bool)),X4: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),X4))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X4))
| ~ preorder(fun(X0,fun(X1,bool))) )
| ~ spl18_108
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1691]) ).
tff(f20262,plain,
( spl18_430
| ~ spl18_109
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1845,f1791,f1731,f20260]) ).
tff(f20260,plain,
( spl18_430
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| ( big_linorder_Max(X0,aa(X0,fun(X0,bool),X2,X1)) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,aa(X0,fun(X0,bool),X2,X1))),X1))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),X2,X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_430])]) ).
tff(f1845,plain,
( ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| ( big_linorder_Max(X0,aa(X0,fun(X0,bool),X2,X1)) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,aa(X0,fun(X0,bool),X2,X1))),X1))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),X2,X1))
| ~ linorder(X0) )
| ~ spl18_109
| ~ spl18_112 ),
inference(superposition,[],[f1732,f1792]) ).
tff(f19864,plain,
( spl18_429
| ~ spl18_27
| ~ spl18_121 ),
inference(avatar_split_clause,[],[f2024,f2014,f769,f19862]) ).
tff(f19862,plain,
( spl18_429
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X0,fun(X1,X2)),X4: fun(X0,fun(X1,X2)),X5: X0] :
( ( aa(X0,fun(X1,X2),aa(fun(X0,fun(X1,X2)),fun(X0,fun(X1,X2)),aa(fun(X0,fun(X1,X2)),fun(fun(X0,fun(X1,X2)),fun(X0,fun(X1,X2))),minus_minus(fun(X0,fun(X1,X2))),X3),X4),X5) = aa(fun(X1,X2),fun(X1,X2),aa(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),minus_minus(fun(X1,X2)),aa(X0,fun(X1,X2),X3,X5)),aa(X0,fun(X1,X2),X4,X5)) )
| ~ cl_Groups_Ominus(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_429])]) ).
tff(f769,plain,
( spl18_27
<=> ! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
tff(f2014,plain,
( spl18_121
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: fun(X1,X0),X2: X1] :
( ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X4),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X4,X2)),aa(X1,X0,X3,X2)) )
| ~ cl_Groups_Ominus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_121])]) ).
tff(f2024,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X1,X2)),X4: fun(X0,fun(X1,X2)),X5: X0] :
( ( aa(X0,fun(X1,X2),aa(fun(X0,fun(X1,X2)),fun(X0,fun(X1,X2)),aa(fun(X0,fun(X1,X2)),fun(fun(X0,fun(X1,X2)),fun(X0,fun(X1,X2))),minus_minus(fun(X0,fun(X1,X2))),X3),X4),X5) = aa(fun(X1,X2),fun(X1,X2),aa(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),minus_minus(fun(X1,X2)),aa(X0,fun(X1,X2),X3,X5)),aa(X0,fun(X1,X2),X4,X5)) )
| ~ cl_Groups_Ominus(X2) )
| ~ spl18_27
| ~ spl18_121 ),
inference(resolution,[],[f2015,f770]) ).
tff(f770,plain,
( ! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) )
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f769]) ).
tff(f2015,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
( ~ cl_Groups_Ominus(X0)
| ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X4),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X4,X2)),aa(X1,X0,X3,X2)) ) )
| ~ spl18_121 ),
inference(avatar_component_clause,[],[f2014]) ).
tff(f19860,plain,
( spl18_428
| ~ spl18_104
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1804,f1791,f1624,f19858]) ).
tff(f19858,plain,
( spl18_428
<=> ! [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),aa(X3,fun(X0,fun(X1,X2)),aa(fun(X0,fun(X3,fun(X1,X2))),fun(X3,fun(X0,fun(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,[spl18_428])]) ).
tff(f1804,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),aa(X3,fun(X0,fun(X1,X2)),aa(fun(X0,fun(X3,fun(X1,X2))),fun(X3,fun(X0,fun(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)) )
| ~ spl18_104
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1625]) ).
tff(f19829,plain,
( spl18_427
| ~ spl18_97
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1940,f1915,f1542,f19827]) ).
tff(f19827,plain,
( spl18_427
<=> ! [X0: $tType,X2: X0,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| pp(aa(X0,bool,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))),X2))
| ~ pp(aa(X0,bool,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_427])]) ).
tff(f1940,plain,
( ! [X0: $tType,X2: X0,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| pp(aa(X0,bool,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))),X2))
| ~ pp(aa(X0,bool,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))),X2)) )
| ~ spl18_97
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1543]) ).
tff(f18669,plain,
( ~ spl18_8
| ~ spl18_180
| spl18_425 ),
inference(avatar_split_clause,[],[f18613,f18609,f4339,f682]) ).
tff(f4339,plain,
( spl18_180
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_180])]) ).
tff(f18609,plain,
( spl18_425
<=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),li)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_425])]) ).
tff(f18613,plain,
( ~ linorder(int)
| ~ spl18_180
| spl18_425 ),
inference(resolution,[],[f18611,f4340]) ).
tff(f4340,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ linorder(X0) )
| ~ spl18_180 ),
inference(avatar_component_clause,[],[f4339]) ).
tff(f18611,plain,
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),li))
| spl18_425 ),
inference(avatar_component_clause,[],[f18609]) ).
tff(f18640,plain,
( spl18_1
| ~ spl18_181
| ~ spl18_357
| ~ spl18_423
| spl18_425 ),
inference(avatar_split_clause,[],[f18639,f18609,f18600,f12557,f4376,f647]) ).
tff(f12557,plain,
( spl18_357
<=> ( li = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_357])]) ).
tff(f18600,plain,
( spl18_423
<=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_423])]) ).
tff(f18639,plain,
( pp(fFalse)
| ~ spl18_181
| ~ spl18_357
| ~ spl18_423
| spl18_425 ),
inference(forward_demodulation,[],[f18638,f18621]) ).
tff(f18621,plain,
( ( fFalse = aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),li) )
| ~ spl18_181
| spl18_425 ),
inference(resolution,[],[f18611,f4377]) ).
tff(f18638,plain,
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),li))
| ~ spl18_357
| ~ spl18_423 ),
inference(forward_demodulation,[],[f18601,f12559]) ).
tff(f12559,plain,
( ( li = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs) )
| ~ spl18_357 ),
inference(avatar_component_clause,[],[f12557]) ).
tff(f18601,plain,
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))
| ~ spl18_423 ),
inference(avatar_component_clause,[],[f18600]) ).
tff(f18636,plain,
( ~ spl18_4
| spl18_423
| spl18_426
| ~ spl18_125
| ~ spl18_158 ),
inference(avatar_split_clause,[],[f2684,f2678,f2124,f18634,f18600,f662]) ).
tff(f662,plain,
( spl18_4
<=> ordered_ab_group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
tff(f18634,plain,
( spl18_426
<=> ! [X0: int,X1: int] :
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_426])]) ).
tff(f2684,plain,
( ! [X0: int,X1: int] :
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),X0),X1))
| pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))
| ~ ordered_ab_group_add(int) )
| ~ spl18_125
| ~ spl18_158 ),
inference(superposition,[],[f2125,f2680]) ).
tff(f18612,plain,
( ~ spl18_425
| ~ spl18_357
| spl18_423 ),
inference(avatar_split_clause,[],[f18607,f18600,f12557,f18609]) ).
tff(f18607,plain,
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),li))
| ~ spl18_357
| spl18_423 ),
inference(forward_demodulation,[],[f18602,f12559]) ).
tff(f18602,plain,
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))
| spl18_423 ),
inference(avatar_component_clause,[],[f18600]) ).
tff(f18606,plain,
( ~ spl18_4
| ~ spl18_423
| spl18_424
| ~ spl18_125
| ~ spl18_158 ),
inference(avatar_split_clause,[],[f2683,f2678,f2124,f18604,f18600,f662]) ).
tff(f18604,plain,
( spl18_424
<=> ! [X0: int,X1: int] :
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1) )
| pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_424])]) ).
tff(f2683,plain,
( ! [X0: int,X1: int] :
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))
| pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),X0),X1))
| ~ ordered_ab_group_add(int) )
| ~ spl18_125
| ~ spl18_158 ),
inference(superposition,[],[f2125,f2680]) ).
tff(f18598,plain,
( spl18_422
| ~ spl18_94
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1855,f1791,f1243,f18596]) ).
tff(f18596,plain,
( spl18_422
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_422])]) ).
tff(f1243,plain,
( spl18_94
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).
tff(f1855,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1)) )
| ~ spl18_94
| ~ spl18_112 ),
inference(superposition,[],[f1244,f1792]) ).
tff(f1244,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,X2) )
| ~ spl18_94 ),
inference(avatar_component_clause,[],[f1243]) ).
tff(f18594,plain,
( spl18_421
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1818,f1791,f18592]) ).
tff(f18592,plain,
( spl18_421
<=> ! [X1: $tType,X2: $tType,X6: $tType,X0: $tType,X3: fun(X0,fun(X2,X1)),X4: fun(X0,X2),X7: fun(X0,fun(X1,X6)),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(fun(X0,X2),fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(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),aa(X0,X2,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_421])]) ).
tff(f1818,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X7: fun(X0,fun(X1,X6)),X4: fun(X0,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(fun(X0,X2),fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(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),aa(X0,X2,X4,X5))) )
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1792]) ).
tff(f18590,plain,
( spl18_420
| ~ spl18_105
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1805,f1791,f1628,f18588]) ).
tff(f18588,plain,
( spl18_420
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: fun(X0,X3),X4: 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),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)),aa(X0,X1,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_420])]) ).
tff(f1805,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: fun(X0,X1),X4: fun(X3,fun(X1,X2)),X5: fun(X0,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(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)),aa(X0,X1,X7,X6)) )
| ~ spl18_105
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1629]) ).
tff(f18586,plain,
( spl18_419
| ~ spl18_35
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f10390,f7358,f809,f18584]) ).
tff(f18584,plain,
( spl18_419
<=> ! [X0: fun(bool,bool)] :
( ( combk(bool,bool,fFalse) != X0 )
| ( fconj = combk(fun(bool,bool),bool,X0) )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,combk(fun(bool,bool),bool,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_419])]) ).
tff(f7358,plain,
( spl18_244
<=> ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_244])]) ).
tff(f10390,plain,
( ! [X0: fun(bool,bool)] :
( ( combk(bool,bool,fFalse) != X0 )
| ( fconj = combk(fun(bool,bool),bool,X0) )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,combk(fun(bool,bool),bool,X0)) ) )
| ~ spl18_35
| ~ spl18_244 ),
inference(superposition,[],[f7359,f810]) ).
tff(f7359,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,X0) ) )
| ~ spl18_244 ),
inference(avatar_component_clause,[],[f7358]) ).
tff(f18501,plain,
( spl18_418
| ~ spl18_101
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1937,f1915,f1599,f18499]) ).
tff(f18499,plain,
( spl18_418
<=> ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK14(fun(X0,bool),X0,X1,member(X0))),big_linorder_Max(X0,sK15(fun(X0,bool),X0,X1,member(X0)))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),X0,X1,member(X0)))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_418])]) ).
tff(f1937,plain,
( ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK14(fun(X0,bool),X0,X1,member(X0))),big_linorder_Max(X0,sK15(fun(X0,bool),X0,X1,member(X0)))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),X0,X1,member(X0)))
| ~ linorder(X0) )
| ~ spl18_101
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1600]) ).
tff(f18469,plain,
( spl18_417
| ~ spl18_90
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2151,f2124,f1216,f18467]) ).
tff(f18467,plain,
( spl18_417
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) != X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ ordered_ab_group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_417])]) ).
tff(f1216,plain,
( spl18_90
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),combk(bool,X0,fFalse)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).
tff(f2151,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) != X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_90
| ~ spl18_125 ),
inference(superposition,[],[f2125,f1217]) ).
tff(f1217,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),combk(bool,X0,fFalse)) = X1 )
| ~ spl18_90 ),
inference(avatar_component_clause,[],[f1216]) ).
tff(f18465,plain,
( spl18_416
| ~ spl18_90
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2142,f2124,f1216,f18463]) ).
tff(f18463,plain,
( spl18_416
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) != X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| ~ ordered_ab_group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_416])]) ).
tff(f2142,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] :
( ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) != X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_90
| ~ spl18_125 ),
inference(superposition,[],[f2125,f1217]) ).
tff(f18299,plain,
( spl18_415
| ~ spl18_35
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f7482,f7149,f809,f18297]) ).
tff(f7149,plain,
( spl18_239
<=> ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,X0,fconj) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_239])]) ).
tff(f7482,plain,
( ! [X0: fun(bool,bool)] :
( ( combk(bool,bool,fFalse) != X0 )
| ( fconj = combk(fun(bool,bool),bool,X0) )
| ( fTrue = sK13(fun(bool,bool),bool,combk(fun(bool,bool),bool,X0),fconj) ) )
| ~ spl18_35
| ~ spl18_239 ),
inference(superposition,[],[f7150,f810]) ).
tff(f7150,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,X0,fconj) ) )
| ~ spl18_239 ),
inference(avatar_component_clause,[],[f7149]) ).
tff(f17995,plain,
( spl18_414
| ~ spl18_63
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f2187,f2174,f984,f17993]) ).
tff(f17993,plain,
( spl18_414
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2))))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_414])]) ).
tff(f2187,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2))))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_128 ),
inference(resolution,[],[f2175,f985]) ).
tff(f17991,plain,
( spl18_413
| ~ spl18_62
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f2186,f2174,f980,f17989]) ).
tff(f17989,plain,
( spl18_413
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2))))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_413])]) ).
tff(f2186,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2))))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_128 ),
inference(resolution,[],[f2175,f981]) ).
tff(f17987,plain,
( spl18_412
| ~ spl18_112
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2153,f2124,f1791,f17985]) ).
tff(f17985,plain,
( spl18_412
<=> ! [X0: $tType,X4: X0,X3: X0,X2: fun(X0,X0),X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X4) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),aa(X0,X0,X2,X1)))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_412])]) ).
tff(f2153,plain,
( ! [X0: $tType,X2: fun(X0,X0),X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X4) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),aa(X0,X0,X2,X1)))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordered_ab_group_add(X0) )
| ~ spl18_112
| ~ spl18_125 ),
inference(superposition,[],[f2125,f1792]) ).
tff(f17983,plain,
( spl18_411
| ~ spl18_112
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2144,f2124,f1791,f17981]) ).
tff(f17981,plain,
( spl18_411
<=> ! [X0: $tType,X4: X0,X3: X0,X2: fun(X0,X0),X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X4) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),aa(X0,X0,X2,X1)))
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_411])]) ).
tff(f2144,plain,
( ! [X0: $tType,X2: fun(X0,X0),X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X4) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),aa(X0,X0,X2,X1)))
| ~ ordered_ab_group_add(X0) )
| ~ spl18_112
| ~ spl18_125 ),
inference(superposition,[],[f2125,f1792]) ).
tff(f17979,plain,
( spl18_410
| ~ spl18_111
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2027,f2018,f1753,f17977]) ).
tff(f17977,plain,
( spl18_410
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_410])]) ).
tff(f2027,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) )
| ~ linorder(X0) )
| ~ spl18_111
| ~ spl18_122 ),
inference(resolution,[],[f2019,f1754]) ).
tff(f17958,plain,
( spl18_409
| ~ spl18_80
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1941,f1915,f1124,f17956]) ).
tff(f17956,plain,
( spl18_409
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| finite_finite1(X0,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_409])]) ).
tff(f1941,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(fun(X0,bool),bool))] :
( pp(aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool,aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(fun(X0,bool),bool))),ord_less_eq(fun(X0,bool))),X1))
| finite_finite1(X0,sK14(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool))))
| ~ finite_finite1(X0,sK15(fun(X0,bool),fun(X0,bool),X1,ord_less_eq(fun(X0,bool)))) )
| ~ spl18_80
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1125]) ).
tff(f17954,plain,
( spl18_408
| ~ spl18_97
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1849,f1791,f1542,f17952]) ).
tff(f17952,plain,
( spl18_408
<=> ! [X0: $tType,X3: X0,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),X2,X1),X3))
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_408])]) ).
tff(f1849,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),X2,X1),X3))
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_97
| ~ spl18_112 ),
inference(superposition,[],[f1543,f1792]) ).
tff(f17950,plain,
( spl18_407
| ~ spl18_100
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1677,f1628,f1585,f17948]) ).
tff(f17948,plain,
( spl18_407
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X3: fun(X2,bool),X4: fun(product_prod(X0,X1),X2),X6: X1] :
( pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6))))
| ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,sK11(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_407])]) ).
tff(f1585,plain,
( spl18_100
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK11(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).
tff(f1677,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,bool),X6: X1,X4: fun(product_prod(X0,X1),X2),X5: X0] :
( pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6))))
| ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,sK11(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4))))) )
| ~ spl18_100
| ~ spl18_105 ),
inference(forward_demodulation,[],[f1675,f1629]) ).
tff(f1675,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,bool),X6: X1,X4: fun(product_prod(X0,X1),X2),X5: X0] :
( ~ pp(aa(X2,bool,X3,aa(product_prod(X0,X1),X2,X4,sK11(X0,X1,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4)))))
| pp(aa(product_prod(X0,X1),bool,aa(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool),aa(fun(X2,bool),fun(fun(product_prod(X0,X1),X2),fun(product_prod(X0,X1),bool)),combb(X2,bool,product_prod(X0,X1)),X3),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6))) )
| ~ spl18_100
| ~ spl18_105 ),
inference(superposition,[],[f1586,f1629]) ).
tff(f1586,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( ~ pp(aa(product_prod(X0,X1),bool,X2,sK11(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7))) )
| ~ spl18_100 ),
inference(avatar_component_clause,[],[f1585]) ).
tff(f17946,plain,
( spl18_406
| ~ spl18_100
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1663,f1624,f1585,f17944]) ).
tff(f17944,plain,
( spl18_406
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X3: fun(product_prod(X0,X1),fun(X2,bool)),X4: X2,X6: X1] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6)),X4))
| ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,sK11(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_406])]) ).
tff(f1663,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(product_prod(X0,X1),fun(X2,bool)),X6: X1,X4: X2,X5: X0] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6)),X4))
| ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,sK11(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),X4)) )
| ~ spl18_100
| ~ spl18_104 ),
inference(forward_demodulation,[],[f1661,f1625]) ).
tff(f1661,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(product_prod(X0,X1),fun(X2,bool)),X6: X1,X4: X2,X5: X0] :
( ~ pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),X3,sK11(X0,X1,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4))),X4))
| pp(aa(product_prod(X0,X1),bool,aa(X2,fun(product_prod(X0,X1),bool),aa(fun(product_prod(X0,X1),fun(X2,bool)),fun(X2,fun(product_prod(X0,X1),bool)),combc(product_prod(X0,X1),X2,bool),X3),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X6))) )
| ~ spl18_100
| ~ spl18_104 ),
inference(superposition,[],[f1586,f1625]) ).
tff(f17246,plain,
( spl18_405
| ~ spl18_105
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1826,f1791,f1628,f17244]) ).
tff(f17244,plain,
( spl18_405
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X2),X5: fun(fun(X0,X2),X0),X3: fun(X2,X1)] : ( aa(X2,X1,X3,aa(X0,X2,X4,aa(fun(X0,X2),X0,X5,X4))) = aa(fun(X0,X2),X1,aa(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1),aa(fun(fun(X0,X2),fun(X0,X1)),fun(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1)),combs(fun(X0,X2),X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3)),X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_405])]) ).
tff(f1826,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X5: fun(fun(X0,X2),X0)] : ( aa(X2,X1,X3,aa(X0,X2,X4,aa(fun(X0,X2),X0,X5,X4))) = aa(fun(X0,X2),X1,aa(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1),aa(fun(fun(X0,X2),fun(X0,X1)),fun(fun(fun(X0,X2),X0),fun(fun(X0,X2),X1)),combs(fun(X0,X2),X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3)),X5),X4) )
| ~ spl18_105
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1629]) ).
tff(f17224,plain,
( ~ spl18_20
| spl18_403 ),
inference(avatar_contradiction_clause,[],[f17222]) ).
tff(f17222,plain,
( $false
| ~ spl18_20
| spl18_403 ),
inference(resolution,[],[f17216,f742]) ).
tff(f742,plain,
( ! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1))
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f741]) ).
tff(f741,plain,
( spl18_20
<=> ! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
tff(f17216,plain,
( ~ finite_finite1(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as)))
| spl18_403 ),
inference(avatar_component_clause,[],[f17214]) ).
tff(f17214,plain,
( spl18_403
<=> finite_finite1(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_403])]) ).
tff(f17221,plain,
( ~ spl18_402
| ~ spl18_403
| spl18_404
| ~ spl18_101
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f2207,f2197,f1599,f17218,f17214,f17210]) ).
tff(f17210,plain,
( spl18_402
<=> linorder(product_prod(int,list(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_402])]) ).
tff(f17218,plain,
( spl18_404
<=> pp(aa(product_prod(int,list(int)),bool,aa(product_prod(int,list(int)),fun(product_prod(int,list(int)),bool),ord_less_eq(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),big_linorder_Max(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_404])]) ).
tff(f2197,plain,
( spl18_129
<=> pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_129])]) ).
tff(f2207,plain,
( pp(aa(product_prod(int,list(int)),bool,aa(product_prod(int,list(int)),fun(product_prod(int,list(int)),bool),ord_less_eq(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),big_linorder_Max(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as)))))
| ~ finite_finite1(product_prod(int,list(int)),set(product_prod(int,list(int)),lbounds(as)))
| ~ linorder(product_prod(int,list(int)))
| ~ spl18_101
| ~ spl18_129 ),
inference(resolution,[],[f2199,f1600]) ).
tff(f2199,plain,
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as))))
| ~ spl18_129 ),
inference(avatar_component_clause,[],[f2197]) ).
tff(f16073,plain,
( spl18_401
| ~ spl18_2
| ~ spl18_141 ),
inference(avatar_split_clause,[],[f2378,f2375,f652,f16071]) ).
tff(f16071,plain,
( spl18_401
<=> ! [X2: list(int),X0: list(int),X1: list(int)] : ( aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),minus_minus(list(int)),X0),X1)),X2) = aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X0),X2)),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_401])]) ).
tff(f652,plain,
( spl18_2
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
tff(f2375,plain,
( spl18_141
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_141])]) ).
tff(f2378,plain,
( ! [X2: list(int),X0: list(int),X1: list(int)] : ( aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),minus_minus(list(int)),X0),X1)),X2) = aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X0),X2)),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),X2)) )
| ~ spl18_2
| ~ spl18_141 ),
inference(resolution,[],[f2376,f654]) ).
tff(f654,plain,
( ring(int)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f652]) ).
tff(f2376,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ~ ring(X0)
| ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) ) )
| ~ spl18_141 ),
inference(avatar_component_clause,[],[f2375]) ).
tff(f16069,plain,
( spl18_400
| ~ spl18_82
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2283,f2231,f1132,f16067]) ).
tff(f16067,plain,
( spl18_400
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_400])]) ).
tff(f1132,plain,
( spl18_82
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).
tff(f2283,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) )
| ~ spl18_82
| ~ spl18_132 ),
inference(resolution,[],[f2232,f1133]) ).
tff(f1133,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_82 ),
inference(avatar_component_clause,[],[f1132]) ).
tff(f16065,plain,
( spl18_399
| ~ spl18_81
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2282,f2231,f1128,f16063]) ).
tff(f16063,plain,
( spl18_399
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_399])]) ).
tff(f1128,plain,
( spl18_81
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).
tff(f2282,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X1))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) )
| ~ spl18_81
| ~ spl18_132 ),
inference(resolution,[],[f2232,f1129]) ).
tff(f1129,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_81 ),
inference(avatar_component_clause,[],[f1128]) ).
tff(f16061,plain,
( spl18_398
| ~ spl18_22
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f10383,f7358,f749,f16059]) ).
tff(f16059,plain,
( spl18_398
<=> ! [X0: bool,X1: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,X0) != aa(bool,fun(bool,bool),X1,X0) )
| ( fconj = X1 )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,X1) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_398])]) ).
tff(f10383,plain,
( ! [X0: bool,X1: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,X0) != aa(bool,fun(bool,bool),X1,X0) )
| ( fconj = X1 )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,X1) )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_244 ),
inference(superposition,[],[f7359,f750]) ).
tff(f16057,plain,
( spl18_397
| ~ spl18_82
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2267,f2227,f1132,f16055]) ).
tff(f16055,plain,
( spl18_397
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_397])]) ).
tff(f2267,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) )
| ~ spl18_82
| ~ spl18_131 ),
inference(resolution,[],[f2228,f1133]) ).
tff(f16053,plain,
( spl18_396
| ~ spl18_81
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2266,f2227,f1128,f16051]) ).
tff(f16051,plain,
( spl18_396
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_396])]) ).
tff(f2266,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))),X2))
| ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) ) )
| ~ spl18_81
| ~ spl18_131 ),
inference(resolution,[],[f2228,f1129]) ).
tff(f16049,plain,
( spl18_395
| ~ spl18_105
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1817,f1791,f1628,f16047]) ).
tff(f16047,plain,
( spl18_395
<=> ! [X1: $tType,X2: $tType,X6: $tType,X0: $tType,X3: fun(X2,X1),X4: fun(X0,X2),X7: fun(X0,fun(X1,X6)),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(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,X3,aa(X0,X2,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_395])]) ).
tff(f1817,plain,
( ! [X6: $tType,X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X7: fun(X0,fun(X1,X6)),X4: fun(X0,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(fun(X0,X2),fun(X0,X1),aa(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4)),X5) = aa(X1,X6,aa(X0,fun(X1,X6),X7,X5),aa(X2,X1,X3,aa(X0,X2,X4,X5))) )
| ~ spl18_105
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1629]) ).
tff(f16045,plain,
( spl18_394
| ~ spl18_104
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1816,f1791,f1624,f16043]) ).
tff(f16043,plain,
( spl18_394
<=> ! [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),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),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,[spl18_394])]) ).
tff(f1816,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),aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),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)) )
| ~ spl18_104
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1625]) ).
tff(f15952,plain,
( spl18_393
| ~ spl18_111
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1895,f1872,f1753,f15950]) ).
tff(f15950,plain,
( spl18_393
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
| ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_393])]) ).
tff(f1895,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
| ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = X1 ) )
| ~ spl18_111
| ~ spl18_115 ),
inference(resolution,[],[f1873,f1754]) ).
tff(f15948,plain,
( spl18_392
| ~ spl18_101
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1846,f1791,f1599,f15946]) ).
tff(f15946,plain,
( spl18_392
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,aa(X0,fun(X0,bool),X2,X1))))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),X2,X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_392])]) ).
tff(f1846,plain,
( ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,aa(X0,fun(X0,bool),X2,X1))))
| ~ finite_finite1(X0,aa(X0,fun(X0,bool),X2,X1))
| ~ linorder(X0) )
| ~ spl18_101
| ~ spl18_112 ),
inference(superposition,[],[f1600,f1792]) ).
tff(f15837,plain,
( spl18_391
| ~ spl18_22
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f7474,f7149,f749,f15835]) ).
tff(f15835,plain,
( spl18_391
<=> ! [X0: bool,X1: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,X0) != aa(bool,fun(bool,bool),X1,X0) )
| ( fconj = X1 )
| ( fTrue = sK13(fun(bool,bool),bool,X1,fconj) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_391])]) ).
tff(f7474,plain,
( ! [X0: bool,X1: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,X0) != aa(bool,fun(bool,bool),X1,X0) )
| ( fconj = X1 )
| ( fTrue = sK13(fun(bool,bool),bool,X1,fconj) )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_239 ),
inference(superposition,[],[f7150,f750]) ).
tff(f15833,plain,
( spl18_390
| ~ spl18_69
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2452,f2437,f1047,f15831]) ).
tff(f15831,plain,
( spl18_390
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,combk(bool,product_prod(X0,X1),fFalse),X2)),sK17(X1,X0,combk(bool,product_prod(X0,X1),fFalse),X2))),X2))
| ( combk(bool,product_prod(X0,X1),fFalse) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_390])]) ).
tff(f1047,plain,
( spl18_69
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).
tff(f2452,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,combk(bool,product_prod(X0,X1),fFalse),X2)),sK17(X1,X0,combk(bool,product_prod(X0,X1),fFalse),X2))),X2))
| ( combk(bool,product_prod(X0,X1),fFalse) = X2 ) )
| ~ spl18_69
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1048]) ).
tff(f1048,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse)))
| ~ spl18_69 ),
inference(avatar_component_clause,[],[f1047]) ).
tff(f15829,plain,
( spl18_389
| ~ spl18_69
| ~ spl18_144 ),
inference(avatar_split_clause,[],[f2444,f2437,f1047,f15827]) ).
tff(f15827,plain,
( spl18_389
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,combk(bool,product_prod(X0,X1),fFalse))),sK17(X1,X0,X2,combk(bool,product_prod(X0,X1),fFalse)))),X2))
| ( combk(bool,product_prod(X0,X1),fFalse) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_389])]) ).
tff(f2444,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK16(X1,X0,X2,combk(bool,product_prod(X0,X1),fFalse))),sK17(X1,X0,X2,combk(bool,product_prod(X0,X1),fFalse)))),X2))
| ( combk(bool,product_prod(X0,X1),fFalse) = X2 ) )
| ~ spl18_69
| ~ spl18_144 ),
inference(resolution,[],[f2438,f1048]) ).
tff(f15783,plain,
( spl18_388
| ~ spl18_84
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1856,f1791,f1176,f15781]) ).
tff(f15781,plain,
( spl18_388
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1))
| ~ finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_388])]) ).
tff(f1176,plain,
( spl18_84
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).
tff(f1856,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),aa(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool))),combs(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool))),X2),X1))
| ~ finite_finite1(X0,X1) )
| ~ spl18_84
| ~ spl18_112 ),
inference(superposition,[],[f1177,f1792]) ).
tff(f1177,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) )
| ~ spl18_84 ),
inference(avatar_component_clause,[],[f1176]) ).
