TSTP Solution File: LCL806_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL806_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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:32 EDT 2024
% Result : Theorem 1.31s 0.60s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 400
% Syntax : Number of formulae : 980 ( 296 unt; 90 typ; 0 def)
% Number of atoms : 2133 ( 553 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1979 ( 736 ~; 725 |; 179 &)
% ( 212 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 28 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 86 ( 39 >; 47 *; 0 +; 0 <<)
% Number of predicates : 189 ( 187 usr; 182 prp; 0-3 aty)
% Number of functors : 80 ( 80 usr; 35 con; 0-6 aty)
% Number of variables : 2056 (1913 !; 101 ?;2056 :)
% ( 42 !>; 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(fun(X0,fun(X1,X2)),fun(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(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
typing: fun(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,
fAll:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_27,type,
fFalse: bool ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_31,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_33,type,
t2: type ).
tff(func_def_34,type,
t1: type ).
tff(func_def_35,type,
t_a: type ).
tff(func_def_36,type,
t: type ).
tff(func_def_37,type,
ts: list(type) ).
tff(func_def_38,type,
a: dB ).
tff(func_def_39,type,
as: list(dB) ).
tff(func_def_40,type,
b: dB ).
tff(func_def_41,type,
bs: list(dB) ).
tff(func_def_42,type,
e: fun(nat,type) ).
tff(func_def_43,type,
ea: fun(nat,type) ).
tff(func_def_44,type,
i: nat ).
tff(func_def_45,type,
ia: nat ).
tff(func_def_46,type,
n: nat ).
tff(func_def_47,type,
rs: list(dB) ).
tff(func_def_48,type,
t3: dB ).
tff(func_def_49,type,
u: dB ).
tff(func_def_50,type,
ua: dB ).
tff(func_def_51,type,
sK2: fun(nat,type) ).
tff(func_def_52,type,
sK3: type ).
tff(func_def_53,type,
sK4: dB ).
tff(func_def_54,type,
sK5: nat ).
tff(func_def_55,type,
sK6: type ).
tff(func_def_56,type,
sK7: type ).
tff(func_def_57,type,
sK8: list(type) ).
tff(func_def_58,type,
sK9: dB > dB ).
tff(func_def_59,type,
sK10: dB > list(dB) ).
tff(func_def_60,type,
sK11: dB > nat ).
tff(func_def_61,type,
sK12: dB > dB ).
tff(func_def_62,type,
sK13: dB > dB ).
tff(func_def_63,type,
sK14: dB > list(dB) ).
tff(func_def_64,type,
sK15: ( dB * fun(nat,type) ) > type ).
tff(func_def_65,type,
sK16: ( dB * fun(nat,type) ) > type ).
tff(func_def_66,type,
sK17: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_67,type,
sK18: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_68,type,
sK19: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_69,type,
sK20: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_70,type,
sK21: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_71,type,
sK22: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_72,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_73,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_74,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_75,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_76,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_77,type,
sK28: ( 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(f2575,plain,
$false,
inference(avatar_sat_refutation,[],[f529,f534,f539,f544,f548,f552,f557,f562,f567,f572,f577,f581,f585,f598,f602,f607,f611,f615,f619,f624,f628,f644,f648,f652,f659,f671,f676,f681,f685,f693,f697,f701,f705,f709,f713,f717,f724,f730,f734,f738,f758,f762,f766,f770,f774,f778,f807,f811,f815,f822,f826,f831,f835,f839,f846,f850,f858,f863,f868,f872,f876,f880,f897,f901,f905,f909,f921,f925,f936,f940,f944,f948,f960,f967,f973,f977,f988,f992,f996,f1008,f1012,f1029,f1034,f1038,f1042,f1046,f1058,f1062,f1066,f1078,f1082,f1086,f1090,f1094,f1098,f1179,f1183,f1187,f1195,f1201,f1206,f1210,f1215,f1354,f1359,f1364,f1374,f1389,f1393,f1397,f1421,f1426,f1431,f1449,f1453,f1457,f1461,f1465,f1505,f1516,f1523,f1533,f1537,f1545,f1550,f1556,f1561,f1579,f1583,f1591,f1595,f1612,f1622,f1626,f1631,f1635,f1661,f1675,f1686,f1698,f1703,f1726,f1730,f1741,f1752,f1769,f1797,f1811,f1815,f1825,f1838,f1848,f1852,f1873,f1880,f1885,f1892,f1897,f1906,f1911,f1915,f1919,f1923,f1982,f1987,f1993,f2015,f2020,f2469,f2498,f2502,f2520,f2528,f2539,f2544,f2548,f2573,f2574]) ).
tff(f2574,plain,
( ~ spl29_4
| ~ spl29_7
| spl29_8
| ~ spl29_20
| ~ spl29_163
| ~ spl29_180 ),
inference(avatar_split_clause,[],[f2569,f2546,f1913,f621,f559,f554,f541]) ).
tff(f541,plain,
( spl29_4
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).
tff(f554,plain,
( spl29_7
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).
tff(f559,plain,
( spl29_8
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).
tff(f621,plain,
( spl29_20
<=> ( fTrue = aa(dB,bool,it,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).
tff(f1913,plain,
( spl29_163
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_163])]) ).
tff(f2546,plain,
( spl29_180
<=> ! [X0: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_180])]) ).
tff(f2569,plain,
( ~ pp(fTrue)
| ~ spl29_7
| spl29_8
| ~ spl29_20
| ~ spl29_163
| ~ spl29_180 ),
inference(duplicate_literal_removal,[],[f2568]) ).
tff(f2568,plain,
( ~ pp(fTrue)
| ~ pp(fTrue)
| ~ spl29_7
| spl29_8
| ~ spl29_20
| ~ spl29_163
| ~ spl29_180 ),
inference(forward_demodulation,[],[f2567,f1960]) ).
tff(f1960,plain,
( ( fTrue = aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t) )
| ~ spl29_7
| ~ spl29_163 ),
inference(resolution,[],[f1914,f556]) ).
tff(f556,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
| ~ spl29_7 ),
inference(avatar_component_clause,[],[f554]) ).
tff(f1914,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| ~ spl29_163 ),
inference(avatar_component_clause,[],[f1913]) ).
tff(f2567,plain,
( ~ pp(fTrue)
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
| spl29_8
| ~ spl29_20
| ~ spl29_180 ),
inference(forward_demodulation,[],[f2556,f623]) ).
tff(f623,plain,
( ( fTrue = aa(dB,bool,it,sK4) )
| ~ spl29_20 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f2556,plain,
( ~ pp(aa(dB,bool,it,sK4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
| spl29_8
| ~ spl29_180 ),
inference(resolution,[],[f2547,f561]) ).
tff(f561,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
| spl29_8 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f2547,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t)) )
| ~ spl29_180 ),
inference(avatar_component_clause,[],[f2546]) ).
tff(f2573,plain,
( spl29_181
| ~ spl29_24
| ~ spl29_41 ),
inference(avatar_split_clause,[],[f779,f756,f650,f2571]) ).
tff(f2571,plain,
( spl29_181
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK10(X0))
| ~ sP1(X0)
| sP1(abs(sK9(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_181])]) ).
tff(f650,plain,
( spl29_24
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_24])]) ).
tff(f756,plain,
( spl29_41
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK9(X0)))
| listsp(dB,it,sK10(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_41])]) ).
tff(f779,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK10(X0))
| ~ sP1(X0)
| sP1(abs(sK9(X0))) )
| ~ spl29_24
| ~ spl29_41 ),
inference(resolution,[],[f757,f651]) ).
tff(f651,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl29_24 ),
inference(avatar_component_clause,[],[f650]) ).
tff(f757,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| sP0(X0)
| listsp(dB,it,sK10(X0))
| ~ sP1(X0) )
| ~ spl29_41 ),
inference(avatar_component_clause,[],[f756]) ).
tff(f2548,plain,
( spl29_180
| ~ spl29_27
| ~ spl29_144 ),
inference(avatar_split_clause,[],[f1745,f1739,f673,f2546]) ).
tff(f673,plain,
( spl29_27
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).
tff(f1739,plain,
( spl29_144
<=> ! [X4: nat,X3: dB,X2: type,X1: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_144])]) ).
tff(f1745,plain,
( ! [X0: dB] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t))
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5))) )
| ~ spl29_27
| ~ spl29_144 ),
inference(resolution,[],[f1740,f675]) ).
tff(f675,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b),sK3))
| ~ spl29_27 ),
inference(avatar_component_clause,[],[f673]) ).
tff(f1740,plain,
( ! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4))) )
| ~ spl29_144 ),
inference(avatar_component_clause,[],[f1739]) ).
tff(f2544,plain,
( spl29_179
| ~ spl29_27
| ~ spl29_38 ),
inference(avatar_split_clause,[],[f751,f728,f673,f2541]) ).
tff(f2541,plain,
( spl29_179
<=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_179])]) ).
tff(f728,plain,
( spl29_38
<=> ! [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,[spl29_38])]) ).
tff(f751,plain,
( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b)))
| ~ spl29_27
| ~ spl29_38 ),
inference(resolution,[],[f729,f675]) ).
tff(f729,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl29_38 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f2539,plain,
( spl29_178
| ~ spl29_16
| ~ spl29_41 ),
inference(avatar_split_clause,[],[f780,f756,f605,f2537]) ).
tff(f2537,plain,
( spl29_178
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK10(X0))
| ~ sP1(X0)
| sP1(sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_178])]) ).
tff(f605,plain,
( spl29_16
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).
tff(f780,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK10(X0))
| ~ sP1(X0)
| sP1(sK9(X0)) )
| ~ spl29_16
| ~ spl29_41 ),
inference(resolution,[],[f757,f606]) ).
tff(f606,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl29_16 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f2528,plain,
( spl29_176
| spl29_177
| ~ spl29_18
| ~ spl29_38 ),
inference(avatar_split_clause,[],[f752,f728,f613,f2526,f2522]) ).
tff(f2522,plain,
( spl29_176
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_176])]) ).
tff(f2526,plain,
( spl29_177
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_177])]) ).
tff(f613,plain,
( spl29_18
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_18])]) ).
tff(f752,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl29_18
| ~ spl29_38 ),
inference(superposition,[],[f729,f614]) ).
tff(f614,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl29_18 ),
inference(avatar_component_clause,[],[f613]) ).
tff(f2520,plain,
( spl29_175
| ~ spl29_1
| ~ spl29_172 ),
inference(avatar_split_clause,[],[f2483,f2467,f526,f2517]) ).
tff(f2517,plain,
( spl29_175
<=> sP1(abs(abs(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_175])]) ).
tff(f526,plain,
( spl29_1
<=> pp(aa(dB,bool,it,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
tff(f2467,plain,
( spl29_172
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_172])]) ).
