TSTP Solution File: LCL814_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL814_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 : n018.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 : Tue Apr 30 13:49:56 EDT 2024
% Result : Theorem 2.39s 0.72s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 566
% Syntax : Number of formulae : 1775 ( 298 unt; 81 typ; 0 def)
% Number of atoms : 4562 ( 943 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 5095 (2227 ~;2192 |; 162 &)
% ( 391 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 92 ( 42 >; 50 *; 0 +; 0 <<)
% Number of predicates : 368 ( 366 usr; 361 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 26 con; 0-6 aty)
% Number of variables : 3727 (3598 !; 88 ?;3727 :)
% ( 41 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
listset:
!>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_18,type,
set_Cons:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
typing: fun(nat,type) > fun(dB,fun(type,bool)) ).
tff(func_def_23,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fTrue: bool ).
tff(func_def_28,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
t2: type ).
tff(func_def_32,type,
t1: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t: type ).
tff(func_def_35,type,
ts: list(type) ).
tff(func_def_36,type,
a: dB ).
tff(func_def_37,type,
as: list(dB) ).
tff(func_def_38,type,
e: fun(nat,type) ).
tff(func_def_39,type,
ea: fun(nat,type) ).
tff(func_def_40,type,
i: nat ).
tff(func_def_41,type,
ia: nat ).
tff(func_def_42,type,
n: nat ).
tff(func_def_43,type,
rs: list(dB) ).
tff(func_def_44,type,
t3: dB ).
tff(func_def_45,type,
u: dB ).
tff(func_def_46,type,
ua: dB ).
tff(func_def_47,type,
sK2: type ).
tff(func_def_48,type,
sK3: list(type) ).
tff(func_def_49,type,
sK4: dB > dB ).
tff(func_def_50,type,
sK5: dB > list(dB) ).
tff(func_def_51,type,
sK6: dB > nat ).
tff(func_def_52,type,
sK7: dB > dB ).
tff(func_def_53,type,
sK8: dB > dB ).
tff(func_def_54,type,
sK9: dB > list(dB) ).
tff(func_def_55,type,
sK10: ( dB * fun(nat,type) ) > type ).
tff(func_def_56,type,
sK11: ( dB * fun(nat,type) ) > type ).
tff(func_def_57,type,
sK12: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_58,type,
sK13: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_59,type,
sK14: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_60,type,
sK15: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_61,type,
sK16: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_62,type,
sK17: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_63,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_64,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_65,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_66,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_67,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_68,type,
sK23: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: dB > $o ).
tff(pred_def_6,type,
sP1: dB > $o ).
tff(f5840,plain,
$false,
inference(avatar_sat_refutation,[],[f530,f535,f540,f544,f548,f552,f557,f562,f567,f571,f575,f586,f590,f595,f599,f604,f608,f612,f616,f620,f640,f644,f648,f656,f667,f672,f677,f683,f690,f696,f701,f708,f713,f717,f721,f726,f741,f745,f749,f754,f759,f764,f769,f773,f777,f781,f800,f804,f809,f818,f822,f827,f833,f849,f855,f863,f869,f877,f881,f885,f889,f893,f898,f902,f911,f919,f923,f927,f931,f936,f943,f947,f955,f960,f965,f971,f975,f980,f984,f989,f998,f1008,f1030,f1035,f1044,f1049,f1054,f1059,f1069,f1075,f1083,f1089,f1096,f1101,f1105,f1120,f1126,f1130,f1136,f1140,f1144,f1148,f1153,f1174,f1180,f1184,f1190,f1197,f1202,f1211,f1216,f1223,f1228,f1235,f1239,f1246,f1251,f1258,f1264,f1268,f1274,f1279,f1285,f1292,f1300,f1307,f1317,f1324,f1338,f1345,f1352,f1369,f1376,f1385,f1390,f1399,f1405,f1410,f1414,f1418,f1422,f1432,f1504,f1508,f1512,f1531,f1537,f1541,f1554,f1558,f1587,f1596,f1602,f1616,f1622,f1635,f1642,f1652,f1659,f1667,f1674,f1678,f1684,f1697,f1703,f1711,f1718,f1726,f1735,f1741,f1749,f1755,f1768,f1773,f1782,f1787,f1827,f1905,f1913,f1928,f1936,f1940,f1948,f1964,f1968,f1972,f1978,f2006,f2028,f2034,f2045,f2054,f2063,f2078,f2082,f2096,f2100,f2108,f2114,f2125,f2134,f2139,f2148,f2156,f2160,f2164,f2172,f2177,f2191,f2202,f2207,f2216,f2221,f2230,f2243,f2250,f2255,f2692,f2719,f2739,f2747,f2758,f2762,f2766,f2770,f2774,f2782,f2786,f2802,f2807,f2811,f2815,f2834,f2852,f2860,f2864,f2868,f2873,f2878,f2882,f2888,f2931,f2967,f2968,f2969,f2970,f2971,f2972,f2973,f2974,f2975,f2976,f2977,f2978,f2979,f2980,f2981,f2982,f2983,f2984,f2985,f2986,f2987,f2988,f2989,f2990,f2991,f2992,f2993,f2994,f2995,f3598,f3617,f3621,f3625,f3633,f3639,f3643,f3647,f3651,f3655,f3660,f3665,f3697,f3719,f3726,f3731,f3736,f3741,f3745,f3774,f3779,f3784,f3802,f3807,f3811,f3815,f3819,f3823,f3827,f3905,f3909,f3913,f3917,f3921,f3925,f4085,f4090,f4094,f4099,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4523,f4527,f4531,f4593,f4598,f4602,f4606,f4610,f4614,f4683,f4695,f4700,f4740,f4744,f4748,f4757,f4763,f4768,f4773,f4777,f4781,f4812,f4817,f4822,f4826,f4830,f4834,f4838,f4945,f4949,f4953,f4957,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5071,f5128,f5132,f5136,f5182,f5186,f5190,f5194,f5198,f5202,f5207,f5211,f5215,f5240,f5478,f5483,f5494,f5498,f5502,f5506,f5510,f5514,f5822,f5826,f5830,f5834,f5838,f5839]) ).
tff(f5839,plain,
( ~ spl24_3
| spl24_12
| ~ spl24_13
| ~ spl24_30
| ~ spl24_353 ),
inference(avatar_split_clause,[],[f5805,f5504,f693,f588,f583,f537]) ).
tff(f537,plain,
( spl24_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).
tff(f583,plain,
( spl24_12
<=> pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_12])]) ).
tff(f588,plain,
( spl24_13
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_13])]) ).
tff(f693,plain,
( spl24_30
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_30])]) ).
tff(f5504,plain,
( spl24_353
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_353])]) ).
tff(f5805,plain,
( ~ pp(fTrue)
| spl24_12
| ~ spl24_13
| ~ spl24_30
| ~ spl24_353 ),
inference(forward_demodulation,[],[f5791,f702]) ).
tff(f702,plain,
( ( fTrue = aa(dB,bool,combc(dB,type,bool,typing(e),t),u) )
| ~ spl24_13
| ~ spl24_30 ),
inference(resolution,[],[f695,f589]) ).
tff(f589,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl24_13 ),
inference(avatar_component_clause,[],[f588]) ).
tff(f695,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl24_30 ),
inference(avatar_component_clause,[],[f693]) ).
tff(f5791,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| spl24_12
| ~ spl24_353 ),
inference(resolution,[],[f5505,f585]) ).
tff(f585,plain,
( ~ pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts))
| spl24_12 ),
inference(avatar_component_clause,[],[f583]) ).
tff(f5505,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl24_353 ),
inference(avatar_component_clause,[],[f5504]) ).
tff(f5838,plain,
( spl24_360
| ~ spl24_53
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1499,f1420,f996,f831,f5836]) ).
tff(f5836,plain,
( spl24_360
<=> ! [X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_360])]) ).
tff(f831,plain,
( spl24_53
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_53])]) ).
tff(f996,plain,
( spl24_81
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_81])]) ).
tff(f1420,plain,
( spl24_141
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X0)),X4: X0,X3: X1,X2: list(X1)] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_141])]) ).
tff(f1499,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),X0),X1) )
| ( X0 = X3 ) )
| ~ spl24_53
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1477,f997]) ).
tff(f997,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl24_81 ),
inference(avatar_component_clause,[],[f996]) ).
tff(f1477,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),X1) != foldl(dB,dB,app,X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ( X0 = X3 ) )
| ~ spl24_53
| ~ spl24_141 ),
inference(superposition,[],[f832,f1421]) ).
tff(f1421,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_141 ),
inference(avatar_component_clause,[],[f1420]) ).
tff(f832,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) )
| ( X0 = X2 ) )
| ~ spl24_53 ),
inference(avatar_component_clause,[],[f831]) ).
tff(f5834,plain,
( spl24_359
| ~ spl24_50
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1485,f1420,f996,f816,f5832]) ).
tff(f5832,plain,
( spl24_359
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_359])]) ).
tff(f816,plain,
( spl24_50
<=> ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_50])]) ).
tff(f1485,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_50
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1463,f997]) ).
tff(f1463,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1)))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_50
| ~ spl24_141 ),
inference(superposition,[],[f817,f1421]) ).
tff(f817,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl24_50 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f5830,plain,
( spl24_358
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1482,f1420,f996,f573,f5828]) ).
tff(f5828,plain,
( spl24_358
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_358])]) ).
tff(f573,plain,
( spl24_11
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_11])]) ).
tff(f1482,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X4),X2),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1460,f997]) ).
tff(f1460,plain,
( ! [X0: $tType,X2: bool,X3: list(X0),X1: fun(bool,fun(X0,bool)),X4: X0] :
( ( fFalse = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X4),X3) )
| ( fTrue = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_11
| ~ spl24_141 ),
inference(superposition,[],[f1421,f574]) ).
tff(f574,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f573]) ).
tff(f5826,plain,
( spl24_357
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1481,f1420,f996,f573,f5824]) ).
tff(f5824,plain,
( spl24_357
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_357])]) ).
tff(f1481,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) )
| ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) ) )
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1458,f997]) ).
tff(f1458,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fFalse = foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) )
| ( fTrue = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3),X4) ) )
| ~ spl24_11
| ~ spl24_141 ),
inference(superposition,[],[f1421,f574]) ).
tff(f5822,plain,
( spl24_356
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1480,f1420,f996,f573,f5820]) ).
tff(f5820,plain,
( spl24_356
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: bool,X1: fun(bool,fun(X0,bool))] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_356])]) ).
tff(f1480,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( fTrue = aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) )
| ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) ) )
| ~ spl24_11
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1456,f997]) ).
tff(f1456,plain,
( ! [X0: $tType,X2: bool,X3: X0,X1: fun(bool,fun(X0,bool)),X4: list(X0)] :
( ( foldl(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = foldl(bool,X0,X1,fFalse,X4) )
| ( fTrue = aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) ) )
| ~ spl24_11
| ~ spl24_141 ),
inference(superposition,[],[f1421,f574]) ).
tff(f5514,plain,
( spl24_355
| ~ spl24_217
| ~ spl24_347 ),
inference(avatar_split_clause,[],[f5451,f5238,f2248,f5512]) ).
tff(f5512,plain,
( spl24_355
<=> ! [X2: bool,X0: bool,X1: bool] :
( ( X0 != X1 )
| ( aa(bool,bool,combi(bool),X1) = X0 )
| ( X0 = X2 )
| ( fTrue = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_355])]) ).
tff(f2248,plain,
( spl24_217
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_217])]) ).
tff(f5238,plain,
( spl24_347
<=> ! [X0: bool] :
( ( fTrue != X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_347])]) ).
tff(f5451,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( X0 != X1 )
| ( aa(bool,bool,combi(bool),X1) = X0 )
| ( X0 = X2 )
| ( fTrue = X2 ) )
| ~ spl24_217
| ~ spl24_347 ),
inference(superposition,[],[f5239,f2249]) ).
tff(f2249,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl24_217 ),
inference(avatar_component_clause,[],[f2248]) ).
tff(f5239,plain,
( ! [X0: bool] :
( ( fTrue != X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_347 ),
inference(avatar_component_clause,[],[f5238]) ).
tff(f5510,plain,
( spl24_354
| ~ spl24_33
| ~ spl24_181 ),
inference(avatar_split_clause,[],[f1930,f1926,f710,f5508]) ).
tff(f5508,plain,
( spl24_354
<=> ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_354])]) ).
tff(f710,plain,
( spl24_33
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_33])]) ).
tff(f1926,plain,
( spl24_181
<=> ! [X2: nat,X4: dB,X0: list(type),X5: fun(nat,type),X3: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_181])]) ).
tff(f1930,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),sK3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl24_33
| ~ spl24_181 ),
inference(resolution,[],[f1927,f712]) ).
tff(f712,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK3))
| ~ spl24_33 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f1927,plain,
( ! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4)) )
| ~ spl24_181 ),
inference(avatar_component_clause,[],[f1926]) ).
tff(f5506,plain,
( spl24_353
| ~ spl24_32
| ~ spl24_181 ),
inference(avatar_split_clause,[],[f1929,f1926,f705,f5504]) ).
tff(f705,plain,
( spl24_32
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_32])]) ).
tff(f1929,plain,
( ! [X0: dB] :
( pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),i),as)),ts))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),X0)) )
| ~ spl24_32
| ~ spl24_181 ),
inference(resolution,[],[f1927,f707]) ).
tff(f707,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts))
| ~ spl24_32 ),
inference(avatar_component_clause,[],[f705]) ).
tff(f5502,plain,
( spl24_352
| ~ spl24_81
| ~ spl24_150 ),
inference(avatar_split_clause,[],[f1567,f1556,f996,f5500]) ).
tff(f5500,plain,
( spl24_352
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,X1),X5: X0,X3: fun(X1,X2)] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_352])]) ).
tff(f1556,plain,
( spl24_150
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_150])]) ).
tff(f1567,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X2),X4: fun(X0,X1),X5: X0] : ( aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5) )
| ~ spl24_81
| ~ spl24_150 ),
inference(superposition,[],[f1557,f997]) ).
tff(f1557,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) )
| ~ spl24_150 ),
inference(avatar_component_clause,[],[f1556]) ).
tff(f5498,plain,
( spl24_351
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1012,f996,f5496]) ).
tff(f5496,plain,
( spl24_351
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X3,fun(X0,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_351])]) ).
tff(f1012,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X3,fun(X0,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7) )
| ~ spl24_81 ),
inference(superposition,[],[f997,f997]) ).
tff(f5494,plain,
( spl24_350
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1011,f996,f5492]) ).
tff(f5492,plain,
( spl24_350
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: X3,X4: fun(X0,fun(X3,fun(X1,X2))),X7: X1,X6: X0] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_350])]) ).
tff(f1011,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X0,X7: X1,X4: fun(X0,fun(X3,fun(X1,X2))),X5: X3] : ( aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7) )
| ~ spl24_81 ),
inference(superposition,[],[f997,f997]) ).
tff(f5483,plain,
( spl24_349
| ~ spl24_23
| ~ spl24_151 ),
inference(avatar_split_clause,[],[f1588,f1584,f646,f5480]) ).
tff(f5480,plain,
( spl24_349
<=> sP1(abs(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_349])]) ).
tff(f646,plain,
( spl24_23
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_23])]) ).
tff(f1584,plain,
( spl24_151
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_151])]) ).
tff(f1588,plain,
( sP1(abs(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_23
| ~ spl24_151 ),
inference(resolution,[],[f1586,f647]) ).
tff(f647,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl24_23 ),
inference(avatar_component_clause,[],[f646]) ).
tff(f1586,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))))
| ~ spl24_151 ),
inference(avatar_component_clause,[],[f1584]) ).
tff(f5478,plain,
( spl24_348
| ~ spl24_81
| ~ spl24_149 ),
inference(avatar_split_clause,[],[f1561,f1552,f996,f5476]) ).
tff(f5476,plain,
( spl24_348
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_348])]) ).
tff(f1552,plain,
( spl24_149
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_149])]) ).
tff(f1561,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X2 = X4 ) )
| ~ spl24_81
| ~ spl24_149 ),
inference(superposition,[],[f1553,f997]) ).
tff(f1553,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 = X3 ) )
| ~ spl24_149 ),
inference(avatar_component_clause,[],[f1552]) ).
tff(f5240,plain,
( spl24_347
| spl24_298
| ~ spl24_334 ),
inference(avatar_split_clause,[],[f5149,f5069,f4595,f5238]) ).
tff(f4595,plain,
( spl24_298
<=> ( fTrue = aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_298])]) ).
tff(f5069,plain,
( spl24_334
<=> ! [X0: bool] :
( ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_334])]) ).
tff(f5149,plain,
( ! [X0: bool] :
( ( fTrue != X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| spl24_298
| ~ spl24_334 ),
inference(superposition,[],[f4597,f5070]) ).
tff(f5070,plain,
( ! [X0: bool] :
( ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_334 ),
inference(avatar_component_clause,[],[f5069]) ).
tff(f4597,plain,
( ( fTrue != aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) )
| spl24_298 ),
inference(avatar_component_clause,[],[f4595]) ).
tff(f5215,plain,
( spl24_346
| ~ spl24_74
| ~ spl24_155 ),
inference(avatar_split_clause,[],[f1623,f1620,f958,f5213]) ).
tff(f5213,plain,
( spl24_346
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_346])]) ).
tff(f958,plain,
( spl24_74
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_74])]) ).
tff(f1620,plain,
( spl24_155
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_155])]) ).
tff(f1623,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK15(X1,X3,var(X2),X0),X1) ) )
| ~ spl24_74
| ~ spl24_155 ),
inference(resolution,[],[f1621,f959]) ).
tff(f959,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl24_74 ),
inference(avatar_component_clause,[],[f958]) ).
tff(f1621,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl24_155 ),
inference(avatar_component_clause,[],[f1620]) ).
tff(f5211,plain,
( spl24_345
| ~ spl24_74
| ~ spl24_153 ),
inference(avatar_split_clause,[],[f1603,f1600,f958,f5209]) ).
tff(f5209,plain,
( spl24_345
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_345])]) ).
tff(f1600,plain,
( spl24_153
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_153])]) ).
tff(f1603,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK14(X1,X3,var(X2),X0),X1) ) )
| ~ spl24_74
| ~ spl24_153 ),
inference(resolution,[],[f1601,f959]) ).
tff(f1601,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1))) )
| ~ spl24_153 ),
inference(avatar_component_clause,[],[f1600]) ).
tff(f5207,plain,
( spl24_344
| ~ spl24_16
| ~ spl24_151 ),
inference(avatar_split_clause,[],[f1589,f1584,f602,f5204]) ).
tff(f5204,plain,
( spl24_344
<=> sP1(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_344])]) ).
tff(f602,plain,
( spl24_16
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_16])]) ).
tff(f1589,plain,
( sP1(foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl24_16
| ~ spl24_151 ),
inference(resolution,[],[f1586,f603]) ).
tff(f603,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl24_16 ),
inference(avatar_component_clause,[],[f602]) ).
tff(f5202,plain,
( spl24_343
| ~ spl24_22
| ~ spl24_145 ),
inference(avatar_split_clause,[],[f1527,f1510,f642,f5200]) ).
tff(f5200,plain,
( spl24_343
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X1,combi(X0),X3,X2)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_343])]) ).
tff(f642,plain,
( spl24_22
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_22])]) ).
tff(f1510,plain,
( spl24_145
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_145])]) ).
tff(f1527,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK22(X0,X0,X1,combi(X0),X3,X2)) = X3 ) )
| ~ spl24_22
| ~ spl24_145 ),
inference(superposition,[],[f1511,f643]) ).
tff(f643,plain,
( ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 )
| ~ spl24_22 ),
inference(avatar_component_clause,[],[f642]) ).
tff(f1511,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl24_145 ),
inference(avatar_component_clause,[],[f1510]) ).
tff(f5198,plain,
( spl24_342
| ~ spl24_81
| ~ spl24_145 ),
inference(avatar_split_clause,[],[f1526,f1510,f996,f5196]) ).
tff(f5196,plain,
( spl24_342
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X0,X3,X5,X4,X2,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_342])]) ).
tff(f1526,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK22(X0,X3,X5,X4,X2,X1)) = X2 ) )
| ~ spl24_81
| ~ spl24_145 ),
inference(superposition,[],[f1511,f997]) ).
tff(f5194,plain,
( spl24_341
| ~ spl24_22
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1523,f1506,f642,f5192]) ).
tff(f5192,plain,
( spl24_341
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK20(X0,X0,X3,X2,X1,combi(X0))) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_341])]) ).
tff(f1506,plain,
( spl24_144
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_144])]) ).
tff(f1523,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( map(X0,X0,combi(X0),sK20(X0,X0,X3,X2,X1,combi(X0))) = X3 ) )
| ~ spl24_22
| ~ spl24_144 ),
inference(superposition,[],[f1507,f643]) ).
tff(f1507,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ~ spl24_144 ),
inference(avatar_component_clause,[],[f1506]) ).
tff(f5190,plain,
( spl24_340
| ~ spl24_81
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1522,f1506,f996,f5188]) ).
tff(f5188,plain,
( spl24_340
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK20(X3,X0,X2,X1,X5,X4)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_340])]) ).
tff(f1522,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( map(X3,X0,X4,sK20(X3,X0,X2,X1,X5,X4)) = X2 ) )
| ~ spl24_81
| ~ spl24_144 ),
inference(superposition,[],[f1507,f997]) ).
tff(f5186,plain,
( spl24_339
| ~ spl24_81
| ~ spl24_143 ),
inference(avatar_split_clause,[],[f1515,f1502,f996,f5184]) ).
tff(f5184,plain,
( spl24_339
<=> ! [X0: $tType,X4: list(X0),X3: X0,X2: list(X0),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_339])]) ).
tff(f1502,plain,
( spl24_143
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_143])]) ).
tff(f1515,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( X1 = X3 ) )
| ~ spl24_81
| ~ spl24_143 ),
inference(superposition,[],[f1503,f997]) ).
tff(f1503,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X2 = X4 ) )
| ~ spl24_143 ),
inference(avatar_component_clause,[],[f1502]) ).
