TSTP Solution File: LCL815_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL815_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 : n028.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 13:49:58 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 390
% Syntax : Number of formulae : 1061 ( 266 unt; 81 typ; 0 def)
% Number of atoms : 2404 ( 539 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2404 ( 980 ~; 945 |; 155 &)
% ( 221 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 92 ( 42 >; 50 *; 0 +; 0 <<)
% Number of predicates : 202 ( 200 usr; 195 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 26 con; 0-6 aty)
% Number of variables : 2289 (2160 !; 88 ?;2289 :)
% ( 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,
t: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t1: 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(f2080,plain,
$false,
inference(avatar_sat_refutation,[],[f529,f534,f539,f543,f547,f552,f557,f562,f566,f570,f580,f584,f589,f593,f597,f601,f605,f609,f623,f628,f632,f636,f649,f655,f660,f665,f670,f676,f682,f688,f694,f699,f704,f708,f712,f717,f727,f731,f736,f741,f746,f751,f755,f759,f763,f782,f786,f791,f799,f803,f808,f814,f828,f834,f841,f846,f851,f858,f862,f866,f870,f874,f879,f887,f893,f900,f904,f908,f912,f918,f924,f928,f936,f941,f947,f952,f956,f961,f965,f970,f978,f1004,f1010,f1018,f1023,f1028,f1033,f1041,f1047,f1055,f1061,f1067,f1072,f1076,f1091,f1098,f1104,f1108,f1114,f1118,f1122,f1126,f1131,f1152,f1158,f1162,f1168,f1172,f1178,f1183,f1191,f1196,f1203,f1208,f1216,f1220,f1227,f1232,f1239,f1245,f1249,f1255,f1262,f1269,f1276,f1283,f1292,f1299,f1310,f1317,f1323,f1340,f1347,f1355,f1360,f1403,f1409,f1414,f1418,f1422,f1426,f1436,f1508,f1512,f1516,f1535,f1541,f1545,f1558,f1562,f1591,f1600,f1606,f1620,f1626,f1639,f1646,f1656,f1663,f1671,f1678,f1682,f1688,f1701,f1707,f1715,f1722,f1730,f1739,f1745,f1753,f1759,f1772,f1777,f1787,f1792,f1832,f1910,f1918,f1933,f1941,f1945,f1953,f1969,f1973,f1977,f1983,f2011,f2033,f2039,f2050,f2059,f2068,f2079]) ).
tff(f2079,plain,
( ~ spl24_95
| spl24_24
| ~ spl24_116 ),
inference(avatar_split_clause,[],[f1221,f1218,f652,f1088]) ).
tff(f1088,plain,
( spl24_95
<=> 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_95])]) ).
tff(f652,plain,
( spl24_24
<=> pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_24])]) ).
tff(f1218,plain,
( spl24_116
<=> ! [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_116])]) ).
tff(f1221,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_24
| ~ spl24_116 ),
inference(resolution,[],[f1219,f654]) ).
tff(f654,plain,
( ~ pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts))
| spl24_24 ),
inference(avatar_component_clause,[],[f652]) ).
tff(f1219,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_116 ),
inference(avatar_component_clause,[],[f1218]) ).
tff(f2068,plain,
spl24_194,
inference(avatar_split_clause,[],[f524,f2066]) ).
tff(f2066,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(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),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,[],[f523,f446]) ).
tff(f446,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,[],[f191]) ).
tff(f191,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
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),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,[],[f465,f446]) ).
tff(f465,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,[],[f307]) ).
tff(f307,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])],[f247,f306]) ).
tff(f306,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(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(flattening,[],[f246]) ).
tff(f246,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,[],[f204]) ).
tff(f204,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,[],[f71]) ).
tff(f71,axiom,
! [X4: type,X6: list(type),X17: type,X60: list(dB),X7: list(dB),X5: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X7),X60)),X17))
=> ( pp(aa(list(type),bool,typings(X8,X7),X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X5),X7)),X4))
=> ? [X61: list(type)] :
( pp(aa(list(type),bool,typings(X8,X60),X61))
& ( foldr(type,type,fun1,X61,X17) = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_var__app__types) ).
tff(f2059,plain,
( spl24_193
| ~ spl24_81
| ~ spl24_192 ),
inference(avatar_split_clause,[],[f2055,f2048,f976,f2057]) ).
tff(f2057,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(f976,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(f2048,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(f2055,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,[],[f2054,f977]) ).
tff(f977,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,[],[f976]) ).
tff(f2054,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,[],[f2053,f977]) ).
tff(f2053,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,[],[f2052,f977]) ).
tff(f2052,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,[],[f2051,f977]) ).
tff(f2051,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,[],[f2049,f977]) ).
tff(f2049,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,[],[f2048]) ).
tff(f2050,plain,
spl24_192,
inference(avatar_split_clause,[],[f442,f2048]) ).
tff(f442,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,[],[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(flattening,[],[f236]) ).
tff(f236,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,[],[f189]) ).
tff(f189,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,[],[f47]) ).
tff(f47,axiom,
! [X24: dB,X4: type,X17: type,X42: dB,X28: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),X42),aa(type,type,aa(type,fun(type,type),fun1,X17),X4)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),X24),X17))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),aa(dB,dB,aa(dB,fun(dB,dB),app,X42),X24)),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_App) ).
tff(f2039,plain,
( spl24_191
| ~ spl24_81
| ~ spl24_190 ),
inference(avatar_split_clause,[],[f2035,f2031,f976,f2037]) ).
tff(f2037,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(f2031,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(f2035,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,[],[f2034,f977]) ).
tff(f2034,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,[],[f2032,f977]) ).
tff(f2032,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,[],[f2031]) ).
tff(f2033,plain,
spl24_190,
inference(avatar_split_clause,[],[f400,f2031]) ).
tff(f400,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,[],[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(flattening,[],[f221]) ).
tff(f221,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,[],[f164]) ).
tff(f164,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,[],[f81]) ).
tff(f81,axiom,
! [X56: list(dB),X42: dB,X55: 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,X55),X42),zero_zero(nat)),X56)))
=> ( pp(aa(dB,bool,it,X42))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X55)),X42),X56))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Beta) ).
tff(f2011,plain,
spl24_189,
inference(avatar_split_clause,[],[f520,f2009]) ).
tff(f2009,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(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(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,[],[f519,f446]) ).
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),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,[],[f518,f446]) ).
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(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,[],[f517,f446]) ).
tff(f517,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,[],[f502,f446]) ).
tff(f502,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,[],[f464]) ).
tff(f464,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,[],[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(flattening,[],[f244]) ).
tff(f244,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,[],[f203]) ).
tff(f203,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,[],[f31]) ).
tff(f31,axiom,
! [X5: nat,X4: type,X23: dB,X34: fun(nat,type),X17: type,X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),X17))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X34),X23),X4))
=> ( ( shift(type,X34,X5,X4) = X8 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X34),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X24),X23),X5)),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_subst__lemma) ).
tff(f1983,plain,
( spl24_188
| ~ spl24_81
| ~ spl24_187 ),
inference(avatar_split_clause,[],[f1979,f1975,f976,f1981]) ).
tff(f1981,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(f1975,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(f1979,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,[],[f1978,f977]) ).
tff(f1978,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,[],[f1976,f977]) ).
tff(f1976,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,[],[f1975]) ).
tff(f1977,plain,
spl24_187,
inference(avatar_split_clause,[],[f479,f1975]) ).
tff(f479,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,[],[f265]) ).
tff(f265,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])],[f263,f264]) ).
tff(f264,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(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 ) ) )
& ( ? [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,[],[f262]) ).
tff(f262,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,[],[f248]) ).
tff(f248,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(f1973,plain,
spl24_186,
inference(avatar_split_clause,[],[f457,f1971]) ).
tff(f1971,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(f457,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,[],[f305]) ).
tff(f305,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])],[f303,f304]) ).
tff(f304,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(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 ) ) )
& ( ? [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,[],[f302]) ).
tff(f302,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,[],[f199]) ).
tff(f199,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,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType,X1: $tType,X64: list(X1),X46: fun(X1,X0),X45: list(X0),X27: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X27),X45) = map(X1,X0,X46,X64) )
<=> ? [X66: X1,X67: list(X1)] :
( ( map(X1,X0,X46,X67) = X45 )
& ( aa(X1,X0,X46,X66) = X27 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X66),X67) = X64 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Cons__eq__map__conv) ).
tff(f1969,plain,
spl24_185,
inference(avatar_split_clause,[],[f453,f1967]) ).
tff(f1967,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(f453,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,[],[f301]) ).
tff(f301,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])],[f299,f300]) ).
tff(f300,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(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 ) ) )
& ( ? [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,[],[f298]) ).
tff(f298,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,[],[f198]) ).
tff(f198,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,[],[f78]) ).
tff(f78,axiom,
! [X1: $tType,X0: $tType,X64: list(X0),X65: X0,X45: list(X1),X46: fun(X1,X0)] :
( ( map(X1,X0,X46,X45) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X65),X64) )
<=> ? [X66: X1,X67: list(X1)] :
( ( map(X1,X0,X46,X67) = X64 )
& ( aa(X1,X0,X46,X66) = X65 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X66),X67) = X45 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_map__eq__Cons__conv) ).
tff(f1953,plain,
( spl24_184
| ~ spl24_81
| ~ spl24_183 ),
inference(avatar_split_clause,[],[f1949,f1943,f976,f1951]) ).
tff(f1951,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(f1943,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(f1949,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,[],[f1948,f977]) ).
tff(f1948,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,[],[f1947,f977]) ).
tff(f1947,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,[],[f1946,f977]) ).
tff(f1946,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,[],[f1944,f977]) ).
tff(f1944,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,[],[f1943]) ).