tff(f15779,plain,
( spl18_387
| ~ spl18_80
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1850,f1791,f1124,f15777]) ).
tff(f15777,plain,
( spl18_387
<=> ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_387])]) ).
tff(f1850,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),fun(X0,bool)),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),bool)),combs(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X2),X1))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),X2,X1)) )
| ~ spl18_80
| ~ spl18_112 ),
inference(superposition,[],[f1125,f1792]) ).
tff(f15647,plain,
( spl18_386
| ~ spl18_28
| ~ spl18_121 ),
inference(avatar_split_clause,[],[f2023,f2014,f776,f15645]) ).
tff(f15645,plain,
( spl18_386
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,list(X1)),X4: X0,X3: fun(X0,list(X1))] :
( ( aa(X0,list(X1),aa(fun(X0,list(X1)),fun(X0,list(X1)),aa(fun(X0,list(X1)),fun(fun(X0,list(X1)),fun(X0,list(X1))),minus_minus(fun(X0,list(X1))),X2),X3),X4) = aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),minus_minus(list(X1)),aa(X0,list(X1),X2,X4)),aa(X0,list(X1),X3,X4)) )
| ~ cl_Groups_Ominus(X1)
| ~ zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_386])]) ).
tff(f776,plain,
( spl18_28
<=> ! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
tff(f2023,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,list(X1)),X3: fun(X0,list(X1)),X4: X0] :
( ( aa(X0,list(X1),aa(fun(X0,list(X1)),fun(X0,list(X1)),aa(fun(X0,list(X1)),fun(fun(X0,list(X1)),fun(X0,list(X1))),minus_minus(fun(X0,list(X1))),X2),X3),X4) = aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),minus_minus(list(X1)),aa(X0,list(X1),X2,X4)),aa(X0,list(X1),X3,X4)) )
| ~ cl_Groups_Ominus(X1)
| ~ zero(X1) )
| ~ spl18_28
| ~ spl18_121 ),
inference(resolution,[],[f2015,f777]) ).
tff(f777,plain,
( ! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) )
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f776]) ).
tff(f15643,plain,
( spl18_385
| ~ spl18_107
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1857,f1791,f1684,f15641]) ).
tff(f15641,plain,
( spl18_385
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: fun(X1,X0),X2: X1] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) != aa(X1,product_prod(X1,X0),aa(fun(X1,X0),fun(X1,product_prod(X1,X0)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(fun(X1,X0),fun(X1,product_prod(X1,X0))),combs(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X3),X2) )
| ( aa(X1,X0,X3,X2) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_385])]) ).
tff(f1684,plain,
( spl18_107
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: X0,X2: X1] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).
tff(f1857,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: X1,X5: X0] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) != aa(X1,product_prod(X1,X0),aa(fun(X1,X0),fun(X1,product_prod(X1,X0)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(fun(X1,X0),fun(X1,product_prod(X1,X0))),combs(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X3),X2) )
| ( aa(X1,X0,X3,X2) = X5 ) )
| ~ spl18_107
| ~ spl18_112 ),
inference(superposition,[],[f1685,f1792]) ).
tff(f1685,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) )
| ( X2 = X4 ) )
| ~ spl18_107 ),
inference(avatar_component_clause,[],[f1684]) ).
tff(f15639,plain,
( spl18_384
| ~ spl18_108
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1776,f1753,f1690,f15637]) ).
tff(f15637,plain,
( spl18_384
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),X2))
| ~ preorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_384])]) ).
tff(f1776,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),X2))
| ~ preorder(fun(X0,bool)) )
| ~ spl18_108
| ~ spl18_111 ),
inference(resolution,[],[f1754,f1691]) ).
tff(f15635,plain,
( spl18_383
| ~ spl18_75
| ~ spl18_99 ),
inference(avatar_split_clause,[],[f1581,f1568,f1089,f15633]) ).
tff(f15633,plain,
( spl18_383
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),X1,sK13(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1)) )
| ( aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_383])]) ).
tff(f1581,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),X1,sK13(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1)) )
| ( aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)) = X1 ) )
| ~ spl18_75
| ~ spl18_99 ),
inference(superposition,[],[f1090,f1569]) ).
tff(f15631,plain,
( spl18_382
| ~ spl18_75
| ~ spl18_99 ),
inference(avatar_split_clause,[],[f1580,f1568,f1089,f15629]) ).
tff(f15629,plain,
( spl18_382
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),X1,sK13(fun(X0,bool),fun(X0,bool),X1,aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)))) )
| ( aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_382])]) ).
tff(f1580,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),X1,sK13(fun(X0,bool),fun(X0,bool),X1,aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)))) )
| ( aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)) = X1 ) )
| ~ spl18_75
| ~ spl18_99 ),
inference(superposition,[],[f1090,f1569]) ).
tff(f15509,plain,
( spl18_381
| ~ spl18_86
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1930,f1915,f1187,f15507]) ).
tff(f15507,plain,
( spl18_381
<=> ! [X0: $tType,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),ord_less_eq(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK15(X0,X0,X1,ord_less_eq(X0))),sK14(X0,X0,X1,ord_less_eq(X0))))
| ( sK14(X0,X0,X1,ord_less_eq(X0)) = sK15(X0,X0,X1,ord_less_eq(X0)) )
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_381])]) ).
tff(f1930,plain,
( ! [X0: $tType,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),ord_less_eq(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK15(X0,X0,X1,ord_less_eq(X0))),sK14(X0,X0,X1,ord_less_eq(X0))))
| ( sK14(X0,X0,X1,ord_less_eq(X0)) = sK15(X0,X0,X1,ord_less_eq(X0)) )
| ~ order(X0) )
| ~ spl18_86
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1188]) ).
tff(f15505,plain,
( spl18_380
| ~ spl18_108
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1929,f1915,f1690,f15503]) ).
tff(f15503,plain,
( spl18_380
<=> ! [X0: $tType,X2: X0,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),ord_less_eq(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK15(X0,X0,X1,ord_less_eq(X0))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK14(X0,X0,X1,ord_less_eq(X0))),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_380])]) ).
tff(f1929,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),ord_less_eq(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK15(X0,X0,X1,ord_less_eq(X0))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK14(X0,X0,X1,ord_less_eq(X0))),X2))
| ~ preorder(X0) )
| ~ spl18_108
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1691]) ).
tff(f15501,plain,
( spl18_41
| ~ spl18_379
| ~ spl18_176 ),
inference(avatar_split_clause,[],[f13822,f4253,f15498,f841]) ).
tff(f841,plain,
( spl18_41
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).
tff(f15498,plain,
( spl18_379
<=> ( fTrue = sK5(bool,fNot) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_379])]) ).
tff(f4253,plain,
( spl18_176
<=> ! [X0: bool] :
( ( sK5(bool,fNot) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_176])]) ).
tff(f13822,plain,
( ! [X0: bool] :
( ( fTrue != sK5(bool,fNot) )
| ( fTrue = X0 ) )
| ~ spl18_176 ),
inference(equality_factoring,[],[f4254]) ).
tff(f4254,plain,
( ! [X0: bool] :
( ( sK5(bool,fNot) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_176 ),
inference(avatar_component_clause,[],[f4253]) ).
tff(f15416,plain,
( spl18_378
| ~ spl18_63
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1608,f1599,f984,f15414]) ).
tff(f15414,plain,
( spl18_378
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_378])]) ).
tff(f1608,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_101 ),
inference(resolution,[],[f1600,f985]) ).
tff(f15412,plain,
( spl18_377
| ~ spl18_62
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1607,f1599,f980,f15410]) ).
tff(f15410,plain,
( spl18_377
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_377])]) ).
tff(f1607,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))))
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)))
| ~ linorder(X0)
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_101 ),
inference(resolution,[],[f1600,f981]) ).
tff(f15131,plain,
( ~ spl18_14
| spl18_376
| ~ spl18_104
| ~ spl18_110
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f2435,f2384,f1749,f1624,f15129,f712]) ).
tff(f712,plain,
( spl18_14
<=> ord(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
tff(f15129,plain,
( spl18_376
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)),aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_376])]) ).
tff(f2435,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)),aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ ord(bool) )
| ~ spl18_104
| ~ spl18_110
| ~ spl18_143 ),
inference(forward_demodulation,[],[f2434,f1625]) ).
tff(f2434,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1),X3)),aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ ord(bool) )
| ~ spl18_104
| ~ spl18_110
| ~ spl18_143 ),
inference(forward_demodulation,[],[f2419,f1625]) ).
tff(f2419,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1),X3)),aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2),X3)))
| ~ ord(bool) )
| ~ spl18_110
| ~ spl18_143 ),
inference(resolution,[],[f2385,f1750]) ).
tff(f15127,plain,
( spl18_375
| ~ spl18_63
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1674,f1628,f984,f15125]) ).
tff(f15125,plain,
( spl18_375
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: fun(X1,bool)] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK6(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)))))
| ( combk(bool,X0,fFalse) = aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_375])]) ).
tff(f1674,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1)] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK6(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)))))
| ( combk(bool,X0,fFalse) = aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3) ) )
| ~ spl18_63
| ~ spl18_105 ),
inference(superposition,[],[f985,f1629]) ).
tff(f15123,plain,
( spl18_374
| ~ spl18_62
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1673,f1628,f980,f15121]) ).
tff(f15121,plain,
( spl18_374
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: fun(X1,bool)] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK5(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)))))
| ( combk(bool,X0,fFalse) = aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_374])]) ).
tff(f1673,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,X1)] :
( pp(aa(X1,bool,X2,aa(X0,X1,X3,sK5(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)))))
| ( combk(bool,X0,fFalse) = aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3) ) )
| ~ spl18_62
| ~ spl18_105 ),
inference(superposition,[],[f981,f1629]) ).
tff(f14356,plain,
( spl18_373
| ~ spl18_106
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1859,f1791,f1680,f14354]) ).
tff(f14354,plain,
( spl18_373
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: fun(X1,X0),X2: X1] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) != aa(X1,product_prod(X1,X0),aa(fun(X1,X0),fun(X1,product_prod(X1,X0)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(fun(X1,X0),fun(X1,product_prod(X1,X0))),combs(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X3),X2) )
| ( X2 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_373])]) ).
tff(f1680,plain,
( spl18_106
<=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).
tff(f1859,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: X1,X5: X0] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) != aa(X1,product_prod(X1,X0),aa(fun(X1,X0),fun(X1,product_prod(X1,X0)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(fun(X1,X0),fun(X1,product_prod(X1,X0))),combs(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X3),X2) )
| ( X2 = X4 ) )
| ~ spl18_106
| ~ spl18_112 ),
inference(superposition,[],[f1681,f1792]) ).
tff(f1681,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) )
| ( X3 = X5 ) )
| ~ spl18_106 ),
inference(avatar_component_clause,[],[f1680]) ).
tff(f14352,plain,
( spl18_372
| ~ spl18_63
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1764,f1749,f984,f14350]) ).
tff(f14350,plain,
( spl18_372
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,sK6(fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2)),X3)))
| ~ ord(X0)
| ( aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2) = combk(bool,fun(X1,X0),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_372])]) ).
tff(f1764,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,sK6(fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2)),X3)))
| ~ ord(X0)
| ( aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2) = combk(bool,fun(X1,X0),fFalse) ) )
| ~ spl18_63
| ~ spl18_110 ),
inference(resolution,[],[f1750,f985]) ).
tff(f14348,plain,
( spl18_371
| ~ spl18_62
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1763,f1749,f980,f14346]) ).
tff(f14346,plain,
( spl18_371
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,sK5(fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2)),X3)))
| ~ ord(X0)
| ( aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2) = combk(bool,fun(X1,X0),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_371])]) ).
tff(f1763,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,sK5(fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2)),X3)))
| ~ ord(X0)
| ( aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X2) = combk(bool,fun(X1,X0),fFalse) ) )
| ~ spl18_62
| ~ spl18_110 ),
inference(resolution,[],[f1750,f981]) ).
tff(f13476,plain,
( spl18_370
| ~ spl18_137
| ~ spl18_359
| ~ spl18_366 ),
inference(avatar_split_clause,[],[f13458,f13455,f12672,f2321,f13474]) ).
tff(f13474,plain,
( spl18_370
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ( aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) = combk(bool,X0,fTrue) )
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK5(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_370])]) ).
tff(f2321,plain,
( spl18_137
<=> ( fTrue = aa(bool,bool,fNot,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_137])]) ).
tff(f12672,plain,
( spl18_359
<=> ! [X0: bool] : ( fFalse = aa(bool,bool,fNot,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_359])]) ).
tff(f13455,plain,
( spl18_366
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK5(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_366])]) ).
tff(f13458,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1] :
( ( aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) = combk(bool,X0,fTrue) )
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK5(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3)) )
| ~ spl18_137
| ~ spl18_359
| ~ spl18_366 ),
inference(forward_demodulation,[],[f13456,f13227]) ).
tff(f13227,plain,
( ( fFalse = fTrue )
| ~ spl18_137
| ~ spl18_359 ),
inference(superposition,[],[f12673,f2323]) ).
tff(f2323,plain,
( ( fTrue = aa(bool,bool,fNot,fFalse) )
| ~ spl18_137 ),
inference(avatar_component_clause,[],[f2321]) ).
tff(f12673,plain,
( ! [X0: bool] : ( fFalse = aa(bool,bool,fNot,X0) )
| ~ spl18_359 ),
inference(avatar_component_clause,[],[f12672]) ).
tff(f13456,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK5(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) ) )
| ~ spl18_366 ),
inference(avatar_component_clause,[],[f13455]) ).
tff(f13471,plain,
( spl18_369
| ~ spl18_35
| ~ spl18_99
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1862,f1791,f1568,f809,f13469]) ).
tff(f13469,plain,
( spl18_369
<=> ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( fFalse = aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_369])]) ).
tff(f1862,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( fFalse = aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X2),X1) )
| ~ spl18_35
| ~ spl18_99
| ~ spl18_112 ),
inference(forward_demodulation,[],[f1802,f810]) ).
tff(f1802,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( aa(X0,bool,combk(bool,X0,fFalse),aa(fun(X0,bool),X0,X2,X1)) = aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X2),X1) )
| ~ spl18_99
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1569]) ).
tff(f13467,plain,
( spl18_368
| ~ spl18_108
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1833,f1791,f1690,f13465]) ).
tff(f13465,plain,
( spl18_368
<=> ! [X0: $tType,X3: X0,X2: fun(X0,X0),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),ord_less_eq(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X0,X0,X2,X1)),X3))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_368])]) ).
tff(f1833,plain,
( ! [X0: $tType,X2: fun(X0,X0),X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),ord_less_eq(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X0,X0,X2,X1)),X3))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ preorder(X0) )
| ~ spl18_108
| ~ spl18_112 ),
inference(superposition,[],[f1691,f1792]) ).
tff(f13462,plain,
( spl18_367
| ~ spl18_63
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1660,f1624,f984,f13460]) ).
tff(f13460,plain,
( spl18_367
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK6(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_367])]) ).
tff(f1660,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK6(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) ) )
| ~ spl18_63
| ~ spl18_104 ),
inference(superposition,[],[f985,f1625]) ).
tff(f13457,plain,
( spl18_366
| ~ spl18_62
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1659,f1624,f980,f13455]) ).
tff(f1659,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK5(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))),X3))
| ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3) ) )
| ~ spl18_62
| ~ spl18_104 ),
inference(superposition,[],[f981,f1625]) ).
tff(f13408,plain,
( spl18_365
| ~ spl18_71
| ~ spl18_140 ),
inference(avatar_split_clause,[],[f2361,f2337,f1061,f13406]) ).
tff(f13406,plain,
( spl18_365
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_365])]) ).
tff(f2361,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2),X1)) )
| ~ spl18_71
| ~ spl18_140 ),
inference(resolution,[],[f2338,f1062]) ).
tff(f13324,plain,
( spl18_364
| ~ spl18_86
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1924,f1915,f1187,f13322]) ).
tff(f13322,plain,
( spl18_364
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),X2))
| ( X2 = X3 )
| ~ order(fun(X0,fun(X1,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_364])]) ).
tff(f1924,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),X2))
| ( X2 = X3 )
| ~ order(fun(X0,fun(X1,bool))) )
| ~ spl18_86
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1188]) ).
tff(f12879,plain,
( spl18_363
| ~ spl18_35
| ~ spl18_89
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1861,f1791,f1212,f809,f12877]) ).
tff(f12877,plain,
( spl18_363
<=> ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( fFalse = aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_363])]) ).
tff(f1861,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( fFalse = aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1)),X2),X1) )
| ~ spl18_35
| ~ spl18_89
| ~ spl18_112 ),
inference(forward_demodulation,[],[f1801,f810]) ).
tff(f1801,plain,
( ! [X0: $tType,X2: fun(fun(X0,bool),X0),X1: fun(X0,bool)] : ( aa(fun(X0,bool),bool,aa(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),X0),fun(fun(X0,bool),bool)),combs(fun(X0,bool),X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1)),X2),X1) = aa(X0,bool,combk(bool,X0,fFalse),aa(fun(X0,bool),X0,X2,X1)) )
| ~ spl18_89
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1213]) ).
tff(f12875,plain,
( spl18_362
| ~ spl18_104
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1825,f1791,f1624,f12873]) ).
tff(f12873,plain,
( spl18_362
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(X0,fun(X2,X1),X3,aa(X2,X0,X5,X4)),X4) = 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),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3)),X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_362])]) ).
tff(f1825,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,fun(X2,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,aa(X0,fun(X2,X1),X3,aa(X2,X0,X5,X4)),X4) = 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),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3)),X5),X4) )
| ~ spl18_104
| ~ spl18_112 ),
inference(superposition,[],[f1792,f1625]) ).
tff(f12704,plain,
( spl18_361
| ~ spl18_83
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f2183,f2174,f1156,f12702]) ).
tff(f12702,plain,
( spl18_361
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ linorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_361])]) ).
tff(f2183,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ linorder(fun(X0,bool)) )
| ~ spl18_83
| ~ spl18_128 ),
inference(resolution,[],[f2175,f1157]) ).
tff(f12700,plain,
( spl18_360
| ~ spl18_83
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2161,f2128,f1156,f12698]) ).
tff(f12698,plain,
( spl18_360
<=> ! [X1: $tType,X0: $tType,X5: fun(X1,fun(X0,bool)),X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,X3),X4))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2),X5))
| ~ linorder(fun(X1,fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_360])]) ).
tff(f2161,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0,X5: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,X3),X4))
| pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2),X5))
| ~ linorder(fun(X1,fun(X0,bool))) )
| ~ spl18_83
| ~ spl18_126 ),
inference(resolution,[],[f2129,f1157]) ).
tff(f12674,plain,
( spl18_359
| ~ spl18_35
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f5951,f4210,f809,f12672]) ).
tff(f4210,plain,
( spl18_171
<=> ( fNot = combk(bool,bool,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_171])]) ).
tff(f5951,plain,
( ! [X0: bool] : ( fFalse = aa(bool,bool,fNot,X0) )
| ~ spl18_35
| ~ spl18_171 ),
inference(superposition,[],[f810,f4212]) ).
tff(f4212,plain,
( ( fNot = combk(bool,bool,fFalse) )
| ~ spl18_171 ),
inference(avatar_component_clause,[],[f4210]) ).
tff(f12563,plain,
( ~ spl18_5
| spl18_357
| spl18_358
| ~ spl18_85
| ~ spl18_158 ),
inference(avatar_split_clause,[],[f2685,f2678,f1180,f12561,f12557,f667]) ).
tff(f667,plain,
( spl18_5
<=> group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
tff(f12561,plain,
( spl18_358
<=> ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_358])]) ).
tff(f1180,plain,
( spl18_85
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0] :
( ( X3 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X2) )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).
tff(f2685,plain,
( ! [X0: int] :
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) )
| ( li = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs) )
| ~ group_add(int) )
| ~ spl18_85
| ~ spl18_158 ),
inference(superposition,[],[f1181,f2680]) ).
tff(f1181,plain,
( ! [X0: $tType,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X2) )
| ( X3 = X4 )
| ~ group_add(X0) )
| ~ spl18_85 ),
inference(avatar_component_clause,[],[f1180]) ).
tff(f12555,plain,
( spl18_356
| ~ spl18_52
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f2219,f2202,f902,f12552]) ).
tff(f12552,plain,
( spl18_356
<=> pp(aa(fun(fun(product_prod(int,list(int)),bool),bool),bool,fEx(fun(product_prod(int,list(int)),bool)),aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_356])]) ).
tff(f2202,plain,
( spl18_130
<=> pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_130])]) ).
tff(f2219,plain,
( pp(aa(fun(fun(product_prod(int,list(int)),bool),bool),bool,fEx(fun(product_prod(int,list(int)),bool)),aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1))))
| ~ spl18_52
| ~ spl18_130 ),
inference(resolution,[],[f2204,f903]) ).
tff(f2204,plain,
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as))))
| ~ spl18_130 ),
inference(avatar_component_clause,[],[f2202]) ).
tff(f12550,plain,
( spl18_355
| ~ spl18_52
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f2209,f2197,f902,f12547]) ).
tff(f12547,plain,
( spl18_355
<=> pp(aa(fun(fun(product_prod(int,list(int)),bool),bool),bool,fEx(fun(product_prod(int,list(int)),bool)),aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_355])]) ).
tff(f2209,plain,
( pp(aa(fun(fun(product_prod(int,list(int)),bool),bool),bool,fEx(fun(product_prod(int,list(int)),bool)),aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks))))
| ~ spl18_52
| ~ spl18_129 ),
inference(resolution,[],[f2199,f903]) ).
tff(f12532,plain,
( spl18_354
| ~ spl18_18
| ~ spl18_30
| ~ spl18_70
| ~ spl18_89
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2155,f2124,f1212,f1053,f784,f732,f12530]) ).
tff(f12530,plain,
( spl18_354
<=> ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) )
| ~ ordered_ab_group_add(fun(X0,bool))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_354])]) ).
tff(f732,plain,
( spl18_18
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
tff(f1053,plain,
( spl18_70
<=> ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).
tff(f2155,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool)] :
( ~ pp(fTrue)
| ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_30
| ~ spl18_70
| ~ spl18_89
| ~ spl18_125 ),
inference(forward_demodulation,[],[f2150,f1058]) ).
tff(f1058,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( fTrue = aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1) )
| ~ spl18_30
| ~ spl18_70 ),
inference(resolution,[],[f1054,f785]) ).
tff(f1054,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1))
| ~ spl18_70 ),
inference(avatar_component_clause,[],[f1053]) ).
tff(f2150,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ ordered_ab_group_add(fun(X0,bool)) )
| ~ spl18_89
| ~ spl18_125 ),
inference(superposition,[],[f2125,f1213]) ).
tff(f12528,plain,
( spl18_353
| ~ spl18_72
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1978,f1919,f1066,f12526]) ).
tff(f12526,plain,
( spl18_353
<=> ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),X1),member(X0)))
| ~ pp(aa(X0,bool,sK15(fun(X0,bool),X0,member(X0),X1),sK14(fun(X0,bool),X0,member(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_353])]) ).
tff(f1978,plain,
( ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),X1),member(X0)))
| ~ pp(aa(X0,bool,sK15(fun(X0,bool),X0,member(X0),X1),sK14(fun(X0,bool),X0,member(X0),X1))) )
| ~ spl18_72
| ~ spl18_118 ),
inference(resolution,[],[f1920,f1067]) ).
tff(f12517,plain,
( spl18_352
| ~ spl18_71
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1938,f1915,f1061,f12515]) ).
tff(f12515,plain,
( spl18_352
<=> ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| pp(aa(X0,bool,sK15(fun(X0,bool),X0,X1,member(X0)),sK14(fun(X0,bool),X0,X1,member(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_352])]) ).
tff(f1938,plain,
( ! [X0: $tType,X1: fun(X0,fun(fun(X0,bool),bool))] :
( pp(aa(fun(X0,fun(fun(X0,bool),bool)),bool,aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(fun(X0,bool),bool)),bool),ord_less_eq(fun(X0,fun(fun(X0,bool),bool))),member(X0)),X1))
| pp(aa(X0,bool,sK15(fun(X0,bool),X0,X1,member(X0)),sK14(fun(X0,bool),X0,X1,member(X0)))) )
| ~ spl18_71
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1062]) ).
tff(f12513,plain,
( spl18_351
| ~ spl18_86
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1834,f1791,f1187,f12511]) ).
tff(f12511,plain,
( spl18_351
<=> ! [X0: $tType,X2: fun(X0,X0),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),ord_less_eq(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X0,X0,X2,X1)),X1))
| ( aa(X0,X0,X2,X1) = X1 )
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_351])]) ).
tff(f1834,plain,
( ! [X0: $tType,X2: fun(X0,X0),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),ord_less_eq(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X0,X0,X2,X1)),X1))
| ( aa(X0,X0,X2,X1) = X1 )
| ~ order(X0) )
| ~ spl18_86
| ~ spl18_112 ),
inference(superposition,[],[f1188,f1792]) ).
tff(f12275,plain,
( spl18_350
| spl18_1
| ~ spl18_35
| ~ spl18_99
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1971,f1915,f1568,f809,f647,f12273]) ).
tff(f12273,plain,
( spl18_350
<=> ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] : pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_350])]) ).
tff(f1971,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( pp(fFalse)
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X1)) )
| ~ spl18_35
| ~ spl18_99
| ~ spl18_117 ),
inference(forward_demodulation,[],[f1955,f810]) ).
tff(f1955,plain,
( ! [X0: $tType,X1: fun(fun(X0,bool),fun(X0,bool))] :
( pp(aa(X0,bool,combk(bool,X0,fFalse),sK15(X0,fun(X0,bool),X1,aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)))))
| pp(aa(fun(fun(X0,bool),fun(X0,bool)),bool,aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(fun(X0,bool),fun(X0,bool)),bool),ord_less_eq(fun(fun(X0,bool),fun(X0,bool))),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse))),X1)) )
| ~ spl18_99
| ~ spl18_117 ),
inference(superposition,[],[f1916,f1569]) ).
tff(f12271,plain,
( spl18_349
| ~ spl18_110
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1922,f1915,f1749,f12269]) ).
tff(f12269,plain,
( spl18_349
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,fun(X1,bool)),X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),X2,X4)),aa(X0,fun(X1,bool),X3,X4)))
| ~ ord(fun(X1,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_349])]) ).
tff(f1922,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X0,fun(X1,bool)),X4: X0] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,X3,X2)),sK15(X1,X0,X3,X2)))
| pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),aa(X0,fun(X1,bool),X2,X4)),aa(X0,fun(X1,bool),X3,X4)))
| ~ ord(fun(X1,bool)) )
| ~ spl18_110
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1750]) ).
tff(f12267,plain,
( spl18_348
| ~ spl18_109
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1892,f1864,f1731,f12265]) ).
tff(f12265,plain,
( spl18_348
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| ( big_linorder_Max(X0,X2) = sK2(X0,X1,X2) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK2(X0,X1,X2),X2)),sK2(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_348])]) ).
tff(f1892,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| ( big_linorder_Max(X0,X2) = sK2(X0,X1,X2) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK2(X0,X1,X2),X2)),sK2(X0,X1,X2))) )
| ~ spl18_109
| ~ spl18_113 ),
inference(duplicate_literal_removal,[],[f1876]) ).
tff(f1876,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| ( big_linorder_Max(X0,X2) = sK2(X0,X1,X2) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK2(X0,X1,X2),X2)),sK2(X0,X1,X2)))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) )
| ~ spl18_109
| ~ spl18_113 ),
inference(resolution,[],[f1865,f1732]) ).
tff(f12263,plain,
( ~ spl18_345
| spl18_346
| spl18_347
| ~ spl18_22
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f2140,f2124,f749,f12261,f12258,f12254]) ).
tff(f12254,plain,
( spl18_345
<=> ordered_ab_group_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_345])]) ).
tff(f12258,plain,
( spl18_346
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),X0),X1))
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_346])]) ).
tff(f12261,plain,
( spl18_347
<=> ! [X2: bool,X3: bool] :
( ( fFalse != aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X2),X3) )
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_347])]) ).
tff(f2140,plain,
( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
( ( fFalse != aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X2),X3) )
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),X2),X3))
| pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),X0),X1))
| ~ ordered_ab_group_add(bool)
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) )
| ~ spl18_22
| ~ spl18_125 ),
inference(superposition,[],[f2125,f750]) ).
tff(f12104,plain,
( ~ spl18_14
| spl18_344
| ~ spl18_22
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2112,f2048,f749,f12102,f712]) ).
tff(f12102,plain,
( spl18_344
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X2,sK4(bool,X0,X1,X2))),fFalse))
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X1,X2)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_344])]) ).
tff(f2112,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X2,sK4(bool,X0,X1,X2))),fFalse))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ ord(bool)
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X1,X2)) ) )
| ~ spl18_22
| ~ spl18_124 ),
inference(superposition,[],[f2049,f750]) ).
tff(f12049,plain,
( spl18_343
| ~ spl18_18
| ~ spl18_30
| ~ spl18_202
| ~ spl18_342 ),
inference(avatar_split_clause,[],[f12045,f12042,f6065,f784,f732,f12047]) ).
tff(f12047,plain,
( spl18_343
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_343])]) ).
tff(f6065,plain,
( spl18_202
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] : pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_202])]) ).
tff(f12042,plain,
( spl18_342
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK4(bool,X0,X2,X1))))
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_342])]) ).
tff(f12045,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(fTrue)
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ spl18_30
| ~ spl18_202
| ~ spl18_342 ),
inference(forward_demodulation,[],[f12043,f6071]) ).
tff(f6071,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] : ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X1,X2)) )
| ~ spl18_30
| ~ spl18_202 ),
inference(resolution,[],[f6066,f785]) ).
tff(f6066,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] : pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,X1)))
| ~ spl18_202 ),
inference(avatar_component_clause,[],[f6065]) ).
tff(f12043,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK4(bool,X0,X2,X1))))
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ spl18_342 ),
inference(avatar_component_clause,[],[f12042]) ).