tff(f5182,plain,
( spl24_338
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1453,f1420,f996,f5180]) ).
tff(f5180,plain,
( spl24_338
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: list(X0),X2: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_338])]) ).
tff(f1453,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X1)),X3: X1,X4: X0,X5: list(X0)] : ( foldl(X1,X0,X2,X3,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X5),X4)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5) )
| ~ spl24_81
| ~ spl24_141 ),
inference(superposition,[],[f1421,f997]) ).
tff(f5136,plain,
( spl24_337
| ~ spl24_45
| ~ spl24_140 ),
inference(avatar_split_clause,[],[f1444,f1416,f775,f5134]) ).
tff(f5134,plain,
( spl24_337
<=> ! [X0: $tType,X4: bool,X3: list(X0),X2: X0,X1: fun(X0,fun(bool,bool))] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_337])]) ).
tff(f775,plain,
( spl24_45
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_45])]) ).
tff(f1416,plain,
( spl24_140
<=> ! [X1: $tType,X0: $tType,X5: fun(X0,fun(X1,X1)),X4: X0,X3: list(X0),X2: X1] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_140])]) ).
tff(f1444,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(bool,bool)),X4: bool] :
( ~ pp(foldr(X0,bool,X1,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X2),X4))
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(X0,fun(bool,bool),X1,X2))) )
| ~ spl24_45
| ~ spl24_140 ),
inference(superposition,[],[f776,f1417]) ).
tff(f1417,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) )
| ~ spl24_140 ),
inference(avatar_component_clause,[],[f1416]) ).
tff(f776,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl24_45 ),
inference(avatar_component_clause,[],[f775]) ).
tff(f5132,plain,
( spl24_336
| ~ spl24_81
| ~ spl24_140 ),
inference(avatar_split_clause,[],[f1440,f1416,f996,f5130]) ).
tff(f5130,plain,
( spl24_336
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X1),X5: X0,X2: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_336])]) ).
tff(f1440,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,X0)),X3: X1,X4: list(X1),X5: X0] : ( foldr(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3) )
| ~ spl24_81
| ~ spl24_140 ),
inference(superposition,[],[f1417,f997]) ).
tff(f5128,plain,
( spl24_335
| ~ spl24_45
| ~ spl24_115 ),
inference(avatar_split_clause,[],[f1240,f1237,f775,f5126]) ).
tff(f5126,plain,
( spl24_335
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_335])]) ).
tff(f1237,plain,
( spl24_115
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_115])]) ).
tff(f1240,plain,
( ! [X2: list(type),X3: nat,X0: fun(nat,type),X1: list(dB),X4: type] :
( ~ pp(aa(list(type),bool,typings(X0,X1),X2))
| pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,X0,X3,X4),map(dB,dB,combc(dB,nat,dB,lift,X3),X1)))) )
| ~ spl24_45
| ~ spl24_115 ),
inference(resolution,[],[f1238,f776]) ).
tff(f1238,plain,
( ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) )
| ~ spl24_115 ),
inference(avatar_component_clause,[],[f1237]) ).
tff(f5071,plain,
( spl24_334
| ~ spl24_18
| ~ spl24_289 ),
inference(avatar_split_clause,[],[f4460,f4145,f610,f5069]) ).
tff(f610,plain,
( spl24_18
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_18])]) ).
tff(f4145,plain,
( spl24_289
<=> ! [X0: bool] :
( ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_289])]) ).
tff(f4460,plain,
( ! [X0: bool] :
( ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_18
| ~ spl24_289 ),
inference(superposition,[],[f611,f4146]) ).
tff(f4146,plain,
( ! [X0: bool] :
( ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = X0 ) )
| ~ spl24_289 ),
inference(avatar_component_clause,[],[f4145]) ).
tff(f611,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl24_18 ),
inference(avatar_component_clause,[],[f610]) ).
tff(f5052,plain,
( spl24_333
| ~ spl24_74
| ~ spl24_171 ),
inference(avatar_split_clause,[],[f1742,f1739,f958,f5050]) ).
tff(f5050,plain,
( spl24_333
<=> ! [X0: fun(nat,type),X3: list(dB),X2: nat,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_333])]) ).
tff(f1739,plain,
( spl24_171
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_171])]) ).
tff(f1742,plain,
( ! [X2: nat,X3: list(dB),X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),foldl(dB,dB,app,var(X2),X3)))
| ( aa(nat,type,X0,X2) = foldr(type,type,fun1,sK16(X1,X3,X2,X0),X1) ) )
| ~ spl24_74
| ~ spl24_171 ),
inference(resolution,[],[f1740,f959]) ).
tff(f1740,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1))) )
| ~ spl24_171 ),
inference(avatar_component_clause,[],[f1739]) ).
tff(f5048,plain,
( spl24_332
| ~ spl24_74
| ~ spl24_147 ),
inference(avatar_split_clause,[],[f1542,f1535,f958,f5046]) ).
tff(f5046,plain,
( spl24_332
<=> ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK12(X1,var(X2),X0)),X2) = sK13(X1,var(X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_332])]) ).
tff(f1535,plain,
( spl24_147
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_147])]) ).
tff(f1542,plain,
( ! [X2: nat,X0: fun(nat,type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),abs(var(X2))))
| ( aa(nat,type,shift(type,X0,zero_zero(nat),sK12(X1,var(X2),X0)),X2) = sK13(X1,var(X2),X0) ) )
| ~ spl24_74
| ~ spl24_147 ),
inference(resolution,[],[f1536,f959]) ).
tff(f1536,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1))) )
| ~ spl24_147 ),
inference(avatar_component_clause,[],[f1535]) ).
tff(f5044,plain,
( spl24_331
| ~ spl24_26
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1483,f1420,f996,f670,f5042]) ).
tff(f5042,plain,
( spl24_331
<=> ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_331])]) ).
tff(f670,plain,
( spl24_26
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_26])]) ).
tff(f1483,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_26
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1461,f997]) ).
tff(f1461,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] :
( sP1(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1))
| ~ listsp(dB,it,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)) )
| ~ spl24_26
| ~ spl24_141 ),
inference(superposition,[],[f671,f1421]) ).
tff(f671,plain,
( ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) )
| ~ spl24_26 ),
inference(avatar_component_clause,[],[f670]) ).
tff(f5040,plain,
( spl24_330
| ~ spl24_22
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1428,f1412,f642,f5038]) ).
tff(f5038,plain,
( spl24_330
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X1,combi(X0),X3,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_330])]) ).
tff(f1412,plain,
( spl24_139
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_139])]) ).
tff(f1428,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK21(X0,X0,X1,combi(X0),X3,X2)) = X2 ) )
| ~ spl24_22
| ~ spl24_139 ),
inference(superposition,[],[f1413,f643]) ).
tff(f1413,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) )
| ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl24_139 ),
inference(avatar_component_clause,[],[f1412]) ).
tff(f5036,plain,
( spl24_329
| ~ spl24_81
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1427,f1412,f996,f5034]) ).
tff(f5034,plain,
( spl24_329
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X0,X3,X5,X4,X2,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_329])]) ).
tff(f1427,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK21(X0,X3,X5,X4,X2,X1)) = X1 ) )
| ~ spl24_81
| ~ spl24_139 ),
inference(superposition,[],[f1413,f997]) ).
tff(f5032,plain,
( spl24_328
| ~ spl24_22
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1425,f1408,f642,f5030]) ).
tff(f5030,plain,
( spl24_328
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK19(X0,X0,X3,X2,X1,combi(X0))) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_328])]) ).
tff(f1408,plain,
( spl24_138
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_138])]) ).
tff(f1425,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 )
| ( aa(X0,X0,combi(X0),sK19(X0,X0,X3,X2,X1,combi(X0))) = X2 ) )
| ~ spl24_22
| ~ spl24_138 ),
inference(superposition,[],[f1409,f643]) ).
tff(f1409,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) )
| ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl24_138 ),
inference(avatar_component_clause,[],[f1408]) ).
tff(f5028,plain,
( spl24_327
| ~ spl24_81
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1424,f1408,f996,f5026]) ).
tff(f5026,plain,
( spl24_327
<=> ! [X0: $tType,X3: $tType,X4: fun(X3,X0),X5: list(X3),X2: list(X0),X1: X0] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK19(X3,X0,X2,X1,X5,X4)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_327])]) ).
tff(f1424,plain,
( ! [X0: $tType,X3: $tType,X2: list(X0),X1: X0,X4: fun(X3,X0),X5: list(X3)] :
( ( map(X3,X0,X4,X5) != aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) )
| ( aa(X3,X0,X4,sK19(X3,X0,X2,X1,X5,X4)) = X1 ) )
| ~ spl24_81
| ~ spl24_138 ),
inference(superposition,[],[f1409,f997]) ).
tff(f5024,plain,
( spl24_326
| ~ spl24_11
| ~ spl24_81
| ~ spl24_131 ),
inference(avatar_split_clause,[],[f1364,f1350,f996,f573,f5022]) ).
tff(f5022,plain,
( spl24_326
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: fun(X0,fun(list(X0),bool)),X1: bool] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_326])]) ).
tff(f1350,plain,
( spl24_131
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_131])]) ).
tff(f1364,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(X0,bool,combc(X0,list(X0),bool,X2,X3),X4) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_11
| ~ spl24_81
| ~ spl24_131 ),
inference(forward_demodulation,[],[f1359,f997]) ).
tff(f1359,plain,
( ! [X0: $tType,X2: fun(X0,fun(list(X0),bool)),X3: list(X0),X1: bool,X4: X0] :
( ( fFalse = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X2,X4),X3) )
| ( fTrue = list_case(bool,X0,X1,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4)) ) )
| ~ spl24_11
| ~ spl24_131 ),
inference(superposition,[],[f1351,f574]) ).
tff(f1351,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_131 ),
inference(avatar_component_clause,[],[f1350]) ).
tff(f4957,plain,
( spl24_325
| ~ spl24_135
| ~ spl24_191 ),
inference(avatar_split_clause,[],[f2035,f2032,f1388,f4955]) ).
tff(f4955,plain,
( spl24_325
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0))))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_325])]) ).
tff(f1388,plain,
( spl24_135
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_135])]) ).
tff(f2032,plain,
( spl24_191
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_191])]) ).
tff(f2035,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0))))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_135
| ~ spl24_191 ),
inference(resolution,[],[f2033,f1389]) ).
tff(f1389,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_135 ),
inference(avatar_component_clause,[],[f1388]) ).
tff(f2033,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_191 ),
inference(avatar_component_clause,[],[f2032]) ).
tff(f4953,plain,
( spl24_324
| ~ spl24_43
| ~ spl24_178 ),
inference(avatar_split_clause,[],[f1877,f1825,f767,f4951]) ).
tff(f4951,plain,
( spl24_324
<=> ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_324])]) ).
tff(f767,plain,
( spl24_43
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_43])]) ).
tff(f1825,plain,
( spl24_178
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_178])]) ).
tff(f1877,plain,
( ! [X2: dB,X0: dB,X1: fun(dB,dB)] : ( abs(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl24_43
| ~ spl24_178 ),
inference(superposition,[],[f768,f1826]) ).
tff(f1826,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl24_178 ),
inference(avatar_component_clause,[],[f1825]) ).
tff(f768,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl24_43 ),
inference(avatar_component_clause,[],[f767]) ).
tff(f4949,plain,
( spl24_323
| ~ spl24_44
| ~ spl24_178 ),
inference(avatar_split_clause,[],[f1876,f1825,f771,f4947]) ).
tff(f4947,plain,
( spl24_323
<=> ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_323])]) ).
tff(f771,plain,
( spl24_44
<=> ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_44])]) ).
tff(f1876,plain,
( ! [X2: nat,X0: dB,X1: fun(dB,dB)] : ( var(X2) != aa(dB,dB,aa(fun(dB,dB),fun(dB,dB),aa(fun(dB,fun(dB,dB)),fun(fun(dB,dB),fun(dB,dB)),combs(dB,dB,dB),app),X1),X0) )
| ~ spl24_44
| ~ spl24_178 ),
inference(superposition,[],[f772,f1826]) ).
tff(f772,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) )
| ~ spl24_44 ),
inference(avatar_component_clause,[],[f771]) ).
tff(f4945,plain,
( spl24_322
| ~ spl24_25
| ~ spl24_131 ),
inference(avatar_split_clause,[],[f1353,f1350,f665,f4943]) ).
tff(f4943,plain,
( spl24_322
<=> ! [X0: $tType,X5: X0,X4: list(nat),X3: fun(list(nat),X0),X2: nat,X1: fun(nat,fun(list(nat),X0))] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_322])]) ).
tff(f665,plain,
( spl24_25
<=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).
tff(f1353,plain,
( ! [X0: $tType,X2: nat,X3: fun(list(nat),X0),X1: fun(nat,fun(list(nat),X0)),X4: list(nat),X5: X0] : ( list_case(X0,nat,X5,shift(fun(list(nat),X0),X1,X2,X3),aa(nat,list(nat),combc(nat,list(nat),list(nat),cons(nat),X4),X2)) = aa(list(nat),X0,X3,X4) )
| ~ spl24_25
| ~ spl24_131 ),
inference(superposition,[],[f1351,f666]) ).
tff(f666,plain,
( ! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 )
| ~ spl24_25 ),
inference(avatar_component_clause,[],[f665]) ).
tff(f4838,plain,
( spl24_321
| ~ spl24_45
| ~ spl24_159 ),
inference(avatar_split_clause,[],[f1660,f1657,f775,f4836]) ).
tff(f4836,plain,
( spl24_321
<=> ! [X4: type,X0: fun(nat,type),X3: nat,X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_321])]) ).
tff(f1657,plain,
( spl24_159
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_159])]) ).
tff(f1660,plain,
( ! [X2: dB,X3: nat,X0: fun(nat,type),X1: type,X4: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X0),X1),X2))
| pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,X0,X3,X4)),X1))) )
| ~ spl24_45
| ~ spl24_159 ),
inference(resolution,[],[f1658,f776]) ).
tff(f1658,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3)) )
| ~ spl24_159 ),
inference(avatar_component_clause,[],[f1657]) ).
tff(f4834,plain,
( spl24_320
| ~ spl24_67
| ~ spl24_140 ),
inference(avatar_split_clause,[],[f1447,f1416,f921,f4832]) ).
tff(f4832,plain,
( spl24_320
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_320])]) ).
tff(f921,plain,
( spl24_67
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_67])]) ).
tff(f1447,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0] : ( foldr(X0,list(X0),cons(X0),X2,X3) != foldr(X0,list(X0),cons(X0),aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1),X3) )
| ~ spl24_67
| ~ spl24_140 ),
inference(superposition,[],[f922,f1417]) ).
tff(f922,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 )
| ~ spl24_67 ),
inference(avatar_component_clause,[],[f921]) ).
tff(f4830,plain,
( spl24_319
| ~ spl24_23
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1391,f1388,f646,f4828]) ).
tff(f4828,plain,
( spl24_319
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_319])]) ).
tff(f1391,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(abs(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0)))) )
| ~ spl24_23
| ~ spl24_135 ),
inference(resolution,[],[f1389,f647]) ).
tff(f4826,plain,
( spl24_318
| ~ spl24_81
| ~ spl24_131 ),
inference(avatar_split_clause,[],[f1358,f1350,f996,f4824]) ).
tff(f4824,plain,
( spl24_318
<=> ! [X1: $tType,X0: $tType,X5: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_318])]) ).
tff(f1358,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X4),X3)) = aa(X0,X1,combc(X0,list(X0),X1,X2,X4),X3) )
| ~ spl24_81
| ~ spl24_131 ),
inference(superposition,[],[f1351,f997]) ).
tff(f4822,plain,
( spl24_317
| ~ spl24_111
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1309,f1304,f1214,f4819]) ).
tff(f4819,plain,
( spl24_317
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK14(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_317])]) ).
tff(f1214,plain,
( spl24_111
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_111])]) ).
tff(f1304,plain,
( spl24_126
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_126])]) ).
tff(f1309,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK14(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl24_111
| ~ spl24_126 ),
inference(resolution,[],[f1306,f1215]) ).
tff(f1215,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl24_111 ),
inference(avatar_component_clause,[],[f1214]) ).
tff(f1306,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl24_126 ),
inference(avatar_component_clause,[],[f1304]) ).
tff(f4817,plain,
( spl24_316
| ~ spl24_113
| ~ spl24_126 ),
inference(avatar_split_clause,[],[f1308,f1304,f1226,f4814]) ).
tff(f4814,plain,
( spl24_316
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_316])]) ).
tff(f1226,plain,
( spl24_113
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_113])]) ).
tff(f1308,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK15(t1,as,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),shift(type,e,i,t))))
| ~ spl24_113
| ~ spl24_126 ),
inference(resolution,[],[f1306,f1227]) ).
tff(f1227,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl24_113 ),
inference(avatar_component_clause,[],[f1226]) ).
tff(f4812,plain,
( spl24_315
| ~ spl24_3
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2454,f2248,f537,f4810]) ).
tff(f4810,plain,
( spl24_315
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_315])]) ).
tff(f2454,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl24_3
| ~ spl24_217 ),
inference(superposition,[],[f539,f2249]) ).
tff(f539,plain,
( pp(fTrue)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f537]) ).
tff(f4781,plain,
( spl24_314
| ~ spl24_43
| ~ spl24_208 ),
inference(avatar_split_clause,[],[f2184,f2170,f767,f4779]) ).
tff(f4779,plain,
( spl24_314
<=> ! [X4: dB,X0: dB,X3: dB,X2: dB,X1: nat] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_314])]) ).
tff(f2170,plain,
( spl24_208
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_208])]) ).
tff(f2184,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: dB] : ( abs(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl24_43
| ~ spl24_208 ),
inference(superposition,[],[f768,f2171]) ).
tff(f2171,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl24_208 ),
inference(avatar_component_clause,[],[f2170]) ).
tff(f4777,plain,
( spl24_313
| ~ spl24_44
| ~ spl24_208 ),
inference(avatar_split_clause,[],[f2183,f2170,f771,f4775]) ).
tff(f4775,plain,
( spl24_313
<=> ! [X4: nat,X0: dB,X3: dB,X2: dB,X1: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_313])]) ).
tff(f2183,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: nat,X4: nat] : ( var(X4) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X3),X0)),X1),X2) )
| ~ spl24_44
| ~ spl24_208 ),
inference(superposition,[],[f772,f2171]) ).
tff(f4773,plain,
( spl24_312
| ~ spl24_130
| ~ spl24_157 ),
inference(avatar_split_clause,[],[f1644,f1640,f1342,f4770]) ).
tff(f4770,plain,
( spl24_312
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK17(foldr(type,type,fun1,sK3,t1),a,var(i),shift(type,e,i,t))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_312])]) ).
tff(f1342,plain,
( spl24_130
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_130])]) ).
tff(f1640,plain,
( spl24_157
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_157])]) ).
tff(f1644,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK17(foldr(type,type,fun1,sK3,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl24_130
| ~ spl24_157 ),
inference(resolution,[],[f1641,f1344]) ).
tff(f1344,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_130 ),
inference(avatar_component_clause,[],[f1342]) ).
tff(f1641,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_157 ),
inference(avatar_component_clause,[],[f1640]) ).
tff(f4768,plain,
( spl24_311
| ~ spl24_124
| ~ spl24_157 ),
inference(avatar_split_clause,[],[f1643,f1640,f1289,f4765]) ).
tff(f4765,plain,
( spl24_311
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK17(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_311])]) ).
tff(f1289,plain,
( spl24_124
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_124])]) ).
tff(f1643,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK17(foldr(type,type,fun1,ts,t1),a,var(i),shift(type,e,i,t))),a))
| ~ spl24_124
| ~ spl24_157 ),
inference(resolution,[],[f1641,f1291]) ).
tff(f1291,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_124 ),
inference(avatar_component_clause,[],[f1289]) ).
tff(f4763,plain,
( spl24_310
| ~ spl24_16
| ~ spl24_135 ),
inference(avatar_split_clause,[],[f1392,f1388,f602,f4761]) ).
tff(f4761,plain,
( spl24_310
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_310])]) ).
tff(f1392,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))) )
| ~ spl24_16
| ~ spl24_135 ),
inference(resolution,[],[f1389,f603]) ).
tff(f4757,plain,
( spl24_309
| ~ spl24_13
| ~ spl24_14 ),
inference(avatar_split_clause,[],[f622,f593,f588,f4755]) ).
tff(f4755,plain,
( spl24_309
<=> ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_309])]) ).
tff(f593,plain,
( spl24_14
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_14])]) ).
tff(f622,plain,
( ! [X0: nat] : ( fTrue = aa(dB,bool,it,var(X0)) )
| ~ spl24_13
| ~ spl24_14 ),
inference(resolution,[],[f589,f594]) ).
tff(f594,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl24_14 ),
inference(avatar_component_clause,[],[f593]) ).
tff(f4748,plain,
( spl24_308
| ~ spl24_135
| ~ spl24_188 ),
inference(avatar_split_clause,[],[f1979,f1976,f1388,f4746]) ).
tff(f4746,plain,
( spl24_308
<=> ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_308])]) ).
tff(f1976,plain,
( spl24_188
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_188])]) ).
tff(f1979,plain,
( ! [X0: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)))
| ~ pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_135
| ~ spl24_188 ),
inference(resolution,[],[f1977,f1389]) ).
tff(f1977,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_188 ),
inference(avatar_component_clause,[],[f1976]) ).
tff(f4744,plain,
( spl24_307
| ~ spl24_72
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1490,f1420,f996,f945,f4742]) ).
tff(f4742,plain,
( spl24_307
<=> ! [X4: dB,X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_307])]) ).
tff(f945,plain,
( spl24_72
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_72])]) ).
tff(f1490,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl24_72
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1468,f997]) ).
tff(f1468,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: dB] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X4) )
| ~ spl24_72
| ~ spl24_141 ),
inference(superposition,[],[f946,f1421]) ).
tff(f946,plain,
( ! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) )
| ~ spl24_72 ),
inference(avatar_component_clause,[],[f945]) ).
tff(f4740,plain,
( spl24_306
| ~ spl24_23
| ~ spl24_133 ),
inference(avatar_split_clause,[],[f1377,f1373,f646,f4737]) ).