tff(f2483,plain,
( sP1(abs(abs(sK4)))
| ~ spl29_1
| ~ spl29_172 ),
inference(resolution,[],[f2468,f528]) ).
tff(f528,plain,
( pp(aa(dB,bool,it,sK4))
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f526]) ).
tff(f2468,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl29_172 ),
inference(avatar_component_clause,[],[f2467]) ).
tff(f2502,plain,
( spl29_174
| ~ spl29_50
| ~ spl29_81 ),
inference(avatar_split_clause,[],[f1022,f1010,f819,f2500]) ).
tff(f2500,plain,
( spl29_174
<=> ! [X0: list(dB)] : ( rs = list_case(list(dB),dB,X0,cons(dB),rs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_174])]) ).
tff(f819,plain,
( spl29_50
<=> ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_50])]) ).
tff(f1010,plain,
( spl29_81
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_81])]) ).
tff(f1022,plain,
( ! [X0: list(dB)] : ( rs = list_case(list(dB),dB,X0,cons(dB),rs) )
| ~ spl29_50
| ~ spl29_81 ),
inference(superposition,[],[f1011,f821]) ).
tff(f821,plain,
( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
| ~ spl29_50 ),
inference(avatar_component_clause,[],[f819]) ).
tff(f1011,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) )
| ~ spl29_81 ),
inference(avatar_component_clause,[],[f1010]) ).
tff(f2498,plain,
( spl29_173
| ~ spl29_13
| ~ spl29_18 ),
inference(avatar_split_clause,[],[f638,f613,f583,f2496]) ).
tff(f2496,plain,
( spl29_173
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_173])]) ).
tff(f583,plain,
( spl29_13
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_13])]) ).
tff(f638,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl29_13
| ~ spl29_18 ),
inference(superposition,[],[f614,f584]) ).
tff(f584,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl29_13 ),
inference(avatar_component_clause,[],[f583]) ).
tff(f2469,plain,
( spl29_172
| ~ spl29_24
| ~ spl29_28 ),
inference(avatar_split_clause,[],[f686,f679,f650,f2467]) ).
tff(f679,plain,
( spl29_28
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_28])]) ).
tff(f686,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl29_24
| ~ spl29_28 ),
inference(resolution,[],[f680,f651]) ).
tff(f680,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl29_28 ),
inference(avatar_component_clause,[],[f679]) ).
tff(f2020,plain,
( spl29_171
| ~ spl29_14
| ~ spl29_38 ),
inference(avatar_split_clause,[],[f744,f728,f596,f2017]) ).
tff(f2017,plain,
( spl29_171
<=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_171])]) ).
tff(f596,plain,
( spl29_14
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).
tff(f744,plain,
( pp(aa(fun(dB,bool),bool,fEx(dB),it))
| ~ spl29_14
| ~ spl29_38 ),
inference(resolution,[],[f729,f597]) ).
tff(f597,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl29_14 ),
inference(avatar_component_clause,[],[f596]) ).
tff(f2015,plain,
( spl29_170
| ~ spl29_13 ),
inference(avatar_split_clause,[],[f586,f583,f2013]) ).
tff(f2013,plain,
( spl29_170
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_170])]) ).
tff(f586,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl29_13 ),
inference(superposition,[],[f584,f584]) ).
tff(f1993,plain,
( spl29_169
| ~ spl29_7
| ~ spl29_38 ),
inference(avatar_split_clause,[],[f750,f728,f554,f1990]) ).
tff(f1990,plain,
( spl29_169
<=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_169])]) ).
tff(f750,plain,
( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4)))
| ~ spl29_7
| ~ spl29_38 ),
inference(resolution,[],[f729,f556]) ).
tff(f1987,plain,
( spl29_168
| ~ spl29_22
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f666,f650,f642,f1985]) ).
tff(f1985,plain,
( spl29_168
<=> ! [X0: dB] :
( sP1(abs(sK13(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_168])]) ).
tff(f642,plain,
( spl29_22
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK13(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).
tff(f666,plain,
( ! [X0: dB] :
( sP1(abs(sK13(X0)))
| ~ sP0(X0) )
| ~ spl29_22
| ~ spl29_24 ),
inference(resolution,[],[f651,f643]) ).
tff(f643,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK13(X0)))
| ~ sP0(X0) )
| ~ spl29_22 ),
inference(avatar_component_clause,[],[f642]) ).
tff(f1982,plain,
( spl29_166
| ~ spl29_167
| ~ spl29_13 ),
inference(avatar_split_clause,[],[f594,f583,f1979,f1976]) ).
tff(f1976,plain,
( spl29_166
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_166])]) ).
tff(f1979,plain,
( spl29_167
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_167])]) ).
tff(f594,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl29_13 ),
inference(equality_factoring,[],[f584]) ).
tff(f1923,plain,
( spl29_165
| ~ spl29_17
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f660,f650,f609,f1921]) ).
tff(f1921,plain,
( spl29_165
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_165])]) ).
tff(f609,plain,
( spl29_17
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).
tff(f660,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl29_17
| ~ spl29_24 ),
inference(resolution,[],[f651,f610]) ).
tff(f610,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl29_17 ),
inference(avatar_component_clause,[],[f609]) ).
tff(f1919,plain,
( spl29_164
| ~ spl29_16
| ~ spl29_22 ),
inference(avatar_split_clause,[],[f653,f642,f605,f1917]) ).
tff(f1917,plain,
( spl29_164
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK13(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_164])]) ).
tff(f653,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK13(X0)) )
| ~ spl29_16
| ~ spl29_22 ),
inference(resolution,[],[f643,f606]) ).
tff(f1915,plain,
( spl29_163
| spl29_2
| ~ spl29_13 ),
inference(avatar_split_clause,[],[f587,f583,f531,f1913]) ).
tff(f531,plain,
( spl29_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
tff(f587,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl29_2
| ~ spl29_13 ),
inference(superposition,[],[f533,f584]) ).
tff(f533,plain,
( ~ pp(fFalse)
| spl29_2 ),
inference(avatar_component_clause,[],[f531]) ).
tff(f1911,plain,
( ~ spl29_162
| spl29_8
| ~ spl29_17 ),
inference(avatar_split_clause,[],[f635,f609,f559,f1908]) ).
tff(f1908,plain,
( spl29_162
<=> sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_162])]) ).
tff(f635,plain,
( ~ sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))
| spl29_8
| ~ spl29_17 ),
inference(resolution,[],[f610,f561]) ).
tff(f1906,plain,
( spl29_161
| ~ spl29_122
| ~ spl29_158 ),
inference(avatar_split_clause,[],[f1887,f1882,f1531,f1903]) ).
tff(f1903,plain,
( spl29_161
<=> listsp(dB,it,rs) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_161])]) ).
tff(f1531,plain,
( spl29_122
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_122])]) ).
tff(f1882,plain,
( spl29_158
<=> 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),
introduced(avatar_definition,[new_symbols(naming,[spl29_158])]) ).
tff(f1887,plain,
( listsp(dB,it,rs)
| ~ spl29_122
| ~ spl29_158 ),
inference(resolution,[],[f1884,f1532]) ).
tff(f1532,plain,
( ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| listsp(X0,X2,X3) )
| ~ spl29_122 ),
inference(avatar_component_clause,[],[f1531]) ).
tff(f1884,plain,
( 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fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,typ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| ~ spl29_158 ),
inference(avatar_component_clause,[],[f1882]) ).
tff(f1897,plain,
spl29_160,
inference(avatar_split_clause,[],[f352,f1894]) ).
tff(f1894,plain,
( spl29_160
<=> 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introduced(avatar_definition,[new_symbols(naming,[spl29_160])]) ).
tff(f352,plain,
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inference(cnf_transformation,[],[f41]) ).
tff(f41,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(n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aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__096listsp_A_I_Ft_O_A_IALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_A_G_A_IEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_J_Aas_096) ).
tff(f1892,plain,
spl29_159,
inference(avatar_split_clause,[],[f351,f1889]) ).
tff(f1889,plain,
( spl29_159
<=> 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introduced(avatar_definition,[new_symbols(naming,[spl29_159])]) ).
tff(f351,plain,
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inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))))),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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)))),bs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Cons_I2_J) ).
tff(f1885,plain,
spl29_158,
inference(avatar_split_clause,[],[f350,f1882]) ).
tff(f350,plain,
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inference(cnf_transformation,[],[f45]) ).
tff(f45,axiom,
listsp(dB,aa(fun(dB,bool),fun(dB,bool),aa(fun(dB,fun(bool,bool)),fun(fun(dB,bool),fun(dB,bool)),combs(dB,bool,bool),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fconj),it)),aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,typ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file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Var_Ohyps) ).
tff(f1880,plain,
spl29_157,
inference(avatar_split_clause,[],[f349,f1877]) ).
tff(f1877,plain,
( spl29_157
<=> 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),
introduced(avatar_definition,[new_symbols(naming,[spl29_157])]) ).