tff(f1945,plain,
spl24_183,
inference(avatar_split_clause,[],[f386,f1943]) ).
tff(f386,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,[],[f151]) ).
tff(f151,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,[],[f45]) ).
tff(f45,axiom,
! [X15: nat,X16: dB,X14: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X14),X16)),X15) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X14),X15)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_lift_Osimps_I2_J) ).
tff(f1941,plain,
( spl24_182
| ~ spl24_20
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f644,f634,f626,f1939]) ).
tff(f1939,plain,
( spl24_182
<=> ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_182])]) ).
tff(f626,plain,
( spl24_20
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_20])]) ).
tff(f634,plain,
( spl24_22
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_22])]) ).
tff(f644,plain,
( ! [X0: dB] :
( sP1(abs(sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_20
| ~ spl24_22 ),
inference(resolution,[],[f635,f627]) ).
tff(f627,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl24_20 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f635,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl24_22 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f1933,plain,
spl24_181,
inference(avatar_split_clause,[],[f508,f1931]) ).
tff(f1931,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(f508,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,[],[f452,f446]) ).
tff(f452,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,[],[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(flattening,[],[f238]) ).
tff(f238,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,[],[f197]) ).
tff(f197,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,[],[f34]) ).
tff(f34,axiom,
! [X6: list(type),X7: list(dB),X5: nat,X17: type,X23: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X23),X17))
=> ( pp(aa(list(type),bool,typings(shift(type,X8,X5,X17),X7),X6))
=> pp(aa(list(type),bool,typings(X8,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X23),X5),X7)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_substs__lemma) ).
tff(f1918,plain,
( spl24_180
| ~ spl24_81
| ~ spl24_179 ),
inference(avatar_split_clause,[],[f1914,f1908,f976,f1916]) ).
tff(f1916,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(f1908,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(f1914,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,[],[f1913,f977]) ).
tff(f1913,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,[],[f1912,f977]) ).
tff(f1912,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,[],[f1911,f977]) ).
tff(f1911,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,[],[f1909,f977]) ).
tff(f1909,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,[],[f1908]) ).
tff(f1910,plain,
spl24_179,
inference(avatar_split_clause,[],[f416,f1908]) ).
tff(f416,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,[],[f282]) ).
tff(f282,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])],[f227,f281]) ).
tff(f281,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(f227,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,[],[f175]) ).
tff(f175,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,[],[f61]) ).
tff(f61,axiom,
! [X17: type,X23: dB,X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),aa(dB,dB,aa(dB,fun(dB,dB),app,X24),X23)),X17))
=> ~ ! [X51: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),aa(type,type,aa(type,fun(type,type),fun1,X51),X17)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X23),X51)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_typing__elims_I2_J) ).
tff(f1832,plain,
spl24_178,
inference(avatar_split_clause,[],[f451,f1830]) ).
tff(f1830,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(f451,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,[],[f196]) ).
tff(f196,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/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1792,plain,
( spl24_177
| ~ spl24_81
| ~ spl24_176 ),
inference(avatar_split_clause,[],[f1788,f1785,f976,f1790]) ).
tff(f1790,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(f1785,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(f1788,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,[],[f1786,f977]) ).
tff(f1786,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,[],[f1785]) ).
tff(f1787,plain,
spl24_176,
inference(avatar_split_clause,[],[f436,f1785]) ).
tff(f436,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,[],[f183]) ).
tff(f183,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,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X1: $tType,X45: list(X1),X27: X1,X46: fun(X1,X0)] : ( map(X1,X0,X46,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X27),X45)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X46,X27)),map(X1,X0,X46,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_map_Osimps_I2_J) ).
tff(f1777,plain,
( spl24_175
| ~ spl24_81
| ~ spl24_174 ),
inference(avatar_split_clause,[],[f1773,f1770,f976,f1775]) ).
tff(f1775,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(f1770,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(f1773,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,[],[f1771,f977]) ).
tff(f1771,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,[],[f1770]) ).
tff(f1772,plain,
spl24_174,
inference(avatar_split_clause,[],[f395,f1770]) ).
tff(f395,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,[],[f217]) ).
tff(f217,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,[],[f160]) ).
tff(f160,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,[],[f57]) ).
tff(f57,axiom,
! [X6: list(type),X7: list(dB),X8: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X7),X6))
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),typing(X8)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_lists__typings) ).
tff(f1759,plain,
( spl24_173
| ~ spl24_81
| ~ spl24_172 ),
inference(avatar_split_clause,[],[f1755,f1751,f976,f1757]) ).
tff(f1757,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(f1751,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(f1755,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,[],[f1754,f977]) ).
tff(f1754,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,[],[f1752,f977]) ).
tff(f1752,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,[],[f1751]) ).
tff(f1753,plain,
spl24_172,
inference(avatar_split_clause,[],[f440,f1751]) ).
tff(f440,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,[],[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(flattening,[],[f232]) ).
tff(f232,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,[],[f187]) ).
tff(f187,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,[],[f55]) ).
tff(f55,axiom,
! [X7: list(dB),X17: type,X6: list(type),X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),foldr(type,type,fun1,X6,X17)))
=> ( pp(aa(list(type),bool,typings(X8,X7),X6))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X24,X7)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list__app__typeI) ).
tff(f1745,plain,
( spl24_171
| ~ spl24_81
| ~ spl24_170 ),
inference(avatar_split_clause,[],[f1741,f1737,f976,f1743]) ).
tff(f1743,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(f1737,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(f1741,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,[],[f1740,f977]) ).
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(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl24_81
| ~ spl24_170 ),
inference(forward_demodulation,[],[f1738,f977]) ).
tff(f1738,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,[],[f1737]) ).
tff(f1739,plain,
spl24_170,
inference(avatar_split_clause,[],[f414,f1737]) ).
tff(f414,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,[],[f280]) ).
tff(f280,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])],[f226,f279]) ).
tff(f279,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(f226,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,[],[f174]) ).
tff(f174,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,[],[f62]) ).
tff(f62,axiom,
! [X17: type,X7: list(dB),X5: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X5),X7)),X17))
=> ~ ! [X36: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),var(X5)),foldr(type,type,fun1,X36,X17)))
=> ~ pp(aa(list(type),bool,typings(X8,X7),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_var__app__typesE) ).
tff(f1730,plain,
( spl24_168
| ~ spl24_169
| ~ spl24_10 ),
inference(avatar_split_clause,[],[f576,f568,f1727,f1724]) ).
tff(f1724,plain,
( spl24_168
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_168])]) ).
tff(f1727,plain,
( spl24_169
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_169])]) ).
tff(f568,plain,
( spl24_10
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_10])]) ).
tff(f576,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl24_10 ),
inference(equality_factoring,[],[f569]) ).
tff(f569,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f568]) ).
tff(f1722,plain,
( spl24_167
| ~ spl24_81
| ~ spl24_166 ),
inference(avatar_split_clause,[],[f1718,f1713,f976,f1720]) ).
tff(f1720,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(f1713,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(f1718,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,[],[f1717,f977]) ).
tff(f1717,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,[],[f1716,f977]) ).
tff(f1716,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,[],[f1714,f977]) ).
tff(f1714,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,[],[f1713]) ).
tff(f1715,plain,
spl24_166,
inference(avatar_split_clause,[],[f413,f1713]) ).
tff(f413,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,[],[f225]) ).
tff(f225,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,[],[f173]) ).
tff(f173,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,[],[f85]) ).
tff(f85,axiom,
! [X4: type,X24: dB,X17: type,X28: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X28,zero_zero(nat),X17)),X24),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),abs(X24)),aa(type,type,aa(type,fun(type,type),fun1,X17),X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Abs) ).
tff(f1707,plain,
( spl24_165
| ~ spl24_81
| ~ spl24_164 ),
inference(avatar_split_clause,[],[f1703,f1699,f976,f1705]) ).
tff(f1705,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(f1699,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(f1703,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,[],[f1702,f977]) ).
tff(f1702,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,[],[f1700,f977]) ).
tff(f1700,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,[],[f1699]) ).
tff(f1701,plain,
spl24_164,
inference(avatar_split_clause,[],[f385,f1699]) ).
tff(f385,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,[],[f150]) ).
tff(f150,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X5: nat,X7: list(dB),X24: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X24,X7)),X5) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X24),X5),map(dB,dB,combc(dB,nat,dB,lift,X5),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lift__map) ).
tff(f1688,plain,
( spl24_163
| ~ spl24_81
| ~ spl24_162 ),
inference(avatar_split_clause,[],[f1684,f1680,f976,f1686]) ).
tff(f1686,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(f1680,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(f1684,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,[],[f1683,f977]) ).
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),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,[],[f1681,f977]) ).
tff(f1681,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,[],[f1680]) ).
tff(f1682,plain,
spl24_162,
inference(avatar_split_clause,[],[f441,f1680]) ).
tff(f441,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,[],[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(flattening,[],[f234]) ).
tff(f234,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,[],[f188]) ).
tff(f188,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,[],[f51]) ).
tff(f51,axiom,
! [X4: type,X17: type,X7: list(dB),X5: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X5),X7)),X17))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,var(X5),X7)),X4))
=> ( X4 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_var__app__type__eq) ).
tff(f1678,plain,
( spl24_161
| ~ spl24_81
| ~ spl24_160 ),
inference(avatar_split_clause,[],[f1672,f1668,f976,f1675]) ).
tff(f1675,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,t1))),fEx(type)),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_161])]) ).
tff(f1668,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,t1))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_160])]) ).
tff(f1672,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,t1))),fEx(type)),as)
| ~ spl24_81
| ~ spl24_160 ),
inference(forward_demodulation,[],[f1670,f977]) ).
tff(f1670,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,t1))),as)
| ~ spl24_160 ),
inference(avatar_component_clause,[],[f1668]) ).
tff(f1671,plain,
spl24_160,
inference(avatar_split_clause,[],[f334,f1668]) ).