tff(f4737,plain,
( spl24_306
<=> sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_306])]) ).
tff(f1373,plain,
( spl24_133
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_133])]) ).
tff(f1377,plain,
( sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_23
| ~ spl24_133 ),
inference(resolution,[],[f1375,f647]) ).
tff(f1375,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_133 ),
inference(avatar_component_clause,[],[f1373]) ).
tff(f4700,plain,
( spl24_305
| ~ spl24_16
| ~ spl24_133 ),
inference(avatar_split_clause,[],[f1378,f1373,f602,f4697]) ).
tff(f4697,plain,
( spl24_305
<=> sP1(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_305])]) ).
tff(f1378,plain,
( sP1(aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u))
| ~ spl24_16
| ~ spl24_133 ),
inference(resolution,[],[f1375,f603]) ).
tff(f4695,plain,
( spl24_304
| ~ spl24_81
| ~ spl24_107 ),
inference(avatar_split_clause,[],[f1192,f1188,f996,f4693]) ).
tff(f4693,plain,
( spl24_304
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_304])]) ).
tff(f1188,plain,
( spl24_107
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_107])]) ).
tff(f1192,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)) = X2 )
| ~ spl24_81
| ~ spl24_107 ),
inference(superposition,[],[f1189,f997]) ).
tff(f1189,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl24_107 ),
inference(avatar_component_clause,[],[f1188]) ).
tff(f4683,plain,
( spl24_303
| ~ spl24_63
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1025,f996,f896,f4681]) ).
tff(f4681,plain,
( spl24_303
<=> ! [X0: $tType,X3: nat,X2: X0,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_303])]) ).
tff(f896,plain,
( spl24_63
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_63])]) ).
tff(f1025,plain,
( ! [X0: $tType,X2: X0,X3: nat,X1: fun(X0,fun(nat,type))] : pp(aa(dB,bool,combc(dB,type,bool,typing(aa(X0,fun(nat,type),X1,X2)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)),var(X3)))
| ~ spl24_63
| ~ spl24_81 ),
inference(superposition,[],[f897,f997]) ).
tff(f897,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl24_63 ),
inference(avatar_component_clause,[],[f896]) ).
tff(f4614,plain,
( spl24_302
| ~ spl24_60
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1494,f1420,f996,f883,f4612]) ).
tff(f4612,plain,
( spl24_302
<=> ! [X4: list(dB),X0: dB,X3: dB,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_302])]) ).
tff(f883,plain,
( spl24_60
<=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_60])]) ).
tff(f1494,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl24_60
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1472,f997]) ).
tff(f1472,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl24_60
| ~ spl24_141 ),
inference(superposition,[],[f884,f1421]) ).
tff(f884,plain,
( ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) )
| ( X1 = X3 ) )
| ~ spl24_60 ),
inference(avatar_component_clause,[],[f883]) ).
tff(f4610,plain,
( spl24_301
| ~ spl24_61
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1486,f1420,f996,f887,f4608]) ).
tff(f4608,plain,
( spl24_301
<=> ! [X4: list(dB),X0: nat,X3: nat,X2: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_301])]) ).
tff(f887,plain,
( spl24_61
<=> ! [X0: list(dB),X3: nat,X2: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_61])]) ).
tff(f1486,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ( X0 = X3 ) )
| ~ spl24_61
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1464,f997]) ).
tff(f1464,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: list(dB),X4: list(dB)] :
( ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) )
| ( X0 = X3 ) )
| ~ spl24_61
| ~ spl24_141 ),
inference(superposition,[],[f888,f1421]) ).
tff(f888,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_61 ),
inference(avatar_component_clause,[],[f887]) ).
tff(f4606,plain,
( spl24_300
| ~ spl24_23
| ~ spl24_109 ),
inference(avatar_split_clause,[],[f1203,f1200,f646,f4604]) ).
tff(f4604,plain,
( spl24_300
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_300])]) ).
tff(f1200,plain,
( spl24_109
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_109])]) ).
tff(f1203,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2)))) )
| ~ spl24_23
| ~ spl24_109 ),
inference(resolution,[],[f1201,f647]) ).
tff(f1201,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_109 ),
inference(avatar_component_clause,[],[f1200]) ).
tff(f4602,plain,
( spl24_299
| ~ spl24_11
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1115,f1103,f573,f4600]) ).
tff(f4600,plain,
( spl24_299
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_299])]) ).
tff(f1103,plain,
( spl24_95
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_95])]) ).
tff(f1115,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X1,X2)) ) )
| ~ spl24_11
| ~ spl24_95 ),
inference(superposition,[],[f1104,f574]) ).
tff(f1104,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl24_95 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f4598,plain,
( spl24_168
| ~ spl24_298
| ~ spl24_289 ),
inference(avatar_split_clause,[],[f4483,f4145,f4595,f1720]) ).
tff(f1720,plain,
( spl24_168
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_168])]) ).
tff(f4483,plain,
( ! [X0: bool] :
( ( fTrue != aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) )
| ( fTrue = X0 ) )
| ~ spl24_289 ),
inference(equality_factoring,[],[f4146]) ).
tff(f4593,plain,
( spl24_297
| ~ spl24_11
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1110,f1103,f573,f4591]) ).
tff(f4591,plain,
( spl24_297
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_297])]) ).
tff(f1110,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK18(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK18(bool,X0,X2,X1)) ) )
| ~ spl24_11
| ~ spl24_95 ),
inference(superposition,[],[f1104,f574]) ).
tff(f4531,plain,
( spl24_296
| ~ spl24_16
| ~ spl24_109 ),
inference(avatar_split_clause,[],[f1204,f1200,f602,f4529]) ).
tff(f4529,plain,
( spl24_296
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_296])]) ).
tff(f1204,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) )
| ~ spl24_16
| ~ spl24_109 ),
inference(resolution,[],[f1201,f603]) ).
tff(f4527,plain,
( spl24_295
| ~ spl24_45
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1018,f996,f775,f4525]) ).
tff(f4525,plain,
( spl24_295
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_295])]) ).
tff(f1018,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X1,fun(X0,bool),X2,X3))) )
| ~ spl24_45
| ~ spl24_81 ),
inference(superposition,[],[f776,f997]) ).
tff(f4523,plain,
( spl24_294
| ~ spl24_45
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1017,f996,f775,f4521]) ).
tff(f4521,plain,
( spl24_294
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_294])]) ).
tff(f1017,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X1,bool,X2,X3))) )
| ~ spl24_45
| ~ spl24_81 ),
inference(superposition,[],[f776,f997]) ).
tff(f4163,plain,
( spl24_293
| ~ spl24_67
| ~ spl24_177 ),
inference(avatar_split_clause,[],[f1804,f1785,f921,f4161]) ).
tff(f4161,plain,
( spl24_293
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_293])]) ).
tff(f1785,plain,
( spl24_177
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_177])]) ).
tff(f1804,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X4),X3)) )
| ~ spl24_67
| ~ spl24_177 ),
inference(superposition,[],[f922,f1786]) ).
tff(f1786,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_177 ),
inference(avatar_component_clause,[],[f1785]) ).
tff(f4159,plain,
( spl24_292
| ~ spl24_90
| ~ spl24_163 ),
inference(avatar_split_clause,[],[f1688,f1682,f1072,f4157]) ).
tff(f4157,plain,
( spl24_292
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_292])]) ).
tff(f1072,plain,
( spl24_90
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_90])]) ).
tff(f1682,plain,
( spl24_163
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_163])]) ).
tff(f1688,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t_a = X0 ) )
| ~ spl24_90
| ~ spl24_163 ),
inference(resolution,[],[f1683,f1074]) ).
tff(f1074,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_90 ),
inference(avatar_component_clause,[],[f1072]) ).
tff(f1683,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl24_163 ),
inference(avatar_component_clause,[],[f1682]) ).
tff(f4155,plain,
( spl24_291
| ~ spl24_92
| ~ spl24_163 ),
inference(avatar_split_clause,[],[f1687,f1682,f1086,f4153]) ).
tff(f4153,plain,
( spl24_291
<=> ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t1 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_291])]) ).
tff(f1086,plain,
( spl24_92
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_92])]) ).
tff(f1687,plain,
( ! [X0: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),X0),foldl(dB,dB,app,var(i),rs)))
| ( t1 = X0 ) )
| ~ spl24_92
| ~ spl24_163 ),
inference(resolution,[],[f1683,f1088]) ).
tff(f1088,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_92 ),
inference(avatar_component_clause,[],[f1086]) ).
tff(f4151,plain,
( spl24_290
| ~ spl24_81
| ~ spl24_103 ),
inference(avatar_split_clause,[],[f1167,f1151,f996,f4149]) ).
tff(f4149,plain,
( spl24_290
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_290])]) ).
tff(f1151,plain,
( spl24_103
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_103])]) ).
tff(f1167,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_81
| ~ spl24_103 ),
inference(superposition,[],[f1152,f997]) ).
tff(f1152,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 = X2 ) )
| ~ spl24_103 ),
inference(avatar_component_clause,[],[f1151]) ).
tff(f4147,plain,
( spl24_289
| ~ spl24_3
| spl24_12
| ~ spl24_217 ),
inference(avatar_split_clause,[],[f2520,f2248,f583,f537,f4145]) ).
tff(f2520,plain,
( ! [X0: bool] :
( ~ pp(fTrue)
| ( aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts) = X0 )
| ( fTrue = X0 ) )
| spl24_12
| ~ spl24_217 ),
inference(superposition,[],[f585,f2249]) ).
tff(f4143,plain,
( spl24_288
| ~ spl24_81
| ~ spl24_102 ),
inference(avatar_split_clause,[],[f1164,f1146,f996,f4141]) ).
tff(f4141,plain,
( spl24_288
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_288])]) ).
tff(f1146,plain,
( spl24_102
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_102])]) ).
tff(f1164,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_81
| ~ spl24_102 ),
inference(superposition,[],[f1147,f997]) ).
tff(f1147,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X1 = X3 ) )
| ~ spl24_102 ),
inference(avatar_component_clause,[],[f1146]) ).
tff(f4139,plain,
( spl24_287
| ~ spl24_81
| ~ spl24_101 ),
inference(avatar_split_clause,[],[f1160,f1142,f996,f4137]) ).
tff(f4137,plain,
( spl24_287
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_287])]) ).
tff(f1142,plain,
( spl24_101
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_101])]) ).
tff(f1160,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_81
| ~ spl24_101 ),
inference(superposition,[],[f1143,f997]) ).
tff(f1143,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_101 ),
inference(avatar_component_clause,[],[f1142]) ).
tff(f4135,plain,
( spl24_286
| ~ spl24_81
| ~ spl24_100 ),
inference(avatar_split_clause,[],[f1155,f1138,f996,f4133]) ).
tff(f4133,plain,
( spl24_286
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_286])]) ).
tff(f1138,plain,
( spl24_100
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_100])]) ).
tff(f1155,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl24_81
| ~ spl24_100 ),
inference(superposition,[],[f1139,f997]) ).
tff(f1139,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl24_100 ),
inference(avatar_component_clause,[],[f1138]) ).
tff(f4131,plain,
( spl24_285
| ~ spl24_11
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1016,f996,f573,f4129]) ).
tff(f4129,plain,
( spl24_285
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X1,fun(X0,bool))] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_285])]) ).
tff(f1016,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) )
| ( fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4) ) )
| ~ spl24_11
| ~ spl24_81 ),
inference(superposition,[],[f997,f574]) ).
tff(f4127,plain,
( spl24_284
| ~ spl24_11
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1009,f996,f573,f4125]) ).
tff(f4125,plain,
( spl24_284
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(X0,fun(X1,bool))] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_284])]) ).
tff(f1009,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: X1,X4: X0] :
( ( fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) )
| ( fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4) ) )
| ~ spl24_11
| ~ spl24_81 ),
inference(superposition,[],[f997,f574]) ).
tff(f4099,plain,
( spl24_283
| ~ spl24_46
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1496,f1420,f996,f779,f4097]) ).
tff(f4097,plain,
( spl24_283
<=> ! [X4: list(dB),X0: dB,X3: nat,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_283])]) ).
tff(f779,plain,
( spl24_46
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_46])]) ).
tff(f1496,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X0)),X1) )
| ~ spl24_46
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1474,f997]) ).
tff(f1474,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,var(X3),X4) != foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X0)),X2),X1) )
| ~ spl24_46
| ~ spl24_141 ),
inference(superposition,[],[f780,f1421]) ).
tff(f780,plain,
( ! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) )
| ~ spl24_46 ),
inference(avatar_component_clause,[],[f779]) ).
tff(f4094,plain,
( spl24_282
| ~ spl24_46
| ~ spl24_81
| ~ spl24_141 ),
inference(avatar_split_clause,[],[f1484,f1420,f996,f779,f4092]) ).
tff(f4092,plain,
( spl24_282
<=> ! [X4: list(dB),X0: nat,X3: dB,X2: dB,X1: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_282])]) ).
tff(f1484,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,abs(X3),X4) != foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1) )
| ~ spl24_46
| ~ spl24_81
| ~ spl24_141 ),
inference(forward_demodulation,[],[f1462,f997]) ).
tff(f1462,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: list(dB),X4: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(X0)),X2),X1) != foldl(dB,dB,app,abs(X3),X4) )
| ~ spl24_46
| ~ spl24_141 ),
inference(superposition,[],[f780,f1421]) ).
tff(f4090,plain,
( spl24_281
| ~ spl24_45
| ~ spl24_130 ),
inference(avatar_split_clause,[],[f1346,f1342,f775,f4087]) ).
tff(f4087,plain,
( spl24_281
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_281])]) ).
tff(f1346,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1))))
| ~ spl24_45
| ~ spl24_130 ),
inference(resolution,[],[f1344,f776]) ).
tff(f4085,plain,
( spl24_280
| ~ spl24_45
| ~ spl24_124 ),
inference(avatar_split_clause,[],[f1293,f1289,f775,f4082]) ).
tff(f4082,plain,
( spl24_280
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_280])]) ).
tff(f1293,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1))))
| ~ spl24_45
| ~ spl24_124 ),
inference(resolution,[],[f1291,f776]) ).
tff(f3925,plain,
( spl24_279
| ~ spl24_66
| ~ spl24_149 ),
inference(avatar_split_clause,[],[f1559,f1552,f916,f3923]) ).
tff(f3923,plain,
( spl24_279
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_279])]) ).
tff(f916,plain,
( spl24_66
<=> ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_66])]) ).
tff(f1559,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( as = X1 ) )
| ~ spl24_66
| ~ spl24_149 ),
inference(superposition,[],[f1553,f918]) ).
tff(f918,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl24_66 ),
inference(avatar_component_clause,[],[f916]) ).
tff(f3921,plain,
( spl24_278
| ~ spl24_18
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1112,f1103,f610,f3919]) ).
tff(f3919,plain,
( spl24_278
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK18(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_278])]) ).
tff(f1112,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK18(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl24_18
| ~ spl24_95 ),
inference(superposition,[],[f1104,f611]) ).
tff(f3917,plain,
( spl24_277
| ~ spl24_21
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2709,f2690,f638,f3915]) ).
tff(f3915,plain,
( spl24_277
<=> ! [X0: dB] :
( sP1(abs(abs(sK8(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_277])]) ).
tff(f638,plain,
( spl24_21
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_21])]) ).
tff(f2690,plain,
( spl24_219
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_219])]) ).
tff(f2709,plain,
( ! [X0: dB] :
( sP1(abs(abs(sK8(X0))))
| ~ sP0(X0) )
| ~ spl24_21
| ~ spl24_219 ),
inference(resolution,[],[f2691,f639]) ).
tff(f639,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_21 ),
inference(avatar_component_clause,[],[f638]) ).
tff(f2691,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl24_219 ),
inference(avatar_component_clause,[],[f2690]) ).
tff(f3913,plain,
( spl24_276
| ~ spl24_11
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1111,f1103,f573,f3911]) ).
tff(f3911,plain,
( spl24_276
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK18(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_276])]) ).
tff(f1111,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK18(X0,bool,X1,X2) ) )
| ~ spl24_11
| ~ spl24_95 ),
inference(superposition,[],[f1104,f574]) ).
tff(f3909,plain,
( spl24_275
| ~ spl24_18
| ~ spl24_95 ),
inference(avatar_split_clause,[],[f1107,f1103,f610,f3907]) ).
tff(f3907,plain,
( spl24_275
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK18(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_275])]) ).
tff(f1107,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK18(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK18(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl24_18
| ~ spl24_95 ),
inference(superposition,[],[f1104,f611]) ).
tff(f3905,plain,
( spl24_274
| ~ spl24_45
| ~ spl24_88 ),
inference(avatar_split_clause,[],[f1061,f1057,f775,f3903]) ).
tff(f3903,plain,
( spl24_274
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_274])]) ).
tff(f1057,plain,
( spl24_88
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_88])]) ).
tff(f1061,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,fun(X0,bool),bool,member(X0),X1))) )
| ~ spl24_45
| ~ spl24_88 ),
inference(resolution,[],[f1058,f776]) ).
tff(f1058,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_88 ),
inference(avatar_component_clause,[],[f1057]) ).
tff(f3827,plain,
( spl24_273
| ~ spl24_43
| ~ spl24_184 ),
inference(avatar_split_clause,[],[f1956,f1946,f767,f3825]) ).
tff(f3825,plain,
( spl24_273
<=> ! [X2: dB,X0: nat,X1: dB,X3: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_273])]) ).
tff(f1946,plain,
( spl24_184
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_184])]) ).
tff(f1956,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( abs(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl24_43
| ~ spl24_184 ),
inference(superposition,[],[f768,f1947]) ).
tff(f1947,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl24_184 ),
inference(avatar_component_clause,[],[f1946]) ).
tff(f3823,plain,
( spl24_272
| ~ spl24_44
| ~ spl24_184 ),
inference(avatar_split_clause,[],[f1955,f1946,f771,f3821]) ).
tff(f3821,plain,
( spl24_272
<=> ! [X2: dB,X0: nat,X1: dB,X3: nat] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_272])]) ).
tff(f1955,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( var(X3) != aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X2),X1)) )
| ~ spl24_44
| ~ spl24_184 ),
inference(superposition,[],[f772,f1947]) ).
tff(f3819,plain,
( spl24_271
| ~ spl24_66
| ~ spl24_145 ),
inference(avatar_split_clause,[],[f1524,f1510,f916,f3817]) ).
tff(f3817,plain,
( spl24_271
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_271])]) ).
tff(f1524,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK22(dB,X0,X2,X1,as,a)) ) )
| ~ spl24_66
| ~ spl24_145 ),
inference(superposition,[],[f1511,f918]) ).
tff(f3815,plain,
( spl24_270
| ~ spl24_66
| ~ spl24_144 ),
inference(avatar_split_clause,[],[f1520,f1506,f916,f3813]) ).
tff(f3813,plain,
( spl24_270
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK20(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_270])]) ).
tff(f1520,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( as = map(X0,dB,X1,sK20(X0,dB,as,a,X2,X1)) ) )
| ~ spl24_66
| ~ spl24_144 ),
inference(superposition,[],[f1507,f918]) ).
tff(f3811,plain,
( spl24_269
| ~ spl24_66
| ~ spl24_143 ),
inference(avatar_split_clause,[],[f1513,f1502,f916,f3809]) ).
tff(f3809,plain,
( spl24_269
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_269])]) ).
tff(f1513,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),X1) )
| ( a = X0 ) )
| ~ spl24_66
| ~ spl24_143 ),
inference(superposition,[],[f1503,f918]) ).
tff(f3807,plain,
( spl24_268
| ~ spl24_90
| ~ spl24_113 ),
inference(avatar_split_clause,[],[f1230,f1226,f1072,f3804]) ).
tff(f3804,plain,
( spl24_268
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_268])]) ).
tff(f1230,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK15(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl24_90
| ~ spl24_113 ),
inference(resolution,[],[f1227,f1074]) ).
tff(f3802,plain,
( spl24_267
| ~ spl24_92
| ~ spl24_113 ),
inference(avatar_split_clause,[],[f1229,f1226,f1086,f3799]) ).
tff(f3799,plain,
( spl24_267
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_267])]) ).
tff(f1229,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK15(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl24_92
| ~ spl24_113 ),
inference(resolution,[],[f1227,f1088]) ).
tff(f3784,plain,
( spl24_266
| ~ spl24_90
| ~ spl24_111 ),
inference(avatar_split_clause,[],[f1218,f1214,f1072,f3781]) ).
tff(f3781,plain,
( spl24_266
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_266])]) ).
tff(f1218,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK14(t_a,rs,var(i),shift(type,ea,ia,t))))
| ~ spl24_90
| ~ spl24_111 ),
inference(resolution,[],[f1215,f1074]) ).
tff(f3779,plain,
( spl24_265
| ~ spl24_92
| ~ spl24_111 ),
inference(avatar_split_clause,[],[f1217,f1214,f1086,f3776]) ).
tff(f3776,plain,
( spl24_265
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK14(t1,rs,var(i),shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_265])]) ).
tff(f1217,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK14(t1,rs,var(i),shift(type,e,i,t))))
| ~ spl24_92
| ~ spl24_111 ),
inference(resolution,[],[f1215,f1088]) ).
tff(f3774,plain,
( spl24_264
| ~ spl24_25
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1010,f996,f665,f3772]) ).
tff(f3772,plain,
( spl24_264
<=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_264])]) ).
tff(f1010,plain,
( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: X0] : ( aa(nat,X1,combc(nat,X0,X1,shift(fun(X0,X1),X2,X3,X4),X5),X3) = aa(X0,X1,X4,X5) )
| ~ spl24_25
| ~ spl24_81 ),
inference(superposition,[],[f997,f666]) ).
tff(f3745,plain,
( spl24_263
| ~ spl24_66
| ~ spl24_139 ),
inference(avatar_split_clause,[],[f1426,f1412,f916,f3743]) ).
tff(f3743,plain,
( spl24_263
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(dB,X0,X2,X1,as,a)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_263])]) ).
