TSTP Solution File: COM111_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM111_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 : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:47:48 EDT 2024
% Result : Theorem 2.57s 0.68s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 461
% Syntax : Number of formulae : 1303 ( 272 unt; 76 typ; 0 def)
% Number of atoms : 3076 ( 893 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3091 (1242 ~;1321 |; 83 &)
% ( 290 <=>; 155 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 24 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 48 ( 31 >; 17 *; 0 +; 0 <<)
% Number of predicates : 271 ( 269 usr; 251 prp; 0-2 aty)
% Number of functors : 54 ( 54 usr; 13 con; 0-5 aty)
% Number of variables : 2545 (2429 !; 44 ?;2545 :)
% ( 72 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
atom: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
big_linorder_Max:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_1,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_2,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).
tff(func_def_3,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_4,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_5,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_6,type,
div_mod:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_7,type,
minus_minus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_8,type,
plus_plus:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_9,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_10,type,
iprod:
!>[X0: $tType] : fun(list(X0),fun(list(X0),X0)) ).
tff(func_def_11,type,
filter:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_15,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_16,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_17,type,
atom_case:
!>[X0: $tType] : ( ( fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) ) > fun(atom,X0) ) ).
tff(func_def_18,type,
divisor: fun(atom,int) ).
tff(func_def_19,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_20,type,
zlcms: list(int) > int ).
tff(func_def_21,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_22,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_25,type,
fFalse: bool ).
tff(func_def_26,type,
fTrue: bool ).
tff(func_def_27,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_28,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
a: atom ).
tff(func_def_32,type,
as: list(atom) ).
tff(func_def_33,type,
li: int ).
tff(func_def_34,type,
lks: list(int) ).
tff(func_def_35,type,
x: int ).
tff(func_def_36,type,
xs: list(int) ).
tff(func_def_37,type,
sK0: int ).
tff(func_def_38,type,
sK1: list(int) ).
tff(func_def_39,type,
sK2:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > X0 ) ).
tff(func_def_40,type,
sK3:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_41,type,
sK4:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_42,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_43,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_44,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_45,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_46,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_47,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_48,type,
sK11:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(X1,bool) ) > X1 ) ).
tff(func_def_49,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_50,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X1) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_div:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
finite_finite:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
linord2061991079up_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
finite_finite1:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_18,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f5028,plain,
$false,
inference(avatar_sat_refutation,[],[f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f654,f659,f664,f669,f674,f679,f684,f689,f694,f699,f703,f707,f711,f715,f719,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f766,f772,f776,f780,f784,f794,f798,f802,f806,f812,f819,f823,f827,f831,f835,f843,f847,f851,f857,f861,f865,f869,f873,f877,f881,f885,f900,f904,f908,f920,f924,f928,f932,f936,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1126,f1130,f1163,f1167,f1171,f1175,f1217,f1221,f1225,f1231,f1235,f1239,f1243,f1282,f1286,f1290,f1314,f1338,f1342,f1356,f1360,f1364,f1370,f1374,f1378,f1382,f1386,f1415,f1419,f1423,f1478,f1482,f1486,f1509,f1513,f1558,f1562,f1589,f1593,f1616,f1620,f1624,f1628,f1650,f1654,f1658,f1662,f1766,f1771,f1775,f1781,f1785,f1790,f1830,f1847,f1865,f1938,f1986,f1995,f2000,f2005,f2044,f2048,f2052,f2056,f2060,f2064,f2078,f2089,f2093,f2104,f2114,f2143,f2153,f2169,f2175,f2180,f2194,f2200,f2206,f2211,f2216,f2222,f2228,f2234,f2257,f2264,f2277,f2321,f2325,f2370,f2374,f2378,f2391,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2554,f2558,f2562,f2596,f2622,f2623,f2624,f2625,f2626,f2627,f2628,f2629,f2630,f2631,f2632,f3570,f3574,f3617,f3628,f3636,f3659,f3673,f3677,f3681,f3685,f3689,f3768,f3772,f3776,f3780,f3784,f3788,f3793,f3797,f3984,f3995,f3999,f4075,f4079,f4083,f4087,f4091,f4092,f4166,f4174,f4182,f4186,f4194,f4198,f4202,f4206,f4300,f4308,f4312,f4316,f4320,f4521,f4526,f4530,f4534,f4538,f4634,f4638,f4642,f4704,f4708,f4712,f4716,f4720,f4724,f4733,f4749,f4753,f4757,f4761,f4863,f4962]) ).
tff(f4962,plain,
( spl14_165
| ~ spl14_247 ),
inference(avatar_contradiction_clause,[],[f4961]) ).
tff(f4961,plain,
( $false
| spl14_165
| ~ spl14_247 ),
inference(trivial_inequality_removal,[],[f4956]) ).