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,t1))),as),
inference(cnf_transformation,[],[f36]) ).
tff(f36,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,t1))),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__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(f1663,plain,
( spl24_159
| ~ spl24_81
| ~ spl24_158 ),
inference(avatar_split_clause,[],[f1659,f1654,f976,f1661]) ).
tff(f1661,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(f1654,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(f1659,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,[],[f1658,f977]) ).
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(type,bool,aa(dB,fun(type,bool),typing(X4),X3),X2)) )
| ~ spl24_81
| ~ spl24_158 ),
inference(forward_demodulation,[],[f1657,f977]) ).
tff(f1657,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,[],[f1655,f977]) ).
tff(f1655,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,[],[f1654]) ).
tff(f1656,plain,
spl24_158,
inference(avatar_split_clause,[],[f439,f1654]) ).
tff(f439,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,[],[f231]) ).
tff(f231,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,[],[f186]) ).
tff(f186,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,[],[f26]) ).
tff(f26,axiom,
! [X4: type,X5: nat,X17: type,X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),X17))
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,X5,X4)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X24),X5)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lift__type) ).
tff(f1646,plain,
( spl24_157
| ~ spl24_81
| ~ spl24_156 ),
inference(avatar_split_clause,[],[f1642,f1637,f976,f1644]) ).
tff(f1644,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(f1637,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(f1642,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,[],[f1641,f977]) ).
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,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,[],[f1640,f977]) ).
tff(f1640,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,[],[f1638,f977]) ).
tff(f1638,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,[],[f1637]) ).
tff(f1639,plain,
spl24_156,
inference(avatar_split_clause,[],[f417,f1637]) ).
tff(f417,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,[],[f282]) ).
tff(f1626,plain,
( spl24_155
| ~ spl24_81
| ~ spl24_154 ),
inference(avatar_split_clause,[],[f1622,f1618,f976,f1624]) ).
tff(f1624,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(f1618,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(f1622,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,[],[f1621,f977]) ).
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(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_81
| ~ spl24_154 ),
inference(forward_demodulation,[],[f1619,f977]) ).
tff(f1619,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,[],[f1618]) ).
tff(f1620,plain,
spl24_154,
inference(avatar_split_clause,[],[f411,f1618]) ).
tff(f411,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,[],[f278]) ).
tff(f278,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])],[f224,f277]) ).
tff(f277,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(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(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,[],[f73]) ).
tff(f73,axiom,
! [X17: type,X7: list(dB),X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X24,X7)),X17))
=> ? [X36: list(type)] :
( pp(aa(list(type),bool,typings(X8,X7),X36))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),foldr(type,type,fun1,X36,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list__app__typeD) ).
tff(f1606,plain,
( spl24_153
| ~ spl24_81
| ~ spl24_152 ),
inference(avatar_split_clause,[],[f1602,f1598,f976,f1604]) ).
tff(f1604,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(f1598,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(f1602,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,[],[f1601,f977]) ).
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(type,bool,aa(dB,fun(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl24_81
| ~ spl24_152 ),
inference(forward_demodulation,[],[f1599,f977]) ).
tff(f1599,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,[],[f1598]) ).
tff(f1600,plain,
spl24_152,
inference(avatar_split_clause,[],[f409,f1598]) ).
tff(f409,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,[],[f276]) ).
tff(f276,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])],[f223,f275]) ).
tff(f275,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(f223,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,[],[f171]) ).
tff(f171,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,[],[f72]) ).
tff(f72,axiom,
! [X17: type,X7: list(dB),X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),foldl(dB,dB,app,X24,X7)),X17))
=> ~ ! [X36: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),X24),foldr(type,type,fun1,X36,X17)))
=> ~ pp(aa(list(type),bool,typings(X8,X7),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_list__app__typeE) ).
tff(f1591,plain,
spl24_151,
inference(avatar_split_clause,[],[f333,f1588]) ).
tff(f1588,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(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,[],[f39]) ).
tff(f39,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/sandbox2/benchmark/theBenchmark.p',fact_38__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(f1562,plain,
spl24_150,
inference(avatar_split_clause,[],[f450,f1560]) ).
tff(f1560,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(f450,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,[],[f195]) ).
tff(f195,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/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1558,plain,
spl24_149,
inference(avatar_split_clause,[],[f444,f1556]) ).
tff(f1556,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(f444,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,[],[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(flattening,[],[f296]) ).
tff(f296,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,[],[f190]) ).
tff(f190,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,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X52: list(X0),X53: X0,X54: list(X0),X47: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X47),X54) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X53),X52) )
<=> ( ( X52 = X54 )
& ( X47 = X53 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_list_Oinject) ).
tff(f1545,plain,
( spl24_148
| ~ spl24_15
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f639,f634,f595,f1543]) ).
tff(f1543,plain,
( spl24_148
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_148])]) ).
tff(f595,plain,
( spl24_15
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_15])]) ).
tff(f639,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl24_15
| ~ spl24_22 ),
inference(resolution,[],[f635,f596]) ).
tff(f596,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl24_15 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f1541,plain,
( spl24_147
| ~ spl24_81
| ~ spl24_146 ),
inference(avatar_split_clause,[],[f1537,f1533,f976,f1539]) ).
tff(f1539,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(f1533,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(f1537,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,[],[f1536,f977]) ).
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(type,bool,aa(dB,fun(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl24_81
| ~ spl24_146 ),
inference(forward_demodulation,[],[f1534,f977]) ).
tff(f1534,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,[],[f1533]) ).
tff(f1535,plain,
spl24_146,
inference(avatar_split_clause,[],[f398,f1533]) ).
tff(f398,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,[],[f272]) ).
tff(f272,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])],[f219,f271]) ).
tff(f271,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(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))
& ( 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,[],[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] :
( ( 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,[],[f92]) ).
tff(f92,axiom,
! [X17: type,X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),abs(X24)),X17))
=> ~ ! [X51: type,X75: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X51),X75) = X17 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,zero_zero(nat),X51)),X24),X75)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_typing__elims_I3_J) ).
tff(f1516,plain,
spl24_145,
inference(avatar_split_clause,[],[f459,f1514]) ).
tff(f1514,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(f459,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,[],[f305]) ).
tff(f1512,plain,
spl24_144,
inference(avatar_split_clause,[],[f455,f1510]) ).
tff(f1510,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(f455,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,[],[f301]) ).
tff(f1508,plain,
spl24_143,
inference(avatar_split_clause,[],[f443,f1506]) ).
tff(f1506,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(f443,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,[],[f297]) ).
tff(f1436,plain,
( spl24_142
| ~ spl24_14
| ~ spl24_20 ),
inference(avatar_split_clause,[],[f637,f626,f591,f1434]) ).
tff(f1434,plain,
( spl24_142
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_142])]) ).
tff(f591,plain,
( spl24_14
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_14])]) ).
tff(f637,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) )
| ~ spl24_14
| ~ spl24_20 ),
inference(resolution,[],[f627,f592]) ).
tff(f592,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl24_14 ),
inference(avatar_component_clause,[],[f591]) ).
tff(f1426,plain,
spl24_141,
inference(avatar_split_clause,[],[f507,f1424]) ).
tff(f1424,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(f507,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,[],[f449,f446]) ).
tff(f449,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,[],[f194]) ).
tff(f194,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,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X1: $tType,X45: list(X1),X27: X1,X47: X0,X46: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X46,X47,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X27),X45)) = foldl(X0,X1,X46,aa(X1,X0,aa(X0,fun(X1,X0),X46,X47),X27),X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_foldl__Cons) ).
tff(f1422,plain,
spl24_140,
inference(avatar_split_clause,[],[f506,f1420]) ).
tff(f1420,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(f506,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,[],[f448,f446]) ).
tff(f448,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,[],[f193]) ).
tff(f193,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,[],[f70]) ).
tff(f70,axiom,
! [X1: $tType,X0: $tType,X47: X0,X45: list(X1),X27: X1,X46: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X46,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X27),X45),X47) = aa(X0,X0,aa(X1,fun(X0,X0),X46,X27),foldr(X1,X0,X46,X45,X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_foldr_Osimps_I2_J) ).
tff(f1418,plain,
spl24_139,
inference(avatar_split_clause,[],[f458,f1416]) ).
tff(f1416,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(f458,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,[],[f305]) ).
tff(f1414,plain,
spl24_138,
inference(avatar_split_clause,[],[f454,f1412]) ).
tff(f1412,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(f454,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,[],[f301]) ).
tff(f1409,plain,
( spl24_137
| ~ spl24_81
| ~ spl24_136 ),
inference(avatar_split_clause,[],[f1405,f1401,f976,f1407]) ).
tff(f1407,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(f1401,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(f1405,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,[],[f1404,f977]) ).
tff(f1404,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,[],[f1402,f977]) ).
tff(f1402,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,[],[f1401]) ).
tff(f1403,plain,
spl24_136,
inference(avatar_split_clause,[],[f396,f1401]) ).
tff(f396,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,[],[f270]) ).
tff(f270,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])],[f218,f269]) ).
tff(f269,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(f218,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,[],[f161]) ).
tff(f161,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,[],[f93]) ).
tff(f93,axiom,
! [X17: type,X24: dB,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),abs(X24)),X17))
=> ~ ! [X75: type,X76: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,X8,zero_zero(nat),X75)),X24),X76)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_abs__typeE) ).
tff(f1360,plain,
( spl24_135
| ~ spl24_81
| ~ spl24_134 ),
inference(avatar_split_clause,[],[f1356,f1353,f976,f1358]) ).
tff(f1358,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(f1353,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(f1356,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,[],[f1354,f977]) ).
tff(f1354,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,[],[f1353]) ).
tff(f1355,plain,
spl24_134,
inference(avatar_split_clause,[],[f355,f1353]) ).