tff(f349,plain,
listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(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inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
listsp(dB,aa(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool),aa(fun(fun(fun(nat,type),bool),bool),fun(fun(dB,fun(fun(nat,type),bool)),fun(dB,bool)),combb(fun(fun(nat,type),bool),bool,dB),fAll(fun(nat,type))),aa(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool)),aa(fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),fun(fun(dB,fun(fun(nat,type),fun(type,bool))),fun(dB,fun(fun(nat,type),bool))),combb(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool),dB),aa(fun(fun(type,bool),bool),fun(fun(fun(nat,type),fun(type,bool)),fun(fun(nat,type),bool)),combb(fun(type,bool),bool,fun(nat,type)),fAll(type))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(dB,fun(fun(nat,type),fun(type,bool)))),combb(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool)),dB),aa(fun(fun(type,fun(dB,bool)),fun(type,bool)),fun(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(fun(nat,type),fun(type,bool))),combb(fun(type,fun(dB,bool)),fun(type,bool),fun(nat,type)),aa(fun(fun(dB,bool),bool),fun(fun(type,fun(dB,bool)),fun(type,bool)),combb(fun(dB,bool),bool,type),fAll(dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool)))),aa(fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,bool))))),combb(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool))),dB),aa(fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool)),fun(nat,type)),aa(fun(fun(dB,fun(nat,bool)),fun(dB,bool)),fun(fun(type,fun(dB,fun(nat,bool))),fun(type,fun(dB,bool))),combb(fun(dB,fun(nat,bool)),fun(dB,bool),type),aa(fun(fun(nat,bool),bool),fun(fun(dB,fun(nat,bool)),fun(dB,bool)),combb(fun(nat,bool),bool,dB),fAll(nat))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),combs(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(dB,fun(nat,bool))))),dB),combs(fun(nat,type),fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(dB,fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(type,fun(dB,fun(nat,bool)))),fun(nat,type)),combc(type,fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),aa(fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))))),combb(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),dB),aa(fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),fun(fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))))),combb(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(nat,type)),aa(fun(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(type,fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,bool),fun(nat,bool)),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),type),combb(fun(nat,bool),fun(nat,bool),dB)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(dB,fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool)))),dB),aa(fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),fun(fun(nat,type),fun(type,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(type,fun(nat,fun(bool,bool))),fun(type,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),type),combs(nat,bool,bool)))),aa(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),aa(fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),fun(fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))))),combb(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool)))),dB),aa(fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),fun(fun(fun(nat,type),fun(type,fun(nat,bool))),fun(fun(nat,type),fun(type,fun(nat,fun(bool,bool))))),combb(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool))),fun(nat,type)),aa(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(type,fun(nat,bool)),fun(type,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),type),aa(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fimplies)))),aa(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(type,fun(nat,bool))))),combb(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool))),dB),aa(fun(fun(nat,fun(type,bool)),fun(type,fun(nat,bool))),fun(fun(fun(nat,type),fun(nat,fun(type,bool))),fun(fun(nat,type),fun(type,fun(nat,bool)))),combb(fun(nat,fun(type,bool)),fun(type,fun(nat,bool)),fun(nat,type)),combc(nat,type,bool))),aa(fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),fun(dB,fun(fun(nat,type),fun(nat,fun(type,bool)))),combc(fun(nat,type),dB,fun(nat,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool)))),aa(fun(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),fun(fun(nat,type),fun(dB,fun(nat,fun(type,bool))))),combb(fun(nat,fun(dB,fun(type,bool))),fun(dB,fun(nat,fun(type,bool))),fun(nat,type)),combc(nat,dB,fun(type,bool))),aa(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool)))),aa(fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),fun(fun(fun(nat,type),fun(nat,fun(nat,type))),fun(fun(nat,type),fun(nat,fun(dB,fun(type,bool))))),combb(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool))),fun(nat,type)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,fun(nat,type)),fun(nat,fun(dB,fun(type,bool)))),combb(fun(nat,type),fun(dB,fun(type,bool)),nat),typing)),aa(type,fun(fun(nat,type),fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),fun(type,fun(fun(nat,type),fun(nat,fun(nat,type)))),combc(fun(nat,type),type,fun(nat,fun(nat,type))),aa(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type)))),aa(fun(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type)))),fun(fun(fun(nat,type),fun(nat,fun(type,fun(nat,type)))),fun(fun(nat,type),fun(type,fun(nat,fun(nat,type))))),combb(fun(nat,fun(type,fun(nat,type))),fun(type,fun(nat,fun(nat,type))),fun(nat,type)),combc(nat,type,fun(nat,type))),shift(type))),t))))))))))),aa(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(fun(fun(nat,type),fun(dB,fun(nat,bool))),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)),fun(nat,type)),aa(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),combs(dB,fun(nat,bool),fun(nat,bool)),aa(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat)),aa(fun(dB,bool),fun(dB,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies),it))))),aa(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(dB,fun(nat,bool))),fun(dB,fun(fun(nat,type),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool))),dB),aa(fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(dB,fun(nat,bool)),fun(fun(nat,type),fun(dB,fun(nat,bool)))),combc(fun(nat,type),fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),aa(fun(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,type),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))))),combb(fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(nat,bool)),fun(dB,fun(nat,bool))),fun(nat,type)),combs(dB,fun(nat,bool),fun(nat,bool))),aa(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),aa(fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(fun(nat,type),fun(dB,fun(bool,bool))),fun(fun(nat,type),fun(dB,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool))),fun(nat,type)),aa(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(dB,fun(bool,bool)),fun(dB,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),dB),combb(bool,bool,nat))),aa(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool))),aa(fun(fun(dB,bool),fun(dB,fun(bool,bool))),fun(fun(fun(nat,type),fun(dB,bool)),fun(fun(nat,type),fun(dB,fun(bool,bool)))),combb(fun(dB,bool),fun(dB,fun(bool,bool)),fun(nat,type)),aa(fun(bool,fun(bool,bool)),fun(fun(dB,bool),fun(dB,fun(bool,bool))),combb(bool,fun(bool,bool),dB),fimplies)),aa(type,fun(fun(nat,type),fun(dB,bool)),aa(fun(fun(nat,type),fun(type,fun(dB,bool))),fun(type,fun(fun(nat,type),fun(dB,bool))),combc(fun(nat,type),type,fun(dB,bool)),aa(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool))),aa(fun(fun(dB,fun(type,bool)),fun(type,fun(dB,bool))),fun(fun(fun(nat,type),fun(dB,fun(type,bool))),fun(fun(nat,type),fun(type,fun(dB,bool)))),combb(fun(dB,fun(type,bool)),fun(type,fun(dB,bool)),fun(nat,type)),combc(dB,type,bool)),typing)),t)))))),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool))),aa(fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),fun(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,bool)))),combb(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool)),dB),aa(fun(fun(nat,dB),fun(nat,bool)),fun(fun(dB,fun(nat,dB)),fun(dB,fun(nat,bool))),combb(fun(nat,dB),fun(nat,bool),dB),aa(fun(dB,bool),fun(fun(nat,dB),fun(nat,bool)),combb(dB,bool,nat),it))),subst)))))))),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__096listsp_A_I_Ft_O_AALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_Aas_096) ).
tff(f1873,plain,
spl29_156,
inference(avatar_split_clause,[],[f494,f1871]) ).
tff(f1871,plain,
( spl29_156
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),listset(X0,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_156])]) ).
tff(f494,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),listset(X0,X1))))))) ),
inference(definition_unfolding,[],[f405,f408]) ).
tff(f408,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X1)))))) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: fun(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X1)))))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType,X87: fun(list(X0),bool),X49: fun(X0,bool)] : ( set_Cons(X0,X49,X87) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X49)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X87)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_set__Cons__def) ).
tff(f405,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: list(fun(X0,bool)),X2: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType,X88: list(fun(X0,bool)),X49: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X49),X88)) = set_Cons(X0,X49,listset(X0,X88)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_listset_Osimps_I2_J) ).
tff(f1852,plain,
spl29_155,
inference(avatar_split_clause,[],[f452,f1850]) ).
tff(f1850,plain,
( spl29_155
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_155])]) ).
tff(f452,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
| ~ pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
<=> pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X44: list(type),X45: list(dB),X15: dB,X14: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X14,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X15),X45)),X44))
<=> pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15)))),typings(X14,X45)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_typings_Osimps_I2_J) ).
tff(f1848,plain,
spl29_154,
inference(avatar_split_clause,[],[f451,f1846]) ).
tff(f1846,plain,
( spl29_154
<=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_154])]) ).
tff(f451,plain,
! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,aa(fun(list(type),bool),fun(type,fun(list(type),bool)),aa(fun(type,fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(list(type),bool),fun(type,fun(list(type),bool))),combc(type,fun(list(type),bool),fun(list(type),bool)),aa(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool))),aa(fun(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool))),fun(fun(type,fun(bool,bool)),fun(type,fun(fun(list(type),bool),fun(list(type),bool)))),combb(fun(bool,bool),fun(fun(list(type),bool),fun(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun(type,bool),fun(type,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(type,bool),fun(type,fun(bool,bool))),combb(bool,fun(bool,bool),type),fconj),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2)))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1838,plain,
( spl29_151
| spl29_152
| spl29_153
| ~ spl29_25
| ~ spl29_55 ),
inference(avatar_split_clause,[],[f852,f844,f656,f1835,f1831,f1827]) ).
tff(f1827,plain,
( spl29_151
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_151])]) ).
tff(f1831,plain,
( spl29_152
<=> ( sK4 = foldl(dB,dB,app,var(sK11(sK4)),sK10(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_152])]) ).
tff(f1835,plain,
( spl29_153
<=> ( sK4 = abs(sK9(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_153])]) ).
tff(f656,plain,
( spl29_25
<=> sP1(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_25])]) ).
tff(f844,plain,
( spl29_55
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK9(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_55])]) ).
tff(f852,plain,
( ( sK4 = abs(sK9(sK4)) )
| ( sK4 = foldl(dB,dB,app,var(sK11(sK4)),sK10(sK4)) )
| sP0(sK4)
| ~ spl29_25
| ~ spl29_55 ),
inference(resolution,[],[f845,f658]) ).
tff(f658,plain,
( sP1(sK4)
| ~ spl29_25 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f845,plain,
( ! [X0: dB] :
( ~ sP1(X0)
| ( abs(sK9(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
| sP0(X0) )
| ~ spl29_55 ),
inference(avatar_component_clause,[],[f844]) ).
tff(f1825,plain,
spl29_150,
inference(avatar_split_clause,[],[f472,f1823]) ).
tff(f1823,plain,
( spl29_150
<=> ! [X3: type,X4: dB,X0: list(type),X5: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_150])]) ).
tff(f472,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(flattening,[],[f247]) ).
tff(f247,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X5),X2),X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X44: list(type),X45: list(dB),X13: nat,X12: type,X11: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X12))
=> ( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),X13),X12),X45),X44))
=> pp(aa(list(type),bool,typings(X14,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X11)),X13),X45)),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_substs__lemma) ).
tff(f1815,plain,
spl29_149,
inference(avatar_split_clause,[],[f483,f1813]) ).
tff(f1813,plain,
( spl29_149
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X0: dB,X6: type,X2: nat,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_149])]) ).
tff(f483,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X11: dB,X12: type,X13: nat,X14: fun(nat,type),X15: dB,X16: type,X17: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) )
=> ( pp(aa(dB,bool,it,X15))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),X13),X17)),X15),X12))
=> ( pp(aa(dB,bool,it,X11))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X17))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MI1) ).
tff(f1811,plain,
spl29_148,
inference(avatar_split_clause,[],[f482,f1809]) ).
tff(f1809,plain,
( spl29_148
<=> ! [X3: fun(nat,type),X4: dB,X0: dB,X6: type,X5: type,X2: nat,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_148])]) ).
tff(f482,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X2),X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X11: dB,X12: type,X13: nat,X14: fun(nat,type),X15: dB,X16: type,X17: type] :
( ( t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) )
=> ( pp(aa(dB,bool,it,X15))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),X13),X16)),X15),X12))
=> ( pp(aa(dB,bool,it,X11))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X16))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_MI2) ).
tff(f1797,plain,
spl29_147,
inference(avatar_split_clause,[],[f481,f1795]) ).
tff(f1795,plain,
( spl29_147
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_147])]) ).
tff(f481,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X51: list(X2),X52: fun(X2,X1),X53: X0,X54: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X54,X53,map(X2,X1,X52,X51)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X54)),X52),X53,X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_foldl__map) ).
tff(f1769,plain,
spl29_146,
inference(avatar_split_clause,[],[f522,f1767]) ).