tff(f12044,plain,
( ~ spl18_14
| spl18_342
| ~ spl18_22
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2098,f2048,f749,f12042,f712]) ).
tff(f2098,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK4(bool,X0,X2,X1))))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ ord(bool)
| ( fTrue = aa(X0,bool,X1,sK4(bool,X0,X2,X1)) ) )
| ~ spl18_22
| ~ spl18_124 ),
inference(superposition,[],[f2049,f750]) ).
tff(f11992,plain,
( ~ spl18_14
| spl18_341
| ~ spl18_22
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2076,f2044,f749,f11990,f712]) ).
tff(f11990,plain,
( spl18_341
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X2,sK3(bool,X0,X1,X2))),fFalse))
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X1,X2)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_341])]) ).
tff(f2076,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X2,sK3(bool,X0,X1,X2))),fFalse))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ ord(bool)
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X1,X2)) ) )
| ~ spl18_22
| ~ spl18_123 ),
inference(superposition,[],[f2045,f750]) ).
tff(f11937,plain,
( spl18_340
| ~ spl18_18
| ~ spl18_30
| ~ spl18_202
| ~ spl18_338 ),
inference(avatar_split_clause,[],[f11925,f11922,f6065,f784,f732,f11935]) ).
tff(f11935,plain,
( spl18_340
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_340])]) ).
tff(f11922,plain,
( spl18_338
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK3(bool,X0,X2,X1))))
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_338])]) ).
tff(f11925,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(fTrue)
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ spl18_30
| ~ spl18_202
| ~ spl18_338 ),
inference(forward_demodulation,[],[f11923,f6071]) ).
tff(f11923,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK3(bool,X0,X2,X1))))
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X2,X1)) )
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ spl18_338 ),
inference(avatar_component_clause,[],[f11922]) ).
tff(f11930,plain,
( spl18_339
| ~ spl18_30
| ~ spl18_172 ),
inference(avatar_split_clause,[],[f6434,f4228,f784,f11927]) ).
tff(f11927,plain,
( spl18_339
<=> ( fTrue = sK6(bool,fNot) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_339])]) ).
tff(f4228,plain,
( spl18_172
<=> pp(sK6(bool,fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_172])]) ).
tff(f6434,plain,
( ( fTrue = sK6(bool,fNot) )
| ~ spl18_30
| ~ spl18_172 ),
inference(resolution,[],[f4229,f785]) ).
tff(f4229,plain,
( pp(sK6(bool,fNot))
| ~ spl18_172 ),
inference(avatar_component_clause,[],[f4228]) ).
tff(f11924,plain,
( ~ spl18_14
| spl18_338
| ~ spl18_22
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2062,f2044,f749,f11922,f712]) ).
tff(f2062,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,sK3(bool,X0,X2,X1))))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ ord(bool)
| ( fTrue = aa(X0,bool,X1,sK3(bool,X0,X2,X1)) ) )
| ~ spl18_22
| ~ spl18_123 ),
inference(superposition,[],[f2045,f750]) ).
tff(f11920,plain,
( spl18_337
| ~ spl18_83
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f2031,f2018,f1156,f11918]) ).
tff(f11918,plain,
( spl18_337
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_337])]) ).
tff(f2031,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X1)),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ( combk(bool,X0,fFalse) = X1 )
| ~ linorder(X0)
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(fun(X0,bool)) )
| ~ spl18_83
| ~ spl18_122 ),
inference(resolution,[],[f2019,f1157]) ).
tff(f11720,plain,
( spl18_336
| ~ spl18_83
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2089,f2048,f1156,f11718]) ).
tff(f11718,plain,
( spl18_336
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1)
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK4(X1,X0,X3,X2))),aa(X0,X1,X2,sK4(X1,X0,X3,X2))))
| ~ linorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_336])]) ).
tff(f2089,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1)
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK4(X1,X0,X3,X2))),aa(X0,X1,X2,sK4(X1,X0,X3,X2))))
| ~ linorder(X1) )
| ~ spl18_83
| ~ spl18_124 ),
inference(resolution,[],[f2049,f1157]) ).
tff(f11672,plain,
( spl18_1
| ~ spl18_172
| ~ spl18_217 ),
inference(avatar_split_clause,[],[f11671,f6430,f4228,f647]) ).
tff(f6430,plain,
( spl18_217
<=> ( fFalse = sK6(bool,fNot) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_217])]) ).
tff(f11671,plain,
( pp(fFalse)
| ~ spl18_172
| ~ spl18_217 ),
inference(forward_demodulation,[],[f4229,f6432]) ).
tff(f6432,plain,
( ( fFalse = sK6(bool,fNot) )
| ~ spl18_217 ),
inference(avatar_component_clause,[],[f6430]) ).
tff(f11667,plain,
( spl18_335
| ~ spl18_103
| spl18_172 ),
inference(avatar_split_clause,[],[f4232,f4228,f1620,f11665]) ).
tff(f11665,plain,
( spl18_335
<=> ! [X0: bool] :
( ( sK6(bool,fNot) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_335])]) ).
tff(f1620,plain,
( spl18_103
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).
tff(f4232,plain,
( ! [X0: bool] :
( ( sK6(bool,fNot) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_103
| spl18_172 ),
inference(resolution,[],[f4230,f1621]) ).
tff(f1621,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl18_103 ),
inference(avatar_component_clause,[],[f1620]) ).
tff(f4230,plain,
( ~ pp(sK6(bool,fNot))
| spl18_172 ),
inference(avatar_component_clause,[],[f4228]) ).
tff(f11663,plain,
( spl18_334
| ~ spl18_83
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2053,f2044,f1156,f11661]) ).
tff(f11661,plain,
( spl18_334
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1)
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK3(X1,X0,X3,X2))),aa(X0,X1,X2,sK3(X1,X0,X3,X2))))
| ~ linorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_334])]) ).
tff(f2053,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1)
| pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK3(X1,X0,X3,X2))),aa(X0,X1,X2,sK3(X1,X0,X3,X2))))
| ~ linorder(X1) )
| ~ spl18_83
| ~ spl18_123 ),
inference(resolution,[],[f2045,f1157]) ).
tff(f11659,plain,
( spl18_333
| ~ spl18_63
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f1553,f1542,f984,f11657]) ).
tff(f11657,plain,
( spl18_333
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_333])]) ).
tff(f1553,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_97 ),
inference(resolution,[],[f1543,f985]) ).
tff(f11655,plain,
( spl18_332
| ~ spl18_62
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f1552,f1542,f980,f11653]) ).
tff(f11653,plain,
( spl18_332
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_332])]) ).
tff(f1552,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_97 ),
inference(resolution,[],[f1543,f981]) ).
tff(f11625,plain,
( spl18_331
| ~ spl18_85
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1829,f1791,f1180,f11623]) ).
tff(f11623,plain,
( spl18_331
<=> ! [X0: $tType,X3: X0,X2: fun(X0,X0),X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X3) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ( aa(X0,X0,X2,X1) = X1 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_331])]) ).
tff(f1829,plain,
( ! [X0: $tType,X2: fun(X0,X0),X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X3) != aa(X0,X0,aa(fun(X0,X0),fun(X0,X0),aa(fun(X0,fun(X0,X0)),fun(fun(X0,X0),fun(X0,X0)),combs(X0,X0,X0),minus_minus(X0)),X2),X1) )
| ( aa(X0,X0,X2,X1) = X1 )
| ~ group_add(X0) )
| ~ spl18_85
| ~ spl18_112 ),
inference(superposition,[],[f1181,f1792]) ).
tff(f11063,plain,
( spl18_330
| ~ spl18_22
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1994,f1919,f749,f11061]) ).
tff(f11061,plain,
( spl18_330
<=> ! [X0: $tType,X2: fun(X0,fun(bool,bool)),X1: fun(X0,fun(bool,bool))] :
( ~ pp(aa(bool,bool,aa(X0,fun(bool,bool),X1,sK14(bool,X0,X1,X2)),fFalse))
| pp(aa(fun(X0,fun(bool,bool)),bool,aa(fun(X0,fun(bool,bool)),fun(fun(X0,fun(bool,bool)),bool),ord_less_eq(fun(X0,fun(bool,bool))),X2),X1))
| ( fTrue = sK15(bool,X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_330])]) ).
tff(f1994,plain,
( ! [X0: $tType,X2: fun(X0,fun(bool,bool)),X1: fun(X0,fun(bool,bool))] :
( ~ pp(aa(bool,bool,aa(X0,fun(bool,bool),X1,sK14(bool,X0,X1,X2)),fFalse))
| pp(aa(fun(X0,fun(bool,bool)),bool,aa(fun(X0,fun(bool,bool)),fun(fun(X0,fun(bool,bool)),bool),ord_less_eq(fun(X0,fun(bool,bool))),X2),X1))
| ( fTrue = sK15(bool,X0,X1,X2) ) )
| ~ spl18_22
| ~ spl18_118 ),
inference(superposition,[],[f1920,f750]) ).
tff(f11059,plain,
( spl18_329
| ~ spl18_22
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1985,f1919,f749,f11057]) ).
tff(f11057,plain,
( spl18_329
<=> ! [X0: $tType,X2: fun(bool,fun(X0,bool)),X1: fun(bool,fun(X0,bool))] :
( ~ pp(aa(X0,bool,aa(bool,fun(X0,bool),X1,fFalse),sK15(X0,bool,X1,X2)))
| pp(aa(fun(bool,fun(X0,bool)),bool,aa(fun(bool,fun(X0,bool)),fun(fun(bool,fun(X0,bool)),bool),ord_less_eq(fun(bool,fun(X0,bool))),X2),X1))
| ( fTrue = sK14(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_329])]) ).
tff(f1985,plain,
( ! [X0: $tType,X2: fun(bool,fun(X0,bool)),X1: fun(bool,fun(X0,bool))] :
( ~ pp(aa(X0,bool,aa(bool,fun(X0,bool),X1,fFalse),sK15(X0,bool,X1,X2)))
| pp(aa(fun(bool,fun(X0,bool)),bool,aa(fun(bool,fun(X0,bool)),fun(fun(bool,fun(X0,bool)),bool),ord_less_eq(fun(bool,fun(X0,bool))),X2),X1))
| ( fTrue = sK14(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_118 ),
inference(superposition,[],[f1920,f750]) ).
tff(f11055,plain,
( spl18_328
| ~ spl18_22
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1963,f1915,f749,f11053]) ).
tff(f11053,plain,
( spl18_328
<=> ! [X0: $tType,X2: fun(X0,fun(bool,bool)),X1: fun(X0,fun(bool,bool))] :
( pp(aa(bool,bool,aa(X0,fun(bool,bool),X2,sK14(bool,X0,X1,X2)),fFalse))
| pp(aa(fun(X0,fun(bool,bool)),bool,aa(fun(X0,fun(bool,bool)),fun(fun(X0,fun(bool,bool)),bool),ord_less_eq(fun(X0,fun(bool,bool))),X2),X1))
| ( fTrue = sK15(bool,X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_328])]) ).
tff(f1963,plain,
( ! [X0: $tType,X2: fun(X0,fun(bool,bool)),X1: fun(X0,fun(bool,bool))] :
( pp(aa(bool,bool,aa(X0,fun(bool,bool),X2,sK14(bool,X0,X1,X2)),fFalse))
| pp(aa(fun(X0,fun(bool,bool)),bool,aa(fun(X0,fun(bool,bool)),fun(fun(X0,fun(bool,bool)),bool),ord_less_eq(fun(X0,fun(bool,bool))),X2),X1))
| ( fTrue = sK15(bool,X0,X1,X2) ) )
| ~ spl18_22
| ~ spl18_117 ),
inference(superposition,[],[f1916,f750]) ).
tff(f11051,plain,
( spl18_327
| ~ spl18_22
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1954,f1915,f749,f11049]) ).
tff(f11049,plain,
( spl18_327
<=> ! [X0: $tType,X2: fun(bool,fun(X0,bool)),X1: fun(bool,fun(X0,bool))] :
( pp(aa(X0,bool,aa(bool,fun(X0,bool),X2,fFalse),sK15(X0,bool,X1,X2)))
| pp(aa(fun(bool,fun(X0,bool)),bool,aa(fun(bool,fun(X0,bool)),fun(fun(bool,fun(X0,bool)),bool),ord_less_eq(fun(bool,fun(X0,bool))),X2),X1))
| ( fTrue = sK14(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_327])]) ).
tff(f1954,plain,
( ! [X0: $tType,X2: fun(bool,fun(X0,bool)),X1: fun(bool,fun(X0,bool))] :
( pp(aa(X0,bool,aa(bool,fun(X0,bool),X2,fFalse),sK15(X0,bool,X1,X2)))
| pp(aa(fun(bool,fun(X0,bool)),bool,aa(fun(bool,fun(X0,bool)),fun(fun(bool,fun(X0,bool)),bool),ord_less_eq(fun(bool,fun(X0,bool))),X2),X1))
| ( fTrue = sK14(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_117 ),
inference(superposition,[],[f1916,f750]) ).
tff(f11047,plain,
( spl18_326
| ~ spl18_71
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1848,f1791,f1061,f11045]) ).
tff(f11045,plain,
( spl18_326
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),X2,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_326])]) ).
tff(f1848,plain,
( ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),X2,X1),X1)) )
| ~ spl18_71
| ~ spl18_112 ),
inference(superposition,[],[f1062,f1792]) ).
tff(f11043,plain,
( spl18_325
| ~ spl18_72
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1847,f1791,f1066,f11041]) ).
tff(f11041,plain,
( spl18_325
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),X2,X1),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_325])]) ).
tff(f1847,plain,
( ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: X0] :
( pp(aa(X0,bool,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combs(X0,fun(X0,bool),bool),member(X0)),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),X2,X1),X1)) )
| ~ spl18_72
| ~ spl18_112 ),
inference(superposition,[],[f1067,f1792]) ).
tff(f11039,plain,
( spl18_324
| ~ spl18_63
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1720,f1690,f984,f11037]) ).
tff(f11037,plain,
( spl18_324
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_324])]) ).
tff(f1720,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) )
| ~ spl18_63
| ~ spl18_108 ),
inference(resolution,[],[f1691,f985]) ).
tff(f11027,plain,
( spl18_323
| ~ spl18_62
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1719,f1690,f980,f11025]) ).
tff(f11025,plain,
( spl18_323
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_323])]) ).
tff(f1719,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) )
| ~ spl18_62
| ~ spl18_108 ),
inference(resolution,[],[f1691,f981]) ).
tff(f10797,plain,
( spl18_322
| ~ spl18_22
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2107,f2048,f749,f10795]) ).
tff(f10795,plain,
( spl18_322
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(bool,X0,X2,fFalse)),aa(bool,X0,X1,fFalse)))
| pp(aa(fun(bool,X0),bool,aa(fun(bool,X0),fun(fun(bool,X0),bool),ord_less_eq(fun(bool,X0)),X2),X1))
| ~ ord(X0)
| ( fTrue = sK4(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_322])]) ).
tff(f2107,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(bool,X0,X2,fFalse)),aa(bool,X0,X1,fFalse)))
| pp(aa(fun(bool,X0),bool,aa(fun(bool,X0),fun(fun(bool,X0),bool),ord_less_eq(fun(bool,X0)),X2),X1))
| ~ ord(X0)
| ( fTrue = sK4(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_124 ),
inference(superposition,[],[f2049,f750]) ).
tff(f10793,plain,
( spl18_321
| ~ spl18_22
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2071,f2044,f749,f10791]) ).
tff(f10791,plain,
( spl18_321
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(bool,X0,X2,fFalse)),aa(bool,X0,X1,fFalse)))
| pp(aa(fun(bool,X0),bool,aa(fun(bool,X0),fun(fun(bool,X0),bool),ord_less_eq(fun(bool,X0)),X2),X1))
| ~ ord(X0)
| ( fTrue = sK3(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_321])]) ).
tff(f2071,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(bool,X0,X2,fFalse)),aa(bool,X0,X1,fFalse)))
| pp(aa(fun(bool,X0),bool,aa(fun(bool,X0),fun(fun(bool,X0),bool),ord_less_eq(fun(bool,X0)),X2),X1))
| ~ ord(X0)
| ( fTrue = sK3(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_123 ),
inference(superposition,[],[f2045,f750]) ).
tff(f10789,plain,
( spl18_320
| ~ spl18_63
| ~ spl18_86 ),
inference(avatar_split_clause,[],[f1206,f1187,f984,f10787]) ).
tff(f10787,plain,
( spl18_320
<=> ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_320])]) ).
tff(f1206,plain,
( ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK6(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) )
| ~ spl18_63
| ~ spl18_86 ),
inference(resolution,[],[f1188,f985]) ).
tff(f10785,plain,
( spl18_319
| ~ spl18_62
| ~ spl18_86 ),
inference(avatar_split_clause,[],[f1205,f1187,f980,f10783]) ).
tff(f10783,plain,
( spl18_319
<=> ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_319])]) ).
tff(f1205,plain,
( ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1))),X1))
| ( sK5(X0,aa(X0,fun(X0,bool),ord_less_eq(X0),X1)) = X1 )
| ~ order(X0)
| ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),ord_less_eq(X0),X1) ) )
| ~ spl18_62
| ~ spl18_86 ),
inference(resolution,[],[f1188,f981]) ).
tff(f10727,plain,
( spl18_318
| spl18_259
| ~ spl18_201
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f10397,f7358,f6061,f7573,f10724]) ).
tff(f10724,plain,
( spl18_318
<=> ( fTrue = sK13(fun(bool,bool),bool,fconj,bot_bot(fun(bool,fun(bool,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_318])]) ).
tff(f7573,plain,
( spl18_259
<=> ( fconj = bot_bot(fun(bool,fun(bool,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_259])]) ).
tff(f6061,plain,
( spl18_201
<=> ! [X1: $tType,X0: $tType,X2: X1] : ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_201])]) ).
tff(f10397,plain,
( ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,bot_bot(fun(bool,fun(bool,bool)))) )
| ~ spl18_201
| ~ spl18_244 ),
inference(trivial_inequality_removal,[],[f10389]) ).
tff(f10389,plain,
( ( combk(bool,bool,fFalse) != combk(bool,bool,fFalse) )
| ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,bot_bot(fun(bool,fun(bool,bool)))) )
| ~ spl18_201
| ~ spl18_244 ),
inference(superposition,[],[f7359,f6062]) ).
tff(f6062,plain,
( ! [X1: $tType,X0: $tType,X2: X1] : ( combk(bool,X0,fFalse) = aa(X1,fun(X0,bool),bot_bot(fun(X1,fun(X0,bool))),X2) )
| ~ spl18_201 ),
inference(avatar_component_clause,[],[f6061]) ).
tff(f10451,plain,
( spl18_317
| ~ spl18_35
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2114,f2048,f809,f10449]) ).
tff(f10449,plain,
( spl18_317
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK4(X1,X0,combk(X1,X0,X2),X3))),X2))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),combk(X1,X0,X2)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_317])]) ).
tff(f2114,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK4(X1,X0,combk(X1,X0,X2),X3))),X2))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),combk(X1,X0,X2)))
| ~ ord(X1) )
| ~ spl18_35
| ~ spl18_124 ),
inference(superposition,[],[f2049,f810]) ).
tff(f10447,plain,
( spl18_316
| ~ spl18_35
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f2100,f2048,f809,f10445]) ).
tff(f10445,plain,
( spl18_316
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),X2),aa(X0,X1,X3,sK4(X1,X0,X3,combk(X1,X0,X2)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),combk(X1,X0,X2)),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_316])]) ).
tff(f2100,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),X2),aa(X0,X1,X3,sK4(X1,X0,X3,combk(X1,X0,X2)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),combk(X1,X0,X2)),X3))
| ~ ord(X1) )
| ~ spl18_35
| ~ spl18_124 ),
inference(superposition,[],[f2049,f810]) ).
tff(f10443,plain,
( spl18_315
| ~ spl18_35
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2078,f2044,f809,f10441]) ).
tff(f10441,plain,
( spl18_315
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK3(X1,X0,combk(X1,X0,X2),X3))),X2))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),combk(X1,X0,X2)))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_315])]) ).
tff(f2078,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X3,sK3(X1,X0,combk(X1,X0,X2),X3))),X2))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),combk(X1,X0,X2)))
| ~ ord(X1) )
| ~ spl18_35
| ~ spl18_123 ),
inference(superposition,[],[f2045,f810]) ).
tff(f10439,plain,
( spl18_314
| ~ spl18_35
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2064,f2044,f809,f10437]) ).
tff(f10437,plain,
( spl18_314
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),X2),aa(X0,X1,X3,sK3(X1,X0,X3,combk(X1,X0,X2)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),combk(X1,X0,X2)),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_314])]) ).
tff(f2064,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),X2),aa(X0,X1,X3,sK3(X1,X0,X3,combk(X1,X0,X2)))))
| pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),combk(X1,X0,X2)),X3))
| ~ ord(X1) )
| ~ spl18_35
| ~ spl18_123 ),
inference(superposition,[],[f2045,f810]) ).
tff(f10401,plain,
( ~ spl18_7
| spl18_313
| ~ spl18_22
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1885,f1864,f749,f10399,f677]) ).
tff(f677,plain,
( spl18_7
<=> linorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
tff(f10399,plain,
( spl18_313
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X1))
| ( fTrue = sK2(bool,X0,X1) )
| ~ finite_finite1(bool,X1)
| ( big_linorder_Max(bool,X1) = X0 )
| ~ pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_313])]) ).
tff(f1885,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X1))
| ~ pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),X0),X1))
| ( big_linorder_Max(bool,X1) = X0 )
| ~ finite_finite1(bool,X1)
| ~ linorder(bool)
| ( fTrue = sK2(bool,X0,X1) ) )
| ~ spl18_22
| ~ spl18_113 ),
inference(superposition,[],[f1865,f750]) ).
tff(f10382,plain,
( spl18_312
| ~ spl18_52
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1828,f1791,f902,f10380]) ).
tff(f10380,plain,
( spl18_312
<=> ! [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,[spl18_312])]) ).
tff(f1828,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))) )
| ~ spl18_52
| ~ spl18_112 ),
inference(superposition,[],[f903,f1792]) ).
tff(f9581,plain,
( spl18_311
| ~ spl18_17
| ~ spl18_121 ),
inference(avatar_split_clause,[],[f2022,f2014,f727,f9579]) ).
tff(f9579,plain,
( spl18_311
<=> ! [X0: $tType,X3: X0,X2: fun(X0,int),X1: fun(X0,int)] : ( aa(X0,int,aa(fun(X0,int),fun(X0,int),aa(fun(X0,int),fun(fun(X0,int),fun(X0,int)),minus_minus(fun(X0,int)),X1),X2),X3) = aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(X0,int,X1,X3)),aa(X0,int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_311])]) ).
tff(f727,plain,
( spl18_17
<=> cl_Groups_Ominus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
tff(f2022,plain,
( ! [X0: $tType,X2: fun(X0,int),X3: X0,X1: fun(X0,int)] : ( aa(X0,int,aa(fun(X0,int),fun(X0,int),aa(fun(X0,int),fun(fun(X0,int),fun(X0,int)),minus_minus(fun(X0,int)),X1),X2),X3) = aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(X0,int,X1,X3)),aa(X0,int,X2,X3)) )
| ~ spl18_17
| ~ spl18_121 ),
inference(resolution,[],[f2015,f729]) ).
tff(f729,plain,
( cl_Groups_Ominus(int)
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f727]) ).
tff(f9577,plain,
( spl18_310
| ~ spl18_16
| ~ spl18_121 ),
inference(avatar_split_clause,[],[f2021,f2014,f722,f9575]) ).
tff(f9575,plain,
( spl18_310
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),X3) = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),aa(X0,bool,X1,X3)),aa(X0,bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_310])]) ).
tff(f722,plain,
( spl18_16
<=> cl_Groups_Ominus(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
tff(f2021,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] : ( aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),X3) = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),aa(X0,bool,X1,X3)),aa(X0,bool,X2,X3)) )
| ~ spl18_16
| ~ spl18_121 ),
inference(resolution,[],[f2015,f724]) ).
tff(f724,plain,
( cl_Groups_Ominus(bool)
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f722]) ).
tff(f9572,plain,
( spl18_309
| ~ spl18_35
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1987,f1919,f809,f9570]) ).
tff(f9570,plain,
( spl18_309
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: fun(X1,bool)] :
( ~ pp(aa(X1,bool,X2,sK15(X1,X0,combk(fun(X1,bool),X0,X2),X3)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),combk(fun(X1,bool),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_309])]) ).
tff(f1987,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,X2,sK15(X1,X0,combk(fun(X1,bool),X0,X2),X3)))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X3),combk(fun(X1,bool),X0,X2))) )
| ~ spl18_35
| ~ spl18_118 ),
inference(superposition,[],[f1920,f810]) ).
tff(f9568,plain,
( spl18_308
| ~ spl18_35
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1956,f1915,f809,f9566]) ).
tff(f9566,plain,
( spl18_308
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: fun(X1,bool)] :
( pp(aa(X1,bool,X2,sK15(X1,X0,X3,combk(fun(X1,bool),X0,X2))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),combk(fun(X1,bool),X0,X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_308])]) ).
tff(f1956,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,X2,sK15(X1,X0,X3,combk(fun(X1,bool),X0,X2))))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),combk(fun(X1,bool),X0,X2)),X3)) )
| ~ spl18_35
| ~ spl18_117 ),
inference(superposition,[],[f1916,f810]) ).
tff(f9564,plain,
( spl18_307
| ~ spl18_22
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1824,f1791,f749,f9562]) ).
tff(f9562,plain,
( spl18_307
<=> ! [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,[spl18_307])]) ).
tff(f1824,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)) ) )
| ~ spl18_22
| ~ spl18_112 ),
inference(superposition,[],[f1792,f750]) ).
tff(f9560,plain,
( spl18_306
| ~ spl18_22
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1812,f1791,f749,f9558]) ).
tff(f9558,plain,
( spl18_306
<=> ! [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,[spl18_306])]) ).
tff(f1812,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) ) )
| ~ spl18_22
| ~ spl18_112 ),
inference(superposition,[],[f1792,f750]) ).
tff(f9556,plain,
( spl18_305
| ~ spl18_22
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1799,f1791,f749,f9554]) ).
tff(f9554,plain,
( spl18_305
<=> ! [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,[spl18_305])]) ).
tff(f1799,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) ) )
| ~ spl18_22
| ~ spl18_112 ),
inference(superposition,[],[f1792,f750]) ).
tff(f9284,plain,
( spl18_304
| ~ spl18_52
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1931,f1915,f902,f9282]) ).
tff(f9282,plain,
( spl18_304
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,fun(X0,bool)),X2: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,sK14(X0,X1,X3,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_304])]) ).
tff(f1931,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X2),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,sK14(X0,X1,X3,X2)))) )
| ~ spl18_52
| ~ spl18_117 ),
inference(resolution,[],[f1916,f903]) ).
tff(f9280,plain,
( spl18_303
| ~ spl18_67
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1926,f1915,f1027,f9278]) ).
tff(f9278,plain,
( spl18_303
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,bot_bot(fun(X0,fun(X1,bool))),X2)),sK15(X1,X0,bot_bot(fun(X0,fun(X1,bool))),X2)))
| ( bot_bot(fun(X0,fun(X1,bool))) = X2 )
| ~ bot(fun(X0,fun(X1,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_303])]) ).
tff(f1027,plain,
( spl18_67
<=> ! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).
tff(f1926,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,sK14(X1,X0,bot_bot(fun(X0,fun(X1,bool))),X2)),sK15(X1,X0,bot_bot(fun(X0,fun(X1,bool))),X2)))
| ( bot_bot(fun(X0,fun(X1,bool))) = X2 )
| ~ bot(fun(X0,fun(X1,bool))) )
| ~ spl18_67
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1028]) ).
tff(f1028,plain,
( ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ( bot_bot(X0) = X1 )
| ~ bot(X0) )
| ~ spl18_67 ),
inference(avatar_component_clause,[],[f1027]) ).
tff(f9276,plain,
( spl18_302
| ~ spl18_83
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1761,f1749,f1156,f9274]) ).
tff(f9274,plain,
( spl18_302
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X4: fun(X1,X0),X3: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X4,X3)))
| ~ ord(X0)
| pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X4),X2))
| ~ linorder(fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_302])]) ).
tff(f1761,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X4,X3)))
| ~ ord(X0)
| pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X4),X2))
| ~ linorder(fun(X1,X0)) )
| ~ spl18_83
| ~ spl18_110 ),
inference(resolution,[],[f1750,f1157]) ).
tff(f9272,plain,
( spl18_301
| ~ spl18_63
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f1141,f1124,f984,f9270]) ).
tff(f9270,plain,
( spl18_301
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_301])]) ).
tff(f1141,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK6(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_80 ),
inference(resolution,[],[f1125,f985]) ).
tff(f9268,plain,
( spl18_300
| ~ spl18_62
| ~ spl18_80 ),
inference(avatar_split_clause,[],[f1140,f1124,f980,f9266]) ).
tff(f9266,plain,
( spl18_300
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_300])]) ).
tff(f1140,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,sK5(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ( aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_80 ),
inference(resolution,[],[f1125,f981]) ).
tff(f9242,plain,
( spl18_299
| ~ spl18_52
| ~ spl18_165 ),
inference(avatar_split_clause,[],[f2749,f2742,f902,f9239]) ).
tff(f9239,plain,
( spl18_299
<=> pp(aa(fun(fun(int,bool),bool),bool,fEx(fun(int,bool)),aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_299])]) ).
tff(f2742,plain,
( spl18_165
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_165])]) ).
tff(f2749,plain,
( pp(aa(fun(fun(int,bool),bool),bool,fEx(fun(int,bool)),aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)))))
| ~ spl18_52
| ~ spl18_165 ),
inference(resolution,[],[f2744,f903]) ).
tff(f2744,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_165 ),
inference(avatar_component_clause,[],[f2742]) ).