tff(f1426,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK21(dB,X0,X2,X1,as,a)) ) )
| ~ spl24_66
| ~ spl24_139 ),
inference(superposition,[],[f1413,f918]) ).
tff(f3741,plain,
( spl24_262
| ~ spl24_66
| ~ spl24_138 ),
inference(avatar_split_clause,[],[f1423,f1408,f916,f3739]) ).
tff(f3739,plain,
( spl24_262
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK19(X0,dB,as,a,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_262])]) ).
tff(f1423,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,dB)] :
( ( rs != map(X0,dB,X1,X2) )
| ( a = aa(X0,dB,X1,sK19(X0,dB,as,a,X2,X1)) ) )
| ~ spl24_66
| ~ spl24_138 ),
inference(superposition,[],[f1409,f918]) ).
tff(f3736,plain,
( spl24_261
| ~ spl24_90
| ~ spl24_117 ),
inference(avatar_split_clause,[],[f1253,f1249,f1072,f3733]) ).
tff(f3733,plain,
( spl24_261
<=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK16(t_a,rs,i,shift(type,ea,ia,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_261])]) ).
tff(f1249,plain,
( spl24_117
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_117])]) ).
tff(f1253,plain,
( pp(aa(list(type),bool,typings(shift(type,ea,ia,t),rs),sK16(t_a,rs,i,shift(type,ea,ia,t))))
| ~ spl24_90
| ~ spl24_117 ),
inference(resolution,[],[f1250,f1074]) ).
tff(f1250,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl24_117 ),
inference(avatar_component_clause,[],[f1249]) ).
tff(f3731,plain,
( spl24_260
| ~ spl24_92
| ~ spl24_117 ),
inference(avatar_split_clause,[],[f1252,f1249,f1086,f3728]) ).
tff(f3728,plain,
( spl24_260
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK16(t1,rs,i,shift(type,e,i,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_260])]) ).
tff(f1252,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),rs),sK16(t1,rs,i,shift(type,e,i,t))))
| ~ spl24_92
| ~ spl24_117 ),
inference(resolution,[],[f1250,f1088]) ).
tff(f3726,plain,
( spl24_259
| ~ spl24_58
| ~ spl24_101 ),
inference(avatar_split_clause,[],[f1159,f1142,f874,f3724]) ).
tff(f3724,plain,
( spl24_259
<=> ! [X0: type,X1: type] :
( ( t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( foldr(type,type,fun1,ts,t1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_259])]) ).
tff(f874,plain,
( spl24_58
<=> ( t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_58])]) ).
tff(f1159,plain,
( ! [X0: type,X1: type] :
( ( t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( foldr(type,type,fun1,ts,t1) = X1 ) )
| ~ spl24_58
| ~ spl24_101 ),
inference(superposition,[],[f1143,f876]) ).
tff(f876,plain,
( ( t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)) )
| ~ spl24_58 ),
inference(avatar_component_clause,[],[f874]) ).
tff(f3719,plain,
( spl24_258
| ~ spl24_78
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1013,f996,f978,f3717]) ).
tff(f3717,plain,
( spl24_258
<=> ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_258])]) ).
tff(f978,plain,
( spl24_78
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_78])]) ).
tff(f1013,plain,
( ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 )
| ~ spl24_78
| ~ spl24_81 ),
inference(superposition,[],[f997,f979]) ).
tff(f979,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl24_78 ),
inference(avatar_component_clause,[],[f978]) ).
tff(f3697,plain,
( spl24_257
| ~ spl24_17
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2693,f2690,f606,f3695]) ).
tff(f3695,plain,
( spl24_257
<=> ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_257])]) ).
tff(f606,plain,
( spl24_17
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_17])]) ).
tff(f2693,plain,
( ! [X0: dB] :
( sP1(abs(abs(X0)))
| ~ sP1(X0) )
| ~ spl24_17
| ~ spl24_219 ),
inference(resolution,[],[f2691,f607]) ).
tff(f607,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl24_17 ),
inference(avatar_component_clause,[],[f606]) ).
tff(f3665,plain,
( spl24_256
| ~ spl24_45
| ~ spl24_92 ),
inference(avatar_split_clause,[],[f1090,f1086,f775,f3662]) ).
tff(f3662,plain,
( spl24_256
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_256])]) ).
tff(f1090,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t1)))
| ~ spl24_45
| ~ spl24_92 ),
inference(resolution,[],[f1088,f776]) ).
tff(f3660,plain,
( spl24_255
| ~ spl24_45
| ~ spl24_90 ),
inference(avatar_split_clause,[],[f1076,f1072,f775,f3657]) ).
tff(f3657,plain,
( spl24_255
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_255])]) ).
tff(f1076,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a)))
| ~ spl24_45
| ~ spl24_90 ),
inference(resolution,[],[f1074,f776]) ).
tff(f3655,plain,
( spl24_254
| ~ spl24_23
| ~ spl24_84 ),
inference(avatar_split_clause,[],[f1036,f1033,f646,f3653]) ).
tff(f3653,plain,
( spl24_254
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_254])]) ).
tff(f1033,plain,
( spl24_84
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_84])]) ).
tff(f1036,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0))) )
| ~ spl24_23
| ~ spl24_84 ),
inference(resolution,[],[f1034,f647]) ).
tff(f1034,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_84 ),
inference(avatar_component_clause,[],[f1033]) ).
tff(f3651,plain,
( spl24_253
| ~ spl24_72
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1021,f996,f945,f3649]) ).
tff(f3649,plain,
( spl24_253
<=> ! [X2: nat,X0: dB,X1: dB,X3: list(dB)] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_253])]) ).
tff(f1021,plain,
( ! [X2: nat,X3: list(dB),X0: dB,X1: dB] : ( foldl(dB,dB,app,var(X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)) )
| ~ spl24_72
| ~ spl24_81 ),
inference(superposition,[],[f946,f997]) ).
tff(f3647,plain,
( spl24_252
| ~ spl24_23
| ~ spl24_76 ),
inference(avatar_split_clause,[],[f999,f969,f646,f3645]) ).
tff(f3645,plain,
( spl24_252
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK4(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_252])]) ).
tff(f969,plain,
( spl24_76
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_76])]) ).
tff(f999,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(abs(sK4(X0))) )
| ~ spl24_23
| ~ spl24_76 ),
inference(resolution,[],[f970,f647]) ).
tff(f970,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK4(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl24_76 ),
inference(avatar_component_clause,[],[f969]) ).
tff(f3643,plain,
( spl24_251
| ~ spl24_45
| ~ spl24_63 ),
inference(avatar_split_clause,[],[f903,f896,f775,f3641]) ).
tff(f3641,plain,
( spl24_251
<=> ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_251])]) ).
tff(f903,plain,
( ! [X0: fun(nat,type),X1: nat] : pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(X0),aa(nat,type,X0,X1))))
| ~ spl24_45
| ~ spl24_63 ),
inference(resolution,[],[f897,f776]) ).
tff(f3639,plain,
( spl24_250
| ~ spl24_45
| ~ spl24_57 ),
inference(avatar_split_clause,[],[f870,f866,f775,f3636]) ).
tff(f3636,plain,
( spl24_250
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_250])]) ).
tff(f866,plain,
( spl24_57
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_57])]) ).
tff(f870,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),sK2)))
| ~ spl24_45
| ~ spl24_57 ),
inference(resolution,[],[f868,f776]) ).
tff(f868,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK2),a))
| ~ spl24_57 ),
inference(avatar_component_clause,[],[f866]) ).
tff(f3633,plain,
( spl24_249
| ~ spl24_45
| ~ spl24_55 ),
inference(avatar_split_clause,[],[f856,f852,f775,f3630]) ).
tff(f3630,plain,
( spl24_249
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_249])]) ).
tff(f852,plain,
( spl24_55
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_55])]) ).
tff(f856,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(shift(type,e,i,t)),t2)))
| ~ spl24_45
| ~ spl24_55 ),
inference(resolution,[],[f854,f776]) ).
tff(f854,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t2),a))
| ~ spl24_55 ),
inference(avatar_component_clause,[],[f852]) ).
tff(f3625,plain,
( spl24_248
| ~ spl24_16
| ~ spl24_84 ),
inference(avatar_split_clause,[],[f1037,f1033,f602,f3623]) ).
tff(f3623,plain,
( spl24_248
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_248])]) ).
tff(f1037,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) )
| ~ spl24_16
| ~ spl24_84 ),
inference(resolution,[],[f1034,f603]) ).
tff(f3621,plain,
( spl24_247
| ~ spl24_16
| ~ spl24_76 ),
inference(avatar_split_clause,[],[f1000,f969,f602,f3619]) ).
tff(f3619,plain,
( spl24_247
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_247])]) ).
tff(f1000,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK4(X0)) )
| ~ spl24_16
| ~ spl24_76 ),
inference(resolution,[],[f970,f603]) ).
tff(f3617,plain,
( spl24_246
| ~ spl24_23
| ~ spl24_80 ),
inference(avatar_split_clause,[],[f990,f987,f646,f3615]) ).
tff(f3615,plain,
( spl24_246
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_246])]) ).
tff(f987,plain,
( spl24_80
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_80])]) ).
tff(f990,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0))) )
| ~ spl24_23
| ~ spl24_80 ),
inference(resolution,[],[f988,f647]) ).
tff(f988,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_80 ),
inference(avatar_component_clause,[],[f987]) ).
tff(f3598,plain,
( spl24_245
| ~ spl24_14
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2695,f2690,f593,f3596]) ).
tff(f3596,plain,
( spl24_245
<=> ! [X0: nat] : sP1(abs(abs(var(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_245])]) ).
tff(f2695,plain,
( ! [X0: nat] : sP1(abs(abs(var(X0))))
| ~ spl24_14
| ~ spl24_219 ),
inference(resolution,[],[f2691,f594]) ).
tff(f2995,plain,
( ~ spl24_3
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2932]) ).
tff(f2932,plain,
( $false
| ~ spl24_3
| ~ spl24_223 ),
inference(resolution,[],[f2746,f539]) ).
tff(f2746,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl24_223 ),
inference(avatar_component_clause,[],[f2745]) ).
tff(f2745,plain,
( spl24_223
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_223])]) ).
tff(f2994,plain,
( ~ spl24_36
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2933]) ).
tff(f2933,plain,
( $false
| ~ spl24_36
| ~ spl24_223 ),
inference(resolution,[],[f2746,f725]) ).
tff(f725,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl24_36 ),
inference(avatar_component_clause,[],[f724]) ).
tff(f724,plain,
( spl24_36
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_36])]) ).
tff(f2993,plain,
( ~ spl24_14
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2935]) ).
tff(f2935,plain,
( $false
| ~ spl24_14
| ~ spl24_223 ),
inference(resolution,[],[f2746,f594]) ).
tff(f2992,plain,
( ~ spl24_151
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2937]) ).
tff(f2937,plain,
( $false
| ~ spl24_151
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1586]) ).
tff(f2991,plain,
( ~ spl24_203
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2939]) ).
tff(f2939,plain,
( $false
| ~ spl24_203
| ~ spl24_223 ),
inference(resolution,[],[f2746,f2138]) ).
tff(f2138,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_203 ),
inference(avatar_component_clause,[],[f2136]) ).
tff(f2136,plain,
( spl24_203
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_203])]) ).
tff(f2990,plain,
( ~ spl24_133
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2940]) ).
tff(f2940,plain,
( $false
| ~ spl24_133
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1375]) ).
tff(f2989,plain,
( ~ spl24_7
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2941]) ).
tff(f2941,plain,
( $false
| ~ spl24_7
| ~ spl24_223 ),
inference(resolution,[],[f2746,f556]) ).
tff(f556,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl24_7 ),
inference(avatar_component_clause,[],[f554]) ).
tff(f554,plain,
( spl24_7
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_7])]) ).
tff(f2988,plain,
( ~ spl24_9
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2942]) ).
tff(f2942,plain,
( $false
| ~ spl24_9
| ~ spl24_223 ),
inference(resolution,[],[f2746,f566]) ).
tff(f566,plain,
( pp(aa(dB,bool,it,u))
| ~ spl24_9 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f564,plain,
( spl24_9
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_9])]) ).
tff(f2987,plain,
( ~ spl24_8
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2943]) ).
tff(f2943,plain,
( $false
| ~ spl24_8
| ~ spl24_223 ),
inference(resolution,[],[f2746,f561]) ).
tff(f561,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl24_8 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f559,plain,
( spl24_8
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_8])]) ).
tff(f2986,plain,
( ~ spl24_223
| ~ spl24_238 ),
inference(avatar_contradiction_clause,[],[f2947]) ).
tff(f2947,plain,
( $false
| ~ spl24_223
| ~ spl24_238 ),
inference(resolution,[],[f2746,f2863]) ).
tff(f2863,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl24_238 ),
inference(avatar_component_clause,[],[f2862]) ).
tff(f2862,plain,
( spl24_238
<=> ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_238])]) ).
tff(f2985,plain,
( ~ spl24_124
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2948]) ).
tff(f2948,plain,
( $false
| ~ spl24_124
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1291]) ).
tff(f2984,plain,
( ~ spl24_130
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2949]) ).
tff(f2949,plain,
( $false
| ~ spl24_130
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1344]) ).
tff(f2983,plain,
( ~ spl24_63
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2950]) ).
tff(f2950,plain,
( $false
| ~ spl24_63
| ~ spl24_223 ),
inference(resolution,[],[f2746,f897]) ).
tff(f2982,plain,
( ~ spl24_128
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2951]) ).
tff(f2951,plain,
( $false
| ~ spl24_128
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1323]) ).
tff(f1323,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2)),var(i)))
| ~ spl24_128 ),
inference(avatar_component_clause,[],[f1321]) ).
tff(f1321,plain,
( spl24_128
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2)),var(i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_128])]) ).
tff(f2981,plain,
( ~ spl24_55
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2952]) ).
tff(f2952,plain,
( $false
| ~ spl24_55
| ~ spl24_223 ),
inference(resolution,[],[f2746,f854]) ).
tff(f2980,plain,
( ~ spl24_92
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2953]) ).
tff(f2953,plain,
( $false
| ~ spl24_92
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1088]) ).
tff(f2979,plain,
( ~ spl24_126
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2954]) ).
tff(f2954,plain,
( $false
| ~ spl24_126
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1306]) ).
tff(f2978,plain,
( ~ spl24_90
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2955]) ).
tff(f2955,plain,
( $false
| ~ spl24_90
| ~ spl24_223 ),
inference(resolution,[],[f2746,f1074]) ).
tff(f2977,plain,
( ~ spl24_28
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2956]) ).
tff(f2956,plain,
( $false
| ~ spl24_28
| ~ spl24_223 ),
inference(resolution,[],[f2746,f682]) ).
tff(f682,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl24_28 ),
inference(avatar_component_clause,[],[f680]) ).
tff(f680,plain,
( spl24_28
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_28])]) ).
tff(f2976,plain,
( ~ spl24_30
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2957]) ).
tff(f2957,plain,
( $false
| ~ spl24_30
| ~ spl24_223 ),
inference(resolution,[],[f2746,f695]) ).
tff(f2975,plain,
( ~ spl24_57
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2958]) ).
tff(f2958,plain,
( $false
| ~ spl24_57
| ~ spl24_223 ),
inference(resolution,[],[f2746,f868]) ).
tff(f2974,plain,
( ~ spl24_32
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2959]) ).
tff(f2959,plain,
( $false
| ~ spl24_32
| ~ spl24_223 ),
inference(resolution,[],[f2746,f707]) ).
tff(f2973,plain,
( ~ spl24_33
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2960]) ).
tff(f2960,plain,
( $false
| ~ spl24_33
| ~ spl24_223 ),
inference(resolution,[],[f2746,f712]) ).
tff(f2972,plain,
( ~ spl24_223
| ~ spl24_231 ),
inference(avatar_contradiction_clause,[],[f2961]) ).
tff(f2961,plain,
( $false
| ~ spl24_223
| ~ spl24_231 ),
inference(resolution,[],[f2746,f2801]) ).
tff(f2801,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl24_231 ),
inference(avatar_component_clause,[],[f2799]) ).
tff(f2799,plain,
( spl24_231
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_231])]) ).
tff(f2971,plain,
( ~ spl24_223
| ~ spl24_232 ),
inference(avatar_contradiction_clause,[],[f2962]) ).
tff(f2962,plain,
( $false
| ~ spl24_223
| ~ spl24_232 ),
inference(resolution,[],[f2746,f2806]) ).
tff(f2806,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl24_232 ),
inference(avatar_component_clause,[],[f2804]) ).
tff(f2804,plain,
( spl24_232
<=> pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_232])]) ).
tff(f2970,plain,
( ~ spl24_223
| ~ spl24_233 ),
inference(avatar_contradiction_clause,[],[f2963]) ).
tff(f2963,plain,
( $false
| ~ spl24_223
| ~ spl24_233 ),
inference(resolution,[],[f2746,f2810]) ).
tff(f2810,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl24_233 ),
inference(avatar_component_clause,[],[f2809]) ).
tff(f2809,plain,
( spl24_233
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_233])]) ).
tff(f2969,plain,
( ~ spl24_222
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2964]) ).
tff(f2964,plain,
( $false
| ~ spl24_222
| ~ spl24_223 ),
inference(resolution,[],[f2746,f2743]) ).
tff(f2743,plain,
( pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool)))
| ~ spl24_222 ),
inference(avatar_component_clause,[],[f2741]) ).
tff(f2741,plain,
( spl24_222
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_222])]) ).
tff(f2968,plain,
( ~ spl24_218
| ~ spl24_223 ),
inference(avatar_contradiction_clause,[],[f2965]) ).
tff(f2965,plain,
( $false
| ~ spl24_218
| ~ spl24_223 ),
inference(resolution,[],[f2746,f2254]) ).
tff(f2254,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl24_218 ),
inference(avatar_component_clause,[],[f2252]) ).
tff(f2252,plain,
( spl24_218
<=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_218])]) ).
tff(f2967,plain,
( ~ spl24_223
| ~ spl24_237 ),
inference(avatar_contradiction_clause,[],[f2966]) ).
tff(f2966,plain,
( $false
| ~ spl24_223
| ~ spl24_237 ),
inference(resolution,[],[f2746,f2859]) ).
tff(f2859,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as)))
| ~ spl24_237 ),
inference(avatar_component_clause,[],[f2857]) ).
tff(f2857,plain,
( spl24_237
<=> pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_237])]) ).
tff(f2931,plain,
( spl24_223
| spl24_244
| ~ spl24_45
| ~ spl24_49 ),
inference(avatar_split_clause,[],[f812,f807,f775,f2929,f2745]) ).
tff(f2929,plain,
( spl24_244
<=> ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_244])]) ).
tff(f807,plain,
( spl24_49
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_49])]) ).
tff(f812,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),combc(bool,bool,bool,fconj,X0))) )
| ~ spl24_45
| ~ spl24_49 ),
inference(resolution,[],[f808,f776]) ).
tff(f808,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_49 ),
inference(avatar_component_clause,[],[f807]) ).
tff(f2888,plain,
( spl24_243
| ~ spl24_25
| ~ spl24_74
| ~ spl24_128 ),
inference(avatar_split_clause,[],[f1329,f1321,f958,f665,f2885]) ).
tff(f2885,plain,
( spl24_243
<=> ( t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_243])]) ).
tff(f1329,plain,
( ( t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2) )
| ~ spl24_25
| ~ spl24_74
| ~ spl24_128 ),
inference(forward_demodulation,[],[f1325,f666]) ).
tff(f1325,plain,
( ( aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2) = aa(nat,type,shift(type,e,i,t),i) )
| ~ spl24_74
| ~ spl24_128 ),
inference(resolution,[],[f1323,f959]) ).
tff(f2882,plain,
( spl24_242
| ~ spl24_67
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1024,f996,f921,f2880]) ).
tff(f2880,plain,
( spl24_242
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_242])]) ).
tff(f1024,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X2),X1) != X2 )
| ~ spl24_67
| ~ spl24_81 ),
inference(superposition,[],[f922,f997]) ).
tff(f2878,plain,
( spl24_241
| ~ spl24_58
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1015,f996,f874,f2875]) ).
tff(f2875,plain,
( spl24_241
<=> ( t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),t2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_241])]) ).
tff(f1015,plain,
( ( t = aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),t2) )
| ~ spl24_58
| ~ spl24_81 ),
inference(superposition,[],[f997,f876]) ).
tff(f2873,plain,
( spl24_240
| ~ spl24_66
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1014,f996,f916,f2870]) ).
tff(f2870,plain,
( spl24_240
<=> ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_240])]) ).
tff(f1014,plain,
( ( rs = aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),as),a) )
| ~ spl24_66
| ~ spl24_81 ),
inference(superposition,[],[f997,f918]) ).
tff(f2868,plain,
( spl24_239
| ~ spl24_16
| ~ spl24_80 ),
inference(avatar_split_clause,[],[f991,f987,f602,f2866]) ).
tff(f2866,plain,
( spl24_239
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_239])]) ).
tff(f991,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl24_16
| ~ spl24_80 ),
inference(resolution,[],[f988,f603]) ).
tff(f2864,plain,
( spl24_238
| ~ spl24_25
| ~ spl24_63 ),
inference(avatar_split_clause,[],[f905,f896,f665,f2862]) ).
tff(f905,plain,
( ! [X2: type,X0: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl24_25
| ~ spl24_63 ),
inference(superposition,[],[f897,f666]) ).
tff(f2860,plain,
( spl24_237
| ~ spl24_32
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f792,f775,f705,f2857]) ).
tff(f792,plain,
( pp(aa(fun(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,i,t),as)))
| ~ spl24_32
| ~ spl24_45 ),
inference(resolution,[],[f776,f707]) ).
tff(f2852,plain,
( spl24_236
| ~ spl24_58
| ~ spl24_100 ),
inference(avatar_split_clause,[],[f1154,f1138,f874,f2850]) ).
tff(f2850,plain,
( spl24_236
<=> ! [X0: type,X1: type] :
( ( t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( t2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_236])]) ).