tff(f1767,plain,
( spl29_146
<=> ! [X3: fun(nat,type),X4: type,X0: nat,X5: dB,X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1)),X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_146])]) ).
tff(f522,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1)),X5),X4)) ),
inference(equality_resolution,[],[f484]) ).
tff(f484,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,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),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(flattening,[],[f253]) ).
tff(f253,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),aa(fun(nat,type),fun(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))
| ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
=> ( ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),X0),X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[],[f10]) ).
tff(f10,axiom,
! [X13: nat,X18: type,X11: dB,X19: fun(nat,type),X12: type,X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),X12))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X19),X11),X18))
=> ( ( aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X19),X13),X18) = X14 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X19),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13)),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subst__lemma) ).
tff(f1752,plain,
spl29_145,
inference(avatar_split_clause,[],[f428,f1750]) ).
tff(f1750,plain,
( spl29_145
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_145])]) ).
tff(f428,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X13: nat,X11: dB,X45: list(dB),X15: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X15,X45)),X11),X13) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X11)),X13),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_subst__map) ).
tff(f1741,plain,
spl29_144,
inference(avatar_split_clause,[],[f353,f1739]) ).
tff(f353,plain,
! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK6))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f215,f262]) ).
tff(f262,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK6)) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
inference(flattening,[],[f214]) ).
tff(f214,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
inference(ennf_transformation,[],[f122]) ).
tff(f122,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2))
=> ( pp(aa(dB,bool,it,X3))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4))) ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
( ? [X8: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X8))
& ! [X4: fun(nat,type),X5: type,X6: dB,X7: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X7),t)),b),X5))
=> ( pp(aa(dB,bool,it,X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X6),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X6),X7))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Cons_I1_J) ).
tff(f1730,plain,
spl29_143,
inference(avatar_split_clause,[],[f462,f1728]) ).
tff(f1728,plain,
( spl29_143
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_143])]) ).
tff(f462,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X15: dB,X18: type,X12: type,X38: dB,X37: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),X38),aa(type,type,aa(type,fun(type,type),fun1,X12),X18)))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),X15),X12))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),aa(dB,dB,aa(dB,fun(dB,dB),app,X38),X15)),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_App) ).
tff(f1726,plain,
spl29_142,
inference(avatar_split_clause,[],[f348,f1723]) ).
tff(f1723,plain,
( spl29_142
<=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_142])]) ).
tff(f348,plain,
listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))),
inference(cnf_transformation,[],[f22]) ).
tff(f22,axiom,
listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Cons_I3_J) ).
tff(f1703,plain,
spl29_141,
inference(avatar_split_clause,[],[f486,f1701]) ).
tff(f1701,plain,
( spl29_141
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_141])]) ).
tff(f486,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,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),sK28(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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,[sK28])],[f256,f319]) ).
tff(f319,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),sK28(X0,X2,X3,X6)))
& ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f256,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),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f255]) ).
tff(f255,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),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,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),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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,
! [X18: type,X44: list(type),X12: type,X65: list(dB),X45: list(dB),X13: nat,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,foldl(dB,dB,app,var(X13),X45),X65)),X12))
=> ( pp(aa(list(type),bool,typings(X14,X45),X44))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X18))
=> ? [X66: list(type)] :
( pp(aa(list(type),bool,typings(X14,X65),X66))
& ( foldr(type,type,fun1,X66,X12) = X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_var__app__types) ).
tff(f1698,plain,
spl29_140,
inference(avatar_split_clause,[],[f437,f1696]) ).
tff(f1696,plain,
( spl29_140
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_140])]) ).
tff(f437,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X3),zero_zero(nat)),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X18: type,X15: dB,X12: type,X37: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X37),zero_zero(nat)),X12)),X15),X18))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),abs(X15)),aa(type,type,aa(type,fun(type,type),fun1,X12),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Abs) ).
tff(f1686,plain,
spl29_139,
inference(avatar_split_clause,[],[f485,f1684]) ).
tff(f1684,plain,
( spl29_139
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_139])]) ).
tff(f485,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f320]) ).
tff(f1675,plain,
spl29_138,
inference(avatar_split_clause,[],[f459,f1673]) ).
tff(f1673,plain,
( spl29_138
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_138])]) ).
tff(f459,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X18: type,X13: nat,X12: type,X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),X12))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),X13),X18)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X15),X13)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lift__type) ).
tff(f1661,plain,
spl29_137,
inference(avatar_split_clause,[],[f418,f1659]) ).
tff(f1659,plain,
( spl29_137
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_137])]) ).
tff(f418,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f228,f284]) ).
tff(f284,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f228,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4)) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X12: type,X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),abs(X15)),X12))
=> ~ ! [X43: type,X80: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X43),X80) = X12 )
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),zero_zero(nat)),X43)),X15),X80)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_typing__elims_I3_J) ).
tff(f1635,plain,
spl29_136,
inference(avatar_split_clause,[],[f427,f1633]) ).
tff(f1633,plain,
( spl29_136
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_136])]) ).
tff(f427,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X24: nat,X23: dB,X35: dB,X10: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X10),X35)),X23),X24) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X10),X23),X24)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X35),X23),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_subst__App) ).
tff(f1631,plain,
( ~ spl29_135
| ~ spl29_50
| ~ spl29_51 ),
inference(avatar_split_clause,[],[f840,f824,f819,f1628]) ).
tff(f1628,plain,
( spl29_135
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_135])]) ).
tff(f824,plain,
( spl29_51
<=> ! [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,[spl29_51])]) ).
tff(f840,plain,
( ( as != rs )
| ~ spl29_50
| ~ spl29_51 ),
inference(superposition,[],[f825,f821]) ).
tff(f825,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 )
| ~ spl29_51 ),
inference(avatar_component_clause,[],[f824]) ).
tff(f1626,plain,
spl29_134,
inference(avatar_split_clause,[],[f416,f1624]) ).
tff(f1624,plain,
( spl29_134
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_134])]) ).
tff(f416,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f227,f282]) ).
tff(f282,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f227,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X2),zero_zero(nat)),X3)),X1),X4)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X12: type,X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),abs(X15)),X12))
=> ~ ! [X80: type,X81: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),zero_zero(nat)),X80)),X15),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_abs__typeE) ).
tff(f1622,plain,
spl29_133,
inference(avatar_split_clause,[],[f347,f1619]) ).
tff(f1619,plain,
( spl29_133
<=> 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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_133])]) ).
tff(f347,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),as),
inference(cnf_transformation,[],[f29]) ).
tff(f29,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t))),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__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(f1612,plain,
spl29_132,
inference(avatar_split_clause,[],[f458,f1610]) ).
tff(f1610,plain,
( spl29_132
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(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,[spl29_132])]) ).
tff(f458,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,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(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X18: type,X13: nat,X44: list(type),X45: list(dB),X14: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X14,X45),X44))
=> pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X14),X13),X18),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X13),X45)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lift__types) ).
tff(f1595,plain,
spl29_131,
inference(avatar_split_clause,[],[f455,f1593]) ).
tff(f1593,plain,
( spl29_131
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_131])]) ).
tff(f455,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(flattening,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType,X48: fun(X0,bool),X49: fun(X0,bool),X50: list(X0)] :
( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X49)),X48),X50)
<=> ( listsp(X0,X48,X50)
& listsp(X0,X49,X50) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_listsp__conj__eq) ).
tff(f1591,plain,
spl29_130,
inference(avatar_split_clause,[],[f435,f1589]) ).
tff(f1589,plain,
( spl29_130
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_130])]) ).
tff(f435,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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,[sK22])],[f235,f294]) ).
tff(f294,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f235,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4)) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X12: type,X11: dB,X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X11)),X12))
=> ~ ! [X43: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),aa(type,type,aa(type,fun(type,type),fun1,X43),X12)))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_typing__elims_I2_J) ).
tff(f1583,plain,
( spl29_129
| ~ spl29_14
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f661,f650,f596,f1581]) ).
tff(f1581,plain,
( spl29_129
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_129])]) ).
tff(f661,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl29_14
| ~ spl29_24 ),
inference(resolution,[],[f651,f597]) ).
tff(f1579,plain,
spl29_128,
inference(avatar_split_clause,[],[f346,f1576]) ).
tff(f1576,plain,
( spl29_128
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_128])]) ).
tff(f346,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f1561,plain,
spl29_127,
inference(avatar_split_clause,[],[f493,f1558]) ).
tff(f1558,plain,
( spl29_127
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK8,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_127])]) ).
tff(f493,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,sK8,t1))),
inference(definition_unfolding,[],[f357,f329]) ).
tff(f329,plain,
n = i,
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_True) ).
tff(f357,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK8,t1))),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),sK8))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK8,t1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f217,f266]) ).
tff(f266,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) )
=> ( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),sK8))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,sK8,t1))) ) ),
introduced(choice_axiom,[]) ).
tff(f217,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1))) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X0,t1)))
=> ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),X0)) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
~ ! [X46: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,X46,t1)))
=> ~ pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42__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(f1556,plain,
spl29_126,
inference(avatar_split_clause,[],[f492,f1553]) ).
tff(f1553,plain,
( spl29_126
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_126])]) ).
tff(f492,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(i)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))),
inference(definition_unfolding,[],[f355,f329]) ).
tff(f355,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK7))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f216,f264]) ).
tff(f264,plain,
( ? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) )
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK7))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f216,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1)))) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X0),foldr(type,type,fun1,ts,t1))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
~ ! [X47: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),var(n)),aa(type,type,aa(type,fun(type,type),fun1,X47),foldr(type,type,fun1,ts,t1))))
=> ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46__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(f1550,plain,
spl29_125,
inference(avatar_split_clause,[],[f491,f1547]) ).
tff(f1547,plain,
( spl29_125
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_125])]) ).
tff(f491,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t1)),
inference(definition_unfolding,[],[f345,f329]) ).
tff(f345,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49__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(f1545,plain,
spl29_124,
inference(avatar_split_clause,[],[f490,f1542]) ).
tff(f1542,plain,
( spl29_124
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_124])]) ).
tff(f490,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a)),foldr(type,type,fun1,ts,t1))),
inference(definition_unfolding,[],[f344,f329]) ).
tff(f344,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a)),foldr(type,type,fun1,ts,t1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_headT) ).
tff(f1537,plain,
spl29_123,
inference(avatar_split_clause,[],[f454,f1535]) ).
tff(f1535,plain,
( spl29_123
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_123])]) ).
tff(f454,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f308]) ).
tff(f1533,plain,
spl29_122,
inference(avatar_split_clause,[],[f453,f1531]) ).
tff(f453,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
inference(cnf_transformation,[],[f308]) ).
tff(f1523,plain,
spl29_121,
inference(avatar_split_clause,[],[f460,f1521]) ).
tff(f1521,plain,
( spl29_121
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_121])]) ).
tff(f460,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X45: list(dB),X12: type,X44: list(type),X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X44,X12)))
=> ( pp(aa(list(type),bool,typings(X14,X45),X44))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_list__app__typeI) ).