tff(f4956,plain,
( ( div_mod(int,aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as))))),aa(atom,int,divisor,a)) != div_mod(int,aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as))))),aa(atom,int,divisor,a)) )
| spl14_165
| ~ spl14_247 ),
inference(superposition,[],[f2263,f4752]) ).
tff(f4752,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl14_247 ),
inference(avatar_component_clause,[],[f4751]) ).
tff(f4751,plain,
( spl14_247
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_247])]) ).
tff(f2263,plain,
( ( div_mod(int,aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as))))),aa(atom,int,divisor,a)) != div_mod(int,aa(int,int,plus_plus(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)),aa(atom,int,divisor,a))),div_mod(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) )
| spl14_165 ),
inference(avatar_component_clause,[],[f2261]) ).
tff(f2261,plain,
( spl14_165
<=> ( div_mod(int,aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as))))),aa(atom,int,divisor,a)) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)),aa(atom,int,divisor,a))),div_mod(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_165])]) ).
tff(f4863,plain,
( ~ spl14_250
| ~ spl14_93
| spl14_245 ),
inference(avatar_split_clause,[],[f4734,f4730,f1288,f4860]) ).
tff(f4860,plain,
( spl14_250
<=> pp(aa(int,bool,bot_bot(fun(int,bool)),zero_zero(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_250])]) ).
tff(f1288,plain,
( spl14_93
<=> ! [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,[spl14_93])]) ).
tff(f4730,plain,
( spl14_245
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),bot_bot(fun(int,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_245])]) ).
tff(f4734,plain,
( ~ pp(aa(int,bool,bot_bot(fun(int,bool)),zero_zero(int)))
| ~ spl14_93
| spl14_245 ),
inference(resolution,[],[f4732,f1289]) ).
tff(f1289,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)) )
| ~ spl14_93 ),
inference(avatar_component_clause,[],[f1288]) ).
tff(f4732,plain,
( ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),bot_bot(fun(int,bool))))
| spl14_245 ),
inference(avatar_component_clause,[],[f4730]) ).
tff(f4761,plain,
( spl14_249
| ~ spl14_33
| ~ spl14_40
| ~ spl14_112 ),
inference(avatar_split_clause,[],[f1538,f1511,f782,f752,f4759]) ).
tff(f4759,plain,
( spl14_249
<=> ! [X0: $tType,X2: fun(X0,X0),X1: list(X0)] :
( ( map(X0,X0,X2,X1) = X1 )
| ( sK13(X0,X0,combi(X0),X1,X2) != aa(X0,X0,X2,sK13(X0,X0,combi(X0),X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_249])]) ).
tff(f752,plain,
( spl14_33
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_33])]) ).
tff(f782,plain,
( spl14_40
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_40])]) ).
tff(f1511,plain,
( spl14_112
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: list(X1),X2: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| ( aa(X1,X0,X4,sK13(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_112])]) ).
tff(f1538,plain,
( ! [X0: $tType,X2: fun(X0,X0),X1: list(X0)] :
( ( map(X0,X0,X2,X1) = X1 )
| ( sK13(X0,X0,combi(X0),X1,X2) != aa(X0,X0,X2,sK13(X0,X0,combi(X0),X1,X2)) ) )
| ~ spl14_33
| ~ spl14_40
| ~ spl14_112 ),
inference(forward_demodulation,[],[f1529,f783]) ).
tff(f783,plain,
( ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 )
| ~ spl14_40 ),
inference(avatar_component_clause,[],[f782]) ).
tff(f1529,plain,
( ! [X0: $tType,X2: fun(X0,X0),X1: list(X0)] :
( ( sK13(X0,X0,combi(X0),X1,X2) != aa(X0,X0,X2,sK13(X0,X0,combi(X0),X1,X2)) )
| ( map(X0,X0,combi(X0),X1) = map(X0,X0,X2,X1) ) )
| ~ spl14_33
| ~ spl14_112 ),
inference(superposition,[],[f1512,f753]) ).
tff(f753,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl14_33 ),
inference(avatar_component_clause,[],[f752]) ).
tff(f1512,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( aa(X1,X0,X4,sK13(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3,X4)) )
| ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) ) )
| ~ spl14_112 ),
inference(avatar_component_clause,[],[f1511]) ).
tff(f4757,plain,
( spl14_248
| ~ spl14_33
| ~ spl14_40
| ~ spl14_112 ),
inference(avatar_split_clause,[],[f1537,f1511,f782,f752,f4755]) ).
tff(f4755,plain,
( spl14_248
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ( sK13(X0,X0,X1,X2,combi(X0)) != aa(X0,X0,X1,sK13(X0,X0,X1,X2,combi(X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_248])]) ).
tff(f1537,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ( sK13(X0,X0,X1,X2,combi(X0)) != aa(X0,X0,X1,sK13(X0,X0,X1,X2,combi(X0))) ) )
| ~ spl14_33
| ~ spl14_40
| ~ spl14_112 ),
inference(forward_demodulation,[],[f1517,f783]) ).