tff(f1154,plain,
( ! [X0: type,X1: type] :
( ( t != aa(type,type,aa(type,fun(type,type),fun1,X0),X1) )
| ( t2 = X0 ) )
| ~ spl24_58
| ~ spl24_100 ),
inference(superposition,[],[f1139,f876]) ).
tff(f2834,plain,
( spl24_235
| ~ spl24_8
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2706,f2690,f559,f2831]) ).
tff(f2831,plain,
( spl24_235
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_235])]) ).
tff(f2706,plain,
( sP1(abs(abs(ua)))
| ~ spl24_8
| ~ spl24_219 ),
inference(resolution,[],[f2691,f561]) ).
tff(f2815,plain,
( spl24_234
| ~ spl24_25
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f795,f775,f665,f2813]) ).
tff(f2813,plain,
( spl24_234
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_234])]) ).
tff(f795,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) )
| ~ spl24_25
| ~ spl24_45 ),
inference(superposition,[],[f776,f666]) ).
tff(f2811,plain,
( spl24_233
| ~ spl24_36
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f791,f775,f724,f2809]) ).
tff(f791,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),combc(X0,X0,bool,fequal(X0),X1)))
| ~ spl24_36
| ~ spl24_45 ),
inference(resolution,[],[f776,f725]) ).
tff(f2807,plain,
( spl24_232
| ~ spl24_30
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f790,f775,f693,f2804]) ).
tff(f790,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t)))
| ~ spl24_30
| ~ spl24_45 ),
inference(resolution,[],[f776,f695]) ).
tff(f2802,plain,
( spl24_231
| ~ spl24_28
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f789,f775,f680,f2799]) ).
tff(f789,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t)))
| ~ spl24_28
| ~ spl24_45 ),
inference(resolution,[],[f776,f682]) ).
tff(f2786,plain,
( spl24_230
| ~ spl24_11
| ~ spl24_25 ),
inference(avatar_split_clause,[],[f668,f665,f573,f2784]) ).
tff(f2784,plain,
( spl24_230
<=> ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_230])]) ).
tff(f668,plain,
( ! [X2: bool,X0: fun(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) )
| ~ spl24_11
| ~ spl24_25 ),
inference(superposition,[],[f666,f574]) ).
tff(f2782,plain,
( spl24_229
| ~ spl24_9
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2705,f2690,f564,f2779]) ).
tff(f2779,plain,
( spl24_229
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_229])]) ).
tff(f2705,plain,
( sP1(abs(abs(u)))
| ~ spl24_9
| ~ spl24_219 ),
inference(resolution,[],[f2691,f566]) ).
tff(f2774,plain,
( spl24_228
| ~ spl24_43
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1020,f996,f767,f2772]) ).
tff(f2772,plain,
( spl24_228
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_228])]) ).
tff(f1020,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl24_43
| ~ spl24_81 ),
inference(superposition,[],[f768,f997]) ).
tff(f2770,plain,
( spl24_227
| ~ spl24_44
| ~ spl24_81 ),
inference(avatar_split_clause,[],[f1019,f996,f771,f2768]) ).
tff(f2768,plain,
( spl24_227
<=> ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_227])]) ).
tff(f1019,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl24_44
| ~ spl24_81 ),
inference(superposition,[],[f772,f997]) ).
tff(f2766,plain,
( spl24_226
| ~ spl24_23
| ~ spl24_50 ),
inference(avatar_split_clause,[],[f839,f816,f646,f2764]) ).
tff(f2764,plain,
( spl24_226
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_226])]) ).
tff(f839,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl24_23
| ~ spl24_50 ),
inference(resolution,[],[f817,f647]) ).
tff(f2762,plain,
( spl24_225
| ~ spl24_23
| ~ spl24_47 ),
inference(avatar_split_clause,[],[f834,f798,f646,f2760]) ).
tff(f2760,plain,
( spl24_225
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(abs(sK4(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_225])]) ).
tff(f798,plain,
( spl24_47
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_47])]) ).
tff(f834,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(abs(sK4(X0))) )
| ~ spl24_23
| ~ spl24_47 ),
inference(resolution,[],[f799,f647]) ).
tff(f799,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK4(X0)))
| sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) )
| ~ spl24_47 ),
inference(avatar_component_clause,[],[f798]) ).
tff(f2758,plain,
( spl24_224
| ~ spl24_16
| ~ spl24_47 ),
inference(avatar_split_clause,[],[f835,f798,f602,f2756]) ).
tff(f2756,plain,
( spl24_224
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_224])]) ).
tff(f835,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK5(X0))
| ~ sP1(X0)
| sP1(sK4(X0)) )
| ~ spl24_16
| ~ spl24_47 ),
inference(resolution,[],[f799,f603]) ).
tff(f2747,plain,
( spl24_222
| spl24_223
| ~ spl24_18
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f794,f775,f610,f2745,f2741]) ).
tff(f794,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl24_18
| ~ spl24_45 ),
inference(superposition,[],[f776,f611]) ).
tff(f2739,plain,
( spl24_221
| ~ spl24_7
| ~ spl24_219 ),
inference(avatar_split_clause,[],[f2704,f2690,f554,f2736]) ).
tff(f2736,plain,
( spl24_221
<=> sP1(abs(abs(t3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_221])]) ).
tff(f2704,plain,
( sP1(abs(abs(t3)))
| ~ spl24_7
| ~ spl24_219 ),
inference(resolution,[],[f2691,f556]) ).
tff(f2719,plain,
( spl24_220
| ~ spl24_11
| ~ spl24_18 ),
inference(avatar_split_clause,[],[f634,f610,f573,f2717]) ).
tff(f2717,plain,
( spl24_220
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_220])]) ).
tff(f634,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl24_11
| ~ spl24_18 ),
inference(superposition,[],[f611,f574]) ).
tff(f2692,plain,
( spl24_219
| ~ spl24_23
| ~ spl24_34 ),
inference(avatar_split_clause,[],[f733,f715,f646,f2690]) ).
tff(f715,plain,
( spl24_34
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_34])]) ).
tff(f733,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl24_23
| ~ spl24_34 ),
inference(resolution,[],[f716,f647]) ).
tff(f716,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl24_34 ),
inference(avatar_component_clause,[],[f715]) ).
tff(f2255,plain,
( spl24_218
| ~ spl24_14
| ~ spl24_45 ),
inference(avatar_split_clause,[],[f784,f775,f593,f2252]) ).
tff(f784,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl24_14
| ~ spl24_45 ),
inference(resolution,[],[f776,f594]) ).
tff(f2250,plain,
( spl24_217
| ~ spl24_11 ),
inference(avatar_split_clause,[],[f576,f573,f2248]) ).
tff(f576,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl24_11 ),
inference(superposition,[],[f574,f574]) ).
tff(f2243,plain,
( spl24_216
| ~ spl24_81
| ~ spl24_215 ),
inference(avatar_split_clause,[],[f2232,f2228,f996,f2241]) ).
tff(f2241,plain,
( spl24_216
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_216])]) ).
tff(f2228,plain,
( spl24_215
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_215])]) ).
tff(f2232,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) = listset(X0,aa(fun(X0,bool),list(fun(X0,bool)),combc(fun(X0,bool),list(fun(X0,bool)),list(fun(X0,bool)),cons(fun(X0,bool)),X1),X2)) )
| ~ spl24_81
| ~ spl24_215 ),
inference(forward_demodulation,[],[f2231,f997]) ).
tff(f2231,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(fun(X0,bool),bool),fun(list(X0),bool),combc(fun(fun(X0,bool),bool),fun(list(X0),fun(X0,bool)),fun(list(X0),bool),combb(fun(X0,bool),bool,list(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1)))))),fEx(X0))) )
| ~ spl24_81
| ~ spl24_215 ),
inference(forward_demodulation,[],[f2229,f997]) ).
tff(f2229,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) )
| ~ spl24_215 ),
inference(avatar_component_clause,[],[f2228]) ).
tff(f2230,plain,
spl24_215,
inference(avatar_split_clause,[],[f475,f2228]) ).
tff(f475,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),listset(X0,X1))))))) ),
inference(definition_unfolding,[],[f385,f388]) ).
tff(f388,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: fun(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X2))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X1)))))) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType,X82: fun(list(X0),bool),X21: fun(X0,bool)] : ( set_Cons(X0,X21,X82) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0)))),cons(X0))))),combc(X0,fun(list(X0),bool),fun(list(X0),bool),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),combc(X0,fun(X0,bool),bool,member(X0),X21))),combc(list(X0),fun(list(X0),bool),bool,member(list(X0)),X82)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_set__Cons__def) ).
tff(f385,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType,X1: list(fun(X0,bool)),X2: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X83: list(fun(X0,bool)),X21: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X21),X83)) = set_Cons(X0,X21,listset(X0,X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_listset_Osimps_I2_J) ).
tff(f2221,plain,
( spl24_214
| ~ spl24_81
| ~ spl24_213 ),
inference(avatar_split_clause,[],[f2217,f2214,f996,f2219]) ).
tff(f2219,plain,
( spl24_214
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_214])]) ).
tff(f2214,plain,
( spl24_213
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_213])]) ).
tff(f2217,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_81
| ~ spl24_213 ),
inference(forward_demodulation,[],[f2215,f997]) ).
tff(f2215,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_213 ),
inference(avatar_component_clause,[],[f2214]) ).
tff(f2216,plain,
spl24_213,
inference(avatar_split_clause,[],[f433,f2214]) ).
tff(f433,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X5: list(type),X6: list(dB),X22: dB,X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X22),X6)),X5))
<=> pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X10),X22))),typings(X10,X6)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_typings_Osimps_I2_J) ).
tff(f2207,plain,
( spl24_212
| ~ spl24_81
| ~ spl24_211 ),
inference(avatar_split_clause,[],[f2203,f2200,f996,f2205]) ).
tff(f2205,plain,
( spl24_212
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_212])]) ).
tff(f2200,plain,
( spl24_211
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_211])]) ).
tff(f2203,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( ~ pp(aa(list(type),bool,typings(X3,aa(dB,list(dB),combc(dB,list(dB),list(dB),cons(dB),X1),X2)),X0))
| pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
| ~ spl24_81
| ~ spl24_211 ),
inference(forward_demodulation,[],[f2201,f997]) ).
tff(f2201,plain,
( ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) )
| ~ spl24_211 ),
inference(avatar_component_clause,[],[f2200]) ).
tff(f2202,plain,
spl24_211,
inference(avatar_split_clause,[],[f432,f2200]) ).
tff(f432,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun(list(type),bool),fun(list(type),bool),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
inference(cnf_transformation,[],[f294]) ).
tff(f2191,plain,
spl24_210,
inference(avatar_split_clause,[],[f462,f2189]) ).
tff(f2189,plain,
( spl24_210
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_210])]) ).
tff(f462,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X25: list(X2),X27: fun(X2,X1),X15: X0,X40: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X40,X15,map(X2,X1,X27,X25)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X40),X27),X15,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_foldl__map) ).
tff(f2177,plain,
( spl24_209
| ~ spl24_8
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f625,f588,f559,f2174]) ).
tff(f2174,plain,
( spl24_209
<=> ( aa(dB,bool,it,ua) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_209])]) ).
tff(f625,plain,
( ( aa(dB,bool,it,ua) = fTrue )
| ~ spl24_8
| ~ spl24_13 ),
inference(resolution,[],[f589,f561]) ).
tff(f2172,plain,
( spl24_208
| ~ spl24_81
| ~ spl24_207 ),
inference(avatar_split_clause,[],[f2168,f2162,f996,f2170]) ).
tff(f2162,plain,
( spl24_207
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_207])]) ).
tff(f2168,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl24_81
| ~ spl24_207 ),
inference(forward_demodulation,[],[f2167,f997]) ).
tff(f2167,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl24_81
| ~ spl24_207 ),
inference(forward_demodulation,[],[f2166,f997]) ).
tff(f2166,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl24_81
| ~ spl24_207 ),
inference(forward_demodulation,[],[f2165,f997]) ).
tff(f2165,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl24_81
| ~ spl24_207 ),
inference(forward_demodulation,[],[f2163,f997]) ).
tff(f2163,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) )
| ~ spl24_207 ),
inference(avatar_component_clause,[],[f2162]) ).
tff(f2164,plain,
spl24_207,
inference(avatar_split_clause,[],[f409,f2162]) ).
tff(f409,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X50: nat,X51: dB,X58: dB,X30: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X30),X58)),X51),X50) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X30),X51),X50)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X58),X51),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_subst__App) ).
tff(f2160,plain,
spl24_206,
inference(avatar_split_clause,[],[f517,f2158]) ).
tff(f2158,plain,
( spl24_206
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_206])]) ).
tff(f517,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f516,f447]) ).
tff(f447,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X85: X0,X86: X1,X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X84,X86),X85) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X85),X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f516,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f515,f447]) ).
tff(f515,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f514,f447]) ).
tff(f514,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f464,f447]) ).
tff(f464,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X9: dB,X8: type,X7: nat,X10: fun(nat,type),X22: dB,X23: type,X24: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X24),X23) )
=> ( pp(aa(dB,bool,it,X22))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X7,X23)),X22),X8))
=> ( pp(aa(dB,bool,it,X9))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X23))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),X9),X7))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_MI2) ).
tff(f2156,plain,
spl24_205,
inference(avatar_split_clause,[],[f513,f2154]) ).
tff(f2154,plain,
( spl24_205
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_205])]) ).
tff(f513,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f512,f447]) ).
tff(f512,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f511,f447]) ).
tff(f511,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f510,f447]) ).
tff(f510,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f463,f447]) ).
tff(f463,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X9: dB,X8: type,X7: nat,X10: fun(nat,type),X22: dB,X23: type,X24: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X24),X23) )
=> ( pp(aa(dB,bool,it,X22))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X7,X24)),X22),X8))
=> ( pp(aa(dB,bool,it,X9))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X24))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),X9),X7))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_MI1) ).
tff(f2148,plain,
spl24_204,
inference(avatar_split_clause,[],[f436,f2146]) ).
tff(f2146,plain,
( spl24_204
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_204])]) ).
tff(f436,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(flattening,[],[f295]) ).
tff(f295,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X20: fun(X0,bool),X21: fun(X0,bool),X4: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X21)),X20),X4)
<=> ( listsp(X0,X20,X4)
& listsp(X0,X21,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_listsp__conj__eq) ).
tff(f2139,plain,
( spl24_203
| ~ spl24_81
| ~ spl24_201 ),
inference(avatar_split_clause,[],[f2129,f2122,f996,f2136]) ).
tff(f2122,plain,
( spl24_201
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_201])]) ).
tff(f2129,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_81
| ~ spl24_201 ),
inference(forward_demodulation,[],[f2128,f997]) ).
tff(f2128,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_81
| ~ spl24_201 ),
inference(forward_demodulation,[],[f2127,f997]) ).
tff(f2127,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))))
| ~ spl24_81
| ~ spl24_201 ),
inference(forward_demodulation,[],[f2126,f997]) ).
tff(f2126,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))))
| ~ spl24_81
| ~ spl24_201 ),
inference(forward_demodulation,[],[f2124,f997]) ).
tff(f2124,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat))))
| ~ spl24_201 ),
inference(avatar_component_clause,[],[f2122]) ).
tff(f2134,plain,
( spl24_202
| ~ spl24_9
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f624,f588,f564,f2131]) ).
tff(f2131,plain,
( spl24_202
<=> ( aa(dB,bool,it,u) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_202])]) ).
tff(f624,plain,
( ( aa(dB,bool,it,u) = fTrue )
| ~ spl24_9
| ~ spl24_13 ),
inference(resolution,[],[f589,f566]) ).
tff(f2125,plain,
spl24_201,
inference(avatar_split_clause,[],[f335,f2122]) ).
tff(f335,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f2114,plain,
( spl24_200
| ~ spl24_81
| ~ spl24_199 ),
inference(avatar_split_clause,[],[f2110,f2106,f996,f2112]) ).
tff(f2112,plain,
( spl24_200
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_200])]) ).
tff(f2106,plain,
( spl24_199
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_199])]) ).
tff(f2110,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl24_81
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2109,f997]) ).
tff(f2109,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl24_81
| ~ spl24_199 ),
inference(forward_demodulation,[],[f2107,f997]) ).
tff(f2107,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl24_199 ),
inference(avatar_component_clause,[],[f2106]) ).
tff(f2108,plain,
spl24_199,
inference(avatar_split_clause,[],[f408,f2106]) ).
tff(f408,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X7: nat,X9: dB,X6: list(dB),X22: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X22,X6)),X9),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),X9),X7),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X9),X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_subst__map) ).
tff(f2100,plain,
spl24_198,
inference(avatar_split_clause,[],[f435,f2098]) ).
tff(f2098,plain,
( spl24_198
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_198])]) ).
tff(f435,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f296]) ).
tff(f2096,plain,
spl24_197,
inference(avatar_split_clause,[],[f434,f2094]) ).
tff(f2094,plain,
( spl24_197
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_197])]) ).
tff(f434,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f296]) ).
tff(f2082,plain,
spl24_196,
inference(avatar_split_clause,[],[f523,f2080]) ).
tff(f2080,plain,
( spl24_196
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_196])]) ).
tff(f523,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f522,f447]) ).
tff(f522,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f467,f447]) ).
tff(f467,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f248,f307]) ).
tff(f307,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
=> ( pp(aa(list(type),bool,typings(X6,X3),sK23(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f248,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( pp(aa(list(type),bool,typings(X6,X4),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X11: type,X5: list(type),X8: type,X45: list(dB),X6: list(dB),X7: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,foldl(dB,dB,app,var(X7),X6),X45)),X8))
=> ( pp(aa(list(type),bool,typings(X10,X6),X5))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X7),X6)),X11))
=> ? [X46: list(type)] :
( pp(aa(list(type),bool,typings(X10,X45),X46))
& ( foldr(type,type,fun1,X46,X8) = X11 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_var__app__types) ).
tff(f2078,plain,
( spl24_195
| ~ spl24_7
| ~ spl24_13 ),
inference(avatar_split_clause,[],[f623,f588,f554,f2075]) ).
tff(f2075,plain,
( spl24_195
<=> ( aa(dB,bool,it,t3) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_195])]) ).
tff(f623,plain,
( ( aa(dB,bool,it,t3) = fTrue )
| ~ spl24_7
| ~ spl24_13 ),
inference(resolution,[],[f589,f556]) ).
tff(f2063,plain,
spl24_194,
inference(avatar_split_clause,[],[f525,f2061]) ).
tff(f2061,plain,
( spl24_194
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_194])]) ).
tff(f525,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f524,f447]) ).
tff(f524,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f466,f447]) ).
tff(f466,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK23(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f2054,plain,
( spl24_193
| ~ spl24_81
| ~ spl24_192 ),
inference(avatar_split_clause,[],[f2050,f2043,f996,f2052]) ).
tff(f2052,plain,
( spl24_193
<=> ! [X4: fun(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_193])]) ).
tff(f2043,plain,
( spl24_192
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_192])]) ).
tff(f2050,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun1,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl24_81
| ~ spl24_192 ),
inference(forward_demodulation,[],[f2049,f997]) ).
tff(f2049,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl24_81
| ~ spl24_192 ),
inference(forward_demodulation,[],[f2048,f997]) ).
tff(f2048,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_81
| ~ spl24_192 ),
inference(forward_demodulation,[],[f2047,f997]) ).
tff(f2047,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_81
| ~ spl24_192 ),
inference(forward_demodulation,[],[f2046,f997]) ).
tff(f2046,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_81
| ~ spl24_192 ),
inference(forward_demodulation,[],[f2044,f997]) ).
tff(f2044,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) )
| ~ spl24_192 ),
inference(avatar_component_clause,[],[f2043]) ).
tff(f2045,plain,
spl24_192,
inference(avatar_split_clause,[],[f443,f2043]) ).
tff(f443,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(flattening,[],[f237]) ).
tff(f237,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X22: dB,X11: type,X8: type,X31: dB,X28: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),X31),aa(type,type,aa(type,fun(type,type),fun1,X8),X11)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),X22),X8))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),aa(dB,dB,aa(dB,fun(dB,dB),app,X31),X22)),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_App) ).
tff(f2034,plain,
( spl24_191
| ~ spl24_81
| ~ spl24_190 ),
inference(avatar_split_clause,[],[f2030,f2026,f996,f2032]) ).
tff(f2026,plain,
( spl24_190
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_190])]) ).
tff(f2030,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_81
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2029,f997]) ).
tff(f2029,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl24_81
| ~ spl24_190 ),
inference(forward_demodulation,[],[f2027,f997]) ).
tff(f2027,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl24_190 ),
inference(avatar_component_clause,[],[f2026]) ).
tff(f2028,plain,
spl24_190,
inference(avatar_split_clause,[],[f401,f2026]) ).
tff(f401,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f222]) ).
tff(f222,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0)))
=> ( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X47: list(dB),X31: dB,X49: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X49),X31),zero_zero(nat)),X47)))
=> ( pp(aa(dB,bool,it,X31))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X49)),X31),X47))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Beta) ).
tff(f2006,plain,
spl24_189,
inference(avatar_split_clause,[],[f521,f2004]) ).
tff(f2004,plain,
( spl24_189
<=> ! [X2: dB,X3: fun(nat,type),X4: type,X0: nat,X5: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_189])]) ).
tff(f521,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2))) ),
inference(forward_demodulation,[],[f520,f447]) ).
tff(f520,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f519,f447]) ).
tff(f519,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f518,f447]) ).
tff(f518,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f503,f447]) ).
tff(f503,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f465]) ).
tff(f465,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),X1))
=> ( ( shift(type,X3,X0,X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X7: nat,X11: type,X9: dB,X41: fun(nat,type),X8: type,X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),X8))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X41),X9),X11))
=> ( ( shift(type,X41,X7,X11) = X10 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X41),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),X9),X7)),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_subst__lemma) ).
tff(f1978,plain,
( spl24_188
| ~ spl24_81
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f1974,f1970,f996,f1976]) ).
tff(f1970,plain,
( spl24_187
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_187])]) ).
tff(f1974,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_81
| ~ spl24_187 ),
inference(forward_demodulation,[],[f1973,f997]) ).
tff(f1973,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl24_81
| ~ spl24_187 ),
inference(forward_demodulation,[],[f1971,f997]) ).