tff(f1516,plain,
spl29_120,
inference(avatar_split_clause,[],[f433,f1514]) ).
tff(f1514,plain,
( spl29_120
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_120])]) ).
tff(f433,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f234,f292]) ).
tff(f292,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f234,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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,
! [X12: type,X45: list(dB),X13: nat,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X12))
=> ~ ! [X46: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),var(X13)),foldr(type,type,fun1,X46,X12)))
=> ~ pp(aa(list(type),bool,typings(X14,X45),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_var__app__typesE) ).
tff(f1505,plain,
spl29_119,
inference(avatar_split_clause,[],[f461,f1503]) ).
tff(f1503,plain,
( spl29_119
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_119])]) ).
tff(f461,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f243]) ).
tff(f243,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X18: type,X12: type,X45: list(dB),X13: nat,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X12))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X18))
=> ( X12 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_var__app__type__eq) ).
tff(f1465,plain,
spl29_118,
inference(avatar_split_clause,[],[f436,f1463]) ).
tff(f1463,plain,
( spl29_118
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_118])]) ).
tff(f436,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1461,plain,
spl29_117,
inference(avatar_split_clause,[],[f431,f1459]) ).
tff(f1459,plain,
( spl29_117
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_117])]) ).
tff(f431,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f233,f290]) ).
tff(f290,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f233,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X12: type,X45: list(dB),X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12))
=> ? [X46: list(type)] :
( pp(aa(list(type),bool,typings(X14,X45),X46))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X46,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_list__app__typeD) ).
tff(f1457,plain,
spl29_116,
inference(avatar_split_clause,[],[f429,f1455]) ).
tff(f1455,plain,
( spl29_116
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_116])]) ).
tff(f429,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f232,f288]) ).
tff(f288,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f232,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),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(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),aa(fun(nat,type),fun(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,
! [X12: type,X45: list(dB),X15: dB,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12))
=> ~ ! [X46: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X46,X12)))
=> ~ pp(aa(list(type),bool,typings(X14,X45),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_list__app__typeE) ).
tff(f1453,plain,
spl29_115,
inference(avatar_split_clause,[],[f420,f1451]) ).
tff(f1451,plain,
( spl29_115
<=> ! [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,[spl29_115])]) ).
tff(f420,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,[],[f231]) ).
tff(f231,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,[],[f230]) ).
tff(f230,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,[],[f171]) ).
tff(f171,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,[],[f83]) ).
tff(f83,axiom,
! [X61: list(dB),X38: dB,X60: 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,X60),X38),zero_zero(nat)),X61)))
=> ( pp(aa(dB,bool,it,X38))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X60)),X38),X61))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Beta) ).
tff(f1449,plain,
spl29_114,
inference(avatar_split_clause,[],[f407,f1447]) ).
tff(f1447,plain,
( spl29_114
<=> ! [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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_114])]) ).
tff(f407,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,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,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X13: nat,X45: list(dB),X15: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X15,X45)),X13) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X15),X13),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X13),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_lift__map) ).
tff(f1431,plain,
spl29_113,
inference(avatar_split_clause,[],[f488,f1428]) ).
tff(f1428,plain,
( spl29_113
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(i),rs)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_113])]) ).
tff(f488,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(i),rs)),t1)),
inference(definition_unfolding,[],[f342,f329]) ).
tff(f342,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f51]) ).
tff(f51,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_nT) ).
tff(f1426,plain,
spl29_112,
inference(avatar_split_clause,[],[f487,f1423]) ).
tff(f1423,plain,
( spl29_112
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(i),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_112])]) ).
tff(f487,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(i),rs)),t_a)),
inference(definition_unfolding,[],[f341,f329]) ).
tff(f341,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f54]) ).
tff(f54,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),ea),ia),t)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Var_I2_J) ).
tff(f1421,plain,
spl29_111,
inference(avatar_split_clause,[],[f415,f1419]) ).
tff(f1419,plain,
( spl29_111
<=> ! [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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_111])]) ).
tff(f415,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X44: list(type),X45: list(dB),X14: fun(nat,type)] :
( pp(aa(list(type),bool,typings(X14,X45),X44))
=> 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)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14)),X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lists__typings) ).
tff(f1397,plain,
spl29_110,
inference(avatar_split_clause,[],[f499,f1395]) ).
tff(f1395,plain,
( spl29_110
<=> ! [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,[spl29_110])]) ).
tff(f499,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,[],[f376]) ).
tff(f376,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,[],[f278]) ).
tff(f278,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK13(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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f276,f277]) ).
tff(f277,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,sK13(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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f276,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,[],[f275]) ).
tff(f275,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,[],[f257]) ).
tff(f257,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(f1393,plain,
spl29_109,
inference(avatar_split_clause,[],[f477,f1391]) ).
tff(f1391,plain,
( spl29_109
<=> ! [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),sK26(X0,X1,X2,X3,X4,X5)),sK27(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,[spl29_109])]) ).
tff(f477,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(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,[],[f318]) ).
tff(f318,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,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(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,[sK26,sK27])],[f316,f317]) ).
tff(f317,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,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f316,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,[],[f315]) ).
tff(f315,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,[],[f206]) ).
tff(f206,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,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X1: $tType,X67: list(X1),X52: fun(X1,X0),X51: list(X0),X36: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X36),X51) = map(X1,X0,X52,X67) )
<=> ? [X68: X1,X69: list(X1)] :
( ( map(X1,X0,X52,X69) = X51 )
& ( aa(X1,X0,X52,X68) = X36 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X68),X69) = X67 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Cons__eq__map__conv) ).
tff(f1389,plain,
spl29_108,
inference(avatar_split_clause,[],[f473,f1387]) ).
tff(f1387,plain,
( spl29_108
<=> ! [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),sK24(X0,X1,X2,X3,X4,X5)),sK25(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,[spl29_108])]) ).
tff(f473,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(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,[],[f314]) ).
tff(f314,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,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(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,[sK24,sK25])],[f312,f313]) ).
tff(f313,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,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f312,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,[],[f311]) ).
tff(f311,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,[],[f205]) ).
tff(f205,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,[],[f80]) ).
tff(f80,axiom,
! [X1: $tType,X0: $tType,X67: list(X0),X74: X0,X51: list(X1),X52: fun(X1,X0)] :
( ( map(X1,X0,X52,X51) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X74),X67) )
<=> ? [X68: X1,X69: list(X1)] :
( ( map(X1,X0,X52,X69) = X67 )
& ( aa(X1,X0,X52,X68) = X74 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X68),X69) = X51 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_map__eq__Cons__conv) ).
tff(f1374,plain,
spl29_107,
inference(avatar_split_clause,[],[f406,f1372]) ).
tff(f1372,plain,
( spl29_107
<=> ! [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,[spl29_107])]) ).
tff(f406,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,[],[f158]) ).
tff(f158,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,[],[f26]) ).
tff(f26,axiom,
! [X24: nat,X10: dB,X23: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X23),X10)),X24) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X23),X24)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_lift_Osimps_I2_J) ).
tff(f1364,plain,
spl29_106,
inference(avatar_split_clause,[],[f356,f1361]) ).
tff(f1361,plain,
( spl29_106
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_106])]) ).
tff(f356,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK7)),
inference(cnf_transformation,[],[f265]) ).
tff(f1359,plain,
spl29_105,
inference(avatar_split_clause,[],[f354,f1356]) ).
tff(f1356,plain,
( spl29_105
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_105])]) ).
tff(f354,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK6)),
inference(cnf_transformation,[],[f263]) ).
tff(f1354,plain,
spl29_104,
inference(avatar_split_clause,[],[f340,f1351]) ).
tff(f1351,plain,
( spl29_104
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_104])]) ).
tff(f340,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),t2)),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_argT) ).
tff(f1215,plain,
( spl29_103
| ~ spl29_10
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f664,f650,f569,f1212]) ).
tff(f1212,plain,
( spl29_103
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_103])]) ).
tff(f569,plain,
( spl29_10
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_10])]) ).
tff(f664,plain,
( sP1(abs(ua))
| ~ spl29_10
| ~ spl29_24 ),
inference(resolution,[],[f651,f571]) ).
tff(f571,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl29_10 ),
inference(avatar_component_clause,[],[f569]) ).
tff(f1210,plain,
spl29_102,
inference(avatar_split_clause,[],[f471,f1208]) ).
tff(f1208,plain,
( spl29_102
<=> ! [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,[spl29_102])]) ).
tff(f471,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,[],[f203]) ).
tff(f203,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,[],[f108]) ).
tff(f108,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X90: X0,X91: fun(X0,X1),X89: 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),X89),X91),X90) = aa(X1,X2,aa(X0,fun(X1,X2),X89,X90),aa(X0,X1,X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1206,plain,
spl29_101,
inference(avatar_split_clause,[],[f456,f1204]) ).
tff(f1204,plain,
( spl29_101
<=> ! [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,[spl29_101])]) ).
tff(f456,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,[],[f190]) ).
tff(f190,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,X51: list(X1),X36: X1,X52: fun(X1,X0)] : ( map(X1,X0,X52,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X52,X36)),map(X1,X0,X52,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_map_Osimps_I2_J) ).
tff(f1201,plain,
spl29_100,
inference(avatar_split_clause,[],[f417,f1199]) ).
tff(f1199,plain,
( spl29_100
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_100])]) ).
tff(f417,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f1195,plain,
spl29_99,
inference(avatar_split_clause,[],[f434,f1193]) ).
tff(f1193,plain,
( spl29_99
<=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_99])]) ).
tff(f434,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f1187,plain,
spl29_98,
inference(avatar_split_clause,[],[f432,f1185]) ).
tff(f1185,plain,
( spl29_98
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_98])]) ).
tff(f432,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f1183,plain,
spl29_97,
inference(avatar_split_clause,[],[f430,f1181]) ).
tff(f1181,plain,
( spl29_97
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_97])]) ).
tff(f430,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1179,plain,
( spl29_96
| ~ spl29_11
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f663,f650,f574,f1176]) ).
tff(f1176,plain,
( spl29_96
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_96])]) ).
tff(f574,plain,
( spl29_11
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_11])]) ).
tff(f663,plain,
( sP1(abs(u))
| ~ spl29_11
| ~ spl29_24 ),
inference(resolution,[],[f651,f576]) ).
tff(f576,plain,
( pp(aa(dB,bool,it,u))
| ~ spl29_11 ),
inference(avatar_component_clause,[],[f574]) ).
tff(f1098,plain,
spl29_95,
inference(avatar_split_clause,[],[f470,f1096]) ).
tff(f1096,plain,
( spl29_95
<=> ! [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,[spl29_95])]) ).
tff(f470,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,[],[f202]) ).
tff(f202,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,[],[f105]) ).