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,[],[f265]) ).
tff(f1347,plain,
( spl24_133
| ~ spl24_81
| ~ spl24_132 ),
inference(avatar_split_clause,[],[f1342,f1337,f976,f1344]) ).
tff(f1344,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(f1337,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(f1342,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,[],[f1341,f977]) ).
tff(f1341,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,[],[f1339,f977]) ).
tff(f1339,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,[],[f1337]) ).
tff(f1340,plain,
spl24_132,
inference(avatar_split_clause,[],[f332,f1337]) ).
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,[],[f46]) ).
tff(f46,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/sandbox2/benchmark/theBenchmark.p',fact_45__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f1323,plain,
spl24_131,
inference(avatar_split_clause,[],[f505,f1321]) ).
tff(f1321,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(f505,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,[],[f447,f446]) ).
tff(f447,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,[],[f192]) ).
tff(f192,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,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType,X1: $tType,X54: list(X1),X47: X1,X68: fun(X1,fun(list(X1),X0)),X69: X0] : ( list_case(X0,X1,X69,X68,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X47),X54)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X68,X47),X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_list_Osimps_I5_J) ).
tff(f1317,plain,
( spl24_130
| ~ spl24_81
| ~ spl24_129 ),
inference(avatar_split_clause,[],[f1312,f1307,f976,f1314]) ).
tff(f1314,plain,
( spl24_130
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_130])]) ).
tff(f1307,plain,
( spl24_129
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_129])]) ).
tff(f1312,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_81
| ~ spl24_129 ),
inference(forward_demodulation,[],[f1311,f977]) ).
tff(f1311,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,sK3,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_81
| ~ spl24_129 ),
inference(forward_demodulation,[],[f1309,f977]) ).
tff(f1309,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t)))
| ~ spl24_129 ),
inference(avatar_component_clause,[],[f1307]) ).
tff(f1310,plain,
spl24_129,
inference(avatar_split_clause,[],[f473,f1307]) ).
tff(f473,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK3,t))),
inference(definition_unfolding,[],[f338,f313]) ).
tff(f313,plain,
n = i,
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_True) ).
tff(f338,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t))),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f206,f253]) ).
tff(f253,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t))) )
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK3,t))) ) ),
introduced(choice_axiom,[]) ).
tff(f206,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t))) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
~ ! [X36: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X36,t)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X36)) ),
file('/export/starexec/sandbox2/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(f1299,plain,
( spl24_128
| ~ spl24_81
| ~ spl24_127 ),
inference(avatar_split_clause,[],[f1294,f1289,f976,f1296]) ).
tff(f1296,plain,
( spl24_128
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t)),sK2)),var(i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_128])]) ).
tff(f1289,plain,
( spl24_127
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_127])]) ).
tff(f1294,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,combc(type,type,type,fun1,foldr(type,type,fun1,ts,t)),sK2)),var(i)))
| ~ spl24_81
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1293,f977]) ).
tff(f1293,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t))),var(i)))
| ~ spl24_81
| ~ spl24_127 ),
inference(forward_demodulation,[],[f1291,f977]) ).
tff(f1291,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t))))
| ~ spl24_127 ),
inference(avatar_component_clause,[],[f1289]) ).
tff(f1292,plain,
spl24_127,
inference(avatar_split_clause,[],[f472,f1289]) ).
tff(f472,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t)))),
inference(definition_unfolding,[],[f336,f313]) ).
tff(f336,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t)))),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f205,f251]) ).
tff(f251,plain,
( ? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t)))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK2),foldr(type,type,fun1,ts,t)))) ) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t)))) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X0)) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
~ ! [X35: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X35),foldr(type,type,fun1,ts,t))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__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(f1283,plain,
( spl24_126
| ~ spl24_81
| ~ spl24_125 ),
inference(avatar_split_clause,[],[f1278,f1273,f976,f1280]) ).
tff(f1280,plain,
( spl24_126
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),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(f1273,plain,
( spl24_125
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_125])]) ).
tff(f1278,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),var(i)),as)))
| ~ spl24_81
| ~ spl24_125 ),
inference(forward_demodulation,[],[f1277,f977]) ).
tff(f1277,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)))
| ~ spl24_81
| ~ spl24_125 ),
inference(forward_demodulation,[],[f1275,f977]) ).
tff(f1275,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t))
| ~ spl24_125 ),
inference(avatar_component_clause,[],[f1273]) ).
tff(f1276,plain,
spl24_125,
inference(avatar_split_clause,[],[f471,f1273]) ).
tff(f471,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t)),
inference(definition_unfolding,[],[f331,f313]) ).
tff(f331,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48__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(f1269,plain,
( spl24_124
| ~ spl24_81
| ~ spl24_123 ),
inference(avatar_split_clause,[],[f1264,f1259,f976,f1266]) ).
tff(f1266,plain,
( spl24_124
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_124])]) ).
tff(f1259,plain,
( spl24_123
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_123])]) ).
tff(f1264,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(i))))
| ~ spl24_81
| ~ spl24_123 ),
inference(forward_demodulation,[],[f1263,f977]) ).
tff(f1263,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),foldr(type,type,fun1,ts,t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)))
| ~ spl24_81
| ~ spl24_123 ),
inference(forward_demodulation,[],[f1261,f977]) ).
tff(f1261,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t)))
| ~ spl24_123 ),
inference(avatar_component_clause,[],[f1259]) ).
tff(f1262,plain,
spl24_123,
inference(avatar_split_clause,[],[f470,f1259]) ).
tff(f470,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t))),
inference(definition_unfolding,[],[f330,f313]) ).
tff(f330,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t))),
inference(cnf_transformation,[],[f37]) ).
tff(f37,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_headT) ).
tff(f1255,plain,
( spl24_122
| ~ spl24_81
| ~ spl24_121 ),
inference(avatar_split_clause,[],[f1251,f1247,f976,f1253]) ).
tff(f1253,plain,
( spl24_122
<=> ! [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_122])]) ).
tff(f1247,plain,
( spl24_121
<=> ! [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_121])]) ).
tff(f1251,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_121 ),
inference(forward_demodulation,[],[f1250,f977]) ).
tff(f1250,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_121 ),
inference(forward_demodulation,[],[f1248,f977]) ).
tff(f1248,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_121 ),
inference(avatar_component_clause,[],[f1247]) ).
tff(f1249,plain,
spl24_121,
inference(avatar_split_clause,[],[f397,f1247]) ).
tff(f397,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,[],[f272]) ).
tff(f1245,plain,
( spl24_120
| ~ spl24_81
| ~ spl24_119 ),
inference(avatar_split_clause,[],[f1241,f1237,f976,f1243]) ).
tff(f1243,plain,
( spl24_120
<=> ! [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_120])]) ).
tff(f1237,plain,
( spl24_119
<=> ! [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_119])]) ).
tff(f1241,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_119 ),
inference(forward_demodulation,[],[f1240,f977]) ).
tff(f1240,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_119 ),
inference(forward_demodulation,[],[f1238,f977]) ).
tff(f1238,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_119 ),
inference(avatar_component_clause,[],[f1237]) ).
tff(f1239,plain,
spl24_119,
inference(avatar_split_clause,[],[f366,f1237]) ).
tff(f366,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,[],[f133]) ).
tff(f133,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,[],[f97]) ).
tff(f97,axiom,
! [X16: dB,X14: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X14)),X16),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X14),X16),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_beta) ).
tff(f1232,plain,
( spl24_118
| ~ spl24_81
| ~ spl24_117 ),
inference(avatar_split_clause,[],[f1228,f1225,f976,f1230]) ).
tff(f1230,plain,
( spl24_118
<=> ! [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_118])]) ).
tff(f1225,plain,
( spl24_117
<=> ! [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_117])]) ).
tff(f1228,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_117 ),
inference(forward_demodulation,[],[f1226,f977]) ).
tff(f1226,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_117 ),
inference(avatar_component_clause,[],[f1225]) ).
tff(f1227,plain,
spl24_117,
inference(avatar_split_clause,[],[f415,f1225]) ).
tff(f415,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,[],[f280]) ).
tff(f1220,plain,
spl24_116,
inference(avatar_split_clause,[],[f438,f1218]) ).
tff(f438,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,[],[f230]) ).
tff(f230,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,[],[f185]) ).
tff(f185,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,[],[f6]) ).
tff(f6,axiom,
! [X4: type,X5: nat,X6: list(type),X7: list(dB),X8: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X7),X6))
=> pp(aa(list(type),bool,typings(shift(type,X8,X5,X4),map(dB,dB,combc(dB,nat,dB,lift,X5),X7)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_lift__types) ).
tff(f1216,plain,
( ~ spl24_115
| ~ spl24_66
| ~ spl24_67 ),
inference(avatar_split_clause,[],[f913,f902,f897,f1213]) ).
tff(f1213,plain,
( spl24_115
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_115])]) ).
tff(f897,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(f902,plain,
( spl24_67
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_67])]) ).
tff(f913,plain,
( ( as != rs )
| ~ spl24_66
| ~ spl24_67 ),
inference(superposition,[],[f903,f899]) ).
tff(f899,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl24_66 ),
inference(avatar_component_clause,[],[f897]) ).
tff(f903,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 )
| ~ spl24_67 ),
inference(avatar_component_clause,[],[f902]) ).
tff(f1208,plain,
( spl24_114
| ~ spl24_81
| ~ spl24_113 ),
inference(avatar_split_clause,[],[f1204,f1201,f976,f1206]) ).