tff(f1971,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl24_187 ),
inference(avatar_component_clause,[],[f1970]) ).
tff(f1972,plain,
spl24_187,
inference(avatar_split_clause,[],[f480,f1970]) ).
tff(f480,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f357]) ).
tff(f357,plain,
! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f264,f265]) ).
tff(f265,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f264,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f263]) ).
tff(f263,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1968,plain,
spl24_186,
inference(avatar_split_clause,[],[f458,f1966]) ).
tff(f1966,plain,
( spl24_186
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_186])]) ).
tff(f458,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f304,f305]) ).
tff(f305,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
=> ( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK21(X0,X1,X2,X3,X4,X5)),sK22(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f304,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(rectify,[],[f303]) ).
tff(f303,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
<=> ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X1: $tType,X64: list(X1),X27: fun(X1,X0),X25: list(X0),X26: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X26),X25) = map(X1,X0,X27,X64) )
<=> ? [X66: X1,X67: list(X1)] :
( ( map(X1,X0,X27,X67) = X25 )
& ( aa(X1,X0,X27,X66) = X26 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X66),X67) = X64 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Cons__eq__map__conv) ).
tff(f1964,plain,
spl24_185,
inference(avatar_split_clause,[],[f454,f1962]) ).
tff(f1962,plain,
( spl24_185
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_185])]) ).
tff(f454,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f300,f301]) ).
tff(f301,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
=> ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK19(X0,X1,X2,X3,X4,X5)),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f300,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(rectify,[],[f299]) ).
tff(f299,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X0: $tType,X64: list(X0),X65: X0,X25: list(X1),X27: fun(X1,X0)] :
( ( map(X1,X0,X27,X25) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X65),X64) )
<=> ? [X66: X1,X67: list(X1)] :
( ( map(X1,X0,X27,X67) = X64 )
& ( aa(X1,X0,X27,X66) = X65 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X66),X67) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_map__eq__Cons__conv) ).
tff(f1948,plain,
( spl24_184
| ~ spl24_81
| ~ spl24_183 ),
inference(avatar_split_clause,[],[f1944,f1938,f996,f1946]) ).
tff(f1938,plain,
( spl24_183
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_183])]) ).
tff(f1944,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl24_81
| ~ spl24_183 ),
inference(forward_demodulation,[],[f1943,f997]) ).
tff(f1943,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )
| ~ spl24_81
| ~ spl24_183 ),
inference(forward_demodulation,[],[f1942,f997]) ).
tff(f1942,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_81
| ~ spl24_183 ),
inference(forward_demodulation,[],[f1941,f997]) ).
tff(f1941,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_81
| ~ spl24_183 ),
inference(forward_demodulation,[],[f1939,f997]) ).
tff(f1939,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) )
| ~ spl24_183 ),
inference(avatar_component_clause,[],[f1938]) ).
tff(f1940,plain,
spl24_183,
inference(avatar_split_clause,[],[f387,f1938]) ).
tff(f387,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X50: nat,X30: dB,X51: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X51),X30)),X50) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X51),X50)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X30),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_lift_Osimps_I2_J) ).
tff(f1936,plain,
( spl24_182
| ~ spl24_21
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f662,f646,f638,f1934]) ).
tff(f1934,plain,
( spl24_182
<=> ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_182])]) ).
tff(f662,plain,
( ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_21
| ~ spl24_23 ),
inference(resolution,[],[f647,f639]) ).
tff(f1928,plain,
spl24_181,
inference(avatar_split_clause,[],[f509,f1926]) ).
tff(f509,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ),
inference(forward_demodulation,[],[f453,f447]) ).
tff(f453,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3)) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1)),X0)) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X5: list(type),X6: list(dB),X7: nat,X8: type,X9: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X8))
=> ( pp(aa(list(type),bool,typings(shift(type,X10,X7,X8),X6),X5))
=> pp(aa(list(type),bool,typings(X10,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X9),X7),X6)),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_substs__lemma) ).
tff(f1913,plain,
( spl24_180
| ~ spl24_81
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1909,f1903,f996,f1911]) ).
tff(f1911,plain,
( spl24_180
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_180])]) ).
tff(f1903,plain,
( spl24_179
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_179])]) ).
tff(f1909,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) )
| ~ spl24_81
| ~ spl24_179 ),
inference(forward_demodulation,[],[f1908,f997]) ).
tff(f1908,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2)) )
| ~ spl24_81
| ~ spl24_179 ),
inference(forward_demodulation,[],[f1907,f997]) ).
tff(f1907,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),sK17(X0,X1,X2,X3))),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_81
| ~ spl24_179 ),
inference(forward_demodulation,[],[f1906,f997]) ).
tff(f1906,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_81
| ~ spl24_179 ),
inference(forward_demodulation,[],[f1904,f997]) ).
tff(f1904,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_179 ),
inference(avatar_component_clause,[],[f1903]) ).
tff(f1905,plain,
spl24_179,
inference(avatar_split_clause,[],[f417,f1903]) ).
tff(f417,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f228,f282]) ).
tff(f282,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f228,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))
=> ~ ! [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),X4)) ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X8: type,X9: dB,X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X9)),X8))
=> ~ ! [X44: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),aa(type,type,aa(type,fun(type,type),fun1,X44),X8)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X9),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_typing__elims_I2_J) ).
tff(f1827,plain,
spl24_178,
inference(avatar_split_clause,[],[f452,f1825]) ).
tff(f452,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,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X85: X0,X86: fun(X0,X1),X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X84),X86),X85) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X85),aa(X0,X1,X86,X85)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1787,plain,
( spl24_177
| ~ spl24_81
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1783,f1780,f996,f1785]) ).
tff(f1780,plain,
( spl24_176
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_176])]) ).
tff(f1783,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) = map(X1,X0,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) )
| ~ spl24_81
| ~ spl24_176 ),
inference(forward_demodulation,[],[f1781,f997]) ).
tff(f1781,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) )
| ~ spl24_176 ),
inference(avatar_component_clause,[],[f1780]) ).
tff(f1782,plain,
spl24_176,
inference(avatar_split_clause,[],[f437,f1780]) ).
tff(f437,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType,X1: $tType,X25: list(X1),X26: X1,X27: fun(X1,X0)] : ( map(X1,X0,X27,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X26),X25)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X27,X26)),map(X1,X0,X27,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_map_Osimps_I2_J) ).
tff(f1773,plain,
( spl24_175
| ~ spl24_81
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1769,f1766,f996,f1771]) ).
tff(f1771,plain,
( spl24_175
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_175])]) ).
tff(f1766,plain,
( spl24_174
<=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_174])]) ).
tff(f1769,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl24_81
| ~ spl24_174 ),
inference(forward_demodulation,[],[f1767,f997]) ).
tff(f1767,plain,
( ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl24_174 ),
inference(avatar_component_clause,[],[f1766]) ).
tff(f1768,plain,
spl24_174,
inference(avatar_split_clause,[],[f396,f1766]) ).
tff(f396,plain,
! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X2,X1),X0))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X2)),X1) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X5: list(type),X6: list(dB),X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,X6),X5))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X10)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lists__typings) ).
tff(f1755,plain,
( spl24_173
| ~ spl24_81
| ~ spl24_172 ),
inference(avatar_split_clause,[],[f1751,f1747,f996,f1753]) ).
tff(f1753,plain,
( spl24_173
<=> ! [X4: fun(nat,type),X0: list(dB),X3: dB,X2: list(type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_173])]) ).
tff(f1747,plain,
( spl24_172
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_172])]) ).
tff(f1751,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun1,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl24_81
| ~ spl24_172 ),
inference(forward_demodulation,[],[f1750,f997]) ).
tff(f1750,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl24_81
| ~ spl24_172 ),
inference(forward_demodulation,[],[f1748,f997]) ).
tff(f1748,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) )
| ~ spl24_172 ),
inference(avatar_component_clause,[],[f1747]) ).
tff(f1749,plain,
spl24_172,
inference(avatar_split_clause,[],[f441,f1747]) ).
tff(f441,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),foldr(type,type,fun1,X2,X1)))
=> ( pp(aa(list(type),bool,typings(X4,X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X6: list(dB),X8: type,X5: list(type),X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),foldr(type,type,fun1,X5,X8)))
=> ( pp(aa(list(type),bool,typings(X10,X6),X5))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X22,X6)),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list__app__typeI) ).
tff(f1741,plain,
( spl24_171
| ~ spl24_81
| ~ spl24_170 ),
inference(avatar_split_clause,[],[f1737,f1733,f996,f1739]) ).
tff(f1733,plain,
( spl24_170
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_170])]) ).
tff(f1737,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2))) )
| ~ spl24_81
| ~ spl24_170 ),
inference(forward_demodulation,[],[f1736,f997]) ).
tff(f1736,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_81
| ~ spl24_170 ),
inference(forward_demodulation,[],[f1734,f997]) ).
tff(f1734,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_170 ),
inference(avatar_component_clause,[],[f1733]) ).
tff(f1735,plain,
spl24_170,
inference(avatar_split_clause,[],[f415,f1733]) ).
tff(f415,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f227,f280]) ).
tff(f280,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,sK16(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f227,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),var(X2)),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X8: type,X6: list(dB),X7: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X7),X6)),X8))
=> ~ ! [X33: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),var(X7)),foldr(type,type,fun1,X33,X8)))
=> ~ pp(aa(list(type),bool,typings(X10,X6),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_var__app__typesE) ).
tff(f1726,plain,
( spl24_168
| ~ spl24_169
| ~ spl24_11 ),
inference(avatar_split_clause,[],[f581,f573,f1723,f1720]) ).
tff(f1723,plain,
( spl24_169
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_169])]) ).
tff(f581,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl24_11 ),
inference(equality_factoring,[],[f574]) ).
tff(f1718,plain,
( spl24_167
| ~ spl24_81
| ~ spl24_166 ),
inference(avatar_split_clause,[],[f1714,f1709,f996,f1716]) ).
tff(f1716,plain,
( spl24_167
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_167])]) ).
tff(f1709,plain,
( spl24_166
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_166])]) ).
tff(f1714,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1))) )
| ~ spl24_81
| ~ spl24_166 ),
inference(forward_demodulation,[],[f1713,f997]) ).
tff(f1713,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun1,X0),X2)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_81
| ~ spl24_166 ),
inference(forward_demodulation,[],[f1712,f997]) ).
tff(f1712,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_81
| ~ spl24_166 ),
inference(forward_demodulation,[],[f1710,f997]) ).
tff(f1710,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl24_166 ),
inference(avatar_component_clause,[],[f1709]) ).
tff(f1711,plain,
spl24_166,
inference(avatar_split_clause,[],[f414,f1709]) ).
tff(f414,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X11: type,X22: dB,X8: type,X28: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X28,zero_zero(nat),X8)),X22),X11))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),abs(X22)),aa(type,type,aa(type,fun(type,type),fun1,X8),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Abs) ).
tff(f1703,plain,
( spl24_165
| ~ spl24_81
| ~ spl24_164 ),
inference(avatar_split_clause,[],[f1699,f1695,f996,f1701]) ).
tff(f1701,plain,
( spl24_165
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_165])]) ).
tff(f1695,plain,
( spl24_164
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_164])]) ).
tff(f1699,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl24_81
| ~ spl24_164 ),
inference(forward_demodulation,[],[f1698,f997]) ).
tff(f1698,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_81
| ~ spl24_164 ),
inference(forward_demodulation,[],[f1696,f997]) ).
tff(f1696,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl24_164 ),
inference(avatar_component_clause,[],[f1695]) ).
tff(f1697,plain,
spl24_164,
inference(avatar_split_clause,[],[f386,f1695]) ).
tff(f386,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X7: nat,X6: list(dB),X22: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X22,X6)),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X22),X7),map(dB,dB,combc(dB,nat,dB,lift,X7),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_lift__map) ).
tff(f1684,plain,
( spl24_163
| ~ spl24_81
| ~ spl24_162 ),
inference(avatar_split_clause,[],[f1680,f1676,f996,f1682]) ).
tff(f1676,plain,
( spl24_162
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_162])]) ).
tff(f1680,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl24_81
| ~ spl24_162 ),
inference(forward_demodulation,[],[f1679,f997]) ).
tff(f1679,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl24_81
| ~ spl24_162 ),
inference(forward_demodulation,[],[f1677,f997]) ).
tff(f1677,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl24_162 ),
inference(avatar_component_clause,[],[f1676]) ).
tff(f1678,plain,
spl24_162,
inference(avatar_split_clause,[],[f442,f1676]) ).
tff(f442,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f235]) ).
tff(f235,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X11: type,X8: type,X6: list(dB),X7: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X7),X6)),X8))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,var(X7),X6)),X11))
=> ( X8 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_var__app__type__eq) ).
tff(f1674,plain,
( spl24_161
| ~ spl24_81
| ~ spl24_160 ),
inference(avatar_split_clause,[],[f1668,f1664,f996,f1671]) ).
tff(f1671,plain,
( spl24_161
<=> listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t))),fEx(type)),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_161])]) ).
tff(f1664,plain,
( spl24_160
<=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_160])]) ).
tff(f1668,plain,
( listsp(dB,aa(fun(fun(type,bool),bool),fun(dB,bool),combc(fun(fun(type,bool),bool),fun(dB,fun(type,bool)),fun(dB,bool),combb(fun(type,bool),bool,dB),typing(shift(type,e,i,t))),fEx(type)),as)
| ~ spl24_81
| ~ spl24_160 ),
inference(forward_demodulation,[],[f1666,f997]) ).
tff(f1666,plain,
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t))),as)
| ~ spl24_160 ),
inference(avatar_component_clause,[],[f1664]) ).
tff(f1667,plain,
spl24_160,
inference(avatar_split_clause,[],[f334,f1664]) ).
tff(f334,plain,
listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t))),as),
inference(cnf_transformation,[],[f11]) ).
tff(f11,axiom,
listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t))),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096) ).
tff(f1659,plain,
( spl24_159
| ~ spl24_81
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1655,f1650,f996,f1657]) ).
tff(f1650,plain,
( spl24_158
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_158])]) ).
tff(f1655,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) )
| ~ spl24_81
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1654,f997]) ).
tff(f1654,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_81
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1653,f997]) ).
tff(f1653,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_81
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1651,f997]) ).
tff(f1651,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_158 ),
inference(avatar_component_clause,[],[f1650]) ).
tff(f1652,plain,
spl24_158,
inference(avatar_split_clause,[],[f440,f1650]) ).
tff(f440,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X11: type,X7: nat,X8: type,X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),X8))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,X7,X11)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X22),X7)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_lift__type) ).
tff(f1642,plain,
( spl24_157
| ~ spl24_81
| ~ spl24_156 ),
inference(avatar_split_clause,[],[f1638,f1633,f996,f1640]) ).
tff(f1633,plain,
( spl24_156
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_156])]) ).
tff(f1638,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_81
| ~ spl24_156 ),
inference(forward_demodulation,[],[f1637,f997]) ).
tff(f1637,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1)) )
| ~ spl24_81
| ~ spl24_156 ),
inference(forward_demodulation,[],[f1636,f997]) ).
tff(f1636,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK17(X0,X1,X2,X3)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_81
| ~ spl24_156 ),
inference(forward_demodulation,[],[f1634,f997]) ).
tff(f1634,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) )
| ~ spl24_156 ),
inference(avatar_component_clause,[],[f1633]) ).
tff(f1635,plain,
spl24_156,
inference(avatar_split_clause,[],[f418,f1633]) ).
tff(f418,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X1),sK17(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f283]) ).
tff(f1622,plain,
( spl24_155
| ~ spl24_81
| ~ spl24_154 ),
inference(avatar_split_clause,[],[f1618,f1614,f996,f1620]) ).
tff(f1614,plain,
( spl24_154
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_154])]) ).
tff(f1618,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2)) )
| ~ spl24_81
| ~ spl24_154 ),
inference(forward_demodulation,[],[f1617,f997]) ).
tff(f1617,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_81
| ~ spl24_154 ),
inference(forward_demodulation,[],[f1615,f997]) ).
tff(f1615,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_154 ),
inference(avatar_component_clause,[],[f1614]) ).
tff(f1616,plain,
spl24_154,
inference(avatar_split_clause,[],[f412,f1614]) ).
tff(f412,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f225,f278]) ).
tff(f278,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK15(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f225,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X8: type,X6: list(dB),X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X22,X6)),X8))
=> ? [X33: list(type)] :
( pp(aa(list(type),bool,typings(X10,X6),X33))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),foldr(type,type,fun1,X33,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_list__app__typeD) ).
tff(f1602,plain,
( spl24_153
| ~ spl24_81
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1598,f1594,f996,f1600]) ).
tff(f1594,plain,
( spl24_152
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_152])]) ).
tff(f1598,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2)) )
| ~ spl24_81
| ~ spl24_152 ),
inference(forward_demodulation,[],[f1597,f997]) ).
tff(f1597,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_81
| ~ spl24_152 ),
inference(forward_demodulation,[],[f1595,f997]) ).
tff(f1595,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_152 ),
inference(avatar_component_clause,[],[f1594]) ).
tff(f1596,plain,
spl24_152,
inference(avatar_split_clause,[],[f410,f1594]) ).
tff(f410,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f224,f276]) ).
tff(f276,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,sK14(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),X2),foldr(type,type,fun1,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X8: type,X6: list(dB),X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),foldl(dB,dB,app,X22,X6)),X8))
=> ~ ! [X33: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),X22),foldr(type,type,fun1,X33,X8)))
=> ~ pp(aa(list(type),bool,typings(X10,X6),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_list__app__typeE) ).
tff(f1587,plain,
spl24_151,
inference(avatar_split_clause,[],[f333,f1584]) ).
tff(f333,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096IT_A_IVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1558,plain,
spl24_150,
inference(avatar_split_clause,[],[f451,f1556]) ).
tff(f451,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,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X85: X0,X86: fun(X0,X1),X84: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X84),X86),X85) = aa(X1,X2,X84,aa(X0,X1,X86,X85)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1554,plain,
spl24_149,
inference(avatar_split_clause,[],[f445,f1552]) ).
tff(f445,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(flattening,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(nnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X12: list(X0),X13: X0,X14: list(X0),X15: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X15),X14) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X13),X12) )
<=> ( ( X12 = X14 )
& ( X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list_Oinject) ).
tff(f1541,plain,
( spl24_148
| ~ spl24_17
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f657,f646,f606,f1539]) ).
tff(f1539,plain,
( spl24_148
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_148])]) ).
tff(f657,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl24_17
| ~ spl24_23 ),
inference(resolution,[],[f647,f607]) ).
tff(f1537,plain,
( spl24_147
| ~ spl24_81
| ~ spl24_146 ),
inference(avatar_split_clause,[],[f1533,f1529,f996,f1535]) ).
tff(f1529,plain,
( spl24_146
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_146])]) ).
tff(f1533,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1)) )
| ~ spl24_81
| ~ spl24_146 ),
inference(forward_demodulation,[],[f1532,f997]) ).
tff(f1532,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),sK13(X0,X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_81
| ~ spl24_146 ),
inference(forward_demodulation,[],[f1530,f997]) ).
tff(f1530,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_146 ),
inference(avatar_component_clause,[],[f1529]) ).
tff(f1531,plain,
spl24_146,
inference(avatar_split_clause,[],[f399,f1529]) ).
tff(f399,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f220,f272]) ).
tff(f272,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK12(X0,X1,X2))),X1),sK13(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X8: type,X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),abs(X22)),X8))
=> ~ ! [X44: type,X75: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X44),X75) = X8 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,zero_zero(nat),X44)),X22),X75)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_typing__elims_I3_J) ).
tff(f1512,plain,
spl24_145,
inference(avatar_split_clause,[],[f460,f1510]) ).
tff(f460,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK22(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1508,plain,
spl24_144,
inference(avatar_split_clause,[],[f456,f1506]) ).
tff(f456,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f1504,plain,
spl24_143,
inference(avatar_split_clause,[],[f444,f1502]) ).
tff(f444,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1432,plain,
( spl24_142
| ~ spl24_16
| ~ spl24_21 ),
inference(avatar_split_clause,[],[f649,f638,f602,f1430]) ).
tff(f1430,plain,
( spl24_142
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_142])]) ).
tff(f649,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) )
| ~ spl24_16
| ~ spl24_21 ),
inference(resolution,[],[f639,f603]) ).
tff(f1422,plain,
spl24_141,
inference(avatar_split_clause,[],[f508,f1420]) ).
tff(f508,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) = foldl(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f450,f447]) ).
tff(f450,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X1: $tType,X25: list(X1),X26: X1,X15: X0,X27: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X27,X15,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X26),X25)) = foldl(X0,X1,X27,aa(X1,X0,aa(X0,fun(X1,X0),X27,X15),X26),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_foldl__Cons) ).
tff(f1418,plain,
spl24_140,
inference(avatar_split_clause,[],[f507,f1416]) ).
tff(f507,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) = foldr(X0,X1,X5,aa(X0,list(X0),combc(X0,list(X0),list(X0),cons(X0),X3),X4),X2) ),
inference(forward_demodulation,[],[f449,f447]) ).
tff(f449,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X1: $tType,X0: $tType,X15: X0,X25: list(X1),X26: X1,X27: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X27,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X26),X25),X15) = aa(X0,X0,aa(X1,fun(X0,X0),X27,X26),foldr(X1,X0,X27,X25,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_foldr_Osimps_I2_J) ).
tff(f1414,plain,
spl24_139,
inference(avatar_split_clause,[],[f459,f1412]) ).
tff(f459,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK21(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1410,plain,
spl24_138,
inference(avatar_split_clause,[],[f455,f1408]) ).
tff(f455,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f1405,plain,
( spl24_137
| ~ spl24_81
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1401,f1397,f996,f1403]) ).
tff(f1403,plain,
( spl24_137
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_137])]) ).
tff(f1397,plain,
( spl24_136
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_136])]) ).
tff(f1401,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1)) )
| ~ spl24_81
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1400,f997]) ).
tff(f1400,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),sK11(X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_81
| ~ spl24_136 ),
inference(forward_demodulation,[],[f1398,f997]) ).