tff(f105,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X90: X0,X91: fun(X0,X1),X89: 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),X89),X91),X90) = aa(X1,X2,X89,aa(X0,X1,X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1094,plain,
spl29_94,
inference(avatar_split_clause,[],[f469,f1092]) ).
tff(f1092,plain,
( spl29_94
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_94])]) ).
tff(f469,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X90: X0,X91: X1,X89: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X89),X91),X90) = aa(X1,X2,aa(X0,fun(X1,X2),X89,X90),X91) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1090,plain,
spl29_93,
inference(avatar_split_clause,[],[f468,f1088]) ).
tff(f1088,plain,
( spl29_93
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: fun(X0,fun(X1,X0)),X2: list(X1)] : ( 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_93])]) ).
tff(f468,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,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,[],[f70]) ).
tff(f70,axiom,
! [X0: $tType,X1: $tType,X51: list(X1),X36: X1,X53: X0,X52: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X52,X53,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51)) = foldl(X0,X1,X52,aa(X1,X0,aa(X0,fun(X1,X0),X52,X53),X36),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_foldl__Cons) ).
tff(f1086,plain,
spl29_92,
inference(avatar_split_clause,[],[f467,f1084]) ).
tff(f1084,plain,
( spl29_92
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1)),X2: 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_92])]) ).
tff(f467,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,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,[],[f67]) ).
tff(f67,axiom,
! [X1: $tType,X0: $tType,X53: X0,X51: list(X1),X36: X1,X52: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X52,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51),X53) = aa(X0,X0,aa(X1,fun(X0,X0),X52,X36),foldr(X1,X0,X52,X51,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_foldr_Osimps_I2_J) ).
tff(f1082,plain,
spl29_91,
inference(avatar_split_clause,[],[f464,f1080]) ).
tff(f1080,plain,
( spl29_91
<=> ! [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,[spl29_91])]) ).
tff(f464,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,[],[f310]) ).
tff(f310,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,[],[f309]) ).
tff(f309,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,[],[f197]) ).
tff(f197,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,X57: list(X0),X58: X0,X59: list(X0),X53: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X53),X59) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X58),X57) )
<=> ( ( X57 = X59 )
& ( X53 = X58 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_list_Oinject) ).
tff(f1078,plain,
( spl29_90
| ~ spl29_9
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f662,f650,f564,f1075]) ).
tff(f1075,plain,
( spl29_90
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_90])]) ).
tff(f564,plain,
( spl29_9
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).
tff(f662,plain,
( sP1(abs(t3))
| ~ spl29_9
| ~ spl29_24 ),
inference(resolution,[],[f651,f566]) ).
tff(f566,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f1066,plain,
spl29_89,
inference(avatar_split_clause,[],[f479,f1064]) ).
tff(f1064,plain,
( spl29_89
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK27(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,[spl29_89])]) ).
tff(f479,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK27(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,[],[f318]) ).
tff(f1062,plain,
spl29_88,
inference(avatar_split_clause,[],[f475,f1060]) ).
tff(f1060,plain,
( spl29_88
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK25(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,[spl29_88])]) ).
tff(f475,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( map(X0,X1,X5,sK25(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,[],[f314]) ).
tff(f1058,plain,
spl29_87,
inference(avatar_split_clause,[],[f463,f1056]) ).
tff(f1056,plain,
( spl29_87
<=> ! [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,[spl29_87])]) ).
tff(f463,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,[],[f310]) ).
tff(f1046,plain,
( spl29_86
| ~ spl29_14
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f629,f605,f596,f1044]) ).
tff(f1044,plain,
( spl29_86
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_86])]) ).
tff(f629,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl29_14
| ~ spl29_16 ),
inference(resolution,[],[f606,f597]) ).
tff(f1042,plain,
spl29_85,
inference(avatar_split_clause,[],[f478,f1040]) ).
tff(f1040,plain,
( spl29_85
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK26(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,[spl29_85])]) ).
tff(f478,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK26(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,[],[f318]) ).
tff(f1038,plain,
spl29_84,
inference(avatar_split_clause,[],[f474,f1036]) ).
tff(f1036,plain,
( spl29_84
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK24(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,[spl29_84])]) ).
tff(f474,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK24(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,[],[f314]) ).
tff(f1034,plain,
spl29_83,
inference(avatar_split_clause,[],[f358,f1031]) ).
tff(f1031,plain,
( spl29_83
<=> pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_83])]) ).
tff(f358,plain,
pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),sK8)),
inference(cnf_transformation,[],[f267]) ).
tff(f1029,plain,
spl29_82,
inference(avatar_split_clause,[],[f338,f1026]) ).
tff(f1026,plain,
( spl29_82
<=> pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_82])]) ).
tff(f338,plain,
pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),ts)),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
pp(aa(list(type),bool,typings(aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t),as),ts)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_argsT) ).
tff(f1012,plain,
spl29_81,
inference(avatar_split_clause,[],[f466,f1010]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,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,X59: list(X1),X53: X1,X72: fun(X1,fun(list(X1),X0)),X73: X0] : ( list_case(X0,X1,X73,X72,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X53),X59)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X72,X53),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_list_Osimps_I5_J) ).
tff(f1008,plain,
spl29_80,
inference(avatar_split_clause,[],[f374,f1006]) ).
tff(f1006,plain,
( spl29_80
<=> ! [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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_80])]) ).
tff(f374,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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f996,plain,
spl29_79,
inference(avatar_split_clause,[],[f513,f994]) ).
tff(f994,plain,
( spl29_79
<=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_79])]) ).
tff(f513,plain,
! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ),
inference(equality_resolution,[],[f457]) ).
tff(f457,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X12: X0,X14: fun(nat,X0),X20: nat,X13: nat] :
( ( X13 = X20 )
=> ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X14),X13),X12),X20) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_shift__eq) ).
tff(f992,plain,
spl29_78,
inference(avatar_split_clause,[],[f364,f990]) ).
tff(f990,plain,
( spl29_78
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_78])]) ).
tff(f364,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0)) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X45: list(dB)] :
( listsp(dB,it,X45)
=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_lifts__IT) ).
tff(f988,plain,
spl29_77,
inference(avatar_split_clause,[],[f337,f985]) ).
tff(f985,plain,
( spl29_77
<=> 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,[spl29_77])]) ).
tff(f337,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,[],[f18]) ).
tff(f18,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f977,plain,
spl29_76,
inference(avatar_split_clause,[],[f413,f975]) ).
tff(f975,plain,
( spl29_76
<=> ! [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,[spl29_76])]) ).
tff(f413,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,[],[f224]) ).
tff(f224,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,[],[f165]) ).
tff(f165,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,[],[f14]) ).
tff(f14,axiom,
! [X21: nat,X9: nat,X22: dB] :
( pp(aa(dB,bool,it,X22))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),var(X9)),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__Var__IT) ).
tff(f973,plain,
spl29_75,
inference(avatar_split_clause,[],[f404,f971]) ).
tff(f971,plain,
( spl29_75
<=> ! [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,[spl29_75])]) ).
tff(f404,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X23: dB,X24: nat,X10: 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,X10),X24)),X23),X24) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__lift) ).
tff(f967,plain,
spl29_74,
inference(avatar_split_clause,[],[f419,f965]) ).
tff(f965,plain,
( spl29_74
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_74])]) ).
tff(f419,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X12: type,X13: nat,X14: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),var(X13)),X12))
=> ( aa(nat,type,X14,X13) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_typing__elims_I1_J) ).
tff(f960,plain,
spl29_73,
inference(avatar_split_clause,[],[f503,f958]) ).
tff(f958,plain,
( spl29_73
<=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_73])]) ).
tff(f503,plain,
! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f414]) ).
tff(f414,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X12: type,X36: nat,X37: fun(nat,type)] :
( ( aa(nat,type,X37,X36) = X12 )
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),var(X36)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_typing_OVar) ).
tff(f948,plain,
spl29_72,
inference(avatar_split_clause,[],[f449,f946]) ).
tff(f946,plain,
( spl29_72
<=> ! [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,[spl29_72])]) ).
tff(f449,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,[],[f305]) ).
tff(f305,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,[],[f304]) ).
tff(f304,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,[],[f187]) ).
tff(f187,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,[],[f21]) ).
tff(f21,axiom,
! [X31: type,X32: type,X33: type,X34: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X34),X33) = aa(type,type,aa(type,fun(type,type),fun1,X32),X31) )
<=> ( ( X31 = X33 )
& ( X32 = X34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_type_Osimps_I2_J) ).
tff(f944,plain,
spl29_71,
inference(avatar_split_clause,[],[f448,f942]) ).
tff(f942,plain,
( spl29_71
<=> ! [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,[spl29_71])]) ).
tff(f448,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,[],[f305]) ).
tff(f940,plain,
spl29_70,
inference(avatar_split_clause,[],[f446,f938]) ).
tff(f938,plain,
( spl29_70
<=> ! [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,[spl29_70])]) ).
tff(f446,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,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,[],[f302]) ).
tff(f302,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,[],[f186]) ).
tff(f186,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,[],[f19]) ).
tff(f19,axiom,
! [X25: dB,X26: dB,X27: dB,X28: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X27) = aa(dB,dB,aa(dB,fun(dB,dB),app,X26),X25) )
<=> ( ( X25 = X27 )
& ( X26 = X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dB_Osimps_I2_J) ).
tff(f936,plain,
spl29_69,
inference(avatar_split_clause,[],[f445,f934]) ).
tff(f934,plain,
( spl29_69
<=> ! [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,[spl29_69])]) ).
tff(f445,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f303]) ).
tff(f925,plain,
spl29_68,
inference(avatar_split_clause,[],[f438,f923]) ).
tff(f923,plain,
( spl29_68
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_68])]) ).
tff(f438,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f237,f296]) ).
tff(f296,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,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f237,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,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X0: $tType,X54: fun(X0,X1),X52: fun(X0,X1)] :
( ! [X70: X0] : ( aa(X0,X1,X52,X70) = aa(X0,X1,X54,X70) )
=> ( X52 = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f921,plain,
spl29_67,
inference(avatar_split_clause,[],[f373,f919]) ).
tff(f919,plain,
( spl29_67
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_67])]) ).
tff(f373,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f909,plain,
spl29_66,
inference(avatar_split_clause,[],[f424,f907]) ).
tff(f907,plain,
( spl29_66
<=> ! [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,[spl29_66])]) ).
tff(f424,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,[],[f287]) ).
tff(f287,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,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X49: fun(X0,bool),X36: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X36),X49))
<=> pp(aa(X0,bool,X49,X36)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f905,plain,
spl29_65,
inference(avatar_split_clause,[],[f423,f903]) ).
tff(f903,plain,
( spl29_65
<=> ! [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,[spl29_65])]) ).
tff(f423,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,[],[f287]) ).