tff(f9237,plain,
( spl18_298
| ~ spl18_52
| ~ spl18_163 ),
inference(avatar_split_clause,[],[f2716,f2709,f902,f9234]) ).
tff(f9234,plain,
( spl18_298
<=> pp(aa(fun(fun(int,bool),bool),bool,fEx(fun(int,bool)),aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_298])]) ).
tff(f2716,plain,
( pp(aa(fun(fun(int,bool),bool),bool,fEx(fun(int,bool)),aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs)))))
| ~ spl18_52
| ~ spl18_163 ),
inference(resolution,[],[f2711,f903]) ).
tff(f9145,plain,
( spl18_297
| ~ spl18_72
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f2285,f2231,f1066,f9143]) ).
tff(f9143,plain,
( spl18_297
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_297])]) ).
tff(f2285,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3),X1)) )
| ~ spl18_72
| ~ spl18_132 ),
inference(resolution,[],[f2232,f1067]) ).
tff(f9141,plain,
( spl18_296
| ~ spl18_72
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f2269,f2227,f1066,f9139]) ).
tff(f9139,plain,
( spl18_296
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_296])]) ).
tff(f2269,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2),X1)) )
| ~ spl18_72
| ~ spl18_131 ),
inference(resolution,[],[f2228,f1067]) ).
tff(f9137,plain,
( spl18_295
| ~ spl18_52
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1838,f1791,f902,f9135]) ).
tff(f9135,plain,
( spl18_295
<=> ! [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,[spl18_295])]) ).
tff(f1838,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))) )
| ~ spl18_52
| ~ spl18_112 ),
inference(superposition,[],[f903,f1792]) ).
tff(f9023,plain,
( spl18_188
| spl18_1
| spl18_188
| ~ spl18_35
| ~ spl18_201
| ~ spl18_259
| ~ spl18_271
| ~ spl18_292 ),
inference(avatar_split_clause,[],[f8914,f8782,f7921,f7573,f6061,f809,f4579,f647,f4579]) ).
tff(f4579,plain,
( spl18_188
<=> ! [X1: bool] : ~ pp(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_188])]) ).
tff(f7921,plain,
( spl18_271
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0))
| ~ pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_271])]) ).
tff(f8782,plain,
( spl18_292
<=> ! [X1: $tType,X0: $tType,X4: $tType,X3: X0,X5: fun(X0,fun(X1,X4)),X2: X1] : ( aa(X0,X4,aa(fun(X0,X1),fun(X0,X4),aa(fun(X0,fun(X1,X4)),fun(fun(X0,X1),fun(X0,X4)),combs(X0,X1,X4),X5),combk(X1,X0,X2)),X3) = aa(X1,X4,aa(X0,fun(X1,X4),X5,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_292])]) ).
tff(f8914,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| pp(fFalse)
| ~ pp(X1) )
| ~ spl18_35
| ~ spl18_201
| ~ spl18_259
| ~ spl18_271
| ~ spl18_292 ),
inference(forward_demodulation,[],[f8913,f810]) ).
tff(f8913,plain,
( ! [X0: bool,X1: bool] :
( pp(fFalse)
| ~ pp(aa(bool,bool,combk(bool,bool,X0),X1))
| ~ pp(X1) )
| ~ spl18_35
| ~ spl18_201
| ~ spl18_259
| ~ spl18_271
| ~ spl18_292 ),
inference(forward_demodulation,[],[f8912,f810]) ).
tff(f8912,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combk(bool,bool,fFalse),X0))
| ~ pp(aa(bool,bool,combk(bool,bool,X0),X1))
| ~ pp(X1) )
| ~ spl18_201
| ~ spl18_259
| ~ spl18_271
| ~ spl18_292 ),
inference(forward_demodulation,[],[f8890,f8678]) ).
tff(f8678,plain,
( ! [X0: bool] : ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| ~ spl18_201
| ~ spl18_259 ),
inference(superposition,[],[f6062,f7575]) ).
tff(f7575,plain,
( ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ~ spl18_259 ),
inference(avatar_component_clause,[],[f7573]) ).
tff(f8890,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(aa(bool,bool,combk(bool,bool,X0),X1))
| ~ pp(X1) )
| ~ spl18_271
| ~ spl18_292 ),
inference(superposition,[],[f7922,f8783]) ).
tff(f8783,plain,
( ! [X4: $tType,X1: $tType,X0: $tType,X2: X1,X3: X0,X5: fun(X0,fun(X1,X4))] : ( aa(X0,X4,aa(fun(X0,X1),fun(X0,X4),aa(fun(X0,fun(X1,X4)),fun(fun(X0,X1),fun(X0,X4)),combs(X0,X1,X4),X5),combk(X1,X0,X2)),X3) = aa(X1,X4,aa(X0,fun(X1,X4),X5,X3),X2) )
| ~ spl18_292 ),
inference(avatar_component_clause,[],[f8782]) ).
tff(f7922,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0))
| ~ pp(X0) )
| ~ spl18_271 ),
inference(avatar_component_clause,[],[f7921]) ).
tff(f8966,plain,
( ~ spl18_14
| spl18_294
| ~ spl18_110
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1775,f1753,f1749,f8964,f712]) ).
tff(f8964,plain,
( spl18_294
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: fun(X0,bool)] : pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),X3)),aa(X0,bool,X1,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_294])]) ).
tff(f1775,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2),X3)),aa(X0,bool,X1,X3)))
| ~ ord(bool) )
| ~ spl18_110
| ~ spl18_111 ),
inference(resolution,[],[f1754,f1750]) ).
tff(f8788,plain,
( spl18_293
| ~ spl18_101
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1891,f1864,f1599,f8786]) ).
tff(f8786,plain,
( spl18_293
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),big_linorder_Max(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_293])]) ).
tff(f1891,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),big_linorder_Max(X0,X2))) )
| ~ spl18_101
| ~ spl18_113 ),
inference(duplicate_literal_removal,[],[f1877]) ).
tff(f1877,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) )
| ~ spl18_101
| ~ spl18_113 ),
inference(resolution,[],[f1865,f1600]) ).
tff(f8784,plain,
( spl18_292
| ~ spl18_35
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1815,f1791,f809,f8782]) ).
tff(f1815,plain,
( ! [X4: $tType,X1: $tType,X0: $tType,X2: X1,X3: X0,X5: fun(X0,fun(X1,X4))] : ( aa(X0,X4,aa(fun(X0,X1),fun(X0,X4),aa(fun(X0,fun(X1,X4)),fun(fun(X0,X1),fun(X0,X4)),combs(X0,X1,X4),X5),combk(X1,X0,X2)),X3) = aa(X1,X4,aa(X0,fun(X1,X4),X5,X3),X2) )
| ~ spl18_35
| ~ spl18_112 ),
inference(superposition,[],[f1792,f810]) ).
tff(f8780,plain,
( spl18_291
| ~ spl18_35
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1803,f1791,f809,f8778]) ).
tff(f8778,plain,
( spl18_291
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: X0,X5: 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),combk(fun(X1,X2),X0,X3)),X5),X4) = aa(X1,X2,X3,aa(X0,X1,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_291])]) ).
tff(f1803,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: X0,X5: 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),combk(fun(X1,X2),X0,X3)),X5),X4) = aa(X1,X2,X3,aa(X0,X1,X5,X4)) )
| ~ spl18_35
| ~ spl18_112 ),
inference(superposition,[],[f1792,f810]) ).
tff(f8685,plain,
( spl18_290
| ~ spl18_117
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f2157,f2128,f1915,f8683]) ).
tff(f8683,plain,
( spl18_290
<=> ! [X1: $tType,X0: $tType,X5: fun(X1,fun(X0,bool)),X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,X3),X4))
| pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,sK14(X0,X1,X2,X5)),sK15(X0,X1,X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_290])]) ).
tff(f2157,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0,X5: fun(X1,fun(X0,bool))] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,X3),X4))
| pp(aa(X0,bool,aa(X1,fun(X0,bool),X5,sK14(X0,X1,X2,X5)),sK15(X0,X1,X2,X5))) )
| ~ spl18_117
| ~ spl18_126 ),
inference(resolution,[],[f2129,f1916]) ).
tff(f8511,plain,
( spl18_289
| ~ spl18_146
| ~ spl18_148 ),
inference(avatar_split_clause,[],[f2571,f2565,f2514,f8509]) ).
tff(f8509,plain,
( spl18_289
<=> ! [X0: $tType,X2: $tType,X4: X0,X3: fun(X2,fun(X0,bool)),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X2,aa(X0,fun(X2,bool),aa(fun(X2,fun(X0,bool)),fun(X0,fun(X2,bool)),combc(X2,X0,bool),X3),X4))
| ~ pp(aa(X0,bool,X1,X4))
| pp(aa(X0,bool,X1,sK12(X2,X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_289])]) ).
tff(f2571,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: fun(X0,bool),X4: X0] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X2,aa(X0,fun(X2,bool),aa(fun(X2,fun(X0,bool)),fun(X0,fun(X2,bool)),combc(X2,X0,bool),X3),X4))
| ~ pp(aa(X0,bool,X1,X4))
| pp(aa(X0,bool,X1,sK12(X2,X0,X3,X1))) )
| ~ spl18_146
| ~ spl18_148 ),
inference(duplicate_literal_removal,[],[f2568]) ).
tff(f2568,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X2,fun(X0,bool)),X1: fun(X0,bool),X4: X0] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X2,aa(X0,fun(X2,bool),aa(fun(X2,fun(X0,bool)),fun(X0,fun(X2,bool)),combc(X2,X0,bool),X3),X4))
| ~ pp(aa(X0,bool,X1,X4))
| pp(aa(X0,bool,X1,sK12(X2,X0,X3,X1)))
| ~ finite_finite1(X0,X1) )
| ~ spl18_146
| ~ spl18_148 ),
inference(resolution,[],[f2566,f2515]) ).
tff(f8507,plain,
( spl18_288
| ~ spl18_59
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1928,f1915,f948,f8505]) ).
tff(f8505,plain,
( spl18_288
<=> ! [X0: $tType,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),fequal(X0)),X1))
| ( sK14(X0,X0,X1,fequal(X0)) = sK15(X0,X0,X1,fequal(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_288])]) ).
tff(f1928,plain,
( ! [X0: $tType,X1: fun(X0,fun(X0,bool))] :
( pp(aa(fun(X0,fun(X0,bool)),bool,aa(fun(X0,fun(X0,bool)),fun(fun(X0,fun(X0,bool)),bool),ord_less_eq(fun(X0,fun(X0,bool))),fequal(X0)),X1))
| ( sK14(X0,X0,X1,fequal(X0)) = sK15(X0,X0,X1,fequal(X0)) ) )
| ~ spl18_59
| ~ spl18_117 ),
inference(resolution,[],[f1916,f949]) ).
tff(f8503,plain,
( spl18_287
| ~ spl18_83
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f1717,f1690,f1156,f8501]) ).
tff(f8501,plain,
( spl18_287
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
| ~ preorder(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_287])]) ).
tff(f1717,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
| ~ preorder(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ linorder(X0) )
| ~ spl18_83
| ~ spl18_108 ),
inference(resolution,[],[f1691,f1157]) ).
tff(f8320,plain,
( spl18_286
| ~ spl18_52
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1672,f1628,f902,f8318]) ).
tff(f8318,plain,
( spl18_286
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X4: X0,X3: fun(X0,X1)] :
( ~ pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_286])]) ).
tff(f1672,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))) )
| ~ spl18_52
| ~ spl18_105 ),
inference(superposition,[],[f903,f1629]) ).
tff(f8316,plain,
( spl18_285
| ~ spl18_52
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1658,f1624,f902,f8314]) ).
tff(f8314,plain,
( spl18_285
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_285])]) ).
tff(f1658,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3))) )
| ~ spl18_52
| ~ spl18_104 ),
inference(superposition,[],[f903,f1625]) ).
tff(f8312,plain,
( spl18_284
| ~ spl18_91
| spl18_274 ),
inference(avatar_split_clause,[],[f8106,f7991,f1220,f8310]) ).
tff(f8310,plain,
( spl18_284
<=> ! [X0: bool,X1: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) != combk(bool,bool,fFalse) )
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_284])]) ).
tff(f7991,plain,
( spl18_274
<=> ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,fTrue) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_274])]) ).
tff(f8106,plain,
( ! [X0: bool,X1: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) != combk(bool,bool,fFalse) )
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl18_91
| spl18_274 ),
inference(superposition,[],[f7993,f1221]) ).
tff(f7993,plain,
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),fconj,fTrue) )
| spl18_274 ),
inference(avatar_component_clause,[],[f7991]) ).
tff(f8126,plain,
( spl18_283
| ~ spl18_57
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1977,f1919,f940,f8124]) ).
tff(f8124,plain,
( spl18_283
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fconj))
| ~ pp(sK15(bool,bool,fconj,X0))
| ~ pp(sK14(bool,bool,fconj,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_283])]) ).
tff(f940,plain,
( spl18_57
<=> ! [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,[spl18_57])]) ).
tff(f1977,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fconj))
| ~ pp(sK15(bool,bool,fconj,X0))
| ~ pp(sK14(bool,bool,fconj,X0)) )
| ~ spl18_57
| ~ spl18_118 ),
inference(resolution,[],[f1920,f941]) ).
tff(f941,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl18_57 ),
inference(avatar_component_clause,[],[f940]) ).
tff(f8122,plain,
( spl18_282
| ~ spl18_58
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1935,f1915,f944,f8120]) ).
tff(f8120,plain,
( spl18_282
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fdisj),X0))
| pp(sK14(bool,bool,X0,fdisj))
| pp(sK15(bool,bool,X0,fdisj)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_282])]) ).
tff(f1935,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fdisj),X0))
| pp(sK14(bool,bool,X0,fdisj))
| pp(sK15(bool,bool,X0,fdisj)) )
| ~ spl18_58
| ~ spl18_117 ),
inference(resolution,[],[f1916,f945]) ).
tff(f8118,plain,
( spl18_281
| ~ spl18_22
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f1669,f1628,f749,f8116]) ).
tff(f8116,plain,
( spl18_281
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,bool),X4: X0,X3: fun(X0,X1)] :
( ( 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) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_281])]) ).
tff(f1669,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) ) )
| ~ spl18_22
| ~ spl18_105 ),
inference(superposition,[],[f1629,f750]) ).
tff(f8114,plain,
( spl18_280
| ~ spl18_22
| ~ spl18_104 ),
inference(avatar_split_clause,[],[f1655,f1624,f749,f8112]) ).
tff(f8112,plain,
( spl18_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,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_280])]) ).
tff(f1655,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,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X3),X4) ) )
| ~ spl18_22
| ~ spl18_104 ),
inference(superposition,[],[f1625,f750]) ).
tff(f8105,plain,
( spl18_279
| ~ spl18_22
| ~ spl18_102 ),
inference(avatar_split_clause,[],[f1643,f1616,f749,f8103]) ).
tff(f8103,plain,
( spl18_279
<=> ! [X0: $tType,X2: product_prod(X0,bool),X1: fun(product_prod(X0,bool),bool)] :
( ~ pp(aa(product_prod(X0,bool),bool,X1,aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK9(X0,bool,X1)),fFalse)))
| pp(aa(product_prod(X0,bool),bool,X1,X2))
| ( fTrue = sK10(X0,bool,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_279])]) ).
tff(f1643,plain,
( ! [X0: $tType,X2: product_prod(X0,bool),X1: fun(product_prod(X0,bool),bool)] :
( ~ pp(aa(product_prod(X0,bool),bool,X1,aa(bool,product_prod(X0,bool),aa(X0,fun(bool,product_prod(X0,bool)),product_Pair(X0,bool),sK9(X0,bool,X1)),fFalse)))
| pp(aa(product_prod(X0,bool),bool,X1,X2))
| ( fTrue = sK10(X0,bool,X1) ) )
| ~ spl18_22
| ~ spl18_102 ),
inference(superposition,[],[f1617,f750]) ).
tff(f8101,plain,
( spl18_278
| ~ spl18_22
| ~ spl18_102 ),
inference(avatar_split_clause,[],[f1638,f1616,f749,f8099]) ).
tff(f8099,plain,
( spl18_278
<=> ! [X0: $tType,X2: product_prod(bool,X0),X1: fun(product_prod(bool,X0),bool)] :
( ~ pp(aa(product_prod(bool,X0),bool,X1,aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK10(bool,X0,X1))))
| pp(aa(product_prod(bool,X0),bool,X1,X2))
| ( fTrue = sK9(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_278])]) ).
tff(f1638,plain,
( ! [X0: $tType,X2: product_prod(bool,X0),X1: fun(product_prod(bool,X0),bool)] :
( ~ pp(aa(product_prod(bool,X0),bool,X1,aa(X0,product_prod(bool,X0),aa(bool,fun(X0,product_prod(bool,X0)),product_Pair(bool,X0),fFalse),sK10(bool,X0,X1))))
| pp(aa(product_prod(bool,X0),bool,X1,X2))
| ( fTrue = sK9(bool,X0,X1) ) )
| ~ spl18_22
| ~ spl18_102 ),
inference(superposition,[],[f1617,f750]) ).
tff(f8006,plain,
( spl18_277
| ~ spl18_82
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f1736,f1731,f1132,f8004]) ).
tff(f8004,plain,
( spl18_277
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = sK8(X0,X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK8(X0,X1),X1)),sK8(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_277])]) ).
tff(f1736,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = sK8(X0,X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK8(X0,X1),X1)),sK8(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_82
| ~ spl18_109 ),
inference(resolution,[],[f1732,f1133]) ).
tff(f8002,plain,
( spl18_276
| ~ spl18_81
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f1735,f1731,f1128,f8000]) ).
tff(f8000,plain,
( spl18_276
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = sK7(X0,X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK7(X0,X1),X1)),sK7(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_276])]) ).
tff(f1735,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = sK7(X0,X1) )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,sK7(X0,X1),X1)),sK7(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_81
| ~ spl18_109 ),
inference(resolution,[],[f1732,f1129]) ).
tff(f7998,plain,
( spl18_275
| ~ spl18_85
| ~ spl18_89 ),
inference(avatar_split_clause,[],[f1225,f1212,f1180,f7996]) ).
tff(f7996,plain,
( spl18_275
<=> ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) )
| ( X2 = X3 )
| ~ group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_275])]) ).
tff(f1225,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3) )
| ( X2 = X3 )
| ~ group_add(fun(X0,bool)) )
| ~ spl18_85
| ~ spl18_89 ),
inference(superposition,[],[f1181,f1213]) ).
tff(f7994,plain,
( spl18_259
| ~ spl18_274
| ~ spl18_75
| ~ spl18_201
| ~ spl18_258 ),
inference(avatar_split_clause,[],[f7878,f7569,f6061,f1089,f7991,f7573]) ).
tff(f7569,plain,
( spl18_258
<=> ( fTrue = sK13(fun(bool,bool),bool,bot_bot(fun(bool,fun(bool,bool))),fconj) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_258])]) ).
tff(f7878,plain,
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),fconj,fTrue) )
| ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ~ spl18_75
| ~ spl18_201
| ~ spl18_258 ),
inference(forward_demodulation,[],[f7875,f6062]) ).
tff(f7875,plain,
( ( aa(bool,fun(bool,bool),fconj,fTrue) != aa(bool,fun(bool,bool),bot_bot(fun(bool,fun(bool,bool))),fTrue) )
| ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ~ spl18_75
| ~ spl18_258 ),
inference(superposition,[],[f1090,f7571]) ).
tff(f7571,plain,
( ( fTrue = sK13(fun(bool,bool),bool,bot_bot(fun(bool,fun(bool,bool))),fconj) )
| ~ spl18_258 ),
inference(avatar_component_clause,[],[f7569]) ).
tff(f7989,plain,
( spl18_273
| ~ spl18_63
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f1071,f1061,f984,f7987]) ).
tff(f7987,plain,
( spl18_273
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1))
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_273])]) ).
tff(f1071,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,sK6(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1))
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_63
| ~ spl18_71 ),
inference(resolution,[],[f1062,f985]) ).
tff(f7985,plain,
( spl18_272
| ~ spl18_62
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f1070,f1061,f980,f7983]) ).
tff(f7983,plain,
( spl18_272
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1))
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_272])]) ).
tff(f1070,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,sK5(fun(X0,bool),aa(X0,fun(fun(X0,bool),bool),member(X0),X1)),X1))
| ( aa(X0,fun(fun(X0,bool),bool),member(X0),X1) = combk(bool,fun(X0,bool),fFalse) ) )
| ~ spl18_62
| ~ spl18_71 ),
inference(resolution,[],[f1062,f981]) ).
tff(f7923,plain,
( spl18_271
| ~ spl18_57
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1842,f1791,f940,f7921]) ).
tff(f1842,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0))
| ~ pp(X0) )
| ~ spl18_57
| ~ spl18_112 ),
inference(superposition,[],[f941,f1792]) ).
tff(f7919,plain,
( spl18_270
| ~ spl18_58
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1839,f1791,f944,f7917]) ).
tff(f7917,plain,
( spl18_270
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| pp(X0)
| pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_270])]) ).
tff(f1839,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| pp(X0)
| pp(aa(bool,bool,X1,X0)) )
| ~ spl18_58
| ~ spl18_112 ),
inference(superposition,[],[f945,f1792]) ).
tff(f7915,plain,
( spl18_269
| ~ spl18_59
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1832,f1791,f948,f7913]) ).
tff(f7913,plain,
( spl18_269
<=> ! [X0: $tType,X2: fun(X0,X0),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),fequal(X0)),X2),X1))
| ( aa(X0,X0,X2,X1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_269])]) ).
tff(f1832,plain,
( ! [X0: $tType,X2: fun(X0,X0),X1: X0] :
( ~ pp(aa(X0,bool,aa(fun(X0,X0),fun(X0,bool),aa(fun(X0,fun(X0,bool)),fun(fun(X0,X0),fun(X0,bool)),combs(X0,X0,bool),fequal(X0)),X2),X1))
| ( aa(X0,X0,X2,X1) = X1 ) )
| ~ spl18_59
| ~ spl18_112 ),
inference(superposition,[],[f949,f1792]) ).
tff(f7763,plain,
( spl18_268
| ~ spl18_46
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1844,f1791,f867,f7761]) ).
tff(f7761,plain,
( spl18_268
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_268])]) ).
tff(f1844,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) )
| ~ spl18_46
| ~ spl18_112 ),
inference(superposition,[],[f868,f1792]) ).
tff(f7759,plain,
( spl18_267
| ~ spl18_44
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1841,f1791,f859,f7757]) ).
tff(f7757,plain,
( spl18_267
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_267])]) ).
tff(f859,plain,
( spl18_44
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).
tff(f1841,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| ~ pp(aa(bool,bool,X1,X0)) )
| ~ spl18_44
| ~ spl18_112 ),
inference(superposition,[],[f860,f1792]) ).
tff(f860,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) )
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f859]) ).
tff(f7755,plain,
( spl18_266
| ~ spl18_22
| ~ spl18_99 ),
inference(avatar_split_clause,[],[f1571,f1568,f749,f7753]) ).
tff(f7753,plain,
( spl18_266
<=> ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ( combk(bool,X1,X0) = aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),combk(bool,X1,X0)),X2) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_266])]) ).
tff(f1571,plain,
( ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ( combk(bool,X1,X0) = aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),combk(bool,X1,X0)),X2) )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_99 ),
inference(superposition,[],[f1569,f750]) ).
tff(f7751,plain,
( spl18_265
| ~ spl18_83
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f1550,f1542,f1156,f7749]) ).
tff(f7749,plain,
( spl18_265
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| ~ linorder(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_265])]) ).
tff(f1550,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2))
| pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| ~ linorder(fun(X0,bool)) )
| ~ spl18_83
| ~ spl18_97 ),
inference(resolution,[],[f1543,f1157]) ).
tff(f7699,plain,
( spl18_264
| ~ spl18_71
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f2218,f2202,f1061,f7696]) ).
tff(f7696,plain,
( spl18_264
<=> pp(aa(product_prod(int,list(int)),bool,set(product_prod(int,list(int)),lbounds(as)),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_264])]) ).
tff(f2218,plain,
( pp(aa(product_prod(int,list(int)),bool,set(product_prod(int,list(int)),lbounds(as)),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)))
| ~ spl18_71
| ~ spl18_130 ),
inference(resolution,[],[f2204,f1062]) ).
tff(f7694,plain,
( spl18_263
| ~ spl18_71
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f2208,f2197,f1061,f7691]) ).
tff(f7691,plain,
( spl18_263
<=> pp(aa(product_prod(int,list(int)),bool,set(product_prod(int,list(int)),lbounds(as)),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_263])]) ).
tff(f2208,plain,
( pp(aa(product_prod(int,list(int)),bool,set(product_prod(int,list(int)),lbounds(as)),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)))
| ~ spl18_71
| ~ spl18_129 ),
inference(resolution,[],[f2199,f1062]) ).
tff(f7689,plain,
( spl18_262
| ~ spl18_71
| ~ spl18_113 ),
inference(avatar_split_clause,[],[f1878,f1864,f1061,f7687]) ).
tff(f7687,plain,
( spl18_262
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| pp(aa(X0,bool,X2,sK2(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_262])]) ).
tff(f1878,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( big_linorder_Max(X0,X2) = X1 )
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| pp(aa(X0,bool,X2,sK2(X0,X1,X2))) )
| ~ spl18_71
| ~ spl18_113 ),
inference(resolution,[],[f1865,f1062]) ).
tff(f7684,plain,
( spl18_261
| ~ spl18_64
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1837,f1791,f1008,f7682]) ).
tff(f7682,plain,
( spl18_261
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: X1] : ~ 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),bot_bot(fun(X1,fun(X0,bool)))),X3),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_261])]) ).
tff(f1837,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: 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),bot_bot(fun(X1,fun(X0,bool)))),X3),X2))
| ~ spl18_64
| ~ spl18_112 ),
inference(superposition,[],[f1009,f1792]) ).
tff(f7580,plain,
( spl18_260
| ~ spl18_44
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1976,f1919,f859,f7578]) ).
tff(f7578,plain,
( spl18_260
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fdisj))
| ~ pp(sK15(bool,bool,fdisj,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_260])]) ).
tff(f1976,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fdisj))
| ~ pp(sK15(bool,bool,fdisj,X0)) )
| ~ spl18_44
| ~ spl18_118 ),
inference(resolution,[],[f1920,f860]) ).
tff(f7576,plain,
( spl18_258
| spl18_259
| ~ spl18_201
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f7486,f7149,f6061,f7573,f7569]) ).
tff(f7486,plain,
( ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ( fTrue = sK13(fun(bool,bool),bool,bot_bot(fun(bool,fun(bool,bool))),fconj) )
| ~ spl18_201
| ~ spl18_239 ),
inference(trivial_inequality_removal,[],[f7481]) ).
tff(f7481,plain,
( ( combk(bool,bool,fFalse) != combk(bool,bool,fFalse) )
| ( fconj = bot_bot(fun(bool,fun(bool,bool))) )
| ( fTrue = sK13(fun(bool,bool),bool,bot_bot(fun(bool,fun(bool,bool))),fconj) )
| ~ spl18_201
| ~ spl18_239 ),
inference(superposition,[],[f7150,f6062]) ).
tff(f7567,plain,
( spl18_257
| ~ spl18_45
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f1975,f1919,f863,f7565]) ).
tff(f7565,plain,
( spl18_257
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fdisj))
| ~ pp(sK14(bool,bool,fdisj,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_257])]) ).
tff(f863,plain,
( spl18_45
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).
tff(f1975,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),X0),fdisj))
| ~ pp(sK14(bool,bool,fdisj,X0)) )
| ~ spl18_45
| ~ spl18_118 ),
inference(resolution,[],[f1920,f864]) ).
tff(f864,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) )
| ~ spl18_45 ),
inference(avatar_component_clause,[],[f863]) ).
tff(f7563,plain,
( spl18_256
| ~ spl18_46
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1934,f1915,f867,f7561]) ).
tff(f7561,plain,
( spl18_256
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fconj),X0))
| pp(sK15(bool,bool,X0,fconj)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_256])]) ).
tff(f1934,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fconj),X0))
| pp(sK15(bool,bool,X0,fconj)) )
| ~ spl18_46
| ~ spl18_117 ),
inference(resolution,[],[f1916,f868]) ).
tff(f7559,plain,
( spl18_255
| ~ spl18_47
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1933,f1915,f871,f7557]) ).
tff(f7557,plain,
( spl18_255
<=> ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fconj),X0))
| pp(sK14(bool,bool,X0,fconj)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_255])]) ).
tff(f1933,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( pp(aa(fun(bool,fun(bool,bool)),bool,aa(fun(bool,fun(bool,bool)),fun(fun(bool,fun(bool,bool)),bool),ord_less_eq(fun(bool,fun(bool,bool))),fconj),X0))
| pp(sK14(bool,bool,X0,fconj)) )
| ~ spl18_47
| ~ spl18_117 ),
inference(resolution,[],[f1916,f872]) ).
tff(f7555,plain,
( spl18_254
| ~ spl18_97
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f1772,f1753,f1542,f7553]) ).
tff(f7553,plain,
( spl18_254
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_254])]) ).
tff(f1772,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3),X2)) )
| ~ spl18_97
| ~ spl18_111 ),
inference(resolution,[],[f1754,f1543]) ).
tff(f7551,plain,
( spl18_253
| ~ spl18_22
| ~ spl18_96 ),
inference(avatar_split_clause,[],[f1271,f1251,f749,f7549]) ).
tff(f7549,plain,
( spl18_253
<=> ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ~ pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),combk(bool,X1,X0)))
| ( combk(bool,X1,X0) = X2 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_253])]) ).
tff(f1251,plain,
( spl18_96
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).
tff(f1271,plain,
( ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ~ pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),combk(bool,X1,X0)))
| ( combk(bool,X1,X0) = X2 )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_96 ),
inference(superposition,[],[f1252,f750]) ).
tff(f1252,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_96 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f7526,plain,
( ~ spl18_7
| spl18_252
| ~ spl18_22
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f1262,f1247,f749,f7524,f677]) ).