tff(f1398,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_136 ),
inference(avatar_component_clause,[],[f1397]) ).
tff(f1399,plain,
spl24_136,
inference(avatar_split_clause,[],[f397,f1397]) ).
tff(f397,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f219,f270]) ).
tff(f270,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),sK10(X1,X2))),X1),sK11(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f219,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X8: type,X22: dB,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),abs(X22)),X8))
=> ~ ! [X75: type,X76: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X10,zero_zero(nat),X75)),X22),X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_abs__typeE) ).
tff(f1390,plain,
( spl24_135
| ~ spl24_81
| ~ spl24_134 ),
inference(avatar_split_clause,[],[f1386,f1383,f996,f1388]) ).
tff(f1383,plain,
( spl24_134
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_134])]) ).
tff(f1386,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),zero_zero(nat)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_81
| ~ spl24_134 ),
inference(forward_demodulation,[],[f1384,f997]) ).
tff(f1384,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl24_134 ),
inference(avatar_component_clause,[],[f1383]) ).
tff(f1385,plain,
spl24_134,
inference(avatar_split_clause,[],[f355,f1383]) ).
tff(f355,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f1376,plain,
( spl24_133
| ~ spl24_81
| ~ spl24_132 ),
inference(avatar_split_clause,[],[f1371,f1366,f996,f1373]) ).
tff(f1366,plain,
( spl24_132
<=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_132])]) ).
tff(f1371,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),u)))
| ~ spl24_81
| ~ spl24_132 ),
inference(forward_demodulation,[],[f1370,f997]) ).
tff(f1370,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),u)))
| ~ spl24_81
| ~ spl24_132 ),
inference(forward_demodulation,[],[f1368,f997]) ).
tff(f1368,plain,
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))))
| ~ spl24_132 ),
inference(avatar_component_clause,[],[f1366]) ).
tff(f1369,plain,
spl24_132,
inference(avatar_split_clause,[],[f332,f1366]) ).
tff(f332,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f1352,plain,
spl24_131,
inference(avatar_split_clause,[],[f506,f1350]) ).
tff(f506,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) = list_case(X0,X1,X5,X4,aa(X1,list(X1),combc(X1,list(X1),list(X1),cons(X1),X2),X3)) ),
inference(forward_demodulation,[],[f448,f447]) ).
tff(f448,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X1: $tType,X14: list(X1),X15: X1,X59: fun(X1,fun(list(X1),X0)),X60: X0] : ( list_case(X0,X1,X60,X59,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X15),X14)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X59,X15),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_list_Osimps_I5_J) ).
tff(f1345,plain,
( spl24_130
| ~ spl24_81
| ~ spl24_129 ),
inference(avatar_split_clause,[],[f1340,f1335,f996,f1342]) ).
tff(f1335,plain,
( spl24_129
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_129])]) ).
tff(f1340,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_81
| ~ spl24_129 ),
inference(forward_demodulation,[],[f1339,f997]) ).
tff(f1339,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,sK3,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_81
| ~ spl24_129 ),
inference(forward_demodulation,[],[f1337,f997]) ).
tff(f1337,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t1)))
| ~ spl24_129 ),
inference(avatar_component_clause,[],[f1335]) ).
tff(f1338,plain,
spl24_129,
inference(avatar_split_clause,[],[f474,f1335]) ).
tff(f474,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t1))),
inference(definition_unfolding,[],[f338,f314]) ).
tff(f314,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_True) ).
tff(f338,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t1))),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f207,f254]) ).
tff(f254,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) )
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t1))) ) ),
introduced(choice_axiom,[]) ).
tff(f207,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X0)) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
~ ! [X33: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X33,t1)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t),as),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1324,plain,
( spl24_128
| ~ spl24_81
| ~ spl24_127 ),
inference(avatar_split_clause,[],[f1319,f1314,f996,f1321]) ).
tff(f1314,plain,
( spl24_127
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_127])]) ).
tff(f1319,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t1)),sK2)),var(i)))
| ~ spl24_81
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1318,f997]) ).
tff(f1318,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1))),var(i)))
| ~ spl24_81
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1316,f997]) ).
tff(f1316,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1))))
| ~ spl24_127 ),
inference(avatar_component_clause,[],[f1314]) ).
tff(f1317,plain,
spl24_127,
inference(avatar_split_clause,[],[f473,f1314]) ).
tff(f473,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1)))),
inference(definition_unfolding,[],[f336,f314]) ).
tff(f336,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1)))),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f206,f252]) ).
tff(f252,plain,
( ? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f206,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X0)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
~ ! [X32: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X32),foldr(type,type,fun1,ts,t1))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1307,plain,
( spl24_126
| ~ spl24_81
| ~ spl24_125 ),
inference(avatar_split_clause,[],[f1302,f1297,f996,f1304]) ).
tff(f1297,plain,
( spl24_125
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_125])]) ).
tff(f1302,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl24_81
| ~ spl24_125 ),
inference(forward_demodulation,[],[f1301,f997]) ).
tff(f1301,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)))
| ~ spl24_81
| ~ spl24_125 ),
inference(forward_demodulation,[],[f1299,f997]) ).
tff(f1299,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1))
| ~ spl24_125 ),
inference(avatar_component_clause,[],[f1297]) ).
tff(f1300,plain,
spl24_125,
inference(avatar_split_clause,[],[f472,f1297]) ).
tff(f472,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)),
inference(definition_unfolding,[],[f331,f314]) ).
tff(f331,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f1292,plain,
( spl24_124
| ~ spl24_81
| ~ spl24_123 ),
inference(avatar_split_clause,[],[f1287,f1282,f996,f1289]) ).
tff(f1282,plain,
( spl24_123
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_123])]) ).
tff(f1287,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_81
| ~ spl24_123 ),
inference(forward_demodulation,[],[f1286,f997]) ).
tff(f1286,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),foldr(type,type,fun1,ts,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_81
| ~ spl24_123 ),
inference(forward_demodulation,[],[f1284,f997]) ).
tff(f1284,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1)))
| ~ spl24_123 ),
inference(avatar_component_clause,[],[f1282]) ).
tff(f1285,plain,
spl24_123,
inference(avatar_split_clause,[],[f471,f1282]) ).
tff(f471,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))),
inference(definition_unfolding,[],[f330,f314]) ).
tff(f330,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_headT) ).
tff(f1279,plain,
( ~ spl24_122
| ~ spl24_66
| ~ spl24_67 ),
inference(avatar_split_clause,[],[f937,f921,f916,f1276]) ).
tff(f1276,plain,
( spl24_122
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_122])]) ).
tff(f937,plain,
( ( as != rs )
| ~ spl24_66
| ~ spl24_67 ),
inference(superposition,[],[f922,f918]) ).
tff(f1274,plain,
( spl24_121
| ~ spl24_81
| ~ spl24_120 ),
inference(avatar_split_clause,[],[f1270,f1266,f996,f1272]) ).
tff(f1272,plain,
( spl24_121
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_121])]) ).
tff(f1266,plain,
( spl24_120
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_120])]) ).
tff(f1270,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 ) )
| ~ spl24_81
| ~ spl24_120 ),
inference(forward_demodulation,[],[f1269,f997]) ).
tff(f1269,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun1,sK13(X0,X1,X2)),sK12(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_81
| ~ spl24_120 ),
inference(forward_demodulation,[],[f1267,f997]) ).
tff(f1267,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_120 ),
inference(avatar_component_clause,[],[f1266]) ).
tff(f1268,plain,
spl24_120,
inference(avatar_split_clause,[],[f398,f1266]) ).
tff(f398,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK12(X0,X1,X2)),sK13(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f1264,plain,
( spl24_119
| ~ spl24_81
| ~ spl24_118 ),
inference(avatar_split_clause,[],[f1260,f1256,f996,f1262]) ).
tff(f1262,plain,
( spl24_119
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_119])]) ).
tff(f1256,plain,
( spl24_118
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_118])]) ).
tff(f1260,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl24_81
| ~ spl24_118 ),
inference(forward_demodulation,[],[f1259,f997]) ).
tff(f1259,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl24_81
| ~ spl24_118 ),
inference(forward_demodulation,[],[f1257,f997]) ).
tff(f1257,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))
| ~ spl24_118 ),
inference(avatar_component_clause,[],[f1256]) ).
tff(f1258,plain,
spl24_118,
inference(avatar_split_clause,[],[f367,f1256]) ).
tff(f367,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X30: dB,X51: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X51)),X30),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X51),X30),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_beta) ).
tff(f1251,plain,
( spl24_117
| ~ spl24_81
| ~ spl24_116 ),
inference(avatar_split_clause,[],[f1247,f1244,f996,f1249]) ).
tff(f1244,plain,
( spl24_116
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_116])]) ).
tff(f1247,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3))) )
| ~ spl24_81
| ~ spl24_116 ),
inference(forward_demodulation,[],[f1245,f997]) ).
tff(f1245,plain,
( ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_116 ),
inference(avatar_component_clause,[],[f1244]) ).
tff(f1246,plain,
spl24_116,
inference(avatar_split_clause,[],[f416,f1244]) ).
tff(f416,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK16(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1239,plain,
spl24_115,
inference(avatar_split_clause,[],[f439,f1237]) ).
tff(f439,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X4,X3),X2))
=> pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X11: type,X7: nat,X5: list(type),X6: list(dB),X10: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X10,X6),X5))
=> pp(aa(list(type),bool,typings(shift(type,X10,X7,X11),map(dB,dB,combc(dB,nat,dB,lift,X7),X6)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_lift__types) ).
tff(f1235,plain,
( spl24_114
| ~ spl24_14
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f658,f646,f593,f1233]) ).
tff(f1233,plain,
( spl24_114
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_114])]) ).
tff(f658,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl24_14
| ~ spl24_23 ),
inference(resolution,[],[f647,f594]) ).
tff(f1228,plain,
( spl24_113
| ~ spl24_81
| ~ spl24_112 ),
inference(avatar_split_clause,[],[f1224,f1221,f996,f1226]) ).
tff(f1221,plain,
( spl24_112
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_112])]) ).
tff(f1224,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) )
| ~ spl24_81
| ~ spl24_112 ),
inference(forward_demodulation,[],[f1222,f997]) ).
tff(f1222,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_112 ),
inference(avatar_component_clause,[],[f1221]) ).
tff(f1223,plain,
spl24_112,
inference(avatar_split_clause,[],[f413,f1221]) ).
tff(f413,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f1216,plain,
( spl24_111
| ~ spl24_81
| ~ spl24_110 ),
inference(avatar_split_clause,[],[f1212,f1209,f996,f1214]) ).
tff(f1209,plain,
( spl24_110
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_110])]) ).
tff(f1212,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3))) )
| ~ spl24_81
| ~ spl24_110 ),
inference(forward_demodulation,[],[f1210,f997]) ).
tff(f1210,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_110 ),
inference(avatar_component_clause,[],[f1209]) ).
tff(f1211,plain,
spl24_110,
inference(avatar_split_clause,[],[f411,f1209]) ).
tff(f411,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK14(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f277]) ).
tff(f1202,plain,
( spl24_109
| ~ spl24_81
| ~ spl24_108 ),
inference(avatar_split_clause,[],[f1198,f1195,f996,f1200]) ).
tff(f1195,plain,
( spl24_108
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_108])]) ).
tff(f1198,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_81
| ~ spl24_108 ),
inference(forward_demodulation,[],[f1196,f997]) ).
tff(f1196,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl24_108 ),
inference(avatar_component_clause,[],[f1195]) ).
tff(f1197,plain,
spl24_108,
inference(avatar_split_clause,[],[f394,f1195]) ).
tff(f394,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X38: nat,X29: nat,X39: dB] :
( pp(aa(dB,bool,it,X39))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X39),var(X29)),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_subst__Var__IT) ).
tff(f1190,plain,
( spl24_107
| ~ spl24_81
| ~ spl24_106 ),
inference(avatar_split_clause,[],[f1186,f1182,f996,f1188]) ).
tff(f1182,plain,
( spl24_106
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_106])]) ).
tff(f1186,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl24_81
| ~ spl24_106 ),
inference(forward_demodulation,[],[f1185,f997]) ).
tff(f1185,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl24_81
| ~ spl24_106 ),
inference(forward_demodulation,[],[f1183,f997]) ).
tff(f1183,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl24_106 ),
inference(avatar_component_clause,[],[f1182]) ).
tff(f1184,plain,
spl24_106,
inference(avatar_split_clause,[],[f384,f1182]) ).
tff(f384,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X51: dB,X50: nat,X30: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X30),X50)),X51),X50) = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_subst__lift) ).
tff(f1180,plain,
spl24_105,
inference(avatar_split_clause,[],[f328,f1177]) ).
tff(f1177,plain,
( spl24_105
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_105])]) ).
tff(f328,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096listsp_AIT_A_Imap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1174,plain,
spl24_104,
inference(avatar_split_clause,[],[f327,f1171]) ).
tff(f1171,plain,
( spl24_104
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t1))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_104])]) ).
tff(f327,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t1))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t1))),
inference(cnf_transformation,[],[f32]) ).
tff(f32,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t1))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_calculation) ).
tff(f1153,plain,
spl24_103,
inference(avatar_split_clause,[],[f430,f1151]) ).
tff(f430,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f292]) ).
tff(f292,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X52: dB,X53: dB,X54: dB,X55: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X55),X54) = aa(dB,dB,aa(dB,fun(dB,dB),app,X53),X52) )
<=> ( ( X52 = X54 )
& ( X53 = X55 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_dB_Osimps_I2_J) ).
tff(f1148,plain,
spl24_102,
inference(avatar_split_clause,[],[f429,f1146]) ).
tff(f429,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f1144,plain,
spl24_101,
inference(avatar_split_clause,[],[f427,f1142]) ).
tff(f427,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(flattening,[],[f290]) ).
tff(f290,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X16: type,X17: type,X18: type,X19: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X19),X18) = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) )
<=> ( ( X16 = X18 )
& ( X17 = X19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type_Osimps_I2_J) ).
tff(f1140,plain,
spl24_100,
inference(avatar_split_clause,[],[f426,f1138]) ).
tff(f426,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f291]) ).
tff(f1136,plain,
( spl24_99
| ~ spl24_81
| ~ spl24_98 ),
inference(avatar_split_clause,[],[f1132,f1128,f996,f1134]) ).
tff(f1134,plain,
( spl24_99
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_99])]) ).
tff(f1128,plain,
( spl24_98
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_98])]) ).
tff(f1132,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl24_81
| ~ spl24_98 ),
inference(forward_demodulation,[],[f1131,f997]) ).
tff(f1131,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl24_81
| ~ spl24_98 ),
inference(forward_demodulation,[],[f1129,f997]) ).
tff(f1129,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl24_98 ),
inference(avatar_component_clause,[],[f1128]) ).
tff(f1130,plain,
spl24_98,
inference(avatar_split_clause,[],[f393,f1128]) ).
tff(f393,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X58: dB,X30: dB,X51: dB] :
( beta(X51,X30)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X58),X51),aa(dB,dB,aa(dB,fun(dB,dB),app,X58),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_appR) ).
tff(f1126,plain,
( spl24_97
| ~ spl24_81
| ~ spl24_96 ),
inference(avatar_split_clause,[],[f1122,f1118,f996,f1124]) ).
tff(f1124,plain,
( spl24_97
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_97])]) ).
tff(f1118,plain,
( spl24_96
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_96])]) ).
tff(f1122,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl24_81
| ~ spl24_96 ),
inference(forward_demodulation,[],[f1121,f997]) ).
tff(f1121,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl24_81
| ~ spl24_96 ),
inference(forward_demodulation,[],[f1119,f997]) ).
tff(f1119,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl24_96 ),
inference(avatar_component_clause,[],[f1118]) ).
tff(f1120,plain,
spl24_96,
inference(avatar_split_clause,[],[f392,f1118]) ).
tff(f392,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X58: dB,X30: dB,X51: dB] :
( beta(X51,X30)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X51),X58),aa(dB,dB,aa(dB,fun(dB,dB),app,X30),X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_appL) ).
tff(f1105,plain,
spl24_95,
inference(avatar_split_clause,[],[f419,f1103]) ).
tff(f419,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f229,f284]) ).
tff(f284,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f229,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,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X40: fun(X0,X1),X27: fun(X0,X1)] :
( ! [X68: X0] : ( aa(X0,X1,X27,X68) = aa(X0,X1,X40,X68) )
=> ( X27 = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1101,plain,
( spl24_94
| ~ spl24_81
| ~ spl24_93 ),
inference(avatar_split_clause,[],[f1097,f1094,f996,f1099]) ).
tff(f1099,plain,
( spl24_94
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_94])]) ).
tff(f1094,plain,
( spl24_93
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_93])]) ).
tff(f1097,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl24_81
| ~ spl24_93 ),
inference(forward_demodulation,[],[f1095,f997]) ).
tff(f1095,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl24_93 ),
inference(avatar_component_clause,[],[f1094]) ).
tff(f1096,plain,
spl24_93,
inference(avatar_split_clause,[],[f354,f1094]) ).
tff(f354,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f1089,plain,
( spl24_92
| ~ spl24_81
| ~ spl24_91 ),
inference(avatar_split_clause,[],[f1084,f1080,f996,f1086]) ).
tff(f1080,plain,
( spl24_91
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_91])]) ).
tff(f1084,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t1),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_81
| ~ spl24_91 ),
inference(forward_demodulation,[],[f1082,f997]) ).
tff(f1082,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1))
| ~ spl24_91 ),
inference(avatar_component_clause,[],[f1080]) ).
tff(f1083,plain,
spl24_91,
inference(avatar_split_clause,[],[f469,f1080]) ).
tff(f469,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(i),rs)),t1)),
inference(definition_unfolding,[],[f325,f314]) ).
tff(f325,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f26]) ).
tff(f26,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nT) ).
tff(f1075,plain,
( spl24_90
| ~ spl24_81
| ~ spl24_89 ),
inference(avatar_split_clause,[],[f1070,f1066,f996,f1072]) ).
tff(f1066,plain,
( spl24_89
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_89])]) ).
tff(f1070,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_81
| ~ spl24_89 ),
inference(forward_demodulation,[],[f1068,f997]) ).
tff(f1068,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a))
| ~ spl24_89 ),
inference(avatar_component_clause,[],[f1066]) ).
tff(f1069,plain,
spl24_89,
inference(avatar_split_clause,[],[f468,f1066]) ).
tff(f468,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f324,f314]) ).
tff(f324,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f35]) ).
tff(f35,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Var_I2_J) ).
tff(f1059,plain,
( spl24_88
| ~ spl24_81
| ~ spl24_87 ),
inference(avatar_split_clause,[],[f1055,f1052,f996,f1057]) ).
tff(f1052,plain,
( spl24_87
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_87])]) ).
tff(f1055,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_81
| ~ spl24_87 ),
inference(forward_demodulation,[],[f1053,f997]) ).
tff(f1053,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl24_87 ),
inference(avatar_component_clause,[],[f1052]) ).
tff(f1054,plain,
spl24_87,
inference(avatar_split_clause,[],[f405,f1052]) ).
tff(f405,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,[],[f275]) ).
tff(f275,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,[],[f167]) ).
tff(f167,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X21: fun(X0,bool),X26: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X26),X21))
<=> pp(aa(X0,bool,X21,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f1049,plain,
( spl24_86
| ~ spl24_81
| ~ spl24_85 ),
inference(avatar_split_clause,[],[f1045,f1042,f996,f1047]) ).
tff(f1047,plain,
( spl24_86
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_86])]) ).
tff(f1042,plain,
( spl24_85
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_85])]) ).
tff(f1045,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl24_81
| ~ spl24_85 ),
inference(forward_demodulation,[],[f1043,f997]) ).
tff(f1043,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl24_85 ),
inference(avatar_component_clause,[],[f1042]) ).
tff(f1044,plain,
spl24_85,
inference(avatar_split_clause,[],[f404,f1042]) ).
tff(f404,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,[],[f275]) ).
tff(f1035,plain,
( spl24_84
| ~ spl24_81
| ~ spl24_83 ),
inference(avatar_split_clause,[],[f1031,f1028,f996,f1033]) ).
tff(f1028,plain,
( spl24_83
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_83])]) ).
tff(f1031,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_81
| ~ spl24_83 ),
inference(forward_demodulation,[],[f1029,f997]) ).
tff(f1029,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_83 ),
inference(avatar_component_clause,[],[f1028]) ).
tff(f1030,plain,
spl24_83,
inference(avatar_split_clause,[],[f373,f1028]) ).
tff(f373,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X29: nat,X30: dB] :
( pp(aa(dB,bool,it,X30))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X30),var(X29)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_app__Var__IT) ).
tff(f1008,plain,
( spl24_82
| ~ spl24_8
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f661,f646,f559,f1005]) ).
tff(f1005,plain,
( spl24_82
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_82])]) ).
tff(f661,plain,
( sP1(abs(ua))
| ~ spl24_8
| ~ spl24_23 ),
inference(resolution,[],[f647,f561]) ).
tff(f998,plain,
spl24_81,
inference(avatar_split_clause,[],[f447,f996]) ).
tff(f989,plain,
( spl24_80
| ~ spl24_79 ),
inference(avatar_split_clause,[],[f985,f982,f987]) ).
tff(f982,plain,
( spl24_79
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_79])]) ).
tff(f985,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_79 ),
inference(forward_demodulation,[],[f983,f447]) ).
tff(f983,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl24_79 ),
inference(avatar_component_clause,[],[f982]) ).
tff(f984,plain,
spl24_79,
inference(avatar_split_clause,[],[f372,f982]) ).
tff(f372,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X29: nat,X30: dB] :
( pp(aa(dB,bool,it,X30))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X30),X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_lift__IT) ).
tff(f980,plain,
( spl24_78
| ~ spl24_77 ),
inference(avatar_split_clause,[],[f976,f973,f978]) ).
tff(f973,plain,
( spl24_77
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_77])]) ).
tff(f976,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl24_77 ),
inference(forward_demodulation,[],[f974,f447]) ).
tff(f974,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl24_77 ),
inference(avatar_component_clause,[],[f973]) ).