tff(f901,plain,
spl29_64,
inference(avatar_split_clause,[],[f393,f899]) ).
tff(f899,plain,
( spl29_64
<=> ! [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,[spl29_64])]) ).
tff(f393,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,[],[f223]) ).
tff(f223,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,[],[f147]) ).
tff(f147,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,[],[f33]) ).
tff(f33,axiom,
! [X9: nat,X10: dB] :
( pp(aa(dB,bool,it,X10))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X10),var(X9)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_app__Var__IT) ).
tff(f897,plain,
( spl29_63
| ~ spl29_10
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f632,f605,f569,f894]) ).
tff(f894,plain,
( spl29_63
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_63])]) ).
tff(f632,plain,
( sP1(ua)
| ~ spl29_10
| ~ spl29_16 ),
inference(resolution,[],[f606,f571]) ).
tff(f880,plain,
spl29_62,
inference(avatar_split_clause,[],[f392,f878]) ).
tff(f878,plain,
( spl29_62
<=> ! [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,[spl29_62])]) ).
tff(f392,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,[],[f222]) ).
tff(f222,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,[],[f146]) ).
tff(f146,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,[],[f7]) ).
tff(f7,axiom,
! [X9: nat,X10: dB] :
( pp(aa(dB,bool,it,X10))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_lift__IT) ).
tff(f876,plain,
spl29_61,
inference(avatar_split_clause,[],[f384,f874]) ).
tff(f874,plain,
( spl29_61
<=> ! [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,[spl29_61])]) ).
tff(f384,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,[],[f137]) ).
tff(f137,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,[],[f34]) ).
tff(f34,axiom,
! [X35: dB,X24: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X24)),X35),X24) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_subst__eq) ).
tff(f872,plain,
spl29_60,
inference(avatar_split_clause,[],[f368,f870]) ).
tff(f870,plain,
( spl29_60
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK9(X0)))
| ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_60])]) ).
tff(f368,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK9(X0)))
| ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK9(X0)))
& ( abs(sK9(X0)) = X0 ) )
| ( listsp(dB,it,sK10(X0))
& ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f271,f273,f272]) ).
tff(f272,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK9(X0)))
& ( abs(sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f273,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK10(X0))
& ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f271,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,[],[f270]) ).
tff(f270,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,[],[f269]) ).
tff(f269,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,[],[f258]) ).
tff(f258,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f868,plain,
spl29_59,
inference(avatar_split_clause,[],[f336,f865]) ).
tff(f865,plain,
( spl29_59
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_59])]) ).
tff(f336,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_uT) ).
tff(f863,plain,
spl29_58,
inference(avatar_split_clause,[],[f335,f860]) ).
tff(f860,plain,
( spl29_58
<=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_58])]) ).
tff(f335,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Var_I4_J) ).
tff(f858,plain,
( spl29_57
| ~ spl29_11
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f631,f605,f574,f855]) ).
tff(f855,plain,
( spl29_57
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_57])]) ).
tff(f631,plain,
( sP1(u)
| ~ spl29_11
| ~ spl29_16 ),
inference(resolution,[],[f606,f576]) ).
tff(f850,plain,
spl29_56,
inference(avatar_split_clause,[],[f426,f848]) ).
tff(f848,plain,
( spl29_56
<=> ! [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,[spl29_56])]) ).
tff(f426,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,[],[f175]) ).
tff(f175,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,[],[f92]) ).
tff(f92,axiom,
! [X61: list(dB),X55: nat,X15: dB,X38: dB] : ( foldl(dB,dB,app,var(X55),X61) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X38)),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Abs__App__neq__Var__apps) ).
tff(f846,plain,
spl29_55,
inference(avatar_split_clause,[],[f366,f844]) ).
tff(f366,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK9(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f839,plain,
spl29_54,
inference(avatar_split_clause,[],[f443,f837]) ).
tff(f837,plain,
( spl29_54
<=> ! [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,[spl29_54])]) ).
tff(f443,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,[],[f301]) ).
tff(f301,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,[],[f300]) ).
tff(f300,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,[],[f185]) ).
tff(f185,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,
! [X61: list(dB),X55: nat,X56: list(dB),X62: nat] :
( ( foldl(dB,dB,app,var(X62),X56) = foldl(dB,dB,app,var(X55),X61) )
<=> ( ( X56 = X61 )
& ( X55 = X62 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Var__apps__eq__Var__apps__conv) ).
tff(f835,plain,
spl29_53,
inference(avatar_split_clause,[],[f440,f833]) ).
tff(f833,plain,
( spl29_53
<=> ! [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,[spl29_53])]) ).
tff(f440,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,[],[f299]) ).
tff(f299,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,[],[f298]) ).
tff(f298,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,[],[f184]) ).
tff(f184,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,[],[f86]) ).
tff(f86,axiom,
! [X61: list(dB),X38: dB,X56: list(dB),X60: dB] :
( ( foldl(dB,dB,app,abs(X60),X56) = foldl(dB,dB,app,abs(X38),X61) )
<=> ( ( X56 = X61 )
& ( X38 = X60 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Abs__apps__eq__Abs__apps__conv) ).
tff(f831,plain,
( spl29_52
| ~ spl29_9
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f630,f605,f564,f828]) ).
tff(f828,plain,
( spl29_52
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_52])]) ).
tff(f630,plain,
( sP1(t3)
| ~ spl29_9
| ~ spl29_16 ),
inference(resolution,[],[f606,f566]) ).
tff(f826,plain,
spl29_51,
inference(avatar_split_clause,[],[f402,f824]) ).
tff(f402,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,[],[f154]) ).
tff(f154,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,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X64: list(X0),X63: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X63),X64) != X64 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_not__Cons__self2) ).
tff(f822,plain,
spl29_50,
inference(avatar_split_clause,[],[f334,f819]) ).
tff(f334,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54__096rs_A_061_Aa_A_D_Aas_096) ).
tff(f815,plain,
spl29_49,
inference(avatar_split_clause,[],[f442,f813]) ).
tff(f813,plain,
( spl29_49
<=> ! [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,[spl29_49])]) ).
tff(f442,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,[],[f301]) ).
tff(f811,plain,
spl29_48,
inference(avatar_split_clause,[],[f439,f809]) ).
tff(f809,plain,
( spl29_48
<=> ! [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,[spl29_48])]) ).
tff(f439,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,[],[f299]) ).
tff(f807,plain,
spl29_47,
inference(avatar_split_clause,[],[f333,f804]) ).
tff(f804,plain,
( spl29_47
<=> ( t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_47])]) ).
tff(f333,plain,
t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
inference(cnf_transformation,[],[f44]) ).
tff(f44,axiom,
t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_T) ).
tff(f778,plain,
spl29_46,
inference(avatar_split_clause,[],[f421,f776]) ).
tff(f776,plain,
( spl29_46
<=> ! [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,[spl29_46])]) ).
tff(f421,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,[],[f286]) ).
tff(f286,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,[],[f172]) ).
tff(f172,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,
! [X38: dB,X45: list(dB),X60: dB] :
( ( foldl(dB,dB,app,X60,X45) = foldl(dB,dB,app,X38,X45) )
<=> ( X38 = X60 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_apps__eq__tail__conv) ).
tff(f774,plain,
spl29_45,
inference(avatar_split_clause,[],[f412,f772]) ).
tff(f772,plain,
( spl29_45
<=> ! [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,[spl29_45])]) ).
tff(f412,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,[],[f164]) ).
tff(f164,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X92: X0,X63: X0] :
( ( X63 = X92 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X63),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f770,plain,
spl29_44,
inference(avatar_split_clause,[],[f391,f768]) ).
tff(f768,plain,
( spl29_44
<=> ! [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,[spl29_44])]) ).
tff(f391,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,[],[f221]) ).
tff(f221,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,[],[f145]) ).
tff(f145,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X55: nat,X56: list(dB)] :
( listsp(dB,it,X56)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X55),X56))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_IT_OVar) ).
tff(f766,plain,
spl29_43,
inference(avatar_split_clause,[],[f390,f764]) ).
tff(f764,plain,
( spl29_43
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_43])]) ).
tff(f390,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
inference(rectify,[],[f118]) ).
tff(f118,axiom,
! [X91: bool,X89: bool] :
( pp(X91)
| ~ pp(X89)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
tff(f762,plain,
spl29_42,
inference(avatar_split_clause,[],[f385,f760]) ).
tff(f760,plain,
( spl29_42
<=> ! [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,[spl29_42])]) ).
tff(f385,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X91: bool,X89: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91))
| ~ pp(X91)
| ~ pp(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f758,plain,
spl29_41,
inference(avatar_split_clause,[],[f369,f756]) ).
tff(f369,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK9(X0)))
| listsp(dB,it,sK10(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f738,plain,
spl29_40,
inference(avatar_split_clause,[],[f425,f736]) ).
tff(f736,plain,
( spl29_40
<=> ! [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,[spl29_40])]) ).
tff(f425,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,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,[],[f93]) ).
tff(f93,axiom,
! [X61: list(dB),X60: dB,X45: list(dB),X55: nat] : ( foldl(dB,dB,app,var(X55),X45) != foldl(dB,dB,app,abs(X60),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Var__apps__neq__Abs__apps) ).
tff(f734,plain,
spl29_39,
inference(avatar_split_clause,[],[f411,f732]) ).
tff(f732,plain,
( spl29_39
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_39])]) ).
tff(f411,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X0: $tType,X63: X0,X89: fun(X0,bool)] :
( pp(aa(X0,bool,X89,X63))
| ~ pp(aa(fun(X0,bool),bool,fAll(X0),X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fAll_1_1_U) ).
tff(f730,plain,
spl29_38,
inference(avatar_split_clause,[],[f410,f728]) ).
tff(f410,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X63: X0,X89: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X89))
| ~ pp(aa(X0,bool,X89,X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f724,plain,
( spl29_37
| ~ spl29_1
| ~ spl29_24 ),
inference(avatar_split_clause,[],[f665,f650,f526,f721]) ).
tff(f721,plain,
( spl29_37
<=> sP1(abs(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_37])]) ).
tff(f665,plain,
( sP1(abs(sK4))
| ~ spl29_1
| ~ spl29_24 ),
inference(resolution,[],[f651,f528]) ).
tff(f717,plain,
spl29_36,
inference(avatar_split_clause,[],[f400,f715]) ).
tff(f715,plain,
( spl29_36
<=> ! [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,[spl29_36])]) ).
tff(f400,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X41: nat,X39: dB,X40: dB] : ( var(X41) != aa(dB,dB,aa(dB,fun(dB,dB),app,X40),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_dB_Osimps_I5_J) ).
tff(f713,plain,
spl29_35,
inference(avatar_split_clause,[],[f398,f711]) ).
tff(f711,plain,
( spl29_35
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_35])]) ).