tff(f1206,plain,
( spl24_114
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK15(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_114])]) ).
tff(f1201,plain,
( spl24_113
<=> ! [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_113])]) ).
tff(f1204,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_113 ),
inference(forward_demodulation,[],[f1202,f977]) ).
tff(f1202,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_113 ),
inference(avatar_component_clause,[],[f1201]) ).
tff(f1203,plain,
spl24_113,
inference(avatar_split_clause,[],[f412,f1201]) ).
tff(f412,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,[],[f278]) ).
tff(f1196,plain,
( spl24_112
| ~ spl24_81
| ~ spl24_111 ),
inference(avatar_split_clause,[],[f1192,f1189,f976,f1194]) ).
tff(f1194,plain,
( spl24_112
<=> ! [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_112])]) ).
tff(f1189,plain,
( spl24_111
<=> ! [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_111])]) ).
tff(f1192,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_111 ),
inference(forward_demodulation,[],[f1190,f977]) ).
tff(f1190,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_111 ),
inference(avatar_component_clause,[],[f1189]) ).
tff(f1191,plain,
spl24_111,
inference(avatar_split_clause,[],[f410,f1189]) ).
tff(f410,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,[],[f276]) ).
tff(f1183,plain,
( spl24_110
| ~ spl24_81
| ~ spl24_109 ),
inference(avatar_split_clause,[],[f1179,f1176,f976,f1181]) ).
tff(f1181,plain,
( spl24_110
<=> ! [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_110])]) ).
tff(f1176,plain,
( spl24_109
<=> ! [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_109])]) ).
tff(f1179,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_109 ),
inference(forward_demodulation,[],[f1177,f977]) ).
tff(f1177,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_109 ),
inference(avatar_component_clause,[],[f1176]) ).
tff(f1178,plain,
spl24_109,
inference(avatar_split_clause,[],[f393,f1176]) ).
tff(f393,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,[],[f215]) ).
tff(f215,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,[],[f158]) ).
tff(f158,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,[],[f29]) ).
tff(f29,axiom,
! [X31: nat,X29: nat,X32: dB] :
( pp(aa(dB,bool,it,X32))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X32),var(X29)),X31))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_subst__Var__IT) ).
tff(f1172,plain,
( spl24_108
| ~ spl24_11
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f640,f634,f578,f1170]) ).
tff(f1170,plain,
( spl24_108
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_108])]) ).
tff(f578,plain,
( spl24_11
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_11])]) ).
tff(f640,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl24_11
| ~ spl24_22 ),
inference(resolution,[],[f635,f579]) ).
tff(f579,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl24_11 ),
inference(avatar_component_clause,[],[f578]) ).
tff(f1168,plain,
( spl24_107
| ~ spl24_81
| ~ spl24_106 ),
inference(avatar_split_clause,[],[f1164,f1160,f976,f1166]) ).
tff(f1166,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(f1160,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(f1164,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,[],[f1163,f977]) ).
tff(f1163,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,[],[f1161,f977]) ).
tff(f1161,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,[],[f1160]) ).
tff(f1162,plain,
spl24_106,
inference(avatar_split_clause,[],[f383,f1160]) ).
tff(f383,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,[],[f148]) ).
tff(f148,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,[],[f11]) ).
tff(f11,axiom,
! [X14: dB,X15: nat,X16: 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,X16),X15)),X14),X15) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_subst__lift) ).
tff(f1158,plain,
spl24_105,
inference(avatar_split_clause,[],[f328,f1155]) ).
tff(f1155,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,[],[f10]) ).
tff(f10,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/sandbox2/benchmark/theBenchmark.p',fact_9__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(f1152,plain,
spl24_104,
inference(avatar_split_clause,[],[f327,f1149]) ).
tff(f1149,plain,
( spl24_104
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t))) ),
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,t))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t))),var(zero_zero(nat))),foldr(type,type,fun1,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_calculation) ).
tff(f1131,plain,
spl24_103,
inference(avatar_split_clause,[],[f429,f1129]) ).
tff(f1129,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(f429,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,[],[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(flattening,[],[f291]) ).
tff(f291,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,[],[f180]) ).
tff(f180,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,[],[f43]) ).
tff(f43,axiom,
! [X38: dB,X39: dB,X40: dB,X41: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X41),X40) = aa(dB,dB,aa(dB,fun(dB,dB),app,X39),X38) )
<=> ( ( X38 = X40 )
& ( X39 = X41 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_dB_Osimps_I2_J) ).
tff(f1126,plain,
spl24_102,
inference(avatar_split_clause,[],[f428,f1124]) ).
tff(f1124,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(f428,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,[],[f292]) ).
tff(f1122,plain,
spl24_101,
inference(avatar_split_clause,[],[f426,f1120]) ).
tff(f1120,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(f426,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,[],[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(flattening,[],[f289]) ).
tff(f289,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,[],[f179]) ).
tff(f179,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,[],[f9]) ).
tff(f9,axiom,
! [X10: type,X11: type,X12: type,X13: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X13),X12) = aa(type,type,aa(type,fun(type,type),fun1,X11),X10) )
<=> ( ( X10 = X12 )
& ( X11 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_type_Osimps_I2_J) ).
tff(f1118,plain,
spl24_100,
inference(avatar_split_clause,[],[f425,f1116]) ).
tff(f1116,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(f425,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,[],[f290]) ).
tff(f1114,plain,
( spl24_99
| ~ spl24_81
| ~ spl24_98 ),
inference(avatar_split_clause,[],[f1110,f1106,f976,f1112]) ).
tff(f1112,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(f1106,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(f1110,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,[],[f1109,f977]) ).
tff(f1109,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,[],[f1107,f977]) ).
tff(f1107,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,[],[f1106]) ).
tff(f1108,plain,
spl24_98,
inference(avatar_split_clause,[],[f392,f1106]) ).
tff(f392,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,[],[f214]) ).
tff(f214,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,[],[f157]) ).
tff(f157,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,[],[f99]) ).
tff(f99,axiom,
! [X33: dB,X16: dB,X14: dB] :
( beta(X14,X16)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X33),X14),aa(dB,dB,aa(dB,fun(dB,dB),app,X33),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_appR) ).
tff(f1104,plain,
( spl24_97
| ~ spl24_81
| ~ spl24_96 ),
inference(avatar_split_clause,[],[f1100,f1096,f976,f1102]) ).
tff(f1102,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(f1096,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(f1100,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,[],[f1099,f977]) ).
tff(f1099,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,[],[f1097,f977]) ).
tff(f1097,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,[],[f1096]) ).
tff(f1098,plain,
spl24_96,
inference(avatar_split_clause,[],[f391,f1096]) ).
tff(f391,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,[],[f213]) ).
tff(f213,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,[],[f156]) ).
tff(f156,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,
! [X33: dB,X16: dB,X14: dB] :
( beta(X14,X16)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X14),X33),aa(dB,dB,aa(dB,fun(dB,dB),app,X16),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_appL) ).
tff(f1091,plain,
spl24_95,
inference(avatar_split_clause,[],[f325,f1088]) ).
tff(f325,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,[],[f4]) ).
tff(f4,axiom,
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/sandbox2/benchmark/theBenchmark.p',fact_3__096e_A_124_124_N_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_A_058_ATs_096) ).
tff(f1076,plain,
spl24_94,
inference(avatar_split_clause,[],[f418,f1074]) ).
tff(f1074,plain,
( spl24_94
<=> ! [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_94])]) ).
tff(f418,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,[],[f284]) ).
tff(f284,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])],[f228,f283]) ).
tff(f283,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(f228,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,[],[f176]) ).
tff(f176,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,X48: fun(X0,X1),X46: fun(X0,X1)] :
( ! [X62: X0] : ( aa(X0,X1,X46,X62) = aa(X0,X1,X48,X62) )
=> ( X46 = X48 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1072,plain,
( spl24_93
| ~ spl24_81
| ~ spl24_92 ),
inference(avatar_split_clause,[],[f1068,f1065,f976,f1070]) ).
tff(f1070,plain,
( spl24_93
<=> ! [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_93])]) ).
tff(f1065,plain,
( spl24_92
<=> ! [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_92])]) ).
tff(f1068,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_92 ),
inference(forward_demodulation,[],[f1066,f977]) ).
tff(f1066,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_92 ),
inference(avatar_component_clause,[],[f1065]) ).
tff(f1067,plain,
spl24_92,
inference(avatar_split_clause,[],[f354,f1065]) ).