tff(f975,plain,
spl24_77,
inference(avatar_split_clause,[],[f366,f973]) ).
tff(f366,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X58: dB,X50: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X50)),X58),X50) = X58 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_subst__eq) ).
tff(f971,plain,
spl24_76,
inference(avatar_split_clause,[],[f349,f969]) ).
tff(f349,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) )
| ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f259,f261,f260]) ).
tff(f260,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f261,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f259,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f258]) ).
tff(f258,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f965,plain,
( spl24_75
| ~ spl24_9
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f660,f646,f564,f962]) ).
tff(f962,plain,
( spl24_75
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_75])]) ).
tff(f660,plain,
( sP1(abs(u))
| ~ spl24_9
| ~ spl24_23 ),
inference(resolution,[],[f647,f566]) ).
tff(f960,plain,
( spl24_74
| ~ spl24_73 ),
inference(avatar_split_clause,[],[f956,f953,f958]) ).
tff(f953,plain,
( spl24_73
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_73])]) ).
tff(f956,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl24_73 ),
inference(forward_demodulation,[],[f954,f447]) ).
tff(f954,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) )
| ~ spl24_73 ),
inference(avatar_component_clause,[],[f953]) ).
tff(f955,plain,
spl24_73,
inference(avatar_split_clause,[],[f400,f953]) ).
tff(f400,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X8: type,X7: nat,X10: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X10),var(X7)),X8))
=> ( aa(nat,type,X10,X7) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_typing__elims_I1_J) ).
tff(f947,plain,
spl24_72,
inference(avatar_split_clause,[],[f407,f945]) ).
tff(f407,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X47: list(dB),X42: nat,X22: dB,X31: dB] : ( foldl(dB,dB,app,var(X42),X47) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X31)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Abs__App__neq__Var__apps) ).
tff(f943,plain,
spl24_71,
inference(avatar_split_clause,[],[f347,f941]) ).
tff(f941,plain,
( spl24_71
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_71])]) ).
tff(f347,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f936,plain,
( spl24_70
| ~ spl24_7
| ~ spl24_23 ),
inference(avatar_split_clause,[],[f659,f646,f554,f933]) ).
tff(f933,plain,
( spl24_70
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_70])]) ).
tff(f659,plain,
( sP1(abs(t3))
| ~ spl24_7
| ~ spl24_23 ),
inference(resolution,[],[f647,f556]) ).
tff(f931,plain,
spl24_69,
inference(avatar_split_clause,[],[f424,f929]) ).
tff(f929,plain,
( spl24_69
<=> ! [X2: list(dB),X0: list(dB),X1: nat,X3: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_69])]) ).
tff(f424,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(flattening,[],[f288]) ).
tff(f288,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X47: list(dB),X42: nat,X43: list(dB),X48: nat] :
( ( foldl(dB,dB,app,var(X48),X43) = foldl(dB,dB,app,var(X42),X47) )
<=> ( ( X43 = X47 )
& ( X42 = X48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Var__apps__eq__Var__apps__conv) ).
tff(f927,plain,
spl24_68,
inference(avatar_split_clause,[],[f421,f925]) ).
tff(f925,plain,
( spl24_68
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_68])]) ).
tff(f421,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(flattening,[],[f286]) ).
tff(f286,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X47: list(dB),X31: dB,X43: list(dB),X49: dB] :
( ( foldl(dB,dB,app,abs(X49),X43) = foldl(dB,dB,app,abs(X31),X47) )
<=> ( ( X43 = X47 )
& ( X31 = X49 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Abs__apps__eq__Abs__apps__conv) ).
tff(f923,plain,
spl24_67,
inference(avatar_split_clause,[],[f382,f921]) ).
tff(f382,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(cnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType,X35: X0,X36: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X35),X36) != X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_not__Cons__self) ).
tff(f919,plain,
spl24_66,
inference(avatar_split_clause,[],[f323,f916]) ).
tff(f323,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Cons) ).
tff(f911,plain,
spl24_65,
inference(avatar_split_clause,[],[f505,f908]) ).
tff(f908,plain,
( spl24_65
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_65])]) ).
tff(f505,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),t)),
inference(forward_demodulation,[],[f470,f322]) ).
tff(f322,plain,
t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_T) ).
tff(f470,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)))),
inference(definition_unfolding,[],[f329,f314]) ).
tff(f329,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)))),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_varT) ).
tff(f902,plain,
( spl24_64
| ~ spl24_14
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f626,f602,f593,f900]) ).
tff(f900,plain,
( spl24_64
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_64])]) ).
tff(f626,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl24_14
| ~ spl24_16 ),
inference(resolution,[],[f603,f594]) ).
tff(f898,plain,
( spl24_63
| ~ spl24_62 ),
inference(avatar_split_clause,[],[f894,f891,f896]) ).
tff(f891,plain,
( spl24_62
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_62])]) ).
tff(f894,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl24_62 ),
inference(forward_demodulation,[],[f892,f447]) ).
tff(f892,plain,
( ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl24_62 ),
inference(avatar_component_clause,[],[f891]) ).
tff(f893,plain,
spl24_62,
inference(avatar_split_clause,[],[f484,f891]) ).
tff(f484,plain,
! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f395]) ).
tff(f395,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X2),var(X1)),X0)) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X8: type,X26: nat,X28: fun(nat,type)] :
( ( aa(nat,type,X28,X26) = X8 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),var(X26)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_typing_OVar) ).
tff(f889,plain,
spl24_61,
inference(avatar_split_clause,[],[f423,f887]) ).
tff(f423,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f885,plain,
spl24_60,
inference(avatar_split_clause,[],[f420,f883]) ).
tff(f420,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f881,plain,
spl24_59,
inference(avatar_split_clause,[],[f345,f879]) ).
tff(f879,plain,
( spl24_59
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_59])]) ).
tff(f345,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X6: list(dB)] :
( listsp(dB,it,X6)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_lifts__IT) ).
tff(f877,plain,
spl24_58,
inference(avatar_split_clause,[],[f322,f874]) ).
tff(f869,plain,
( spl24_57
| ~ spl24_56 ),
inference(avatar_split_clause,[],[f864,f860,f866]) ).
tff(f860,plain,
( spl24_56
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_56])]) ).
tff(f864,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),sK2),a))
| ~ spl24_56 ),
inference(forward_demodulation,[],[f862,f447]) ).
tff(f862,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),sK2))
| ~ spl24_56 ),
inference(avatar_component_clause,[],[f860]) ).
tff(f863,plain,
spl24_56,
inference(avatar_split_clause,[],[f337,f860]) ).
tff(f337,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),sK2)),
inference(cnf_transformation,[],[f253]) ).
tff(f855,plain,
( spl24_55
| ~ spl24_54 ),
inference(avatar_split_clause,[],[f850,f846,f852]) ).
tff(f846,plain,
( spl24_54
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_54])]) ).
tff(f850,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t)),t2),a))
| ~ spl24_54 ),
inference(forward_demodulation,[],[f848,f447]) ).
tff(f848,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),t2))
| ~ spl24_54 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f849,plain,
spl24_54,
inference(avatar_split_clause,[],[f321,f846]) ).
tff(f321,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),t2)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),a),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_argT) ).
tff(f833,plain,
spl24_53,
inference(avatar_split_clause,[],[f402,f831]) ).
tff(f402,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
inference(nnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X31: dB,X6: list(dB),X49: dB] :
( ( foldl(dB,dB,app,X49,X6) = foldl(dB,dB,app,X31,X6) )
<=> ( X31 = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_apps__eq__tail__conv) ).
tff(f827,plain,
( spl24_52
| ~ spl24_51 ),
inference(avatar_split_clause,[],[f823,f820,f825]) ).
tff(f825,plain,
( spl24_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_52])]) ).
tff(f820,plain,
( spl24_51
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_51])]) ).
tff(f823,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl24_51 ),
inference(forward_demodulation,[],[f821,f447]) ).
tff(f821,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) )
| ~ spl24_51 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f822,plain,
spl24_51,
inference(avatar_split_clause,[],[f391,f820]) ).
tff(f391,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,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X0: $tType,X87: X0,X35: X0] :
( ( X35 = X87 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X35),X87)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f818,plain,
spl24_50,
inference(avatar_split_clause,[],[f371,f816]) ).
tff(f371,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X42: nat,X43: list(dB)] :
( listsp(dB,it,X43)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X42),X43))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_IT_OVar) ).
tff(f809,plain,
( spl24_49
| ~ spl24_48 ),
inference(avatar_split_clause,[],[f805,f802,f807]) ).
tff(f802,plain,
( spl24_48
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_48])]) ).
tff(f805,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_48 ),
inference(forward_demodulation,[],[f803,f447]) ).
tff(f803,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_48 ),
inference(avatar_component_clause,[],[f802]) ).
tff(f804,plain,
spl24_48,
inference(avatar_split_clause,[],[f368,f802]) ).
tff(f368,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X86: bool,X84: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86))
| ~ pp(X86)
| ~ pp(X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f800,plain,
spl24_47,
inference(avatar_split_clause,[],[f350,f798]) ).
tff(f350,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f781,plain,
spl24_46,
inference(avatar_split_clause,[],[f406,f779]) ).
tff(f406,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X47: list(dB),X49: dB,X6: list(dB),X42: nat] : ( foldl(dB,dB,app,var(X42),X6) != foldl(dB,dB,app,abs(X49),X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Var__apps__neq__Abs__apps) ).
tff(f777,plain,
spl24_45,
inference(avatar_split_clause,[],[f390,f775]) ).
tff(f390,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,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X35: X0,X84: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X84))
| ~ pp(aa(X0,bool,X84,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f773,plain,
spl24_44,
inference(avatar_split_clause,[],[f380,f771]) ).
tff(f380,plain,
! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) ),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: dB,X1: dB,X2: nat] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != var(X2) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X61: dB,X62: dB,X63: nat] : ( var(X63) != aa(dB,dB,aa(dB,fun(dB,dB),app,X62),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_dB_Osimps_I4_J) ).
tff(f769,plain,
spl24_43,
inference(avatar_split_clause,[],[f378,f767]) ).
tff(f378,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X72: dB,X73: dB,X74: dB] : ( abs(X72) != aa(dB,dB,aa(dB,fun(dB,dB),app,X74),X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dB_Osimps_I8_J) ).
tff(f764,plain,
( spl24_42
| ~ spl24_41 ),
inference(avatar_split_clause,[],[f760,f757,f762]) ).
tff(f762,plain,
( spl24_42
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_42])]) ).
tff(f757,plain,
( spl24_41
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_41])]) ).
tff(f760,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl24_41 ),
inference(forward_demodulation,[],[f758,f447]) ).
tff(f758,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_41 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f759,plain,
spl24_41,
inference(avatar_split_clause,[],[f370,f757]) ).
tff(f370,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X86: bool,X84: bool] :
( pp(X86)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f754,plain,
( spl24_40
| ~ spl24_39 ),
inference(avatar_split_clause,[],[f750,f747,f752]) ).
tff(f752,plain,
( spl24_40
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_40])]) ).
tff(f747,plain,
( spl24_39
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_39])]) ).
tff(f750,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl24_39 ),
inference(forward_demodulation,[],[f748,f447]) ).
tff(f748,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_39 ),
inference(avatar_component_clause,[],[f747]) ).
tff(f749,plain,
spl24_39,
inference(avatar_split_clause,[],[f369,f747]) ).
tff(f369,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X86: bool,X84: bool] :
( pp(X84)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X86)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f745,plain,
spl24_38,
inference(avatar_split_clause,[],[f348,f743]) ).
tff(f743,plain,
( spl24_38
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_38])]) ).
tff(f348,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f741,plain,
( spl24_37
| ~ spl24_8
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f629,f602,f559,f738]) ).
tff(f738,plain,
( spl24_37
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_37])]) ).
tff(f629,plain,
( sP1(ua)
| ~ spl24_8
| ~ spl24_16 ),
inference(resolution,[],[f603,f561]) ).
tff(f726,plain,
( spl24_36
| ~ spl24_35 ),
inference(avatar_split_clause,[],[f722,f719,f724]) ).
tff(f719,plain,
( spl24_35
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_35])]) ).
tff(f722,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl24_35 ),
inference(forward_demodulation,[],[f720,f447]) ).
tff(f720,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl24_35 ),
inference(avatar_component_clause,[],[f719]) ).
tff(f721,plain,
spl24_35,
inference(avatar_split_clause,[],[f483,f719]) ).
tff(f483,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f389]) ).
tff(f389,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,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X87: X0,X35: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X35),X87))
| ( X35 != X87 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f717,plain,
spl24_34,
inference(avatar_split_clause,[],[f346,f715]) ).
tff(f346,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X39: dB] :
( pp(aa(dB,bool,it,X39))
=> pp(aa(dB,bool,it,abs(X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Lambda) ).
tff(f713,plain,
spl24_33,
inference(avatar_split_clause,[],[f339,f710]) ).
tff(f339,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),sK3)),
inference(cnf_transformation,[],[f255]) ).
tff(f708,plain,
spl24_32,
inference(avatar_split_clause,[],[f320,f705]) ).
tff(f320,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_argsT) ).
tff(f701,plain,
( spl24_31
| ~ spl24_9
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f628,f602,f564,f698]) ).
tff(f698,plain,
( spl24_31
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_31])]) ).
tff(f628,plain,
( sP1(u)
| ~ spl24_9
| ~ spl24_16 ),
inference(resolution,[],[f603,f566]) ).
tff(f696,plain,
( spl24_30
| ~ spl24_29 ),
inference(avatar_split_clause,[],[f691,f687,f693]) ).
tff(f687,plain,
( spl24_29
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_29])]) ).
tff(f691,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t),u))
| ~ spl24_29 ),
inference(forward_demodulation,[],[f689,f447]) ).
tff(f689,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t))
| ~ spl24_29 ),
inference(avatar_component_clause,[],[f687]) ).
tff(f690,plain,
spl24_29,
inference(avatar_split_clause,[],[f319,f687]) ).
tff(f319,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uT) ).
tff(f683,plain,
( spl24_28
| ~ spl24_27 ),
inference(avatar_split_clause,[],[f678,f674,f680]) ).
tff(f674,plain,
( spl24_27
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_27])]) ).
tff(f678,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t),ua))
| ~ spl24_27 ),
inference(forward_demodulation,[],[f676,f447]) ).
tff(f676,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t))
| ~ spl24_27 ),
inference(avatar_component_clause,[],[f674]) ).
tff(f677,plain,
spl24_27,
inference(avatar_split_clause,[],[f318,f674]) ).
tff(f318,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Var_I4_J) ).
tff(f672,plain,
spl24_26,
inference(avatar_split_clause,[],[f479,f670]) ).
tff(f479,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f351]) ).
tff(f351,plain,
! [X2: list(dB),X3: nat,X0: dB] :
( sP1(X0)
| ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ),
inference(cnf_transformation,[],[f262]) ).
tff(f667,plain,
spl24_25,
inference(avatar_split_clause,[],[f494,f665]) ).
tff(f494,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f438]) ).
tff(f438,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X8: X0,X10: fun(nat,X0),X37: nat,X7: nat] :
( ( X7 = X37 )
=> ( aa(nat,X0,shift(X0,X10,X7,X8),X37) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_shift__eq) ).
tff(f656,plain,
( spl24_24
| ~ spl24_7
| ~ spl24_16 ),
inference(avatar_split_clause,[],[f627,f602,f554,f653]) ).
tff(f653,plain,
( spl24_24
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_24])]) ).
tff(f627,plain,
( sP1(t3)
| ~ spl24_7
| ~ spl24_16 ),
inference(resolution,[],[f603,f556]) ).
tff(f648,plain,
spl24_23,
inference(avatar_split_clause,[],[f478,f646]) ).
tff(f478,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f352]) ).
tff(f352,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f262]) ).
tff(f644,plain,
spl24_22,
inference(avatar_split_clause,[],[f365,f642]) ).
tff(f365,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X4: list(X0)] : ( map(X0,X0,combi(X0),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_map__ident) ).
tff(f640,plain,
spl24_21,
inference(avatar_split_clause,[],[f356,f638]) ).
tff(f356,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f620,plain,
spl24_20,
inference(avatar_split_clause,[],[f376,f618]) ).
tff(f618,plain,
( spl24_20
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_20])]) ).
tff(f376,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X56: nat,X57: nat] :
( ( var(X57) = var(X56) )
<=> ( X56 = X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_dB_Osimps_I1_J) ).
tff(f616,plain,
spl24_19,
inference(avatar_split_clause,[],[f374,f614]) ).
tff(f614,plain,
( spl24_19
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_19])]) ).
tff(f374,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X70: dB,X71: dB] :
( ( abs(X71) = abs(X70) )
<=> ( X70 = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_dB_Osimps_I3_J) ).
tff(f612,plain,
spl24_18,
inference(avatar_split_clause,[],[f364,f610]) ).
tff(f364,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X84: X0] : ( aa(X0,X0,combi(X0),X84) = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f608,plain,
spl24_17,
inference(avatar_split_clause,[],[f359,f606]) ).
tff(f359,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f126,f250,f249]) ).
tff(f126,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X15: dB] :
( pp(aa(dB,bool,it,X15))
<=> ( ? [X79: dB,X80: dB,X81: list(dB)] :
( pp(aa(dB,bool,it,X80))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X79),X80),zero_zero(nat)),X81)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X79)),X80),X81) = X15 ) )
| ? [X79: dB] :
( pp(aa(dB,bool,it,X79))
& ( abs(X79) = X15 ) )
| ? [X77: list(dB),X78: nat] :
( listsp(dB,it,X77)
& ( foldl(dB,dB,app,var(X78),X77) = X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_IT_Osimps) ).
tff(f604,plain,
spl24_16,
inference(avatar_split_clause,[],[f358,f602]) ).
tff(f358,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f267]) ).
tff(f599,plain,
spl24_15,
inference(avatar_split_clause,[],[f363,f597]) ).
tff(f597,plain,
( spl24_15
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_15])]) ).
tff(f363,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X69: fun(X0,bool)] : ( collect(X0,X69) = X69 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f595,plain,
spl24_14,
inference(avatar_split_clause,[],[f341,f593]) ).
tff(f341,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X34: nat] : pp(aa(dB,bool,it,var(X34))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Var__IT) ).
tff(f590,plain,
( spl24_13
| spl24_1
| ~ spl24_11 ),
inference(avatar_split_clause,[],[f577,f573,f527,f588]) ).
tff(f527,plain,
( spl24_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_1])]) ).
tff(f577,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl24_1
| ~ spl24_11 ),
inference(superposition,[],[f529,f574]) ).
tff(f529,plain,
( ~ pp(fFalse)
| spl24_1 ),
inference(avatar_component_clause,[],[f527]) ).
tff(f586,plain,
~ spl24_12,
inference(avatar_split_clause,[],[f309,f583]) ).
tff(f309,plain,
~ pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
pp(aa(list(type),bool,typings(e,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f575,plain,
spl24_11,
inference(avatar_split_clause,[],[f342,f573]) ).
tff(f342,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X84: bool] :
( ( fFalse = X84 )
| ( fTrue = X84 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f571,plain,
spl24_10,
inference(avatar_split_clause,[],[f340,f569]) ).
tff(f569,plain,
( spl24_10
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_10])]) ).
tff(f340,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X63: nat] : ( zero_zero(nat) = dB_size(var(X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_dB_Osize_I1_J) ).
tff(f567,plain,
spl24_9,
inference(avatar_split_clause,[],[f317,f564]) ).
tff(f317,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT) ).
tff(f562,plain,
spl24_8,
inference(avatar_split_clause,[],[f316,f559]) ).
tff(f316,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Var_I3_J) ).
tff(f557,plain,
spl24_7,
inference(avatar_split_clause,[],[f315,f554]) ).
tff(f315,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096IT_At_096) ).
tff(f552,plain,
spl24_6,
inference(avatar_split_clause,[],[f361,f550]) ).
tff(f550,plain,
( spl24_6
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_6])]) ).
tff(f361,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X72: dB,X63: nat] : ( var(X63) != abs(X72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_dB_Osimps_I6_J) ).
tff(f548,plain,
spl24_5,
inference(avatar_split_clause,[],[f360,f546]) ).
tff(f546,plain,
( spl24_5
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_5])]) ).
tff(f360,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X30: dB,X29: nat] : ~ beta(var(X29),X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_beta__cases_I1_J) ).
tff(f544,plain,
spl24_4,
inference(avatar_split_clause,[],[f353,f542]) ).
tff(f542,plain,
( spl24_4
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_4])]) ).
tff(f353,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f540,plain,
spl24_3,
inference(avatar_split_clause,[],[f313,f537]) ).
tff(f313,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f535,plain,
spl24_2,
inference(avatar_split_clause,[],[f312,f532]) ).
tff(f532,plain,
( spl24_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).
tff(f312,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f530,plain,
~ spl24_1,
inference(avatar_split_clause,[],[f310,f527]) ).
tff(f310,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL814_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:07:28 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (27374)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40 % (27381)WARNING: value z3 for option sas not known
% 0.22/0.40 % (27382)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.40 % (27380)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.40 % (27381)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.40 % (27379)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.40 % (27383)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.40 % (27385)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.40 % (27384)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.40 % (27385)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (27397)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (27398)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.42 % (27399)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.43 % (27397)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % (27398)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % Exception at run slice level
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.45 % (27406)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.93/0.69 % (27383)First to succeed.
% 2.39/0.72 % (27383)Refutation found. Thanks to Tanya!
% 2.39/0.72 % SZS status Theorem for theBenchmark
% 2.39/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.73 % (27383)------------------------------
% 2.39/0.73 % (27383)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.39/0.73 % (27383)Termination reason: Refutation
% 2.39/0.73
% 2.39/0.73 % (27383)Memory used [KB]: 4680
% 2.39/0.73 % (27383)Time elapsed: 0.322 s
% 2.39/0.73 % (27383)Instructions burned: 820 (million)
% 2.39/0.73 % (27383)------------------------------
% 2.39/0.73 % (27383)------------------------------
% 2.39/0.73 % (27374)Success in time 0.346 s
%------------------------------------------------------------------------------