tff(f7524,plain,
( spl18_252
<=> ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( fTrue = big_linorder_Max(bool,X0) )
| ~ finite_finite1(bool,X0)
| ( combk(bool,bool,fFalse) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_252])]) ).
tff(f1262,plain,
( ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( combk(bool,bool,fFalse) = X0 )
| ~ finite_finite1(bool,X0)
| ~ linorder(bool)
| ( fTrue = big_linorder_Max(bool,X0) ) )
| ~ spl18_22
| ~ spl18_95 ),
inference(superposition,[],[f1248,f750]) ).
tff(f7490,plain,
( spl18_251
| ~ spl18_64
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1932,f1915,f1008,f7488]) ).
tff(f7488,plain,
( spl18_251
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool))] : pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),bot_bot(fun(X1,fun(X0,bool)))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_251])]) ).
tff(f1932,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool))] : pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),bot_bot(fun(X1,fun(X0,bool)))),X2))
| ~ spl18_64
| ~ spl18_117 ),
inference(resolution,[],[f1916,f1009]) ).
tff(f7473,plain,
( spl18_250
| ~ spl18_22
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f1226,f1216,f749,f7471]) ).
tff(f7471,plain,
( spl18_250
<=> ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ( aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),combk(bool,X1,X0)) = X2 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_250])]) ).
tff(f1226,plain,
( ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( ( aa(fun(X1,bool),fun(X1,bool),aa(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X2),combk(bool,X1,X0)) = X2 )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_90 ),
inference(superposition,[],[f1217,f750]) ).
tff(f7437,plain,
( spl18_249
| ~ spl18_47
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1843,f1791,f871,f7435]) ).
tff(f7435,plain,
( spl18_249
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_249])]) ).
tff(f1843,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) )
| ~ spl18_47
| ~ spl18_112 ),
inference(superposition,[],[f872,f1792]) ).
tff(f7433,plain,
( spl18_248
| ~ spl18_45
| ~ spl18_112 ),
inference(avatar_split_clause,[],[f1840,f1791,f863,f7431]) ).
tff(f7431,plain,
( spl18_248
<=> ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| ~ pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_248])]) ).
tff(f1840,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fdisj),X1),X0))
| ~ pp(X0) )
| ~ spl18_45
| ~ spl18_112 ),
inference(superposition,[],[f864,f1792]) ).
tff(f7429,plain,
( ~ spl18_245
| spl18_246
| spl18_247
| ~ spl18_22
| ~ spl18_85 ),
inference(avatar_split_clause,[],[f1183,f1180,f749,f7427,f7424,f7420]) ).
tff(f7420,plain,
( spl18_245
<=> group_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_245])]) ).
tff(f7424,plain,
( spl18_246
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_246])]) ).
tff(f7427,plain,
( spl18_247
<=> ! [X2: bool] : ( fFalse != aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_247])]) ).
tff(f1183,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( fFalse != aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X2),X2) )
| ( X0 = X1 )
| ~ group_add(bool)
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) )
| ~ spl18_22
| ~ spl18_85 ),
inference(superposition,[],[f1181,f750]) ).
tff(f7360,plain,
( spl18_244
| ~ spl18_190
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f6373,f6295,f4678,f7358]) ).
tff(f4678,plain,
( spl18_190
<=> ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_190])]) ).
tff(f6295,plain,
( spl18_210
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK13(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_210])]) ).
tff(f6373,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,fconj,X0) ) )
| ~ spl18_190
| ~ spl18_210 ),
inference(superposition,[],[f6296,f4680]) ).
tff(f4680,plain,
( ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,fFalse) )
| ~ spl18_190 ),
inference(avatar_component_clause,[],[f4678]) ).
tff(f6296,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK13(X0,bool,X1,X2) ) )
| ~ spl18_210 ),
inference(avatar_component_clause,[],[f6295]) ).
tff(f7356,plain,
( spl18_243
| ~ spl18_72
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f1738,f1731,f1066,f7354]) ).
tff(f7354,plain,
( spl18_243
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X2,X1)),X2))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_243])]) ).
tff(f1738,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ( big_linorder_Max(X0,X1) = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X2,X1)),X2))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl18_72
| ~ spl18_109 ),
inference(resolution,[],[f1732,f1067]) ).
tff(f7352,plain,
( spl18_242
| ~ spl18_52
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1151,f1132,f902,f7350]) ).
tff(f7350,plain,
( spl18_242
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_242])]) ).
tff(f1151,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)))) )
| ~ spl18_52
| ~ spl18_82 ),
inference(resolution,[],[f1133,f903]) ).
tff(f7348,plain,
( spl18_241
| ~ spl18_52
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f1145,f1128,f902,f7346]) ).
tff(f7346,plain,
( spl18_241
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_241])]) ).
tff(f1145,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)))) )
| ~ spl18_52
| ~ spl18_81 ),
inference(resolution,[],[f1129,f903]) ).
tff(f7321,plain,
( spl18_240
| ~ spl18_80
| ~ spl18_83 ),
inference(avatar_split_clause,[],[f1162,f1156,f1124,f7319]) ).
tff(f7319,plain,
( spl18_240
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(fun(X0,bool))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_240])]) ).
tff(f1162,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(fun(X0,bool))
| finite_finite1(X0,X1)
| ~ finite_finite1(X0,X2) )
| ~ spl18_80
| ~ spl18_83 ),
inference(resolution,[],[f1157,f1125]) ).
tff(f7151,plain,
( spl18_239
| ~ spl18_190
| ~ spl18_210 ),
inference(avatar_split_clause,[],[f6354,f6295,f4678,f7149]) ).
tff(f6354,plain,
( ! [X0: fun(bool,fun(bool,bool))] :
( ( combk(bool,bool,fFalse) != aa(bool,fun(bool,bool),X0,fFalse) )
| ( fconj = X0 )
| ( fTrue = sK13(fun(bool,bool),bool,X0,fconj) ) )
| ~ spl18_190
| ~ spl18_210 ),
inference(superposition,[],[f6296,f4680]) ).
tff(f7147,plain,
( spl18_238
| ~ spl18_56
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1760,f1749,f936,f7145]) ).
tff(f7145,plain,
( spl18_238
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,bot_bot(fun(X1,X0)),X2)),aa(X1,X0,X3,X2)))
| ~ ord(X0)
| ~ bot(fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_238])]) ).
tff(f936,plain,
( spl18_56
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).
tff(f1760,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,bot_bot(fun(X1,X0)),X2)),aa(X1,X0,X3,X2)))
| ~ ord(X0)
| ~ bot(fun(X1,X0)) )
| ~ spl18_56
| ~ spl18_110 ),
inference(resolution,[],[f1750,f937]) ).
tff(f937,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) )
| ~ spl18_56 ),
inference(avatar_component_clause,[],[f936]) ).
tff(f7143,plain,
( spl18_237
| ~ spl18_82
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1604,f1599,f1132,f7141]) ).
tff(f7141,plain,
( spl18_237
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK8(X0,X1)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_237])]) ).
tff(f1604,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK8(X0,X1)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_82
| ~ spl18_101 ),
inference(resolution,[],[f1600,f1133]) ).
tff(f7139,plain,
( spl18_236
| ~ spl18_81
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1603,f1599,f1128,f7137]) ).
tff(f7137,plain,
( spl18_236
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK7(X0,X1)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_236])]) ).
tff(f1603,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK7(X0,X1)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_81
| ~ spl18_101 ),
inference(resolution,[],[f1600,f1129]) ).
tff(f7135,plain,
( spl18_235
| ~ spl18_22
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1153,f1132,f749,f7133]) ).
tff(f7133,plain,
( spl18_235
<=> ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK8(bool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_235])]) ).
tff(f1153,plain,
( ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK8(bool,X0) ) )
| ~ spl18_22
| ~ spl18_82 ),
inference(superposition,[],[f1133,f750]) ).
tff(f7131,plain,
( spl18_234
| ~ spl18_22
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f1147,f1128,f749,f7129]) ).
tff(f7129,plain,
( spl18_234
<=> ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK7(bool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_234])]) ).
tff(f1147,plain,
( ! [X0: fun(bool,bool)] :
( pp(aa(fun(bool,bool),bool,aa(bool,fun(fun(bool,bool),bool),member(bool),fFalse),X0))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK7(bool,X0) ) )
| ~ spl18_22
| ~ spl18_81 ),
inference(superposition,[],[f1129,f750]) ).
tff(f7109,plain,
( spl18_233
| ~ spl18_117
| ~ spl18_118 ),
inference(avatar_split_clause,[],[f2002,f1919,f1915,f7107]) ).
tff(f7107,plain,
( spl18_233
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool))] : pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_233])]) ).
tff(f2002,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool))] : pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X2))
| ~ spl18_117
| ~ spl18_118 ),
inference(duplicate_literal_removal,[],[f1974]) ).
tff(f1974,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool))] :
( pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X2))
| pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X2),X2)) )
| ~ spl18_117
| ~ spl18_118 ),
inference(resolution,[],[f1920,f1916]) ).
tff(f7045,plain,
( spl18_232
| ~ spl18_52
| ~ spl18_72 ),
inference(avatar_split_clause,[],[f1075,f1066,f902,f7043]) ).
tff(f7043,plain,
( spl18_232
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_232])]) ).
tff(f1075,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),X2))) )
| ~ spl18_52
| ~ spl18_72 ),
inference(resolution,[],[f1067,f903]) ).
tff(f6636,plain,
( spl18_231
| ~ spl18_50
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1759,f1749,f894,f6634]) ).
tff(f6634,plain,
( spl18_231
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X2,X3)))
| ~ ord(X0)
| ~ preorder(fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_231])]) ).
tff(f894,plain,
( spl18_50
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).
tff(f1759,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X2,X3)))
| ~ ord(X0)
| ~ preorder(fun(X1,X0)) )
| ~ spl18_50
| ~ spl18_110 ),
inference(resolution,[],[f1750,f895]) ).
tff(f895,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) )
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f894]) ).
tff(f6632,plain,
( spl18_230
| ~ spl18_53
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1758,f1749,f906,f6630]) ).
tff(f6630,plain,
( spl18_230
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X1,X0)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X2,X3)))
| ~ ord(X0)
| ~ order(fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_230])]) ).
tff(f906,plain,
( spl18_53
<=> ! [X0: $tType,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X2))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).
tff(f1758,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X2,X3)),aa(X1,X0,X2,X3)))
| ~ ord(X0)
| ~ order(fun(X1,X0)) )
| ~ spl18_53
| ~ spl18_110 ),
inference(resolution,[],[f1750,f907]) ).
tff(f907,plain,
( ! [X0: $tType,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X2))
| ~ order(X0) )
| ~ spl18_53 ),
inference(avatar_component_clause,[],[f906]) ).
tff(f6628,plain,
( spl18_229
| ~ spl18_22
| ~ spl18_76 ),
inference(avatar_split_clause,[],[f1106,f1094,f749,f6626]) ).
tff(f6626,plain,
( spl18_229
<=> ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),combk(bool,X1,X0)),X2))
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_229])]) ).
tff(f1094,plain,
( spl18_76
<=> ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),combk(bool,X0,fFalse)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).
tff(f1106,plain,
( ! [X1: $tType,X2: fun(X1,bool),X0: bool] :
( pp(aa(fun(X1,bool),bool,aa(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),combk(bool,X1,X0)),X2))
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_76 ),
inference(superposition,[],[f1095,f750]) ).
tff(f1095,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),combk(bool,X0,fFalse)),X1))
| ~ spl18_76 ),
inference(avatar_component_clause,[],[f1094]) ).
tff(f6624,plain,
( spl18_228
| ~ spl18_22
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f1100,f1089,f749,f6622]) ).
tff(f6622,plain,
( spl18_228
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK13(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK13(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_228])]) ).
tff(f1100,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK13(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK13(bool,X0,X1,X2)) ) )
| ~ spl18_22
| ~ spl18_75 ),
inference(superposition,[],[f1090,f750]) ).
tff(f6614,plain,
( spl18_227
| ~ spl18_22
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f1097,f1089,f749,f6612]) ).
tff(f6612,plain,
( spl18_227
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK13(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK13(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_227])]) ).
tff(f1097,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK13(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK13(bool,X0,X2,X1)) ) )
| ~ spl18_22
| ~ spl18_75 ),
inference(superposition,[],[f1090,f750]) ).
tff(f6610,plain,
( spl18_226
| ~ spl18_59
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f1002,f984,f948,f6608]) ).
tff(f6608,plain,
( spl18_226
<=> ! [X0: $tType,X1: X0] :
( ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) )
| ( sK6(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_226])]) ).
tff(f1002,plain,
( ! [X0: $tType,X1: X0] :
( ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) )
| ( sK6(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) )
| ~ spl18_59
| ~ spl18_63 ),
inference(resolution,[],[f985,f949]) ).
tff(f6606,plain,
( spl18_225
| ~ spl18_59
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f992,f980,f948,f6604]) ).
tff(f6604,plain,
( spl18_225
<=> ! [X0: $tType,X1: X0] :
( ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) )
| ( sK5(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_225])]) ).
tff(f992,plain,
( ! [X0: $tType,X1: X0] :
( ( combk(bool,X0,fFalse) = aa(X0,fun(X0,bool),fequal(X0),X1) )
| ( sK5(X0,aa(X0,fun(X0,bool),fequal(X0),X1)) = X1 ) )
| ~ spl18_59
| ~ spl18_62 ),
inference(resolution,[],[f981,f949]) ).
tff(f6551,plain,
( spl18_224
| ~ spl18_72
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1606,f1599,f1066,f6549]) ).
tff(f6549,plain,
( spl18_224
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_224])]) ).
tff(f1606,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0)
| ~ pp(aa(X0,bool,X2,X1)) )
| ~ spl18_72
| ~ spl18_101 ),
inference(resolution,[],[f1600,f1067]) ).
tff(f6547,plain,
( spl18_223
| ~ spl18_52
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f1056,f1053,f902,f6545]) ).
tff(f6545,plain,
( spl18_223
<=> ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_223])]) ).
tff(f1056,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1)))
| ~ spl18_52
| ~ spl18_70 ),
inference(resolution,[],[f1054,f903]) ).
tff(f6543,plain,
( spl18_222
| ~ spl18_58
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f1000,f984,f944,f6541]) ).
tff(f6541,plain,
( spl18_222
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) )
| pp(X0)
| pp(sK6(bool,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_222])]) ).
tff(f1000,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) )
| pp(X0)
| pp(sK6(bool,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl18_58
| ~ spl18_63 ),
inference(resolution,[],[f985,f945]) ).
tff(f6533,plain,
( ~ spl18_172
| spl18_171
| ~ spl18_32
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f4725,f984,f792,f4210,f4228]) ).
tff(f792,plain,
( spl18_32
<=> ! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).
tff(f4725,plain,
( ( fNot = combk(bool,bool,fFalse) )
| ~ pp(sK6(bool,fNot))
| ~ spl18_32
| ~ spl18_63 ),
inference(resolution,[],[f985,f793]) ).
tff(f793,plain,
( ! [X0: bool] :
( ~ pp(aa(bool,bool,fNot,X0))
| ~ pp(X0) )
| ~ spl18_32 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f6522,plain,
( spl18_221
| ~ spl18_171
| ~ spl18_220 ),
inference(avatar_split_clause,[],[f6518,f6515,f4210,f6520]) ).
tff(f6520,plain,
( spl18_221
<=> ! [X0: bool] :
( ( fNot = aa(bool,fun(bool,bool),fdisj,X0) )
| pp(X0)
| pp(sK5(bool,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_221])]) ).
tff(f6515,plain,
( spl18_220
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) )
| pp(X0)
| pp(sK5(bool,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_220])]) ).
tff(f6518,plain,
( ! [X0: bool] :
( ( fNot = aa(bool,fun(bool,bool),fdisj,X0) )
| pp(X0)
| pp(sK5(bool,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl18_171
| ~ spl18_220 ),
inference(forward_demodulation,[],[f6516,f4212]) ).
tff(f6516,plain,
( ! [X0: bool] :
( pp(sK5(bool,aa(bool,fun(bool,bool),fdisj,X0)))
| pp(X0)
| ( aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) ) )
| ~ spl18_220 ),
inference(avatar_component_clause,[],[f6515]) ).
tff(f6517,plain,
( spl18_220
| ~ spl18_58
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f990,f980,f944,f6515]) ).
tff(f990,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fdisj,X0) = combk(bool,bool,fFalse) )
| pp(X0)
| pp(sK5(bool,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl18_58
| ~ spl18_62 ),
inference(resolution,[],[f981,f945]) ).
tff(f6465,plain,
( spl18_219
| ~ spl18_50
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2052,f2044,f894,f6463]) ).
tff(f6463,plain,
( spl18_219
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X2))
| ~ ord(X1)
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_219])]) ).
tff(f2052,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X2))
| ~ ord(X1)
| ~ preorder(X1) )
| ~ spl18_50
| ~ spl18_123 ),
inference(resolution,[],[f2045,f895]) ).
tff(f6461,plain,
( spl18_218
| ~ spl18_53
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f2051,f2044,f906,f6459]) ).
tff(f6459,plain,
( spl18_218
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X2))
| ~ ord(X1)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_218])]) ).
tff(f2051,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X2))
| ~ ord(X1)
| ~ order(X1) )
| ~ spl18_53
| ~ spl18_123 ),
inference(resolution,[],[f2045,f907]) ).
tff(f6433,plain,
( spl18_217
| spl18_172
| ~ spl18_181 ),
inference(avatar_split_clause,[],[f4571,f4376,f4228,f6430]) ).
tff(f4571,plain,
( ( fFalse = sK6(bool,fNot) )
| spl18_172
| ~ spl18_181 ),
inference(resolution,[],[f4377,f4230]) ).
tff(f6400,plain,
( ~ spl18_20
| spl18_215 ),
inference(avatar_contradiction_clause,[],[f6398]) ).
tff(f6398,plain,
( $false
| ~ spl18_20
| spl18_215 ),
inference(resolution,[],[f6392,f742]) ).
tff(f6392,plain,
( ~ finite_finite1(atom,set(atom,as))
| spl18_215 ),
inference(avatar_component_clause,[],[f6390]) ).
tff(f6390,plain,
( spl18_215
<=> finite_finite1(atom,set(atom,as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_215])]) ).
tff(f6397,plain,
( ~ spl18_214
| ~ spl18_215
| spl18_216
| ~ spl18_66
| ~ spl18_101 ),
inference(avatar_split_clause,[],[f1602,f1599,f1019,f6394,f6390,f6386]) ).
tff(f6386,plain,
( spl18_214
<=> linorder(atom) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_214])]) ).
tff(f1019,plain,
( spl18_66
<=> pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).
tff(f1602,plain,
( pp(aa(atom,bool,aa(atom,fun(atom,bool),ord_less_eq(atom),a),big_linorder_Max(atom,set(atom,as))))
| ~ finite_finite1(atom,set(atom,as))
| ~ linorder(atom)
| ~ spl18_66
| ~ spl18_101 ),
inference(resolution,[],[f1600,f1021]) ).
tff(f1021,plain,
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as)))
| ~ spl18_66 ),
inference(avatar_component_clause,[],[f1019]) ).
tff(f6384,plain,
( spl18_213
| ~ spl18_46
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f999,f984,f867,f6382]) ).
tff(f6382,plain,
( spl18_213
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(sK6(bool,aa(bool,fun(bool,bool),fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_213])]) ).
tff(f999,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(sK6(bool,aa(bool,fun(bool,bool),fconj,X0))) )
| ~ spl18_46
| ~ spl18_63 ),
inference(resolution,[],[f985,f868]) ).
tff(f6380,plain,
( spl18_212
| ~ spl18_46
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f989,f980,f867,f6378]) ).
tff(f6378,plain,
( spl18_212
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(sK5(bool,aa(bool,fun(bool,bool),fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_212])]) ).
tff(f989,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(sK5(bool,aa(bool,fun(bool,bool),fconj,X0))) )
| ~ spl18_46
| ~ spl18_62 ),
inference(resolution,[],[f981,f868]) ).
tff(f6301,plain,
( ~ spl18_14
| spl18_211
| ~ spl18_70
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1756,f1749,f1053,f6299,f712]) ).
tff(f6299,plain,
( spl18_211
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] : pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X1,X2)),aa(X0,bool,X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_211])]) ).
tff(f1756,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,X1,X2)),aa(X0,bool,X1,X2)))
| ~ ord(bool) )
| ~ spl18_70
| ~ spl18_110 ),
inference(resolution,[],[f1750,f1054]) ).
tff(f6297,plain,
( spl18_210
| ~ spl18_22
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f1099,f1089,f749,f6295]) ).
tff(f1099,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK13(X0,bool,X1,X2) ) )
| ~ spl18_22
| ~ spl18_75 ),
inference(superposition,[],[f1090,f750]) ).
tff(f6293,plain,
( spl18_209
| ~ spl18_22
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f1050,f1047,f749,f6291]) ).
tff(f6291,plain,
( spl18_209
<=> ! [X1: $tType,X2: X1,X0: bool] :
( ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X2),combk(bool,X1,X0)))
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_209])]) ).
tff(f1050,plain,
( ! [X1: $tType,X2: X1,X0: bool] :
( ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X2),combk(bool,X1,X0)))
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_69 ),
inference(superposition,[],[f1048,f750]) ).
tff(f6244,plain,
( spl18_208
| ~ spl18_35
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f1101,f1089,f809,f6242]) ).
tff(f6242,plain,
( spl18_208
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK13(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_208])]) ).
tff(f1101,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK13(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl18_35
| ~ spl18_75 ),
inference(superposition,[],[f1090,f810]) ).
tff(f6240,plain,
( spl18_207
| ~ spl18_35
| ~ spl18_75 ),
inference(avatar_split_clause,[],[f1098,f1089,f809,f6238]) ).
tff(f6238,plain,
( spl18_207
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK13(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_207])]) ).
tff(f1098,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK13(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl18_35
| ~ spl18_75 ),
inference(superposition,[],[f1090,f810]) ).
tff(f6236,plain,
( ~ spl18_13
| ~ spl18_19
| spl18_196 ),
inference(avatar_split_clause,[],[f6094,f6022,f737,f707]) ).
tff(f707,plain,
( spl18_13
<=> finite_finite(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
tff(f737,plain,
( spl18_19
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
tff(f6022,plain,
( spl18_196
<=> finite_finite1(bool,fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_196])]) ).
tff(f6094,plain,
( ~ finite_finite(bool)
| ~ spl18_19
| spl18_196 ),
inference(resolution,[],[f6023,f738]) ).
tff(f738,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite(X0) )
| ~ spl18_19 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f6023,plain,
( ~ finite_finite1(bool,fNot)
| spl18_196 ),
inference(avatar_component_clause,[],[f6022]) ).
tff(f6235,plain,
( spl18_206
| ~ spl18_5
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f1092,f1080,f667,f6233]) ).
tff(f6233,plain,
( spl18_206
<=> ! [X0: list(int)] : ( aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),minus_minus(list(int)),X0),nil(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_206])]) ).
tff(f1080,plain,
( spl18_73
<=> ! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X1),nil(X0)) = X1 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).
tff(f1092,plain,
( ! [X0: list(int)] : ( aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),minus_minus(list(int)),X0),nil(int)) = X0 )
| ~ spl18_5
| ~ spl18_73 ),
inference(resolution,[],[f1081,f669]) ).
tff(f669,plain,
( group_add(int)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f667]) ).
tff(f1081,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ group_add(X0)
| ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X1),nil(X0)) = X1 ) )
| ~ spl18_73 ),
inference(avatar_component_clause,[],[f1080]) ).
tff(f6231,plain,
( spl18_205
| ~ spl18_52
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f1023,f1019,f902,f6228]) ).
tff(f6228,plain,
( spl18_205
<=> pp(aa(fun(fun(atom,bool),bool),bool,fEx(fun(atom,bool)),aa(atom,fun(fun(atom,bool),bool),member(atom),a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_205])]) ).
tff(f1023,plain,
( pp(aa(fun(fun(atom,bool),bool),bool,fEx(fun(atom,bool)),aa(atom,fun(fun(atom,bool),bool),member(atom),a)))
| ~ spl18_52
| ~ spl18_66 ),
inference(resolution,[],[f1021,f903]) ).
tff(f6180,plain,
( spl18_204
| ~ spl18_71
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f1259,f1247,f1061,f6178]) ).
tff(f6178,plain,
( spl18_204
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| pp(aa(X0,bool,X1,big_linorder_Max(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_204])]) ).
tff(f1259,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| pp(aa(X0,bool,X1,big_linorder_Max(X0,X1))) )
| ~ spl18_71
| ~ spl18_95 ),
inference(resolution,[],[f1248,f1062]) ).
tff(f6176,plain,
( spl18_203
| ~ spl18_23
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f853,f837,f753,f6174]) ).
tff(f6174,plain,
( spl18_203
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2] :
( ( bot_bot(fun(X0,X1)) = aa(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3) )
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_203])]) ).
tff(f753,plain,
( spl18_23
<=> ! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
tff(f837,plain,
( spl18_40
<=> ! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).
tff(f853,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2] :
( ( bot_bot(fun(X0,X1)) = aa(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3) )
| ~ bot(X1) )
| ~ spl18_23
| ~ spl18_40 ),
inference(resolution,[],[f838,f754]) ).
tff(f754,plain,
( ! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) )
| ~ spl18_23 ),
inference(avatar_component_clause,[],[f753]) ).
tff(f838,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ bot(X1)
| ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) )
| ~ spl18_40 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f6067,plain,
( ~ spl18_14
| spl18_202
| ~ spl18_35
| ~ spl18_76
| ~ spl18_110 ),
inference(avatar_split_clause,[],[f1771,f1749,f1094,f809,f6065,f712]) ).
tff(f1771,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),fFalse),aa(X0,bool,X2,X1)))
| ~ ord(bool) )
| ~ spl18_35
| ~ spl18_76
| ~ spl18_110 ),
inference(forward_demodulation,[],[f1757,f810]) ).
tff(f1757,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less_eq(bool),aa(X0,bool,combk(bool,X0,fFalse),X1)),aa(X0,bool,X2,X1)))
| ~ ord(bool) )
| ~ spl18_76
| ~ spl18_110 ),
inference(resolution,[],[f1750,f1095]) ).
tff(f6063,plain,
( spl18_201
| ~ spl18_62
| ~ spl18_64 ),
inference(avatar_split_clause,[],[f1011,f1008,f980,f6061]) ).
tff(f6059,plain,
( spl18_200
| ~ spl18_22
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f1004,f984,f749,f6057]) ).
tff(f6057,plain,
( spl18_200
<=> ! [X0: fun(bool,bool)] :
( pp(aa(bool,bool,X0,fFalse))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK6(bool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_200])]) ).
tff(f1004,plain,
( ! [X0: fun(bool,bool)] :
( pp(aa(bool,bool,X0,fFalse))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK6(bool,X0) ) )
| ~ spl18_22
| ~ spl18_63 ),
inference(superposition,[],[f985,f750]) ).
tff(f6055,plain,
( spl18_199
| ~ spl18_22
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f994,f980,f749,f6053]) ).
tff(f6053,plain,
( spl18_199
<=> ! [X0: fun(bool,bool)] :
( pp(aa(bool,bool,X0,fFalse))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK5(bool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_199])]) ).
tff(f994,plain,
( ! [X0: fun(bool,bool)] :
( pp(aa(bool,bool,X0,fFalse))
| ( combk(bool,bool,fFalse) = X0 )
| ( fTrue = sK5(bool,X0) ) )
| ~ spl18_22
| ~ spl18_62 ),
inference(superposition,[],[f981,f750]) ).
tff(f6042,plain,
( spl18_198
| spl18_188
| ~ spl18_52
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f971,f940,f902,f4579,f6040]) ).
tff(f6040,plain,
( spl18_198
<=> ! [X1: bool] :
( ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_198])]) ).
tff(f971,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) )
| ~ spl18_52
| ~ spl18_57 ),
inference(resolution,[],[f941,f903]) ).
tff(f6038,plain,
( spl18_197
| ~ spl18_52
| ~ spl18_56 ),
inference(avatar_split_clause,[],[f961,f936,f902,f6036]) ).
tff(f6036,plain,
( spl18_197
<=> ! [X0: $tType] :
( ~ bot(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_197])]) ).
tff(f961,plain,
( ! [X0: $tType] :
( ~ bot(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)))) )
| ~ spl18_52
| ~ spl18_56 ),
inference(resolution,[],[f937,f903]) ).
tff(f6034,plain,
( ~ spl18_170
| spl18_171
| ~ spl18_32
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f4713,f980,f792,f4210,f4206]) ).
tff(f4206,plain,
( spl18_170
<=> pp(sK5(bool,fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_170])]) ).
tff(f4713,plain,
( ( fNot = combk(bool,bool,fFalse) )
| ~ pp(sK5(bool,fNot))
| ~ spl18_32
| ~ spl18_62 ),
inference(resolution,[],[f981,f793]) ).
tff(f6025,plain,
( spl18_196
| ~ spl18_65
| ~ spl18_171 ),
inference(avatar_split_clause,[],[f5944,f4210,f1015,f6022]) ).
tff(f1015,plain,
( spl18_65
<=> ! [X0: $tType] : finite_finite1(X0,combk(bool,X0,fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).
tff(f5944,plain,
( finite_finite1(bool,fNot)
| ~ spl18_65
| ~ spl18_171 ),
inference(superposition,[],[f1016,f4212]) ).
tff(f1016,plain,
( ! [X0: $tType] : finite_finite1(X0,combk(bool,X0,fFalse))
| ~ spl18_65 ),
inference(avatar_component_clause,[],[f1015]) ).
tff(f6006,plain,
( spl18_195
| ~ spl18_52
| ~ spl18_53 ),
inference(avatar_split_clause,[],[f926,f906,f902,f6004]) ).
tff(f6004,plain,
( spl18_195
<=> ! [X0: $tType,X1: X0] :
( ~ order(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_195])]) ).