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,[],[f265]) ).
tff(f1061,plain,
( spl24_91
| ~ spl24_81
| ~ spl24_90 ),
inference(avatar_split_clause,[],[f1056,f1052,f976,f1058]) ).
tff(f1058,plain,
( spl24_91
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_91])]) ).
tff(f1052,plain,
( spl24_90
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_90])]) ).
tff(f1056,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_81
| ~ spl24_90 ),
inference(forward_demodulation,[],[f1054,f977]) ).
tff(f1054,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t))
| ~ spl24_90 ),
inference(avatar_component_clause,[],[f1052]) ).
tff(f1055,plain,
spl24_90,
inference(avatar_split_clause,[],[f468,f1052]) ).
tff(f468,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(i),rs)),t)),
inference(definition_unfolding,[],[f324,f313]) ).
tff(f324,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t)),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nT) ).
tff(f1047,plain,
( spl24_89
| ~ spl24_81
| ~ spl24_88 ),
inference(avatar_split_clause,[],[f1042,f1038,f976,f1044]) ).
tff(f1044,plain,
( spl24_89
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(i),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_89])]) ).
tff(f1038,plain,
( spl24_88
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_88])]) ).
tff(f1042,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(i),rs)))
| ~ spl24_81
| ~ spl24_88 ),
inference(forward_demodulation,[],[f1040,f977]) ).
tff(f1040,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a))
| ~ spl24_88 ),
inference(avatar_component_clause,[],[f1038]) ).
tff(f1041,plain,
spl24_88,
inference(avatar_split_clause,[],[f467,f1038]) ).
tff(f467,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f323,f313]) ).
tff(f323,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Var_I2_J) ).
tff(f1033,plain,
( spl24_87
| ~ spl24_81
| ~ spl24_86 ),
inference(avatar_split_clause,[],[f1029,f1026,f976,f1031]) ).
tff(f1031,plain,
( spl24_87
<=> ! [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_87])]) ).
tff(f1026,plain,
( spl24_86
<=> ! [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_86])]) ).
tff(f1029,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_86 ),
inference(forward_demodulation,[],[f1027,f977]) ).
tff(f1027,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_86 ),
inference(avatar_component_clause,[],[f1026]) ).
tff(f1028,plain,
spl24_86,
inference(avatar_split_clause,[],[f404,f1026]) ).
tff(f404,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,[],[f274]) ).
tff(f274,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,[],[f166]) ).
tff(f166,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,X22: fun(X0,bool),X27: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X27),X22))
<=> pp(aa(X0,bool,X22,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f1023,plain,
( spl24_85
| ~ spl24_81
| ~ spl24_84 ),
inference(avatar_split_clause,[],[f1019,f1016,f976,f1021]) ).
tff(f1021,plain,
( spl24_85
<=> ! [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_85])]) ).
tff(f1016,plain,
( spl24_84
<=> ! [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_84])]) ).
tff(f1019,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_84 ),
inference(forward_demodulation,[],[f1017,f977]) ).
tff(f1017,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_84 ),
inference(avatar_component_clause,[],[f1016]) ).
tff(f1018,plain,
spl24_84,
inference(avatar_split_clause,[],[f403,f1016]) ).
tff(f403,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,[],[f274]) ).
tff(f1010,plain,
( spl24_83
| ~ spl24_81
| ~ spl24_82 ),
inference(avatar_split_clause,[],[f1005,f1002,f976,f1008]) ).
tff(f1008,plain,
( spl24_83
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_83])]) ).
tff(f1002,plain,
( spl24_82
<=> ! [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_82])]) ).
tff(f1005,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_82 ),
inference(forward_demodulation,[],[f1003,f977]) ).
tff(f1003,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_82 ),
inference(avatar_component_clause,[],[f1002]) ).
tff(f1004,plain,
spl24_82,
inference(avatar_split_clause,[],[f372,f1002]) ).
tff(f372,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,[],[f212]) ).
tff(f212,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,[],[f139]) ).
tff(f139,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,[],[f56]) ).
tff(f56,axiom,
! [X29: nat,X16: dB] :
( pp(aa(dB,bool,it,X16))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X16),var(X29)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_app__Var__IT) ).
tff(f978,plain,
spl24_81,
inference(avatar_split_clause,[],[f446,f976]) ).
tff(f970,plain,
( spl24_80
| ~ spl24_79 ),
inference(avatar_split_clause,[],[f966,f963,f968]) ).
tff(f968,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(f963,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(f966,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,[],[f964,f446]) ).
tff(f964,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,[],[f963]) ).
tff(f965,plain,
spl24_79,
inference(avatar_split_clause,[],[f371,f963]) ).
tff(f371,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,[],[f211]) ).
tff(f211,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,[],[f138]) ).
tff(f138,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,[],[f24]) ).
tff(f24,axiom,
! [X29: nat,X16: dB] :
( pp(aa(dB,bool,it,X16))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X16),X29))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lift__IT) ).
tff(f961,plain,
( spl24_78
| ~ spl24_77 ),
inference(avatar_split_clause,[],[f957,f954,f959]) ).
tff(f959,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(f954,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(f957,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,[],[f955,f446]) ).
tff(f955,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,[],[f954]) ).
tff(f956,plain,
spl24_77,
inference(avatar_split_clause,[],[f365,f954]) ).
tff(f365,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,[],[f132]) ).
tff(f132,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,[],[f30]) ).
tff(f30,axiom,
! [X33: dB,X15: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X15)),X33),X15) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_subst__eq) ).
tff(f952,plain,
( spl24_76
| ~ spl24_7
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f643,f634,f554,f949]) ).
tff(f949,plain,
( spl24_76
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_76])]) ).
tff(f554,plain,
( spl24_7
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_7])]) ).
tff(f643,plain,
( sP1(abs(ua))
| ~ spl24_7
| ~ spl24_22 ),
inference(resolution,[],[f635,f556]) ).
tff(f556,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl24_7 ),
inference(avatar_component_clause,[],[f554]) ).
tff(f947,plain,
spl24_75,
inference(avatar_split_clause,[],[f349,f945]) ).
tff(f945,plain,
( spl24_75
<=> ! [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_75])]) ).
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,[],[f261]) ).
tff(f261,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])],[f258,f260,f259]) ).
tff(f259,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(f260,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(f258,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,[],[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(flattening,[],[f256]) ).
tff(f256,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,[],[f249]) ).
tff(f249,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(f941,plain,
( spl24_74
| ~ spl24_73 ),
inference(avatar_split_clause,[],[f937,f934,f939]) ).
tff(f939,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(f934,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(f937,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,[],[f935,f446]) ).
tff(f935,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,[],[f934]) ).
tff(f936,plain,
spl24_73,
inference(avatar_split_clause,[],[f399,f934]) ).
tff(f399,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,[],[f220]) ).
tff(f220,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,[],[f163]) ).
tff(f163,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,[],[f23]) ).
tff(f23,axiom,
! [X17: type,X5: nat,X8: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(X8),var(X5)),X17))
=> ( aa(nat,type,X8,X5) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_typing__elims_I1_J) ).
tff(f928,plain,
spl24_72,
inference(avatar_split_clause,[],[f406,f926]) ).
tff(f926,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(f406,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,[],[f168]) ).
tff(f168,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,[],[f90]) ).
tff(f90,axiom,
! [X56: list(dB),X49: nat,X24: dB,X42: dB] : ( foldl(dB,dB,app,var(X49),X56) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X42)),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Abs__App__neq__Var__apps) ).
tff(f924,plain,
spl24_71,
inference(avatar_split_clause,[],[f347,f922]) ).
tff(f922,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,[],[f261]) ).
tff(f918,plain,
( spl24_70
| ~ spl24_8
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f642,f634,f559,f915]) ).
tff(f915,plain,
( spl24_70
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_70])]) ).
tff(f559,plain,
( spl24_8
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_8])]) ).
tff(f642,plain,
( sP1(abs(u))
| ~ spl24_8
| ~ spl24_22 ),
inference(resolution,[],[f635,f561]) ).
tff(f561,plain,
( pp(aa(dB,bool,it,u))
| ~ spl24_8 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f912,plain,
spl24_69,
inference(avatar_split_clause,[],[f423,f910]) ).
tff(f910,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(f423,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,[],[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(flattening,[],[f287]) ).
tff(f287,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,[],[f178]) ).
tff(f178,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,[],[f66]) ).
tff(f66,axiom,
! [X56: list(dB),X49: nat,X50: list(dB),X57: nat] :
( ( foldl(dB,dB,app,var(X57),X50) = foldl(dB,dB,app,var(X49),X56) )
<=> ( ( X50 = X56 )
& ( X49 = X57 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Var__apps__eq__Var__apps__conv) ).
tff(f908,plain,
spl24_68,
inference(avatar_split_clause,[],[f420,f906]) ).
tff(f906,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(f420,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,[],[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(flattening,[],[f285]) ).
tff(f285,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,[],[f177]) ).
tff(f177,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,[],[f84]) ).
tff(f84,axiom,
! [X56: list(dB),X42: dB,X50: list(dB),X55: dB] :
( ( foldl(dB,dB,app,abs(X55),X50) = foldl(dB,dB,app,abs(X42),X56) )
<=> ( ( X50 = X56 )
& ( X42 = X55 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Abs__apps__eq__Abs__apps__conv) ).
tff(f904,plain,
spl24_67,
inference(avatar_split_clause,[],[f381,f902]) ).
tff(f381,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X58: list(X0),X59: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X59),X58) != X58 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_not__Cons__self2) ).
tff(f900,plain,
spl24_66,
inference(avatar_split_clause,[],[f322,f897]) ).
tff(f322,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Cons) ).
tff(f893,plain,
( spl24_65
| ~ spl24_6
| ~ spl24_22 ),
inference(avatar_split_clause,[],[f641,f634,f549,f890]) ).
tff(f890,plain,
( spl24_65
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_65])]) ).
tff(f549,plain,
( spl24_6
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_6])]) ).
tff(f641,plain,
( sP1(abs(t3))
| ~ spl24_6
| ~ spl24_22 ),
inference(resolution,[],[f635,f551]) ).
tff(f551,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl24_6 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f887,plain,
spl24_64,
inference(avatar_split_clause,[],[f504,f884]) ).
tff(f884,plain,
( spl24_64
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_64])]) ).
tff(f504,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),t1)),
inference(forward_demodulation,[],[f469,f321]) ).
tff(f321,plain,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
t1 = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_T) ).
tff(f469,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)))),
inference(definition_unfolding,[],[f329,f313]) ).
tff(f329,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)))),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_varT) ).
tff(f879,plain,
( spl24_63
| ~ spl24_62 ),
inference(avatar_split_clause,[],[f875,f872,f877]) ).
tff(f877,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(f872,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(f875,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,[],[f873,f446]) ).
tff(f873,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,[],[f872]) ).
tff(f874,plain,
spl24_62,
inference(avatar_split_clause,[],[f483,f872]) ).
tff(f483,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,[],[f394]) ).
tff(f394,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,[],[f216]) ).