tff(f398,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X79: dB,X77: dB,X78: dB] : ( abs(X79) != aa(dB,dB,aa(dB,fun(dB,dB),app,X78),X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dB_Osimps_I8_J) ).
tff(f709,plain,
spl29_34,
inference(avatar_split_clause,[],[f389,f707]) ).
tff(f707,plain,
( spl29_34
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_34])]) ).
tff(f389,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X91: bool,X89: bool] :
( pp(X91)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f705,plain,
spl29_33,
inference(avatar_split_clause,[],[f388,f703]) ).
tff(f703,plain,
( spl29_33
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_33])]) ).
tff(f388,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X91: bool,X89: bool] :
( pp(X89)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f701,plain,
spl29_32,
inference(avatar_split_clause,[],[f387,f699]) ).
tff(f699,plain,
( spl29_32
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_32])]) ).
tff(f387,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X91: bool,X89: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91))
| pp(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
tff(f697,plain,
spl29_31,
inference(avatar_split_clause,[],[f386,f695]) ).
tff(f695,plain,
( spl29_31
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_31])]) ).
tff(f386,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(rectify,[],[f117]) ).
tff(f117,axiom,
! [X89: bool,X91: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91))
| ~ pp(X91) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
tff(f693,plain,
spl29_30,
inference(avatar_split_clause,[],[f367,f691]) ).
tff(f691,plain,
( spl29_30
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK9(X0)) = X0 )
| listsp(dB,it,sK10(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_30])]) ).
tff(f367,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK9(X0)) = X0 )
| listsp(dB,it,sK10(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f685,plain,
spl29_29,
inference(avatar_split_clause,[],[f502,f683]) ).
tff(f683,plain,
( spl29_29
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_29])]) ).
tff(f502,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f409]) ).
tff(f409,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X0: $tType,X92: X0,X63: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X63),X92))
| ( X63 != X92 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f681,plain,
spl29_28,
inference(avatar_split_clause,[],[f365,f679]) ).
tff(f365,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X22: dB] :
( pp(aa(dB,bool,it,X22))
=> pp(aa(dB,bool,it,abs(X22))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Lambda) ).
tff(f676,plain,
spl29_27,
inference(avatar_split_clause,[],[f321,f673]) ).
tff(f321,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b),sK3)),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
& pp(aa(dB,bool,it,sK4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b),sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f213,f260]) ).
tff(f260,plain,
( ? [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
& pp(aa(dB,bool,it,X2))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X0),X3),t)),b),X1)) )
=> ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
& pp(aa(dB,bool,it,sK4))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),sK2),sK5),t)),b),sK3)) ) ),
introduced(choice_axiom,[]) ).
tff(f213,plain,
? [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
& pp(aa(dB,bool,it,X2))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X0),X3),t)),b),X1)) ),
inference(ennf_transformation,[],[f121]) ).
tff(f121,plain,
~ ! [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X0),X3),t)),b),X1)) ),
inference(rectify,[],[f120]) ).
tff(f120,negated_conjecture,
~ ! [X93: fun(nat,type),X94: type,X95: dB,X96: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X95),X96)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X93),X95),t))
| ~ pp(aa(dB,bool,it,X95))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X93),X96),t)),b),X94)) ),
inference(negated_conjecture,[],[f119]) ).
tff(f119,conjecture,
! [X93: fun(nat,type),X94: type,X95: dB,X96: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X95),X96)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X93),X95),t))
| ~ pp(aa(dB,bool,it,X95))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X93),X96),t)),b),X94)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f671,plain,
spl29_26,
inference(avatar_split_clause,[],[f498,f669]) ).
tff(f669,plain,
( spl29_26
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_26])]) ).
tff(f498,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f370]) ).
tff(f370,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,[],[f274]) ).
tff(f659,plain,
( spl29_25
| ~ spl29_1
| ~ spl29_16 ),
inference(avatar_split_clause,[],[f633,f605,f526,f656]) ).
tff(f633,plain,
( sP1(sK4)
| ~ spl29_1
| ~ spl29_16 ),
inference(resolution,[],[f606,f528]) ).
tff(f652,plain,
spl29_24,
inference(avatar_split_clause,[],[f497,f650]) ).
tff(f497,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f371]) ).
tff(f371,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f274]) ).
tff(f648,plain,
spl29_23,
inference(avatar_split_clause,[],[f383,f646]) ).
tff(f646,plain,
( spl29_23
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_23])]) ).
tff(f383,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType,X50: list(X0)] : ( map(X0,X0,combi(X0),X50) = X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_map__ident) ).
tff(f644,plain,
spl29_22,
inference(avatar_split_clause,[],[f375,f642]) ).
tff(f375,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK13(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f628,plain,
spl29_21,
inference(avatar_split_clause,[],[f396,f626]) ).
tff(f626,plain,
( spl29_21
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_21])]) ).
tff(f396,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X29: nat,X30: nat] :
( ( var(X30) = var(X29) )
<=> ( X29 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dB_Osimps_I1_J) ).
tff(f624,plain,
( spl29_20
| spl29_2
| ~ spl29_1
| ~ spl29_13 ),
inference(avatar_split_clause,[],[f592,f583,f526,f531,f621]) ).
tff(f592,plain,
( pp(fFalse)
| ( fTrue = aa(dB,bool,it,sK4) )
| ~ spl29_1
| ~ spl29_13 ),
inference(superposition,[],[f528,f584]) ).
tff(f619,plain,
spl29_19,
inference(avatar_split_clause,[],[f394,f617]) ).
tff(f617,plain,
( spl29_19
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_19])]) ).
tff(f394,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X75: dB,X76: dB] :
( ( abs(X76) = abs(X75) )
<=> ( X75 = X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dB_Osimps_I3_J) ).
tff(f615,plain,
spl29_18,
inference(avatar_split_clause,[],[f382,f613]) ).
tff(f382,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X0: $tType,X89: X0] : ( aa(X0,X0,combi(X0),X89) = X89 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f611,plain,
spl29_17,
inference(avatar_split_clause,[],[f378,f609]) ).
tff(f378,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f131,f258,f257]) ).
tff(f131,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,[],[f96]) ).
tff(f96,axiom,
! [X53: dB] :
( pp(aa(dB,bool,it,X53))
<=> ( ? [X84: dB,X85: dB,X86: list(dB)] :
( pp(aa(dB,bool,it,X85))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X84),X85),zero_zero(nat)),X86)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X84)),X85),X86) = X53 ) )
| ? [X84: dB] :
( pp(aa(dB,bool,it,X84))
& ( abs(X84) = X53 ) )
| ? [X82: list(dB),X83: nat] :
( listsp(dB,it,X82)
& ( foldl(dB,dB,app,var(X83),X82) = X53 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_IT_Osimps) ).
tff(f607,plain,
spl29_16,
inference(avatar_split_clause,[],[f377,f605]) ).
tff(f377,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f602,plain,
spl29_15,
inference(avatar_split_clause,[],[f381,f600]) ).
tff(f600,plain,
( spl29_15
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).
tff(f381,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X71: fun(X0,bool)] : ( collect(X0,X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
tff(f598,plain,
spl29_14,
inference(avatar_split_clause,[],[f360,f596]) ).
tff(f360,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X42: nat] : pp(aa(dB,bool,it,var(X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Var__IT) ).
tff(f585,plain,
spl29_13,
inference(avatar_split_clause,[],[f361,f583]) ).
tff(f361,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X89: bool] :
( ( fFalse = X89 )
| ( fTrue = X89 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f581,plain,
spl29_12,
inference(avatar_split_clause,[],[f359,f579]) ).
tff(f579,plain,
( spl29_12
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_12])]) ).
tff(f359,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X41: nat] : ( zero_zero(nat) = dB_size(var(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dB_Osize_I1_J) ).
tff(f577,plain,
spl29_11,
inference(avatar_split_clause,[],[f332,f574]) ).
tff(f332,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uIT) ).
tff(f572,plain,
spl29_10,
inference(avatar_split_clause,[],[f331,f569]) ).
tff(f331,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Var_I3_J) ).
tff(f567,plain,
spl29_9,
inference(avatar_split_clause,[],[f330,f564]) ).
tff(f330,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096IT_At_096) ).
tff(f562,plain,
~ spl29_8,
inference(avatar_split_clause,[],[f324,f559]) ).
tff(f324,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))),
inference(cnf_transformation,[],[f261]) ).
tff(f557,plain,
spl29_7,
inference(avatar_split_clause,[],[f323,f554]) ).
tff(f323,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t)),
inference(cnf_transformation,[],[f261]) ).
tff(f552,plain,
spl29_6,
inference(avatar_split_clause,[],[f379,f550]) ).
tff(f550,plain,
( spl29_6
<=> ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).
tff(f379,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X41: nat,X79: dB] : ( var(X41) != abs(X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osimps_I7_J) ).
tff(f548,plain,
spl29_5,
inference(avatar_split_clause,[],[f372,f546]) ).
tff(f546,plain,
( spl29_5
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).
tff(f372,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f544,plain,
spl29_4,
inference(avatar_split_clause,[],[f328,f541]) ).
tff(f328,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f539,plain,
spl29_3,
inference(avatar_split_clause,[],[f327,f536]) ).
tff(f536,plain,
( spl29_3
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
tff(f327,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f534,plain,
~ spl29_2,
inference(avatar_split_clause,[],[f325,f531]) ).
tff(f325,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(f529,plain,
spl29_1,
inference(avatar_split_clause,[],[f322,f526]) ).
tff(f322,plain,
pp(aa(dB,bool,it,sK4)),
inference(cnf_transformation,[],[f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL806_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 14:09:27 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (2797)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2800)WARNING: value z3 for option sas not known
% 0.21/0.42 % (2801)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.42 % (2798)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.42 % (2802)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)
% 0.21/0.42 % (2799)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.42 % (2803)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)
% 0.21/0.42 % (2800)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)
% 0.21/0.42 % (2804)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)
% 0.21/0.43 % (2804)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % (2806)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)
% 0.21/0.45 % (2805)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.45 % (2807)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)
% 0.21/0.46 % (2806)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46 % (2805)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46 % Exception at run slice level
% 0.21/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.47 % (2808)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.31/0.57 % (2802)First to succeed.
% 1.31/0.60 % (2802)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2797"
% 1.31/0.60 % (2802)Refutation found. Thanks to Tanya!
% 1.31/0.60 % SZS status Theorem for theBenchmark
% 1.31/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.60 % (2802)------------------------------
% 1.31/0.60 % (2802)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.31/0.60 % (2802)Termination reason: Refutation
% 1.31/0.60
% 1.31/0.60 % (2802)Memory used [KB]: 3058
% 1.31/0.60 % (2802)Time elapsed: 0.181 s
% 1.31/0.60 % (2802)Instructions burned: 478 (million)
% 1.31/0.60 % (2797)Success in time 0.233 s
%------------------------------------------------------------------------------