tff(f926,plain,
( ! [X0: $tType,X1: X0] :
( ~ order(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),X1))) )
| ~ spl18_52
| ~ spl18_53 ),
inference(resolution,[],[f907,f903]) ).
tff(f6002,plain,
( spl18_194
| ~ spl18_50
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f923,f902,f894,f6000]) ).
tff(f6000,plain,
( spl18_194
<=> ! [X0: $tType,X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_194])]) ).
tff(f923,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less_eq(X0),X1)))
| ~ preorder(X0) )
| ~ spl18_50
| ~ spl18_52 ),
inference(resolution,[],[f903,f895]) ).
tff(f5988,plain,
( spl18_193
| ~ spl18_52
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f991,f980,f902,f5986]) ).
tff(f5986,plain,
( spl18_193
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_193])]) ).
tff(f991,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) )
| ~ spl18_52
| ~ spl18_62 ),
inference(resolution,[],[f981,f903]) ).
tff(f5931,plain,
( spl18_192
| spl18_170
| ~ spl18_181 ),
inference(avatar_split_clause,[],[f4570,f4376,f4206,f5928]) ).
tff(f5928,plain,
( spl18_192
<=> ( fFalse = sK5(bool,fNot) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_192])]) ).
tff(f4570,plain,
( ( fFalse = sK5(bool,fNot) )
| spl18_170
| ~ spl18_181 ),
inference(resolution,[],[f4377,f4208]) ).
tff(f4208,plain,
( ~ pp(sK5(bool,fNot))
| spl18_170 ),
inference(avatar_component_clause,[],[f4206]) ).
tff(f4952,plain,
( spl18_191
| ~ spl18_22
| ~ spl18_190 ),
inference(avatar_split_clause,[],[f4748,f4678,f749,f4950]) ).
tff(f4950,plain,
( spl18_191
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,X0) )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_191])]) ).
tff(f4748,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,X0) )
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_190 ),
inference(superposition,[],[f4680,f750]) ).
tff(f4681,plain,
( spl18_190
| spl18_55
| ~ spl18_158
| ~ spl18_181
| ~ spl18_184 ),
inference(avatar_split_clause,[],[f4615,f4400,f4376,f2678,f930,f4678]) ).
tff(f4400,plain,
( spl18_184
<=> ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_184])]) ).
tff(f4615,plain,
( ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,fFalse) )
| spl18_55
| ~ spl18_158
| ~ spl18_181
| ~ spl18_184 ),
inference(forward_demodulation,[],[f4459,f4573]) ).
tff(f4459,plain,
( ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)))) )
| spl18_55
| ~ spl18_158
| ~ spl18_184 ),
inference(forward_demodulation,[],[f4433,f2680]) ).
tff(f4433,plain,
( ( combk(bool,bool,fFalse) = aa(bool,fun(bool,bool),fconj,aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))) )
| spl18_55
| ~ spl18_184 ),
inference(resolution,[],[f4401,f932]) ).
tff(f4401,plain,
( ! [X0: bool] :
( pp(X0)
| ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) ) )
| ~ spl18_184 ),
inference(avatar_component_clause,[],[f4400]) ).
tff(f4655,plain,
( spl18_18
| ~ spl18_30
| ~ spl18_183 ),
inference(avatar_split_clause,[],[f4620,f4396,f784,f732]) ).
tff(f4396,plain,
( spl18_183
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_183])]) ).
tff(f4620,plain,
( pp(fTrue)
| ~ spl18_30
| ~ spl18_183 ),
inference(forward_demodulation,[],[f4397,f4412]) ).
tff(f4412,plain,
( ! [X0: $tType,X1: X0] : ( fTrue = aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)) )
| ~ spl18_30
| ~ spl18_183 ),
inference(resolution,[],[f4397,f785]) ).
tff(f4397,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl18_183 ),
inference(avatar_component_clause,[],[f4396]) ).
tff(f4630,plain,
( ~ spl18_1
| ~ spl18_35
| ~ spl18_62
| ~ spl18_64 ),
inference(avatar_split_clause,[],[f4623,f1008,f980,f809,f647]) ).
tff(f4623,plain,
( ~ pp(fFalse)
| ~ spl18_35
| ~ spl18_62
| ~ spl18_64 ),
inference(forward_demodulation,[],[f4622,f810]) ).
tff(f4622,plain,
( ! [X1: $tType,X2: X1] : ~ pp(aa(X1,bool,combk(bool,X1,fFalse),X2))
| ~ spl18_62
| ~ spl18_64 ),
inference(forward_demodulation,[],[f1009,f1011]) ).
tff(f4613,plain,
( ~ spl18_18
| ~ spl18_188 ),
inference(avatar_contradiction_clause,[],[f4585]) ).
tff(f4585,plain,
( $false
| ~ spl18_18
| ~ spl18_188 ),
inference(resolution,[],[f4580,f734]) ).
tff(f734,plain,
( pp(fTrue)
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f4580,plain,
( ! [X1: bool] : ~ pp(X1)
| ~ spl18_188 ),
inference(avatar_component_clause,[],[f4579]) ).
tff(f4612,plain,
( ~ spl18_168
| ~ spl18_188 ),
inference(avatar_contradiction_clause,[],[f4605]) ).
tff(f4605,plain,
( $false
| ~ spl18_168
| ~ spl18_188 ),
inference(resolution,[],[f4580,f2776]) ).
tff(f2776,plain,
( pp(aa(fun(bool,bool),bool,fEx(bool),fNot))
| ~ spl18_168 ),
inference(avatar_component_clause,[],[f2774]) ).
tff(f2774,plain,
( spl18_168
<=> pp(aa(fun(bool,bool),bool,fEx(bool),fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_168])]) ).
tff(f4611,plain,
( ~ spl18_183
| ~ spl18_188 ),
inference(avatar_contradiction_clause,[],[f4606]) ).
tff(f4606,plain,
( $false
| ~ spl18_183
| ~ spl18_188 ),
inference(resolution,[],[f4580,f4397]) ).
tff(f4584,plain,
( spl18_188
| spl18_189
| ~ spl18_44
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f921,f902,f859,f4582,f4579]) ).
tff(f4582,plain,
( spl18_189
<=> ! [X0: bool] : pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fdisj,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_189])]) ).
tff(f921,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fdisj,X0)))
| ~ pp(X1) )
| ~ spl18_44
| ~ spl18_52 ),
inference(resolution,[],[f903,f860]) ).
tff(f4577,plain,
( spl18_187
| ~ spl18_22
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f890,f887,f749,f4575]) ).
tff(f4575,plain,
( spl18_187
<=> ! [X1: $tType,X0: bool,X3: X1,X2: fun(X1,bool)] :
( ( combk(bool,X1,X0) != X2 )
| ~ pp(aa(X1,bool,X2,X3))
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_187])]) ).
tff(f887,plain,
( spl18_49
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).
tff(f890,plain,
( ! [X1: $tType,X2: fun(X1,bool),X3: X1,X0: bool] :
( ( combk(bool,X1,X0) != X2 )
| ~ pp(aa(X1,bool,X2,X3))
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_49 ),
inference(superposition,[],[f888,f750]) ).
tff(f888,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_49 ),
inference(avatar_component_clause,[],[f887]) ).
tff(f4410,plain,
( spl18_186
| ~ spl18_71
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1150,f1132,f1061,f4408]) ).
tff(f4408,plain,
( spl18_186
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_186])]) ).
tff(f1150,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) )
| ~ spl18_71
| ~ spl18_82 ),
inference(resolution,[],[f1133,f1062]) ).
tff(f4406,plain,
( spl18_185
| ~ spl18_71
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f1144,f1128,f1061,f4404]) ).
tff(f4404,plain,
( spl18_185
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_185])]) ).
tff(f1144,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) )
| ~ spl18_71
| ~ spl18_81 ),
inference(resolution,[],[f1129,f1062]) ).
tff(f4402,plain,
( spl18_184
| ~ spl18_47
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f988,f980,f871,f4400]) ).
tff(f988,plain,
( ! [X0: bool] :
( ( aa(bool,fun(bool,bool),fconj,X0) = combk(bool,bool,fFalse) )
| pp(X0) )
| ~ spl18_47
| ~ spl18_62 ),
inference(resolution,[],[f981,f872]) ).
tff(f4398,plain,
( spl18_183
| ~ spl18_43
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f922,f902,f849,f4396]) ).
tff(f849,plain,
( spl18_43
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
tff(f922,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl18_43
| ~ spl18_52 ),
inference(resolution,[],[f903,f850]) ).
tff(f850,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f849]) ).
tff(f4383,plain,
( ~ spl18_182
| spl18_55
| ~ spl18_158 ),
inference(avatar_split_clause,[],[f2682,f2678,f930,f4380]) ).
tff(f4380,plain,
( spl18_182
<=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_182])]) ).
tff(f2682,plain,
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))))
| spl18_55
| ~ spl18_158 ),
inference(superposition,[],[f932,f2680]) ).
tff(f4378,plain,
( ~ spl18_18
| spl18_181
| ~ spl18_35
| ~ spl18_100
| ~ spl18_174 ),
inference(avatar_split_clause,[],[f4277,f4245,f1585,f809,f4376,f732]) ).
tff(f4245,plain,
( spl18_174
<=> ! [X0: $tType,X2: X0,X1: bool] :
( ( fFalse = X1 )
| ( fTrue = aa(X0,bool,combk(bool,X0,X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_174])]) ).
tff(f4277,plain,
( ! [X2: bool] :
( pp(X2)
| ~ pp(fTrue)
| ( fFalse = X2 ) )
| ~ spl18_35
| ~ spl18_100
| ~ spl18_174 ),
inference(forward_demodulation,[],[f4265,f810]) ).
tff(f4265,plain,
( ! [X1: $tType,X0: $tType,X2: bool,X3: X0,X4: X1] :
( ~ pp(fTrue)
| pp(aa(product_prod(X0,X1),bool,combk(bool,product_prod(X0,X1),X2),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4)))
| ( fFalse = X2 ) )
| ~ spl18_100
| ~ spl18_174 ),
inference(superposition,[],[f1586,f4246]) ).
tff(f4246,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fTrue = aa(X0,bool,combk(bool,X0,X1),X2) )
| ( fFalse = X1 ) )
| ~ spl18_174 ),
inference(avatar_component_clause,[],[f4245]) ).
tff(f4341,plain,
( spl18_180
| ~ spl18_83 ),
inference(avatar_split_clause,[],[f1169,f1156,f4339]) ).
tff(f1169,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ linorder(X0) )
| ~ spl18_83 ),
inference(factoring,[],[f1157]) ).
tff(f4337,plain,
( spl18_179
| ~ spl18_36
| ~ spl18_51 ),
inference(avatar_split_clause,[],[f912,f898,f814,f4335]) ).
tff(f4335,plain,
( spl18_179
<=> ! [X0: $tType,X1: list(X0)] :
( ( set(X0,nil(X0)) != set(X0,X1) )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_179])]) ).
tff(f814,plain,
( spl18_36
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).
tff(f898,plain,
( spl18_51
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).
tff(f912,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( set(X0,nil(X0)) != set(X0,X1) )
| ( nil(X0) = X1 ) )
| ~ spl18_36
| ~ spl18_51 ),
inference(superposition,[],[f899,f815]) ).
tff(f815,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f814]) ).
tff(f899,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( bot_bot(fun(X0,bool)) != set(X0,X1) )
| ( nil(X0) = X1 ) )
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f898]) ).
tff(f4333,plain,
( spl18_178
| ~ spl18_39
| ~ spl18_51 ),
inference(avatar_split_clause,[],[f911,f898,f830,f4331]) ).
tff(f4331,plain,
( spl18_178
<=> ! [X0: $tType,X1: list(X0)] :
( ( combk(bool,X0,fFalse) != set(X0,X1) )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_178])]) ).
tff(f830,plain,
( spl18_39
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).
tff(f911,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( combk(bool,X0,fFalse) != set(X0,X1) )
| ( nil(X0) = X1 ) )
| ~ spl18_39
| ~ spl18_51 ),
inference(superposition,[],[f899,f831]) ).
tff(f831,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f830]) ).
tff(f4321,plain,
( spl18_177
| ~ spl18_35
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f925,f902,f809,f4319]) ).
tff(f4319,plain,
( spl18_177
<=> ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),combk(bool,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_177])]) ).
tff(f925,plain,
( ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),combk(bool,X0,X1))) )
| ~ spl18_35
| ~ spl18_52 ),
inference(superposition,[],[f903,f810]) ).
tff(f4255,plain,
( spl18_176
| ~ spl18_103
| spl18_170 ),
inference(avatar_split_clause,[],[f4214,f4206,f1620,f4253]) ).
tff(f4214,plain,
( ! [X0: bool] :
( ( sK5(bool,fNot) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_103
| spl18_170 ),
inference(resolution,[],[f4208,f1621]) ).
tff(f4251,plain,
( spl18_175
| ~ spl18_35
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f996,f980,f809,f4249]) ).
tff(f4249,plain,
( spl18_175
<=> ! [X0: $tType,X1: bool] :
( pp(X1)
| ( combk(bool,X0,fFalse) = combk(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_175])]) ).
tff(f996,plain,
( ! [X0: $tType,X1: bool] :
( pp(X1)
| ( combk(bool,X0,fFalse) = combk(bool,X0,X1) ) )
| ~ spl18_35
| ~ spl18_62 ),
inference(superposition,[],[f981,f810]) ).
tff(f4247,plain,
( spl18_174
| ~ spl18_22
| ~ spl18_35 ),
inference(avatar_split_clause,[],[f812,f809,f749,f4245]) ).
tff(f812,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fFalse = X1 )
| ( fTrue = aa(X0,bool,combk(bool,X0,X1),X2) ) )
| ~ spl18_22
| ~ spl18_35 ),
inference(superposition,[],[f810,f750]) ).
tff(f4243,plain,
( spl18_173
| ~ spl18_85
| ~ spl18_89
| ~ spl18_99 ),
inference(avatar_split_clause,[],[f1583,f1568,f1212,f1180,f4241]) ).
tff(f4241,plain,
( spl18_173
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ group_add(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_173])]) ).
tff(f1583,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ group_add(fun(X0,bool)) )
| ~ spl18_85
| ~ spl18_89
| ~ spl18_99 ),
inference(trivial_inequality_removal,[],[f1582]) ).
tff(f1582,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != combk(bool,X0,fFalse) )
| ( combk(bool,X0,fFalse) = X1 )
| ~ group_add(fun(X0,bool)) )
| ~ spl18_85
| ~ spl18_89
| ~ spl18_99 ),
inference(forward_demodulation,[],[f1578,f1213]) ).
tff(f1578,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X2) )
| ( combk(bool,X0,fFalse) = X1 )
| ~ group_add(fun(X0,bool)) )
| ~ spl18_85
| ~ spl18_99 ),
inference(superposition,[],[f1181,f1569]) ).
tff(f4231,plain,
( ~ spl18_172
| spl18_171
| ~ spl18_32
| ~ spl18_63 ),
inference(avatar_split_clause,[],[f997,f984,f792,f4210,f4228]) ).
tff(f997,plain,
( ( fNot = combk(bool,bool,fFalse) )
| ~ pp(sK6(bool,fNot))
| ~ spl18_32
| ~ spl18_63 ),
inference(resolution,[],[f985,f793]) ).
tff(f4213,plain,
( ~ spl18_170
| spl18_171
| ~ spl18_32
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f987,f980,f792,f4210,f4206]) ).
tff(f987,plain,
( ( fNot = combk(bool,bool,fFalse) )
| ~ pp(sK5(bool,fNot))
| ~ spl18_32
| ~ spl18_62 ),
inference(resolution,[],[f981,f793]) ).
tff(f3116,plain,
( spl18_41
| ~ spl18_169
| ~ spl18_160 ),
inference(avatar_split_clause,[],[f2930,f2693,f3113,f841]) ).
tff(f3113,plain,
( spl18_169
<=> ( fTrue = bot_bot(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_169])]) ).
tff(f2693,plain,
( spl18_160
<=> ! [X0: bool] :
( ( bot_bot(bool) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_160])]) ).
tff(f2930,plain,
( ! [X0: bool] :
( ( fTrue != bot_bot(bool) )
| ( fTrue = X0 ) )
| ~ spl18_160 ),
inference(equality_factoring,[],[f2694]) ).
tff(f2694,plain,
( ! [X0: bool] :
( ( bot_bot(bool) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_160 ),
inference(avatar_component_clause,[],[f2693]) ).
tff(f2809,plain,
( spl18_18
| ~ spl18_30
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f2799,f849,f784,f732]) ).
tff(f2799,plain,
( pp(fTrue)
| ~ spl18_30
| ~ spl18_43 ),
inference(forward_demodulation,[],[f850,f856]) ).
tff(f856,plain,
( ! [X0: $tType,X1: X0] : ( fTrue = aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X1),X1) )
| ~ spl18_30
| ~ spl18_43 ),
inference(resolution,[],[f850,f785]) ).
tff(f2796,plain,
( spl18_1
| ~ spl18_167 ),
inference(avatar_contradiction_clause,[],[f2778]) ).
tff(f2778,plain,
( $false
| spl18_1
| ~ spl18_167 ),
inference(resolution,[],[f2772,f649]) ).
tff(f649,plain,
( ~ pp(fFalse)
| spl18_1 ),
inference(avatar_component_clause,[],[f647]) ).
tff(f2772,plain,
( ! [X0: bool] : pp(X0)
| ~ spl18_167 ),
inference(avatar_component_clause,[],[f2771]) ).
tff(f2771,plain,
( spl18_167
<=> ! [X0: bool] : pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_167])]) ).
tff(f2795,plain,
( ~ spl18_64
| ~ spl18_167 ),
inference(avatar_contradiction_clause,[],[f2781]) ).
tff(f2781,plain,
( $false
| ~ spl18_64
| ~ spl18_167 ),
inference(resolution,[],[f2772,f1009]) ).
tff(f2794,plain,
( spl18_55
| ~ spl18_167 ),
inference(avatar_contradiction_clause,[],[f2784]) ).
tff(f2784,plain,
( $false
| spl18_55
| ~ spl18_167 ),
inference(resolution,[],[f2772,f932]) ).
tff(f2793,plain,
( ~ spl18_69
| ~ spl18_167 ),
inference(avatar_contradiction_clause,[],[f2785]) ).
tff(f2785,plain,
( $false
| ~ spl18_69
| ~ spl18_167 ),
inference(resolution,[],[f2772,f1048]) ).
tff(f2777,plain,
( spl18_167
| spl18_168
| ~ spl18_31
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f919,f902,f788,f2774,f2771]) ).
tff(f788,plain,
( spl18_31
<=> ! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).
tff(f919,plain,
( ! [X0: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),fNot))
| pp(X0) )
| ~ spl18_31
| ~ spl18_52 ),
inference(resolution,[],[f903,f789]) ).
tff(f789,plain,
( ! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) )
| ~ spl18_31 ),
inference(avatar_component_clause,[],[f788]) ).
tff(f2769,plain,
( spl18_166
| ~ spl18_36
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f833,f830,f814,f2767]) ).
tff(f2767,plain,
( spl18_166
<=> ! [X0: $tType] : ( set(X0,nil(X0)) = combk(bool,X0,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_166])]) ).
tff(f833,plain,
( ! [X0: $tType] : ( set(X0,nil(X0)) = combk(bool,X0,fFalse) )
| ~ spl18_36
| ~ spl18_39 ),
inference(superposition,[],[f831,f815]) ).
tff(f2745,plain,
( spl18_165
| ~ spl18_29
| ~ spl18_158
| ~ spl18_164 ),
inference(avatar_split_clause,[],[f2740,f2735,f2678,f780,f2742]) ).
tff(f2735,plain,
( spl18_164
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_164])]) ).
tff(f2740,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_29
| ~ spl18_158
| ~ spl18_164 ),
inference(forward_demodulation,[],[f2739,f2680]) ).
tff(f2739,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_29
| ~ spl18_164 ),
inference(forward_demodulation,[],[f2737,f781]) ).
tff(f2737,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))))
| ~ spl18_164 ),
inference(avatar_component_clause,[],[f2735]) ).
tff(f2738,plain,
spl18_164,
inference(avatar_split_clause,[],[f619,f2735]) ).
tff(f619,plain,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),
inference(forward_demodulation,[],[f439,f436]) ).
tff(f436,plain,
aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),li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inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),li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file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096li_A_N_A_092_060langle_062lks_Mxs_092_060rangle_062_A_061Max_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f439,plain,
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tff(f17,axiom,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool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file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096Max_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_058_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f2712,plain,
( spl18_163
| ~ spl18_29
| ~ spl18_162 ),
inference(avatar_split_clause,[],[f2707,f2703,f780,f2709]) ).
tff(f2703,plain,
( spl18_162
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_162])]) ).
tff(f2707,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_29
| ~ spl18_162 ),
inference(forward_demodulation,[],[f2705,f781]) ).
tff(f2705,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))))
| ~ spl18_162 ),
inference(avatar_component_clause,[],[f2703]) ).
tff(f2706,plain,
spl18_162,
inference(avatar_split_clause,[],[f438,f2703]) ).
tff(f438,plain,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_058_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f2700,plain,
( spl18_161
| ~ spl18_29
| ~ spl18_159 ),
inference(avatar_split_clause,[],[f2691,f2687,f780,f2697]) ).
tff(f2687,plain,
( spl18_159
<=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_159])]) ).
tff(f2691,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) )
| ~ spl18_29
| ~ spl18_159 ),
inference(forward_demodulation,[],[f2689,f781]) ).
tff(f2689,plain,
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
| ~ spl18_159 ),
inference(avatar_component_clause,[],[f2687]) ).
tff(f2695,plain,
( spl18_160
| spl18_42
| ~ spl18_54
| ~ spl18_91 ),
inference(avatar_split_clause,[],[f1398,f1220,f915,f844,f2693]) ).
tff(f915,plain,
( spl18_54
<=> ( fFalse = bot_bot(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).
tff(f1398,plain,
( ! [X0: bool] :
( ( fFalse = fTrue )
| ( bot_bot(bool) = X0 )
| ( fTrue = X0 ) )
| ~ spl18_54
| ~ spl18_91 ),
inference(superposition,[],[f917,f1221]) ).
tff(f917,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl18_54 ),
inference(avatar_component_clause,[],[f915]) ).
tff(f2690,plain,
spl18_159,
inference(avatar_split_clause,[],[f441,f2687]) ).
tff(f441,plain,
big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)),
inference(cnf_transformation,[],[f346]) ).
tff(f346,plain,
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f259,f345]) ).
tff(f345,plain,
( ? [X0: int,X1: list(int)] :
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as)))) )
=> ( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ) ),
introduced(choice_axiom,[]) ).
tff(f259,plain,
? [X0: int,X1: list(int)] :
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as)))) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
~ ! [X0: int,X1: list(int)] :
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as))))
=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
~ ! [X20: int,X21: list(int)] :
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X20),X21)),set(product_prod(int,list(int)),lbounds(as))))
=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X20),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X21),xs)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096_B_Bthesis_O_A_I_B_Bli_Alks_O_A_091_124_A_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_059_AMax_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_061_Ali_A_N_A_092_060langle_062lks_Mxs_092_060rangle_062_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f2681,plain,
( spl18_158
| ~ spl18_157 ),
inference(avatar_split_clause,[],[f2676,f2672,f2678]) ).
tff(f2672,plain,
( spl18_157
<=> ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_157])]) ).
tff(f2676,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
| ~ spl18_157 ),
inference(forward_demodulation,[],[f2674,f441]) ).
tff(f2674,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) )
| ~ spl18_157 ),
inference(avatar_component_clause,[],[f2672]) ).
tff(f2675,plain,
spl18_157,
inference(avatar_split_clause,[],[f436,f2672]) ).
tff(f2669,plain,
( ~ spl18_156
| ~ spl18_36
| ~ spl18_39
| spl18_155 ),
inference(avatar_split_clause,[],[f2664,f2659,f830,f814,f2666]) ).
tff(f2666,plain,
( spl18_156
<=> ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) = combk(bool,int,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_156])]) ).
tff(f2659,plain,
( spl18_155
<=> ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) = bot_bot(fun(int,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_155])]) ).
tff(f2664,plain,
( ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != combk(bool,int,fFalse) )
| ~ spl18_36
| ~ spl18_39
| spl18_155 ),
inference(forward_demodulation,[],[f2663,f833]) ).
tff(f2663,plain,
( ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != set(int,nil(int)) )
| ~ spl18_36
| spl18_155 ),
inference(forward_demodulation,[],[f2661,f815]) ).
tff(f2661,plain,
( ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != bot_bot(fun(int,bool)) )
| spl18_155 ),
inference(avatar_component_clause,[],[f2659]) ).
tff(f2662,plain,
~ spl18_155,
inference(avatar_split_clause,[],[f435,f2659]) ).
tff(f435,plain,
collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != bot_bot(fun(int,bool)),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != bot_bot(fun(int,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__096_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_126_061_A_123_125_096) ).
tff(f2657,plain,
( spl18_154
| ~ spl18_29
| ~ spl18_153 ),
inference(avatar_split_clause,[],[f2652,f2648,f780,f2654]) ).
tff(f2648,plain,
( spl18_153
<=> finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_153])]) ).
tff(f2652,plain,
( finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))
| ~ spl18_29
| ~ spl18_153 ),
inference(forward_demodulation,[],[f2650,f781]) ).
tff(f2650,plain,
( finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl18_153 ),
inference(avatar_component_clause,[],[f2648]) ).
tff(f2651,plain,
spl18_153,
inference(avatar_split_clause,[],[f434,f2648]) ).
tff(f434,plain,
finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f2591,plain,
spl18_152,
inference(avatar_split_clause,[],[f580,f2589]) ).
tff(f580,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2)))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2)) ),
inference(cnf_transformation,[],[f404]) ).
tff(f404,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2)))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2))
| ~ pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2))) ) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2)))
<=> pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X1: $tType,X0: $tType,X33: fun(product_prod(X0,X1),bool),X34: fun(product_prod(X0,X1),bool)] :
( pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X34)),aa(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(product_prod(X0,X1),bool),fun(X0,fun(X1,bool))),combc(X0,fun(product_prod(X0,X1),bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),aa(fun(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(X0,fun(fun(product_prod(X0,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(product_prod(X0,X1),bool),fun(X1,bool)),X0),combc(X1,fun(product_prod(X0,X1),bool),bool)),aa(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),aa(fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),fun(fun(X0,fun(X1,product_prod(X0,X1))),fun(X0,fun(X1,fun(fun(product_prod(X0,X1),bool),bool)))),combb(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool)),X0),aa(fun(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool)),fun(fun(X1,product_prod(X0,X1)),fun(X1,fun(fun(product_prod(X0,X1),bool),bool))),combb(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),X1),member(product_prod(X0,X1)))),product_Pair(X0,X1)))),X33)))
<=> pp(aa(fun(product_prod(X0,X1),bool),bool,aa(fun(product_prod(X0,X1),bool),fun(fun(product_prod(X0,X1),bool),bool),ord_less_eq(fun(product_prod(X0,X1),bool)),X34),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_pred__subset__eq2) ).
tff(f2587,plain,
spl18_151,
inference(avatar_split_clause,[],[f579,f2585]) ).
tff(f2585,plain,
( spl18_151
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X1,X0),bool),X2: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2))
| ~ pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_151])]) ).
tff(f579,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(fun(product_prod(X1,X0),bool),fun(fun(product_prod(X1,X0),bool),bool),ord_less_eq(fun(product_prod(X1,X0),bool)),X3),X2))
| ~ pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X3)),aa(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(product_prod(X1,X0),bool),fun(X1,fun(X0,bool))),combc(X1,fun(product_prod(X1,X0),bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),aa(fun(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(X1,fun(fun(product_prod(X1,X0),bool),fun(X0,bool)))),combb(fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(product_prod(X1,X0),bool),fun(X0,bool)),X1),combc(X0,fun(product_prod(X1,X0),bool),bool)),aa(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),aa(fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),fun(fun(X1,fun(X0,product_prod(X1,X0))),fun(X1,fun(X0,fun(fun(product_prod(X1,X0),bool),bool)))),combb(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool)),X1),aa(fun(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool)),fun(fun(X0,product_prod(X1,X0)),fun(X0,fun(fun(product_prod(X1,X0),bool),bool))),combb(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),X0),member(product_prod(X1,X0)))),product_Pair(X1,X0)))),X2))) ),
inference(cnf_transformation,[],[f404]) ).
tff(f2581,plain,
spl18_150,
inference(avatar_split_clause,[],[f637,f2579]) ).
tff(f2579,plain,
( spl18_150
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X1,X0)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_150])]) ).
tff(f637,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))) ),
inference(forward_demodulation,[],[f636,f480]) ).
tff(f480,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X26: fun(X0,bool)] : ( collect(X0,X26) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
tff(f636,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f558,f480]) ).
tff(f558,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(ennf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X1,collect(X1,X3))
=> finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3)))) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X1: $tType,X0: $tType,X16: fun(X0,X1),X26: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X26))
=> finite_finite1(X1,collect(X1,aa(fun(X1,fun(X0,bool)),fun(X1,bool),aa(fun(fun(X0,bool),bool),fun(fun(X1,fun(X0,bool)),fun(X1,bool)),combb(fun(X0,bool),bool,X1),fEx(X0)),aa(fun(X0,bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X1,fun(X0,bool))),combc(X1,fun(X0,bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(bool,bool))),fun(X1,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(bool,bool))),fun(X1,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X1),combs(X0,bool,bool)),aa(fun(X1,fun(X0,bool)),fun(X1,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X1,fun(X0,bool)),fun(X1,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X1),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj)),aa(fun(X0,X1),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(X0,X1),fun(X0,bool))),fun(fun(X0,X1),fun(X1,fun(X0,bool))),combc(X1,fun(X0,X1),fun(X0,bool)),aa(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X0,X1),fun(X0,bool))),aa(fun(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool))),fun(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X0,X1),fun(X0,bool)))),combb(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),X1),combb(X1,bool,X0)),fequal(X1))),X16)))),X26)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_finite__image__set) ).