tff(f216,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,[],[f159]) ).
tff(f159,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,[],[f22]) ).
tff(f22,axiom,
! [X17: type,X27: nat,X28: fun(nat,type)] :
( ( aa(nat,type,X28,X27) = X17 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(X28),var(X27)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_typing_OVar) ).
tff(f870,plain,
spl24_61,
inference(avatar_split_clause,[],[f422,f868]) ).
tff(f868,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(f422,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,[],[f288]) ).
tff(f866,plain,
spl24_60,
inference(avatar_split_clause,[],[f419,f864]) ).
tff(f864,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(f419,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,[],[f286]) ).
tff(f862,plain,
spl24_59,
inference(avatar_split_clause,[],[f345,f860]) ).
tff(f860,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,[],[f208]) ).
tff(f208,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,[],[f32]) ).
tff(f32,axiom,
! [X7: list(dB)] :
( listsp(dB,it,X7)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lifts__IT) ).
tff(f858,plain,
spl24_58,
inference(avatar_split_clause,[],[f321,f855]) ).
tff(f855,plain,
( spl24_58
<=> ( t1 = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_58])]) ).
tff(f851,plain,
( spl24_57
| ~ spl24_55 ),
inference(avatar_split_clause,[],[f842,f838,f848]) ).
tff(f848,plain,
( spl24_57
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_57])]) ).
tff(f838,plain,
( spl24_55
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_55])]) ).
tff(f842,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),sK2),a))
| ~ spl24_55 ),
inference(forward_demodulation,[],[f840,f446]) ).
tff(f840,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2))
| ~ spl24_55 ),
inference(avatar_component_clause,[],[f838]) ).
tff(f846,plain,
( spl24_56
| ~ spl24_11
| ~ spl24_14 ),
inference(avatar_split_clause,[],[f610,f591,f578,f844]) ).
tff(f844,plain,
( spl24_56
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_56])]) ).
tff(f610,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl24_11
| ~ spl24_14 ),
inference(resolution,[],[f592,f579]) ).
tff(f841,plain,
spl24_55,
inference(avatar_split_clause,[],[f337,f838]) ).
tff(f337,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),sK2)),
inference(cnf_transformation,[],[f252]) ).
tff(f834,plain,
( spl24_54
| ~ spl24_53 ),
inference(avatar_split_clause,[],[f829,f825,f831]) ).
tff(f831,plain,
( spl24_54
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_54])]) ).
tff(f825,plain,
( spl24_53
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_53])]) ).
tff(f829,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,i,t1)),t2),a))
| ~ spl24_53 ),
inference(forward_demodulation,[],[f827,f446]) ).
tff(f827,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t2))
| ~ spl24_53 ),
inference(avatar_component_clause,[],[f825]) ).
tff(f828,plain,
spl24_53,
inference(avatar_split_clause,[],[f320,f825]) ).
tff(f320,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t2)),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t1)),a),t2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_argT) ).
tff(f814,plain,
spl24_52,
inference(avatar_split_clause,[],[f401,f812]) ).
tff(f812,plain,
( spl24_52
<=> ! [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_52])]) ).
tff(f401,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,[],[f273]) ).
tff(f273,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,[],[f165]) ).
tff(f165,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X42: dB,X7: list(dB),X55: dB] :
( ( foldl(dB,dB,app,X55,X7) = foldl(dB,dB,app,X42,X7) )
<=> ( X42 = X55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_apps__eq__tail__conv) ).
tff(f808,plain,
( spl24_51
| ~ spl24_50 ),
inference(avatar_split_clause,[],[f804,f801,f806]) ).
tff(f806,plain,
( spl24_51
<=> ! [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_51])]) ).
tff(f801,plain,
( spl24_50
<=> ! [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_50])]) ).
tff(f804,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl24_50 ),
inference(forward_demodulation,[],[f802,f446]) ).
tff(f802,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) )
| ~ spl24_50 ),
inference(avatar_component_clause,[],[f801]) ).
tff(f803,plain,
spl24_50,
inference(avatar_split_clause,[],[f390,f801]) ).
tff(f390,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,[],[f155]) ).
tff(f155,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,X59: X0] :
( ( X59 = X87 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X59),X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f799,plain,
spl24_49,
inference(avatar_split_clause,[],[f370,f797]) ).
tff(f797,plain,
( spl24_49
<=> ! [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_49])]) ).
tff(f370,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,[],[f210]) ).
tff(f210,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,[],[f137]) ).
tff(f137,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X49: nat,X50: list(dB)] :
( listsp(dB,it,X50)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X49),X50))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_IT_OVar) ).
tff(f791,plain,
( spl24_48
| ~ spl24_47 ),
inference(avatar_split_clause,[],[f787,f784,f789]) ).
tff(f789,plain,
( spl24_48
<=> ! [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_48])]) ).
tff(f784,plain,
( spl24_47
<=> ! [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_47])]) ).
tff(f787,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_47 ),
inference(forward_demodulation,[],[f785,f446]) ).
tff(f785,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl24_47 ),
inference(avatar_component_clause,[],[f784]) ).
tff(f786,plain,
spl24_47,
inference(avatar_split_clause,[],[f367,f784]) ).
tff(f367,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,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/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f782,plain,
spl24_46,
inference(avatar_split_clause,[],[f350,f780]) ).
tff(f780,plain,
( spl24_46
<=> ! [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_46])]) ).
tff(f350,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f763,plain,
spl24_45,
inference(avatar_split_clause,[],[f405,f761]) ).
tff(f761,plain,
( spl24_45
<=> ! [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_45])]) ).
tff(f405,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,[],[f167]) ).
tff(f167,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,[],[f91]) ).
tff(f91,axiom,
! [X56: list(dB),X55: dB,X7: list(dB),X49: nat] : ( foldl(dB,dB,app,var(X49),X7) != foldl(dB,dB,app,abs(X55),X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Var__apps__neq__Abs__apps) ).
tff(f759,plain,
spl24_44,
inference(avatar_split_clause,[],[f389,f757]) ).
tff(f757,plain,
( spl24_44
<=> ! [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_44])]) ).
tff(f389,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,[],[f154]) ).
tff(f154,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,X59: X0,X84: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X84))
| ~ pp(aa(X0,bool,X84,X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f755,plain,
spl24_43,
inference(avatar_split_clause,[],[f379,f753]) ).
tff(f753,plain,
( spl24_43
<=> ! [X2: dB,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != abs(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_43])]) ).
tff(f379,plain,
! [X2: dB,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != abs(X2) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: dB,X1: dB,X2: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != abs(X2) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X73: dB,X74: dB,X72: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X74),X73) != abs(X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_dB_Osimps_I9_J) ).
tff(f751,plain,
spl24_42,
inference(avatar_split_clause,[],[f377,f749]) ).
tff(f749,plain,
( spl24_42
<=> ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_42])]) ).
tff(f377,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X37: nat,X43: dB,X44: dB] : ( var(X37) != aa(dB,dB,aa(dB,fun(dB,dB),app,X44),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_dB_Osimps_I5_J) ).
tff(f746,plain,
( spl24_41
| ~ spl24_40 ),
inference(avatar_split_clause,[],[f742,f739,f744]) ).
tff(f744,plain,
( spl24_41
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_41])]) ).
tff(f739,plain,
( spl24_40
<=> ! [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_40])]) ).
tff(f742,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl24_40 ),
inference(forward_demodulation,[],[f740,f446]) ).
tff(f740,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_40 ),
inference(avatar_component_clause,[],[f739]) ).
tff(f741,plain,
spl24_40,
inference(avatar_split_clause,[],[f369,f739]) ).
tff(f369,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,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/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f736,plain,
( spl24_39
| ~ spl24_38 ),
inference(avatar_split_clause,[],[f732,f729,f734]) ).
tff(f734,plain,
( spl24_39
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_39])]) ).
tff(f729,plain,
( spl24_38
<=> ! [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_38])]) ).
tff(f732,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl24_38 ),
inference(forward_demodulation,[],[f730,f446]) ).
tff(f730,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl24_38 ),
inference(avatar_component_clause,[],[f729]) ).
tff(f731,plain,
spl24_38,
inference(avatar_split_clause,[],[f368,f729]) ).
tff(f368,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,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/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f727,plain,
spl24_37,
inference(avatar_split_clause,[],[f348,f725]) ).
tff(f725,plain,
( spl24_37
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_37])]) ).
tff(f348,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f717,plain,
( spl24_36
| ~ spl24_35 ),
inference(avatar_split_clause,[],[f713,f710,f715]) ).
tff(f715,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(f710,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(f713,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
| ~ spl24_35 ),
inference(forward_demodulation,[],[f711,f446]) ).
tff(f711,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl24_35 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f712,plain,
spl24_35,
inference(avatar_split_clause,[],[f482,f710]) ).
tff(f482,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f388]) ).
tff(f388,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,[],[f153]) ).
tff(f153,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,X59: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X59),X87))
| ( X59 != X87 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f708,plain,
spl24_34,
inference(avatar_split_clause,[],[f346,f706]) ).
tff(f706,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(f346,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,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,[],[f83]) ).
tff(f83,axiom,
! [X32: dB] :
( pp(aa(dB,bool,it,X32))
=> pp(aa(dB,bool,it,abs(X32))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Lambda) ).
tff(f704,plain,
spl24_33,
inference(avatar_split_clause,[],[f339,f701]) ).
tff(f701,plain,
( spl24_33
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_33])]) ).
tff(f339,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK3)),
inference(cnf_transformation,[],[f254]) ).
tff(f699,plain,
( spl24_32
| ~ spl24_7
| ~ spl24_14 ),
inference(avatar_split_clause,[],[f613,f591,f554,f696]) ).
tff(f696,plain,
( spl24_32
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_32])]) ).