tff(f2575,plain,
spl18_149,
inference(avatar_split_clause,[],[f529,f2573]) ).
tff(f529,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = collect(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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = collect(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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11) = collect(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),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X12))),aa(fun(X0,bool),fun(X0,bool),aa(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_set__diff__eq) ).
tff(f2567,plain,
spl18_148,
inference(avatar_split_clause,[],[f645,f2565]) ).
tff(f645,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5)) ),
inference(forward_demodulation,[],[f644,f480]) ).
tff(f644,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f643,f480]) ).
tff(f643,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f559,f480]) ).
tff(f559,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f396]) ).
tff(f396,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3))))
& pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3))) ) )
& ( ! [X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f394,f395]) ).
tff(f395,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) )
=> ( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3))))
& pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f394,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) ) )
& ( ! [X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(rectify,[],[f393]) ).
tff(f393,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) ) )
& ( ! [X4: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
| ~ pp(aa(X1,bool,X3,X4)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(nnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
<=> ! [X4: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
| ~ pp(aa(X1,bool,X3,X4)) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(ennf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X1,collect(X1,X3))
=> ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
<=> ! [X4: X1] :
( pp(aa(X1,bool,X3,X4))
=> finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4))) ) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X1: $tType,X0: $tType,X37: fun(X1,fun(X0,bool)),X26: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X26))
=> ( finite_finite1(X1,collect(X1,aa(fun(X1,fun(X0,bool)),fun(X1,bool),aa(fun(fun(X0,bool),bool),fun(fun(X1,fun(X0,bool)),fun(X1,bool)),combb(fun(X0,bool),bool,X1),fEx(X0)),aa(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X1),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),X26))),X37))))
<=> ! [X43: X0] :
( pp(aa(X0,bool,X26,X43))
=> finite_finite1(X1,collect(X1,aa(X0,fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),X37),X43))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_finite__Collect__bounded__ex) ).
tff(f2556,plain,
spl18_147,
inference(avatar_split_clause,[],[f640,f2554]) ).
tff(f640,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))) ),
inference(forward_demodulation,[],[f639,f480]) ).
tff(f639,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f638,f480]) ).
tff(f638,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f561,f480]) ).
tff(f561,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK12(X0,X1,X2,X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f396]) ).
tff(f2516,plain,
spl18_146,
inference(avatar_split_clause,[],[f642,f2514]) ).
tff(f642,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3))) ),
inference(forward_demodulation,[],[f641,f480]) ).
tff(f641,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f560,f480]) ).
tff(f560,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| pp(aa(X1,bool,X3,sK12(X0,X1,X2,X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f396]) ).
tff(f2443,plain,
spl18_145,
inference(avatar_split_clause,[],[f582,f2441]) ).
tff(f582,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( X2 = X3 )
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ),
inference(cnf_transformation,[],[f408]) ).
tff(f408,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( ! [X4: X1,X5: X0] :
( ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) ) )
| ( X2 != X3 ) )
& ( ( X2 = X3 )
| ( ( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f406,f407]) ).
tff(f407,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ? [X6: X1,X7: X0] :
( ( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X3)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X3)) ) )
=> ( ( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f406,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( ! [X4: X1,X5: X0] :
( ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) ) )
| ( X2 != X3 ) )
& ( ( X2 = X3 )
| ? [X6: X1,X7: X0] :
( ( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X3)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)),X3)) ) ) ) ),
inference(rectify,[],[f405]) ).
tff(f405,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( ! [X4: X1,X5: X0] :
( ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) ) )
| ( X2 != X3 ) )
& ( ( X2 = X3 )
| ? [X4: X1,X5: X0] :
( ( ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))
| ~ pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) )
& ( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3)) ) ) ) ),
inference(nnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ! [X4: X1,X5: X0] :
( pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X3))
<=> pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)),X2)) )
<=> ( X2 = X3 ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X1: $tType,X0: $tType,X33: fun(product_prod(X0,X1),bool),X34: fun(product_prod(X0,X1),bool)] :
( ! [X17: X0,X35: X1] :
( pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X17),X35)),X34))
<=> pp(aa(fun(product_prod(X0,X1),bool),bool,aa(product_prod(X0,X1),fun(fun(product_prod(X0,X1),bool),bool),member(product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X17),X35)),X33)) )
<=> ( X33 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_pred__equals__eq2) ).
tff(f2439,plain,
spl18_144,
inference(avatar_split_clause,[],[f581,f2437]) ).
tff(f581,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ( X2 = X3 )
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X2))
| pp(aa(fun(product_prod(X1,X0),bool),bool,aa(product_prod(X1,X0),fun(fun(product_prod(X1,X0),bool),bool),member(product_prod(X1,X0)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK16(X0,X1,X2,X3)),sK17(X0,X1,X2,X3))),X3)) ),
inference(cnf_transformation,[],[f408]) ).
tff(f2386,plain,
spl18_143,
inference(avatar_split_clause,[],[f553,f2384]) ).
tff(f553,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(cnf_transformation,[],[f387]) ).
tff(f387,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) )
& ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) ) ),
inference(nnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1)))
<=> pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType,X33: fun(X0,bool),X34: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X34)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X33)))
<=> pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X34),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_pred__subset__eq) ).
tff(f2382,plain,
spl18_142,
inference(avatar_split_clause,[],[f552,f2380]) ).
tff(f552,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))) ),
inference(cnf_transformation,[],[f387]) ).
tff(f2377,plain,
spl18_141,
inference(avatar_split_clause,[],[f448,f2375]) ).
tff(f448,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X4: list(X0),X5: list(X0),X6: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X6),X5)),X4) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X6),X4)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X5),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_iprod__left__diff__distrib) ).
tff(f2339,plain,
spl18_140,
inference(avatar_split_clause,[],[f563,f2337]) ).
tff(f563,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ),
inference(flattening,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ),
inference(ennf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
=> ( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool),X8: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),X12))
=> ( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),X11))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_DiffI) ).
tff(f2335,plain,
spl18_139,
inference(avatar_split_clause,[],[f528,f2333]) ).
tff(f528,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X1) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X1) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11)),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Diff__idemp) ).
tff(f2328,plain,
spl18_138,
inference(avatar_split_clause,[],[f631,f2326]) ).
tff(f631,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| ~ finite_finite1(X0,X1)
| finite_finite1(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),fdisj),X2)),X1)) ),
inference(forward_demodulation,[],[f630,f480]) ).
tff(f630,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(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),fdisj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f629,f480]) ).
tff(f629,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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),fdisj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f551,f480]) ).
tff(f551,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(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),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(cnf_transformation,[],[f386]) ).
tff(f386,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(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),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) )
& ( ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) )
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ) ),
inference(flattening,[],[f385]) ).
tff(f385,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(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),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) )
& ( ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) )
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,collect(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),fdisj),X2)),X1)))
<=> ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType,X37: fun(X0,bool),X26: fun(X0,bool)] :
( finite_finite1(X0,collect(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),fdisj),X26)),X37)))
<=> ( finite_finite1(X0,collect(X0,X37))
& finite_finite1(X0,collect(X0,X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__Collect__disjI) ).
tff(f2324,plain,
( spl18_137
| spl18_1
| ~ spl18_114 ),
inference(avatar_split_clause,[],[f2234,f1868,f647,f2321]) ).
tff(f1868,plain,
( spl18_114
<=> ! [X0: bool] :
( ( fTrue = aa(bool,bool,fNot,X0) )
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_114])]) ).
tff(f2234,plain,
( ( fTrue = aa(bool,bool,fNot,fFalse) )
| spl18_1
| ~ spl18_114 ),
inference(resolution,[],[f1869,f649]) ).
tff(f1869,plain,
( ! [X0: bool] :
( pp(X0)
| ( fTrue = aa(bool,bool,fNot,X0) ) )
| ~ spl18_114 ),
inference(avatar_component_clause,[],[f1868]) ).
tff(f2313,plain,
spl18_136,
inference(avatar_split_clause,[],[f635,f2311]) ).
tff(f635,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X2) ),
inference(forward_demodulation,[],[f634,f480]) ).
tff(f634,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X2)
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ),
inference(forward_demodulation,[],[f549,f480]) ).
tff(f549,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X2))
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ),
inference(cnf_transformation,[],[f386]) ).
tff(f2309,plain,
spl18_135,
inference(avatar_split_clause,[],[f633,f2307]) ).
tff(f633,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(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),fdisj),X2)),X1))
| finite_finite1(X0,X1) ),
inference(forward_demodulation,[],[f632,f480]) ).
tff(f632,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ),
inference(forward_demodulation,[],[f550,f480]) ).
tff(f550,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(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),fdisj),X2)),X1))) ),
inference(cnf_transformation,[],[f386]) ).
tff(f2305,plain,
spl18_134,
inference(avatar_split_clause,[],[f628,f2303]) ).
tff(f628,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| finite_finite1(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)) ),
inference(forward_demodulation,[],[f627,f480]) ).
tff(f627,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f542,f480]) ).
tff(f542,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(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)))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(cnf_transformation,[],[f322]) ).
tff(f322,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,collect(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)))
| ( ~ finite_finite1(X0,collect(X0,X1))
& ~ finite_finite1(X0,collect(X0,X2)) ) ),
inference(ennf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,X1))
| finite_finite1(X0,collect(X0,X2)) )
=> finite_finite1(X0,collect(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))) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X37: fun(X0,bool),X26: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,X37))
| finite_finite1(X0,collect(X0,X26)) )
=> finite_finite1(X0,collect(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),X26)),X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_finite__Collect__conjI) ).
tff(f2301,plain,
spl18_133,
inference(avatar_split_clause,[],[f626,f2299]) ).
tff(f626,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(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)) ),
inference(forward_demodulation,[],[f625,f480]) ).
tff(f625,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(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))
| ~ finite_finite1(X0,collect(X0,X1)) ),
inference(forward_demodulation,[],[f543,f480]) ).
tff(f543,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(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)))
| ~ finite_finite1(X0,collect(X0,X1)) ),
inference(cnf_transformation,[],[f322]) ).
tff(f2233,plain,
spl18_132,
inference(avatar_split_clause,[],[f568,f2231]) ).
tff(f568,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(cnf_transformation,[],[f336]) ).
tff(f336,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(ennf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool),X8: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11)))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_DiffD1) ).
tff(f2229,plain,
spl18_131,
inference(avatar_split_clause,[],[f567,f2227]) ).
tff(f567,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(ennf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
=> ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool),X8: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11)))
=> ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_DiffD2) ).
tff(f2205,plain,
spl18_130,
inference(avatar_split_clause,[],[f440,f2202]) ).
tff(f440,plain,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))),
inference(cnf_transformation,[],[f346]) ).
tff(f2200,plain,
spl18_129,
inference(avatar_split_clause,[],[f433,f2197]) ).
tff(f433,plain,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_calculation_I1_J) ).
tff(f2176,plain,
spl18_128,
inference(avatar_split_clause,[],[f565,f2174]) ).
tff(f565,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2)) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2)) ),
inference(flattening,[],[f331]) ).
tff(f331,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2)) ),
inference(ennf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X0: $tType,X14: X0,X11: fun(X0,bool),X12: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X11))
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X14),X12))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X14),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_in__mono) ).
tff(f2135,plain,
( spl18_127
| ~ spl18_30
| ~ spl18_77 ),
inference(avatar_split_clause,[],[f1173,f1109,f784,f2132]) ).
tff(f2132,plain,
( spl18_127
<=> ( fTrue = aa(atom,bool,set(atom,as),a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_127])]) ).
tff(f1109,plain,
( spl18_77
<=> pp(aa(atom,bool,set(atom,as),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).
tff(f1173,plain,
( ( fTrue = aa(atom,bool,set(atom,as),a) )
| ~ spl18_30
| ~ spl18_77 ),
inference(resolution,[],[f1111,f785]) ).
tff(f1111,plain,
( pp(aa(atom,bool,set(atom,as),a))
| ~ spl18_77 ),
inference(avatar_component_clause,[],[f1109]) ).
tff(f2130,plain,
spl18_126,
inference(avatar_split_clause,[],[f588,f2128]) ).
tff(f588,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0,X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3)) ),
inference(cnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0,X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3)) ),
inference(flattening,[],[f340]) ).
tff(f340,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0,X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| ~ pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3)) ),
inference(ennf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0,X5: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X5,X4),X3))
=> ( pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X5),X2))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3)) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X1: $tType,X37: fun(X0,fun(X1,bool)),X19: X1,X14: X0,X26: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X26,X14),X19))
=> ( pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X26),X37))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X37,X14),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rev__predicate2D) ).
tff(f2126,plain,
spl18_125,
inference(avatar_split_clause,[],[f450,f2124]) ).
tff(f450,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ ordered_ab_group_add(X0) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3)) ) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
| ~ ordered_ab_group_add(X0) ),
inference(nnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
| ~ ordered_ab_group_add(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X4),X3))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X7: X0,X8: X0,X9: X0,X10: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X10),X9) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X8),X7) )
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X10),X9))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X8),X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_diff__eq__diff__less__eq) ).
tff(f2050,plain,
spl18_124,
inference(avatar_split_clause,[],[f502,f2048]) ).
tff(f502,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK4(X0,X1,X2,X3))),aa(X1,X0,X2,sK4(X0,X1,X2,X3))))
| ~ ord(X0) ),
inference(cnf_transformation,[],[f360]) ).
tff(f360,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK4(X0,X1,X2,X3))),aa(X1,X0,X2,sK4(X0,X1,X2,X3)))) )
& ( ! [X5: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X5)),aa(X1,X0,X2,X5)))
| ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2)) ) )
| ~ ord(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f358,f359]) ).
tff(f359,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4)))
=> ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK4(X0,X1,X2,X3))),aa(X1,X0,X2,sK4(X0,X1,X2,X3)))) ),
introduced(choice_axiom,[]) ).
tff(f358,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ? [X4: X1] : ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4))) )
& ( ! [X5: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X5)),aa(X1,X0,X2,X5)))
| ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2)) ) )
| ~ ord(X0) ),
inference(rectify,[],[f357]) ).
tff(f357,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ? [X4: X1] : ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4))) )
& ( ! [X4: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4)))
| ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2)) ) )
| ~ ord(X0) ),
inference(nnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
<=> ! [X4: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4))) )
| ~ ord(X0) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: $tType] :
( ord(X0)
=> ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
<=> ! [X4: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4))) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X1: $tType,X0: $tType] :
( ord(X1)
=> ! [X15: fun(X0,X1),X16: fun(X0,X1)] :
( pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X16),X15))
<=> ! [X17: X0] : pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X16,X17)),aa(X0,X1,X15,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_le__fun__def) ).
tff(f2046,plain,
spl18_123,
inference(avatar_split_clause,[],[f500,f2044]) ).
tff(f500,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK3(X0,X1,X2,X3))),aa(X1,X0,X2,sK3(X0,X1,X2,X3))))
| ~ ord(X0) ),
inference(cnf_transformation,[],[f356]) ).
tff(f356,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK3(X0,X1,X2,X3))),aa(X1,X0,X2,sK3(X0,X1,X2,X3)))) )
| ~ ord(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f299,f355]) ).
tff(f355,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4)))
=> ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,sK3(X0,X1,X2,X3))),aa(X1,X0,X2,sK3(X0,X1,X2,X3)))) ),
introduced(choice_axiom,[]) ).
tff(f299,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ? [X4: X1] : ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4))) )
| ~ ord(X0) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType] :
( ord(X0)
=> ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X4)),aa(X1,X0,X2,X4)))
=> pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2)) ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X1: $tType,X0: $tType] :
( ord(X1)
=> ! [X15: fun(X0,X1),X16: fun(X0,X1)] :
( ! [X32: X0] : pp(aa(X1,bool,aa(X1,fun(X1,bool),ord_less_eq(X1),aa(X0,X1,X16,X32)),aa(X0,X1,X15,X32)))
=> pp(aa(fun(X0,X1),bool,aa(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X16),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_le__funI) ).
tff(f2020,plain,
( spl18_122
| ~ spl18_39
| ~ spl18_119 ),
inference(avatar_split_clause,[],[f2008,f2005,f830,f2018]) ).
tff(f2005,plain,
( spl18_119
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_119])]) ).
tff(f2008,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X2 )
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(X0) )
| ~ spl18_39
| ~ spl18_119 ),
inference(forward_demodulation,[],[f2006,f831]) ).
tff(f2006,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(X0) )
| ~ spl18_119 ),
inference(avatar_component_clause,[],[f2005]) ).
tff(f2016,plain,
spl18_121,
inference(avatar_split_clause,[],[f506,f2014]) ).
tff(f506,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
( ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X4),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X4,X2)),aa(X1,X0,X3,X2)) )
| ~ cl_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] : ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X4),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X4,X2)),aa(X1,X0,X3,X2)) )
| ~ cl_Groups_Ominus(X0) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X0)
=> ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] : ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X4),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X4,X2)),aa(X1,X0,X3,X2)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X0)
=> ! [X14: X1,X11: fun(X1,X0),X12: fun(X1,X0)] : ( aa(X1,X0,aa(fun(X1,X0),fun(X1,X0),aa(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X12),X11),X14) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X1,X0,X12,X14)),aa(X1,X0,X11,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_minus__apply) ).
tff(f2012,plain,
( spl18_120
| ~ spl18_22
| ~ spl18_65 ),
inference(avatar_split_clause,[],[f1064,f1015,f749,f2010]) ).
tff(f2010,plain,
( spl18_120
<=> ! [X1: $tType,X0: bool] :
( finite_finite1(X1,combk(bool,X1,X0))
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_120])]) ).
tff(f1064,plain,
( ! [X1: $tType,X0: bool] :
( finite_finite1(X1,combk(bool,X1,X0))
| ( fTrue = X0 ) )
| ~ spl18_22
| ~ spl18_65 ),
inference(superposition,[],[f1016,f750]) ).
tff(f2007,plain,
spl18_119,
inference(avatar_split_clause,[],[f464,f2005]) ).
tff(f464,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool),X2: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) )
| ~ linorder(X0) ),
inference(flattening,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool),X2: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1)))
| ~ finite_finite1(X0,X1)
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: fun(X0,bool),X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
=> ( ( bot_bot(fun(X0,bool)) != X2 )
=> ( finite_finite1(X0,X1)
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X2)),big_linorder_Max(X0,X1))) ) ) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X41: fun(X0,bool),X42: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X42),X41))
=> ( ( bot_bot(fun(X0,bool)) != X42 )
=> ( finite_finite1(X0,X41)
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),big_linorder_Max(X0,X42)),big_linorder_Max(X0,X41))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Max__mono) ).
tff(f1921,plain,
spl18_118,
inference(avatar_split_clause,[],[f573,f1919]) ).
tff(f573,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f400]) ).
tff(f400,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| ( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3)))
& pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f339,f399]) ).
tff(f399,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( ? [X4: X1,X5: X0] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5))
& pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,X4),X5)) )
=> ( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3)))
& pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f339,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| ? [X4: X1,X5: X0] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5))
& pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,X4),X5)) ) ),
inference(ennf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( ! [X4: X1,X5: X0] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,X4),X5))
=> pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5)) )
=> pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2)) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X1: $tType,X0: $tType,X37: fun(X0,fun(X1,bool)),X26: fun(X0,fun(X1,bool))] :
( ! [X32: X0,X44: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X26,X32),X44))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X37,X32),X44)) )
=> pp(aa(fun(X0,fun(X1,bool)),bool,aa(fun(X0,fun(X1,bool)),fun(fun(X0,fun(X1,bool)),bool),ord_less_eq(fun(X0,fun(X1,bool))),X26),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_predicate2I) ).
tff(f1917,plain,
spl18_117,
inference(avatar_split_clause,[],[f572,f1915]) ).
tff(f572,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: fun(X1,fun(X0,bool))] :
( pp(aa(fun(X1,fun(X0,bool)),bool,aa(fun(X1,fun(X0,bool)),fun(fun(X1,fun(X0,bool)),bool),ord_less_eq(fun(X1,fun(X0,bool))),X3),X2))
| pp(aa(X0,bool,aa(X1,fun(X0,bool),X3,sK14(X0,X1,X2,X3)),sK15(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f400]) ).
tff(f1913,plain,
spl18_116,
inference(avatar_split_clause,[],[f620,f1911]) ).
tff(f620,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))
| ~ finite_finite1(X0,X1) ),
inference(forward_demodulation,[],[f508,f480]) ).
tff(f508,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(fun(X0,bool),collect(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1)))
| ~ finite_finite1(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(fun(X0,bool),collect(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1)))
| ~ finite_finite1(X0,X1) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
=> finite_finite1(fun(X0,bool),collect(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType,X12: fun(X0,bool)] :
( finite_finite1(X0,X12)
=> finite_finite1(fun(X0,bool),collect(fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),bool),aa(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__Collect__subsets) ).
tff(f1874,plain,
spl18_115,
inference(avatar_split_clause,[],[f541,f1872]) ).
tff(f541,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( X1 = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( X1 = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(flattening,[],[f320]) ).
tff(f320,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( X1 = X2 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(ennf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X11))
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X11),X12))
=> ( X11 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_equalityI) ).
tff(f1870,plain,
( spl18_114
| ~ spl18_30
| ~ spl18_31 ),
inference(avatar_split_clause,[],[f807,f788,f784,f1868]) ).
tff(f807,plain,
( ! [X0: bool] :
( ( fTrue = aa(bool,bool,fNot,X0) )
| pp(X0) )
| ~ spl18_30
| ~ spl18_31 ),
inference(resolution,[],[f785,f789]) ).
tff(f1866,plain,
spl18_113,
inference(avatar_split_clause,[],[f461,f1864]) ).
tff(f461,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),X2))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f351]) ).
tff(f351,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),X2)) )
| ~ finite_finite1(X0,X2) )
| ~ linorder(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f273,f350]) ).
tff(f350,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( ? [X3: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
=> ( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ? [X3: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ~ finite_finite1(X0,X2) )
| ~ linorder(X0) ),
inference(flattening,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ? [X3: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ~ finite_finite1(X0,X2) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1)) )
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> ( big_linorder_Max(X0,X2) = X1 ) ) ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X14: X0,X12: fun(X0,bool)] :
( finite_finite1(X0,X12)
=> ( ! [X44: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X44),X12))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X44),X14)) )
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X14),X12))
=> ( big_linorder_Max(X0,X12) = X14 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Max__eqI) ).
tff(f1793,plain,
spl18_112,
inference(avatar_split_clause,[],[f587,f1791]) ).
tff(f587,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,[],[f254]) ).
tff(f254,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,[],[f133]) ).
tff(f133,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X48: X0,X49: fun(X0,X1),X47: 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),X47),X49),X48) = aa(X1,X2,aa(X0,fun(X1,X2),X47,X48),aa(X0,X1,X49,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1755,plain,
spl18_111,
inference(avatar_split_clause,[],[f527,f1753]) ).
tff(f527,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X2)),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)),X2)),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11)),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Diff__subset) ).
tff(f1751,plain,
spl18_110,
inference(avatar_split_clause,[],[f501,f1749]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: X1] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),aa(X1,X0,X3,X5)),aa(X1,X0,X2,X5)))
| ~ pp(aa(fun(X1,X0),bool,aa(fun(X1,X0),fun(fun(X1,X0),bool),ord_less_eq(fun(X1,X0)),X3),X2))
| ~ ord(X0) ),
inference(cnf_transformation,[],[f360]) ).
tff(f1733,plain,
spl18_109,
inference(avatar_split_clause,[],[f462,f1731]) ).
tff(f462,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( big_linorder_Max(X0,X2) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),sK2(X0,X1,X2)),X1))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f351]) ).
tff(f1692,plain,
spl18_108,
inference(avatar_split_clause,[],[f473,f1690]) ).
tff(f473,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2)) )
| ~ preorder(X0) ),
inference(flattening,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X2))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X1)) ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X22: X0,X18: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X18))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X18),X22))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_order__trans) ).
tff(f1686,plain,
spl18_107,
inference(avatar_split_clause,[],[f591,f1684]) ).
tff(f591,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( ( X2 = X4 )
& ( X3 = X5 ) )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(ennf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) )
=> ~ ( ( X3 = X5 )
=> ( X2 != X4 ) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType,X1: $tType,X38: X1,X39: X0,X24: X1,X25: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X25),X24) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X39),X38) )
=> ~ ( ( X25 = X39 )
=> ( X24 != X38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Pair__inject) ).
tff(f1682,plain,
spl18_106,
inference(avatar_split_clause,[],[f590,f1680]) ).
tff(f590,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(cnf_transformation,[],[f344]) ).
tff(f1630,plain,
spl18_105,
inference(avatar_split_clause,[],[f586,f1628]) ).
tff(f586,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,[],[f253]) ).
tff(f253,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,[],[f130]) ).
tff(f130,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X48: X0,X49: fun(X0,X1),X47: 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),X47),X49),X48) = aa(X1,X2,X47,aa(X0,X1,X49,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1626,plain,
spl18_104,
inference(avatar_split_clause,[],[f585,f1624]) ).
tff(f585,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X48: X0,X49: X1,X47: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X47),X49),X48) = aa(X1,X2,aa(X0,fun(X1,X2),X47,X48),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1622,plain,
( spl18_103
| ~ spl18_18
| ~ spl18_91 ),
inference(avatar_split_clause,[],[f1397,f1220,f732,f1620]) ).
tff(f1397,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl18_18
| ~ spl18_91 ),
inference(superposition,[],[f734,f1221]) ).
tff(f1618,plain,
spl18_102,
inference(avatar_split_clause,[],[f555,f1616]) ).
tff(f555,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f392]) ).
tff(f392,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2)))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK11(X0,X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f389,f391,f390]) ).
tff(f390,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f391,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,sK11(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f389,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(rectify,[],[f388]) ).
tff(f388,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
| ? [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
inference(nnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
<=> ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType,X1: $tType,X26: fun(product_prod(X0,X1),bool)] :
( ! [X27: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X26,X27))
<=> ! [X28: X0,X29: X1] : pp(aa(product_prod(X0,X1),bool,X26,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X28),X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_split__paired__All) ).
tff(f1601,plain,
spl18_101,
inference(avatar_split_clause,[],[f460,f1599]) ).
tff(f460,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ finite_finite1(X0,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ finite_finite1(X0,X2) )
| ~ linorder(X0) ),
inference(flattening,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2)))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ finite_finite1(X0,X2) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),big_linorder_Max(X0,X2))) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X14: X0,X12: fun(X0,bool)] :
( finite_finite1(X0,X12)
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X14),X12))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X14),big_linorder_Max(X0,X12))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Max__ge) ).
tff(f1587,plain,
spl18_100,
inference(avatar_split_clause,[],[f554,f1585]) ).
tff(f554,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK11(X0,X1,X2))) ),
inference(cnf_transformation,[],[f392]) ).
tff(f1570,plain,
( spl18_99
| ~ spl18_39
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f1566,f1563,f830,f1568]) ).
tff(f1563,plain,
( spl18_98
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).
tff(f1566,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),combk(bool,X0,fFalse)),X1) )
| ~ spl18_39
| ~ spl18_98 ),
inference(forward_demodulation,[],[f1564,f831]) ).
tff(f1564,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) )
| ~ spl18_98 ),
inference(avatar_component_clause,[],[f1563]) ).
tff(f1565,plain,
spl18_98,
inference(avatar_split_clause,[],[f487,f1563]) ).
tff(f487,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType,X12: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_empty__Diff) ).
tff(f1544,plain,
spl18_97,
inference(avatar_split_clause,[],[f562,f1542]) ).
tff(f562,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(flattening,[],[f325]) ).
tff(f325,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X3,X2))
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
=> pp(aa(X0,bool,X1,X2)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X37: fun(X0,bool),X14: X0,X26: fun(X0,bool)] :
( pp(aa(X0,bool,X26,X14))
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X26),X37))
=> pp(aa(X0,bool,X37,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rev__predicate1D) ).
tff(f1253,plain,
( spl18_96
| ~ spl18_39
| ~ spl18_93 ),
inference(avatar_split_clause,[],[f1241,f1237,f830,f1251]) ).
tff(f1237,plain,
( spl18_93
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).
tff(f1241,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),combk(bool,X0,fFalse)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_39
| ~ spl18_93 ),
inference(forward_demodulation,[],[f1240,f831]) ).
tff(f1240,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) )
| ~ spl18_39
| ~ spl18_93 ),
inference(forward_demodulation,[],[f1238,f831]) ).
tff(f1238,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) )
| ~ spl18_93 ),
inference(avatar_component_clause,[],[f1237]) ).
tff(f1249,plain,
( spl18_95
| ~ spl18_39
| ~ spl18_92 ),
inference(avatar_split_clause,[],[f1235,f1232,f830,f1247]) ).
tff(f1232,plain,
( spl18_92
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).
tff(f1235,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) )
| ~ spl18_39
| ~ spl18_92 ),
inference(forward_demodulation,[],[f1233,f831]) ).
tff(f1233,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) )
| ~ spl18_92 ),
inference(avatar_component_clause,[],[f1232]) ).
tff(f1245,plain,
spl18_94,
inference(avatar_split_clause,[],[f535,f1243]) ).
tff(f535,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ),
inference(cnf_transformation,[],[f381]) ).
tff(f381,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X1) )
& ( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) ) )
| ~ finite_finite1(X0,X2) ),
inference(nnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
<=> finite_finite1(X0,X1) )
| ~ finite_finite1(X0,X2) ),
inference(ennf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
<=> finite_finite1(X0,X1) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X12: fun(X0,bool),X11: fun(X0,bool)] :
( finite_finite1(X0,X11)
=> ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11))
<=> finite_finite1(X0,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_finite__Diff2) ).
tff(f1239,plain,
spl18_93,
inference(avatar_split_clause,[],[f521,f1237]) ).
tff(f521,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
inference(cnf_transformation,[],[f372]) ).