tff(f613,plain,
( sP1(ua)
| ~ spl24_7
| ~ spl24_14 ),
inference(resolution,[],[f592,f556]) ).
tff(f694,plain,
spl24_31,
inference(avatar_split_clause,[],[f319,f691]) ).
tff(f691,plain,
( spl24_31
<=> pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_31])]) ).
tff(f319,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_argsT) ).
tff(f688,plain,
( spl24_30
| ~ spl24_29 ),
inference(avatar_split_clause,[],[f683,f679,f685]) ).
tff(f685,plain,
( spl24_30
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_30])]) ).
tff(f679,plain,
( spl24_29
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_29])]) ).
tff(f683,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ~ spl24_29 ),
inference(forward_demodulation,[],[f681,f446]) ).
tff(f681,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1))
| ~ spl24_29 ),
inference(avatar_component_clause,[],[f679]) ).
tff(f682,plain,
spl24_29,
inference(avatar_split_clause,[],[f318,f679]) ).
tff(f318,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_uT) ).
tff(f676,plain,
( spl24_28
| ~ spl24_27 ),
inference(avatar_split_clause,[],[f671,f667,f673]) ).
tff(f673,plain,
( spl24_28
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_28])]) ).
tff(f667,plain,
( spl24_27
<=> pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_27])]) ).
tff(f671,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua))
| ~ spl24_27 ),
inference(forward_demodulation,[],[f669,f446]) ).
tff(f669,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1))
| ~ spl24_27 ),
inference(avatar_component_clause,[],[f667]) ).
tff(f670,plain,
spl24_27,
inference(avatar_split_clause,[],[f317,f667]) ).
tff(f317,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),typing(ea),ua),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Var_I4_J) ).
tff(f665,plain,
spl24_26,
inference(avatar_split_clause,[],[f478,f663]) ).
tff(f663,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(f478,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,[],[f261]) ).
tff(f660,plain,
( spl24_25
| ~ spl24_8
| ~ spl24_14 ),
inference(avatar_split_clause,[],[f612,f591,f559,f657]) ).
tff(f657,plain,
( spl24_25
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).
tff(f612,plain,
( sP1(u)
| ~ spl24_8
| ~ spl24_14 ),
inference(resolution,[],[f592,f561]) ).
tff(f655,plain,
~ spl24_24,
inference(avatar_split_clause,[],[f308,f652]) ).
tff(f308,plain,
~ pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts)),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts)),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts)),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
pp(aa(list(type),bool,typings(shift(type,e,zero_zero(nat),foldr(type,type,fun1,ts,t)),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))),ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f649,plain,
spl24_23,
inference(avatar_split_clause,[],[f493,f647]) ).
tff(f647,plain,
( spl24_23
<=> ! [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_23])]) ).
tff(f493,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f437]) ).
tff(f437,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,[],[f229]) ).
tff(f229,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,[],[f184]) ).
tff(f184,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,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X17: X0,X8: fun(nat,X0),X18: nat,X5: nat] :
( ( X5 = X18 )
=> ( aa(nat,X0,shift(X0,X8,X5,X17),X18) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_shift__eq) ).
tff(f636,plain,
spl24_22,
inference(avatar_split_clause,[],[f477,f634]) ).
tff(f477,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,[],[f261]) ).
tff(f632,plain,
spl24_21,
inference(avatar_split_clause,[],[f364,f630]) ).
tff(f630,plain,
( spl24_21
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_21])]) ).
tff(f364,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X9: list(X0)] : ( map(X0,X0,combi(X0),X9) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_map__ident) ).
tff(f628,plain,
spl24_20,
inference(avatar_split_clause,[],[f356,f626]) ).
tff(f356,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f623,plain,
( spl24_19
| ~ spl24_6
| ~ spl24_14 ),
inference(avatar_split_clause,[],[f611,f591,f549,f620]) ).
tff(f620,plain,
( spl24_19
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_19])]) ).
tff(f611,plain,
( sP1(t3)
| ~ spl24_6
| ~ spl24_14 ),
inference(resolution,[],[f592,f551]) ).
tff(f609,plain,
spl24_18,
inference(avatar_split_clause,[],[f375,f607]) ).
tff(f607,plain,
( spl24_18
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_18])]) ).
tff(f375,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X19: nat,X20: nat] :
( ( var(X20) = var(X19) )
<=> ( X19 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I1_J) ).
tff(f605,plain,
spl24_17,
inference(avatar_split_clause,[],[f373,f603]) ).
tff(f603,plain,
( spl24_17
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_17])]) ).
tff(f373,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X70: dB,X71: dB] :
( ( abs(X71) = abs(X70) )
<=> ( X70 = X71 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_dB_Osimps_I3_J) ).
tff(f601,plain,
spl24_16,
inference(avatar_split_clause,[],[f363,f599]) ).
tff(f599,plain,
( spl24_16
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_16])]) ).
tff(f363,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,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/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f597,plain,
spl24_15,
inference(avatar_split_clause,[],[f359,f595]) ).
tff(f359,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f126,f249,f248]) ).
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,[],[f94]) ).
tff(f94,axiom,
! [X47: dB] :
( pp(aa(dB,bool,it,X47))
<=> ( ? [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) = X47 ) )
| ? [X79: dB] :
( pp(aa(dB,bool,it,X79))
& ( abs(X79) = X47 ) )
| ? [X77: list(dB),X78: nat] :
( listsp(dB,it,X77)
& ( foldl(dB,dB,app,var(X78),X77) = X47 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_IT_Osimps) ).
tff(f593,plain,
spl24_14,
inference(avatar_split_clause,[],[f358,f591]) ).
tff(f358,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f266]) ).
tff(f589,plain,
( spl24_13
| spl24_1
| ~ spl24_10 ),
inference(avatar_split_clause,[],[f572,f568,f526,f587]) ).
tff(f587,plain,
( spl24_13
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_13])]) ).
tff(f526,plain,
( spl24_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_1])]) ).
tff(f572,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl24_1
| ~ spl24_10 ),
inference(superposition,[],[f528,f569]) ).
tff(f528,plain,
( ~ pp(fFalse)
| spl24_1 ),
inference(avatar_component_clause,[],[f526]) ).
tff(f584,plain,
spl24_12,
inference(avatar_split_clause,[],[f362,f582]) ).
tff(f582,plain,
( spl24_12
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_12])]) ).
tff(f362,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X63: fun(X0,bool)] : ( collect(X0,X63) = X63 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f580,plain,
spl24_11,
inference(avatar_split_clause,[],[f341,f578]) ).
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,[],[f28]) ).
tff(f28,axiom,
! [X30: nat] : pp(aa(dB,bool,it,var(X30))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Var__IT) ).
tff(f570,plain,
spl24_10,
inference(avatar_split_clause,[],[f342,f568]) ).
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/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f566,plain,
spl24_9,
inference(avatar_split_clause,[],[f340,f564]) ).
tff(f564,plain,
( spl24_9
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_9])]) ).
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,[],[f41]) ).
tff(f41,axiom,
! [X37: nat] : ( zero_zero(nat) = dB_size(var(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_dB_Osize_I1_J) ).
tff(f562,plain,
spl24_8,
inference(avatar_split_clause,[],[f316,f559]) ).
tff(f316,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
tff(f557,plain,
spl24_7,
inference(avatar_split_clause,[],[f315,f554]) ).
tff(f315,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Var_I3_J) ).
tff(f552,plain,
spl24_6,
inference(avatar_split_clause,[],[f314,f549]) ).
tff(f314,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096IT_At_096) ).
tff(f547,plain,
spl24_5,
inference(avatar_split_clause,[],[f360,f545]) ).
tff(f545,plain,
( spl24_5
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_5])]) ).
tff(f360,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X72: dB,X37: nat] : ( var(X37) != abs(X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_dB_Osimps_I6_J) ).
tff(f543,plain,
spl24_4,
inference(avatar_split_clause,[],[f353,f541]) ).
tff(f541,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,[],[f261]) ).
tff(f539,plain,
spl24_3,
inference(avatar_split_clause,[],[f312,f536]) ).
tff(f536,plain,
( spl24_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).
tff(f312,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f534,plain,
spl24_2,
inference(avatar_split_clause,[],[f311,f531]) ).
tff(f531,plain,
( spl24_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).
tff(f311,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f529,plain,
~ spl24_1,
inference(avatar_split_clause,[],[f309,f526]) ).
tff(f309,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL815_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:18:14 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % (13058)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39 % (13059)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % (13063)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)
% 0.13/0.40 % Exception at run slice level
% 0.13/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.40 % (13061)WARNING: value z3 for option sas not known
% 0.13/0.40 % (13062)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.40 % (13060)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.40 % (13065)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)
% 0.13/0.40 % (13061)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)
% 0.13/0.40 % (13064)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)
% 0.13/0.41 % Exception at run slice level
% 0.13/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.41 % (13065)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.42 % Exception at run slice level
% 0.13/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.43 % (13067)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)
% 0.13/0.43 % (13066)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.43 % (13068)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)
% 0.13/0.43 % (13067)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.43 % (13066)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.43 % Exception at run slice level
% 0.13/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (13069)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)
% 0.21/0.49 % (13063)First to succeed.
% 0.21/0.52 % (13063)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (13063)------------------------------
% 0.21/0.52 % (13063)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.52 % (13063)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (13063)Memory used [KB]: 2471
% 0.21/0.52 % (13063)Time elapsed: 0.124 s
% 0.21/0.52 % (13063)Instructions burned: 244 (million)
% 0.21/0.52 % (13063)------------------------------
% 0.21/0.52 % (13063)------------------------------
% 0.21/0.52 % (13058)Success in time 0.158 s
%------------------------------------------------------------------------------