tff(f372,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
<=> ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X12: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),bot_bot(fun(X0,bool))))
<=> ( bot_bot(fun(X0,bool)) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_subset__empty) ).
tff(f1234,plain,
spl18_92,
inference(avatar_split_clause,[],[f455,f1232]) ).
tff(f455,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1) )
| ~ linorder(X0) ),
inference(flattening,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
=> ( ( bot_bot(fun(X0,bool)) != X1 )
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1)) ) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X12: fun(X0,bool)] :
( finite_finite1(X0,X12)
=> ( ( bot_bot(fun(X0,bool)) != X12 )
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X12)),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Max__in) ).
tff(f1222,plain,
( spl18_91
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f772,f749,f1220]) ).
tff(f772,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl18_22 ),
inference(superposition,[],[f750,f750]) ).
tff(f1218,plain,
( spl18_90
| ~ spl18_39
| ~ spl18_88 ),
inference(avatar_split_clause,[],[f1199,f1196,f830,f1216]) ).
tff(f1196,plain,
( spl18_88
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).
tff(f1199,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),combk(bool,X0,fFalse)) = X1 )
| ~ spl18_39
| ~ spl18_88 ),
inference(forward_demodulation,[],[f1197,f831]) ).
tff(f1197,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) = X1 )
| ~ spl18_88 ),
inference(avatar_component_clause,[],[f1196]) ).
tff(f1214,plain,
( spl18_89
| ~ spl18_39
| ~ spl18_87 ),
inference(avatar_split_clause,[],[f1194,f1191,f830,f1212]) ).
tff(f1191,plain,
( spl18_87
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).
tff(f1194,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) )
| ~ spl18_39
| ~ spl18_87 ),
inference(forward_demodulation,[],[f1192,f831]) ).
tff(f1192,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) )
| ~ spl18_87 ),
inference(avatar_component_clause,[],[f1191]) ).
tff(f1198,plain,
spl18_88,
inference(avatar_split_clause,[],[f486,f1196]) ).
tff(f486,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) = X1 ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) = X1 ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType,X12: fun(X0,bool)] : ( aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),bot_bot(fun(X0,bool))) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Diff__empty) ).
tff(f1193,plain,
spl18_87,
inference(avatar_split_clause,[],[f485,f1191]) ).
tff(f485,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X12: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Diff__cancel) ).
tff(f1189,plain,
spl18_86,
inference(avatar_split_clause,[],[f467,f1187]) ).
tff(f467,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ order(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ~ order(X0) ),
inference(flattening,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X18: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X18))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X18),X3))
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order__antisym) ).
tff(f1182,plain,
spl18_85,
inference(avatar_split_clause,[],[f595,f1180]) ).
tff(f595,plain,
! [X0: $tType,X2: X0,X3: X0,X4: X0] :
( ( X3 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X2) )
| ~ group_add(X0) ),
inference(equality_resolution,[],[f453]) ).
tff(f453,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( X3 = X4 )
| ( X1 != X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f348]) ).
tff(f348,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( ( X3 = X4 )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( X3 != X4 ) ) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
| ~ group_add(X0) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( X3 = X4 )
<=> ( X1 = X2 ) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
=> ( ( X3 = X4 )
<=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X7: X0,X8: X0,X9: X0,X10: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X10),X9) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X8),X7) )
=> ( ( X9 = X10 )
<=> ( X7 = X8 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_diff__eq__diff__eq) ).
tff(f1178,plain,
spl18_84,
inference(avatar_split_clause,[],[f533,f1176]) ).
tff(f533,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ),
inference(ennf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X11: fun(X0,bool),X12: fun(X0,bool)] :
( finite_finite1(X0,X12)
=> finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__Diff) ).
tff(f1158,plain,
spl18_83,
inference(avatar_split_clause,[],[f459,f1156]) ).
tff(f459,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X18: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X18),X3))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_linorder__linear) ).
tff(f1134,plain,
( spl18_82
| ~ spl18_39
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f1122,f1119,f830,f1132]) ).
tff(f1119,plain,
( spl18_79
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).
tff(f1122,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1)) )
| ~ spl18_39
| ~ spl18_79 ),
inference(forward_demodulation,[],[f1120,f831]) ).
tff(f1120,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
| ~ spl18_79 ),
inference(avatar_component_clause,[],[f1119]) ).
tff(f1130,plain,
( spl18_81
| ~ spl18_39
| ~ spl18_78 ),
inference(avatar_split_clause,[],[f1117,f1114,f830,f1128]) ).
tff(f1114,plain,
( spl18_78
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).
tff(f1117,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) )
| ~ spl18_39
| ~ spl18_78 ),
inference(forward_demodulation,[],[f1115,f831]) ).
tff(f1115,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) )
| ~ spl18_78 ),
inference(avatar_component_clause,[],[f1114]) ).
tff(f1126,plain,
spl18_80,
inference(avatar_split_clause,[],[f534,f1124]) ).
tff(f534,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ),
inference(ennf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> finite_finite1(X0,X1) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X12: fun(X0,bool),X11: fun(X0,bool)] :
( finite_finite1(X0,X11)
=> ( pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X11))
=> finite_finite1(X0,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rev__finite__subset) ).
tff(f1121,plain,
spl18_79,
inference(avatar_split_clause,[],[f526,f1119]) ).
tff(f526,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(cnf_transformation,[],[f380]) ).
tff(f380,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X3: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f378,f379]) ).
tff(f379,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(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f378,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))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X3: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f377]) ).
tff(f377,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))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,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))
<=> ( bot_bot(fun(X0,bool)) != X1 ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType,X12: fun(X0,bool)] :
( ? [X17: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X17),X12))
<=> ( bot_bot(fun(X0,bool)) != X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_ex__in__conv) ).
tff(f1116,plain,
spl18_78,
inference(avatar_split_clause,[],[f523,f1114]) ).
tff(f523,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f376]) ).
tff(f376,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))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f374,f375]) ).
tff(f375,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X3: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f374,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))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ? [X3: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f373]) ).
tff(f373,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))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,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))
<=> ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType,X12: fun(X0,bool)] :
( ! [X17: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X17),X12))
<=> ( bot_bot(fun(X0,bool)) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_all__not__in__conv) ).
tff(f1112,plain,
( spl18_77
| ~ spl18_66
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f1069,f1061,f1019,f1109]) ).
tff(f1069,plain,
( pp(aa(atom,bool,set(atom,as),a))
| ~ spl18_66
| ~ spl18_71 ),
inference(resolution,[],[f1062,f1021]) ).
tff(f1096,plain,
( spl18_76
| ~ spl18_39
| ~ spl18_74 ),
inference(avatar_split_clause,[],[f1087,f1084,f830,f1094]) ).
tff(f1084,plain,
( spl18_74
<=> ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).
tff(f1087,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),combk(bool,X0,fFalse)),X1))
| ~ spl18_39
| ~ spl18_74 ),
inference(forward_demodulation,[],[f1085,f831]) ).
tff(f1085,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1))
| ~ spl18_74 ),
inference(avatar_component_clause,[],[f1084]) ).
tff(f1091,plain,
spl18_75,
inference(avatar_split_clause,[],[f571,f1089]) ).
tff(f571,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK13(X0,X1,X2,X3)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f398]) ).
tff(f398,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK13(X0,X1,X2,X3)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f338,f397]) ).
tff(f397,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,sK13(X0,X1,X2,X3)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f338,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,[],[f246]) ).
tff(f246,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X0: $tType,X15: fun(X0,X1),X16: fun(X0,X1)] :
( ! [X32: X0] : ( aa(X0,X1,X16,X32) = aa(X0,X1,X15,X32) )
=> ( X15 = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f1086,plain,
spl18_74,
inference(avatar_split_clause,[],[f484,f1084]) ).
tff(f484,plain,
! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X12: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_empty__subsetI) ).
tff(f1082,plain,
spl18_73,
inference(avatar_split_clause,[],[f451,f1080]) ).
tff(f451,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X1),nil(X0)) = X1 )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X1),nil(X0)) = X1 )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X1),nil(X0)) = X1 ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X6: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X6),nil(X0)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list__diff__Nil2) ).
tff(f1068,plain,
spl18_72,
inference(avatar_split_clause,[],[f548,f1066]) ).
tff(f548,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,[],[f384]) ).
tff(f384,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,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X12: fun(X0,bool),X14: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X14),X12))
<=> pp(aa(X0,bool,X12,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f1063,plain,
spl18_71,
inference(avatar_split_clause,[],[f547,f1061]) ).
tff(f547,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,[],[f384]) ).
tff(f1055,plain,
spl18_70,
inference(avatar_split_clause,[],[f483,f1053]) ).
tff(f483,plain,
! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X12: fun(X0,bool)] : pp(aa(fun(X0,bool),bool,aa(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_subset__refl) ).
tff(f1049,plain,
( spl18_69
| ~ spl18_39
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f1034,f1031,f830,f1047]) ).
tff(f1031,plain,
( spl18_68
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).
tff(f1034,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),combk(bool,X0,fFalse)))
| ~ spl18_39
| ~ spl18_68 ),
inference(forward_demodulation,[],[f1032,f831]) ).
tff(f1032,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl18_68 ),
inference(avatar_component_clause,[],[f1031]) ).
tff(f1033,plain,
spl18_68,
inference(avatar_split_clause,[],[f481,f1031]) ).
tff(f481,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X8: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X8),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_empty__iff) ).
tff(f1029,plain,
spl18_67,
inference(avatar_split_clause,[],[f456,f1027]) ).
tff(f456,plain,
! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0))) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
=> ( bot_bot(X0) = X1 ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType] :
( bot(X0)
=> ! [X25: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X25),bot_bot(X0)))
=> ( bot_bot(X0) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_le__bot) ).
tff(f1022,plain,
spl18_66,
inference(avatar_split_clause,[],[f432,f1019]) ).
tff(f432,plain,
pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__096a_A_058_Aset_Aas_096) ).
tff(f1017,plain,
( spl18_65
| ~ spl18_21
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f835,f830,f745,f1015]) ).
tff(f745,plain,
( spl18_21
<=> ! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
tff(f835,plain,
( ! [X0: $tType] : finite_finite1(X0,combk(bool,X0,fFalse))
| ~ spl18_21
| ~ spl18_39 ),
inference(superposition,[],[f746,f831]) ).
tff(f746,plain,
( ! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool)))
| ~ spl18_21 ),
inference(avatar_component_clause,[],[f745]) ).
tff(f1010,plain,
spl18_64,
inference(avatar_split_clause,[],[f557,f1008]) ).
tff(f557,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),bot_bot(fun(X0,fun(X1,bool))),X3),X2)),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),bot_bot(fun(X0,fun(X1,bool))),X3),X2)),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType,X1: $tType,X19: X1,X14: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),bot_bot(fun(X0,fun(X1,bool))),X14),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_bot2E) ).
tff(f986,plain,
( spl18_63
| ~ spl18_39
| ~ spl18_61 ),
inference(avatar_split_clause,[],[f960,f957,f830,f984]) ).
tff(f957,plain,
( spl18_61
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK6(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).
tff(f960,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK6(X0,X1))) )
| ~ spl18_39
| ~ spl18_61 ),
inference(forward_demodulation,[],[f958,f831]) ).
tff(f958,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK6(X0,X1))) )
| ~ spl18_61 ),
inference(avatar_component_clause,[],[f957]) ).
tff(f982,plain,
( spl18_62
| ~ spl18_39
| ~ spl18_60 ),
inference(avatar_split_clause,[],[f955,f952,f830,f980]) ).
tff(f952,plain,
( spl18_60
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK5(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).
tff(f955,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK5(X0,X1))) )
| ~ spl18_39
| ~ spl18_60 ),
inference(forward_demodulation,[],[f953,f831]) ).
tff(f953,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK5(X0,X1))) )
| ~ spl18_60 ),
inference(avatar_component_clause,[],[f952]) ).
tff(f959,plain,
spl18_61,
inference(avatar_split_clause,[],[f623,f957]) ).
tff(f623,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK6(X0,X1))) ),
inference(forward_demodulation,[],[f520,f480]) ).
tff(f520,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK6(X0,X1))) ),
inference(cnf_transformation,[],[f371]) ).
tff(f371,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK6(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f369,f370]) ).
tff(f370,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK6(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f369,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f368]) ).
tff(f368,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X26: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X26) )
<=> ! [X17: X0] : ~ pp(aa(X0,bool,X26,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_empty__Collect__eq) ).
tff(f954,plain,
spl18_60,
inference(avatar_split_clause,[],[f621,f952]) ).
tff(f621,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK5(X0,X1))) ),
inference(forward_demodulation,[],[f518,f480]) ).
tff(f518,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK5(X0,X1))) ),
inference(cnf_transformation,[],[f367]) ).
tff(f367,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK5(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f365,f366]) ).
tff(f366,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK5(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f365,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f364]) ).
tff(f364,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X26: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X26) )
<=> ! [X17: X0] : ~ pp(aa(X0,bool,X26,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Collect__empty__eq) ).
tff(f950,plain,
spl18_59,
inference(avatar_split_clause,[],[f532,f948]) ).
tff(f532,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,[],[f219]) ).
tff(f219,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f142]) ).
tff(f142,axiom,
! [X0: $tType,X18: X0,X3: X0] :
( ( X3 = X18 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X3),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f946,plain,
spl18_58,
inference(avatar_split_clause,[],[f491,f944]) ).
tff(f491,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ),
inference(rectify,[],[f139]) ).
tff(f139,axiom,
! [X49: bool,X47: bool] :
( pp(X49)
| pp(X47)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
tff(f942,plain,
spl18_57,
inference(avatar_split_clause,[],[f488,f940]) ).
tff(f488,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f134]) ).
tff(f134,axiom,
! [X49: bool,X47: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49))
| ~ pp(X49)
| ~ pp(X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f938,plain,
spl18_56,
inference(avatar_split_clause,[],[f454,f936]) ).
tff(f454,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1)) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( bot(X0)
=> ! [X25: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_bot__least) ).
tff(f933,plain,
~ spl18_55,
inference(avatar_split_clause,[],[f411,f930]) ).
tff(f411,plain,
~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))),
inference(flattening,[],[f145]) ).
tff(f145,negated_conjecture,
~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))),
inference(negated_conjecture,[],[f144]) ).
tff(f144,conjecture,
pp(aa(int,bool,aa(int,fun(int,bool),ord_less_eq(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),i),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),ks),xs))),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f918,plain,
( spl18_54
| ~ spl18_6
| ~ spl18_35
| ~ spl18_39
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f855,f837,f830,f809,f672,f915]) ).
tff(f672,plain,
( spl18_6
<=> bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
tff(f855,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl18_6
| ~ spl18_35
| ~ spl18_39
| ~ spl18_40 ),
inference(forward_demodulation,[],[f854,f810]) ).
tff(f854,plain,
( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1) )
| ~ spl18_6
| ~ spl18_39
| ~ spl18_40 ),
inference(forward_demodulation,[],[f852,f831]) ).
tff(f852,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool) )
| ~ spl18_6
| ~ spl18_40 ),
inference(resolution,[],[f838,f674]) ).
tff(f674,plain,
( bot(bool)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f672]) ).
tff(f908,plain,
spl18_53,
inference(avatar_split_clause,[],[f600,f906]) ).
tff(f600,plain,
! [X0: $tType,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X2))
| ~ order(X0) ),
inference(equality_resolution,[],[f471]) ).
tff(f471,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ( X1 != X2 )
| ~ order(X0) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
& ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
& pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ( X1 != X2 ) ) )
| ~ order(X0) ),
inference(flattening,[],[f353]) ).
tff(f353,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
& ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
& pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) )
| ( X1 != X2 ) ) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
& pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
& pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X19: X0,X14: X0] :
( ( X14 = X19 )
<=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X19),X14))
& pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X14),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_order__eq__iff) ).
tff(f904,plain,
spl18_52,
inference(avatar_split_clause,[],[f531,f902]) ).
tff(f531,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,[],[f218]) ).
tff(f218,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,[],[f127]) ).
tff(f127,axiom,
! [X0: $tType,X3: X0,X47: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X47))
| ~ pp(aa(X0,bool,X47,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f900,plain,
spl18_51,
inference(avatar_split_clause,[],[f513,f898]) ).
tff(f513,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ),
inference(cnf_transformation,[],[f362]) ).
tff(f362,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: list(X0)] :
( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X40: list(X0)] :
( ( bot_bot(fun(X0,bool)) = set(X0,X40) )
<=> ( nil(X0) = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_set__empty) ).
tff(f896,plain,
spl18_50,
inference(avatar_split_clause,[],[f465,f894]) ).
tff(f465,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType] :
( ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X1),X1)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X3: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less_eq(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_order__refl) ).
tff(f889,plain,
( spl18_49
| ~ spl18_39
| ~ spl18_48 ),
inference(avatar_split_clause,[],[f878,f875,f830,f887]) ).
tff(f875,plain,
( spl18_48
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).
tff(f878,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_39
| ~ spl18_48 ),
inference(forward_demodulation,[],[f876,f831]) ).
tff(f876,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_48 ),
inference(avatar_component_clause,[],[f875]) ).
tff(f877,plain,
spl18_48,
inference(avatar_split_clause,[],[f622,f875]) ).
tff(f622,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ),
inference(forward_demodulation,[],[f517,f480]) ).
tff(f517,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ),
inference(cnf_transformation,[],[f367]) ).
tff(f873,plain,
spl18_47,
inference(avatar_split_clause,[],[f493,f871]) ).
tff(f493,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f135]) ).
tff(f135,axiom,
! [X49: bool,X47: bool] :
( pp(X47)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f869,plain,
spl18_46,
inference(avatar_split_clause,[],[f492,f867]) ).
tff(f492,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f136]) ).
tff(f136,axiom,
! [X49: bool,X47: bool] :
( pp(X49)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f865,plain,
spl18_45,
inference(avatar_split_clause,[],[f490,f863]) ).
tff(f490,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ),
inference(rectify,[],[f137]) ).
tff(f137,axiom,
! [X49: bool,X47: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49))
| ~ pp(X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
tff(f861,plain,
spl18_44,
inference(avatar_split_clause,[],[f489,f859]) ).
tff(f489,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ),
inference(rectify,[],[f138]) ).
tff(f138,axiom,
! [X47: bool,X49: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49))
| ~ pp(X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
tff(f851,plain,
spl18_43,
inference(avatar_split_clause,[],[f609,f849]) ).
tff(f609,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f530]) ).
tff(f530,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,[],[f217]) ).
tff(f217,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f143]) ).
tff(f143,axiom,
! [X0: $tType,X18: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X3),X18))
| ( X3 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f847,plain,
( spl18_41
| ~ spl18_42
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f774,f749,f844,f841]) ).
tff(f774,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl18_22 ),
inference(equality_factoring,[],[f750]) ).
tff(f839,plain,
spl18_40,
inference(avatar_split_clause,[],[f495,f837]) ).
tff(f495,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X1: $tType,X0: $tType] :
( bot(X0)
=> ! [X14: X1] : ( bot_bot(X0) = aa(X1,X0,bot_bot(fun(X1,X0)),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_bot__apply) ).
tff(f832,plain,
( spl18_39
| ~ spl18_29
| ~ spl18_38 ),
inference(avatar_split_clause,[],[f828,f825,f780,f830]) ).
tff(f825,plain,
( spl18_38
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).
tff(f828,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl18_29
| ~ spl18_38 ),
inference(forward_demodulation,[],[f826,f781]) ).
tff(f826,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) )
| ~ spl18_38 ),
inference(avatar_component_clause,[],[f825]) ).
tff(f827,plain,
spl18_38,
inference(avatar_split_clause,[],[f444,f825]) ).
tff(f444,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(cnf_transformation,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_empty__def) ).
tff(f823,plain,
~ spl18_37,
inference(avatar_split_clause,[],[f431,f820]) ).
tff(f820,plain,
( spl18_37
<=> ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).
tff(f431,plain,
lbounds(as) != nil(product_prod(int,list(int))),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
lbounds(as) != nil(product_prod(int,list(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096lbounds_Aas_A_126_061_A_091_093_096) ).
tff(f816,plain,
spl18_36,
inference(avatar_split_clause,[],[f443,f814]) ).
tff(f443,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_List_Oset_Osimps_I1_J) ).
tff(f811,plain,
spl18_35,
inference(avatar_split_clause,[],[f556,f809]) ).
tff(f556,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X1: $tType,X0: $tType,X49: X1,X47: X0] : ( aa(X1,X0,combk(X0,X1,X47),X49) = X47 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f802,plain,
spl18_34,
inference(avatar_split_clause,[],[f510,f800]) ).
tff(f800,plain,
( spl18_34
<=> ! [X1: $tType,X0: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).
tff(f510,plain,
! [X1: $tType,X0: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(flattening,[],[f309]) ).
tff(f309,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType] :
( ( finite_finite(X0)
& finite_finite(X1) )
=> finite_finite(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X45: $tType,X46: $tType] :
( ( finite_finite(X45)
& finite_finite(X46) )
=> finite_finite(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
tff(f798,plain,
spl18_33,
inference(avatar_split_clause,[],[f509,f796]) ).
tff(f796,plain,
( spl18_33
<=> ! [X1: $tType,X0: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).
tff(f509,plain,
! [X1: $tType,X0: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(flattening,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: $tType] :
( ( finite_finite(X0)
& finite_finite(X1) )
=> finite_finite(product_prod(X0,X1)) ),
inference(rectify,[],[f124]) ).
tff(f124,axiom,
! [X45: $tType,X46: $tType] :
( ( finite_finite(X45)
& finite_finite(X46) )
=> finite_finite(product_prod(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
tff(f794,plain,
spl18_32,
inference(avatar_split_clause,[],[f447,f792]) ).
tff(f447,plain,
! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X47: bool] :
( ~ pp(X47)
| ~ pp(aa(bool,bool,fNot,X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
tff(f790,plain,
spl18_31,
inference(avatar_split_clause,[],[f445,f788]) ).
tff(f445,plain,
! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X47: bool] :
( pp(aa(bool,bool,fNot,X47))
| pp(X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
tff(f786,plain,
( spl18_30
| spl18_1
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f773,f749,f647,f784]) ).
tff(f773,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl18_1
| ~ spl18_22 ),
inference(superposition,[],[f649,f750]) ).
tff(f782,plain,
spl18_29,
inference(avatar_split_clause,[],[f480,f780]) ).
tff(f778,plain,
spl18_28,
inference(avatar_split_clause,[],[f478,f776]) ).
tff(f478,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( ( cl_Groups_Ominus(X0)
& zero(X0) )
=> cl_Groups_Ominus(list(X0)) ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X45: $tType] :
( ( cl_Groups_Ominus(X45)
& zero(X45) )
=> cl_Groups_Ominus(list(X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
tff(f771,plain,
spl18_27,
inference(avatar_split_clause,[],[f505,f769]) ).
tff(f505,plain,
! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X1)
=> cl_Groups_Ominus(fun(X0,X1)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X45: $tType,X46: $tType] :
( cl_Groups_Ominus(X46)
=> cl_Groups_Ominus(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
tff(f767,plain,
spl18_26,
inference(avatar_split_clause,[],[f499,f765]) ).
tff(f765,plain,
( spl18_26
<=> ! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
tff(f499,plain,
! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: $tType] :
( ord(X1)
=> ord(fun(X0,X1)) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X45: $tType,X46: $tType] :
( ord(X46)
=> ord(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
tff(f763,plain,
spl18_25,
inference(avatar_split_clause,[],[f498,f761]) ).
tff(f761,plain,
( spl18_25
<=> ! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
tff(f498,plain,
! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType] :
( order(X1)
=> order(fun(X0,X1)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X45: $tType,X46: $tType] :
( order(X46)
=> order(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
tff(f759,plain,
spl18_24,
inference(avatar_split_clause,[],[f497,f757]) ).
tff(f757,plain,
( spl18_24
<=> ! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
tff(f497,plain,
! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X45: $tType,X46: $tType] :
( preorder(X46)
=> preorder(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
tff(f755,plain,
spl18_23,
inference(avatar_split_clause,[],[f494,f753]) ).
tff(f494,plain,
! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: $tType,X1: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X45: $tType,X46: $tType] :
( bot(X46)
=> bot(fun(X45,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
tff(f751,plain,
spl18_22,
inference(avatar_split_clause,[],[f446,f749]) ).
tff(f446,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f141]) ).
tff(f141,axiom,
! [X47: bool] :
( ( fFalse = X47 )
| ( fTrue = X47 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f747,plain,
spl18_21,
inference(avatar_split_clause,[],[f442,f745]) ).
tff(f442,plain,
! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_finite_OemptyI) ).
tff(f743,plain,
spl18_20,
inference(avatar_split_clause,[],[f479,f741]) ).
tff(f479,plain,
! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X40: list(X0)] : finite_finite1(X0,set(X0,X40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_finite__set) ).
tff(f739,plain,
spl18_19,
inference(avatar_split_clause,[],[f474,f737]) ).
tff(f474,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] : finite_finite1(X0,X1)
| ~ finite_finite(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( finite_finite(X0)
=> ! [X1: fun(X0,bool)] : finite_finite1(X0,X1) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] :
( finite_finite(X0)
=> ! [X12: fun(X0,bool)] : finite_finite1(X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__code) ).
tff(f735,plain,
spl18_18,
inference(avatar_split_clause,[],[f430,f732]) ).
tff(f430,plain,
pp(fTrue),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f730,plain,
spl18_17,
inference(avatar_split_clause,[],[f429,f727]) ).
tff(f429,plain,
cl_Groups_Ominus(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
cl_Groups_Ominus(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
tff(f725,plain,
spl18_16,
inference(avatar_split_clause,[],[f428,f722]) ).
tff(f428,plain,
cl_Groups_Ominus(bool),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
cl_Groups_Ominus(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
tff(f720,plain,
spl18_15,
inference(avatar_split_clause,[],[f427,f717]) ).
tff(f717,plain,
( spl18_15
<=> ord(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
tff(f427,plain,
ord(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
ord(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
tff(f715,plain,
spl18_14,
inference(avatar_split_clause,[],[f426,f712]) ).
tff(f426,plain,
ord(bool),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
ord(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
tff(f710,plain,
spl18_13,
inference(avatar_split_clause,[],[f425,f707]) ).
tff(f425,plain,
finite_finite(bool),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
finite_finite(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
tff(f705,plain,
spl18_12,
inference(avatar_split_clause,[],[f424,f702]) ).
tff(f702,plain,
( spl18_12
<=> preorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
tff(f424,plain,
preorder(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
preorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
tff(f700,plain,
spl18_11,
inference(avatar_split_clause,[],[f423,f697]) ).
tff(f697,plain,
( spl18_11
<=> order(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
tff(f423,plain,
order(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
order(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
tff(f695,plain,
spl18_10,
inference(avatar_split_clause,[],[f422,f692]) ).
tff(f692,plain,
( spl18_10
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
tff(f422,plain,
order(bool),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
tff(f690,plain,
spl18_9,
inference(avatar_split_clause,[],[f421,f687]) ).
tff(f687,plain,
( spl18_9
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
tff(f421,plain,
preorder(bool),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
tff(f685,plain,
spl18_8,
inference(avatar_split_clause,[],[f420,f682]) ).
tff(f420,plain,
linorder(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f680,plain,
spl18_7,
inference(avatar_split_clause,[],[f419,f677]) ).
tff(f419,plain,
linorder(bool),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
linorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
tff(f675,plain,
spl18_6,
inference(avatar_split_clause,[],[f418,f672]) ).
tff(f418,plain,
bot(bool),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
tff(f670,plain,
spl18_5,
inference(avatar_split_clause,[],[f417,f667]) ).
tff(f417,plain,
group_add(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
tff(f665,plain,
spl18_4,
inference(avatar_split_clause,[],[f416,f662]) ).
tff(f416,plain,
ordered_ab_group_add(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
ordered_ab_group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
tff(f660,plain,
spl18_3,
inference(avatar_split_clause,[],[f415,f657]) ).
tff(f657,plain,
( spl18_3
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
tff(f415,plain,
zero(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f655,plain,
spl18_2,
inference(avatar_split_clause,[],[f414,f652]) ).
tff(f414,plain,
ring(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f650,plain,
~ spl18_1,
inference(avatar_split_clause,[],[f412,f647]) ).
tff(f412,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f140]) ).
tff(f140,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.20 % Problem : COM099_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.22 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.43 % Computer : n024.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8042.1875MB
% 0.11/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Fri May 3 21:27:53 EDT 2024
% 0.11/0.43 % CPUTime :
% 0.11/0.43 % (22894)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.49 % (22897)WARNING: value z3 for option sas not known
% 0.16/0.49 % (22901)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)
% 0.16/0.49 % (22896)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.49 % (22895)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.49 % (22898)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.49 % (22897)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)
% 0.16/0.49 % (22900)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)
% 0.16/0.49 % (22899)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)
% 0.16/0.50 % (22901)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.50 % Exception at run slice level
% 0.16/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.50 % Exception at run slice level
% 0.16/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.50 % Exception at run slice level
% 0.16/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.51 % (22903)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)
% 0.16/0.51 % (22904)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)
% 0.16/0.51 % (22902)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.52 % (22903)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.52 % (22902)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.52 % Exception at run slice level
% 0.16/0.52 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.54 % (22905)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)
% 61.11/9.26 % (22899)First to succeed.
% 61.57/9.33 % (22899)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22894"
% 61.57/9.34 % (22899)Refutation found. Thanks to Tanya!
% 61.57/9.34 % SZS status Theorem for theBenchmark
% 61.57/9.34 % SZS output start Proof for theBenchmark
% See solution above
% 61.57/9.36 % (22899)------------------------------
% 61.57/9.36 % (22899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 61.57/9.36 % (22899)Termination reason: Refutation
% 61.57/9.36
% 61.57/9.36 % (22899)Memory used [KB]: 56206
% 61.57/9.36 % (22899)Time elapsed: 8.845 s
% 61.57/9.36 % (22899)Instructions burned: 18224 (million)
% 61.57/9.36 % (22894)Success in time 8.891 s
%------------------------------------------------------------------------------