tff(f1517,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( sK13(X0,X0,X1,X2,combi(X0)) != aa(X0,X0,X1,sK13(X0,X0,X1,X2,combi(X0))) )
| ( map(X0,X0,combi(X0),X2) = map(X0,X0,X1,X2) ) )
| ~ spl14_33
| ~ spl14_112 ),
inference(superposition,[],[f1512,f753]) ).
tff(f4753,plain,
( spl14_247
| ~ spl14_13
| ~ spl14_102 ),
inference(avatar_split_clause,[],[f1396,f1376,f661,f4751]) ).
tff(f661,plain,
( spl14_13
<=> semiring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
tff(f1376,plain,
( spl14_102
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_102])]) ).
tff(f1396,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl14_13
| ~ spl14_102 ),
inference(resolution,[],[f1377,f663]) ).
tff(f663,plain,
( semiring_div(int)
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f1377,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) )
| ~ spl14_102 ),
inference(avatar_component_clause,[],[f1376]) ).
tff(f4749,plain,
( spl14_246
| ~ spl14_5
| ~ spl14_101 ),
inference(avatar_split_clause,[],[f1395,f1372,f621,f4747]) ).
tff(f4747,plain,
( spl14_246
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,plus_plus(int,aa(int,int,plus_plus(int,X0),X1)),X2) = aa(int,int,plus_plus(int,X0),aa(int,int,plus_plus(int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_246])]) ).
tff(f621,plain,
( spl14_5
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
tff(f1372,plain,
( spl14_101
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X3),X2)),X1) = aa(X0,X0,plus_plus(X0,X3),aa(X0,X0,plus_plus(X0,X2),X1)) )
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_101])]) ).
tff(f1395,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,plus_plus(int,aa(int,int,plus_plus(int,X0),X1)),X2) = aa(int,int,plus_plus(int,X0),aa(int,int,plus_plus(int,X1),X2)) )
| ~ spl14_5
| ~ spl14_101 ),
inference(resolution,[],[f1373,f623]) ).
tff(f623,plain,
( ab_semigroup_add(int)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f1373,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_add(X0)
| ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X3),X2)),X1) = aa(X0,X0,plus_plus(X0,X3),aa(X0,X0,plus_plus(X0,X2),X1)) ) )
| ~ spl14_101 ),
inference(avatar_component_clause,[],[f1372]) ).
tff(f4733,plain,
( spl14_244
| ~ spl14_245
| ~ spl14_46
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f1346,f1340,f810,f4730,f4726]) ).
tff(f4726,plain,
( spl14_244
<=> ( zero_zero(int) = zlcms(nil(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_244])]) ).
tff(f810,plain,
( spl14_46
<=> ! [X0: $tType] : ( set(X0,nil(X0)) = bot_bot(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_46])]) ).
tff(f1340,plain,
( spl14_96
<=> ! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_96])]) ).
tff(f1346,plain,
( ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),bot_bot(fun(int,bool))))
| ( zero_zero(int) = zlcms(nil(int)) )
| ~ spl14_46
| ~ spl14_96 ),
inference(superposition,[],[f1341,f811]) ).
tff(f811,plain,
( ! [X0: $tType] : ( set(X0,nil(X0)) = bot_bot(fun(X0,bool)) )
| ~ spl14_46 ),
inference(avatar_component_clause,[],[f810]) ).
tff(f1341,plain,
( ! [X0: list(int)] :
( ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0)))
| ( zero_zero(int) = zlcms(X0) ) )
| ~ spl14_96 ),
inference(avatar_component_clause,[],[f1340]) ).
tff(f4724,plain,
( spl14_243
| ~ spl14_24
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1333,f1312,f713,f4722]) ).
tff(f4722,plain,
( spl14_243
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue != aa(X0,bool,X2,sK12(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fFalse = aa(X0,bool,X1,sK12(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_243])]) ).
tff(f713,plain,
( spl14_24
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
tff(f1312,plain,
( spl14_94
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK12(X0,X1,X2,X3)) != aa(X1,X0,X2,sK12(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_94])]) ).
tff(f1333,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue != aa(X0,bool,X2,sK12(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fFalse = aa(X0,bool,X1,sK12(bool,X0,X1,X2)) ) )
| ~ spl14_24
| ~ spl14_94 ),
inference(superposition,[],[f1313,f714]) ).
tff(f714,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f713]) ).
tff(f1313,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK12(X0,X1,X2,X3)) != aa(X1,X0,X2,sK12(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl14_94 ),
inference(avatar_component_clause,[],[f1312]) ).
tff(f4720,plain,
( spl14_242
| ~ spl14_24
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1321,f1312,f713,f4718]) ).
tff(f4718,plain,
( spl14_242
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue != aa(X0,bool,X2,sK12(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fFalse = aa(X0,bool,X1,sK12(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_242])]) ).
tff(f1321,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fTrue != aa(X0,bool,X2,sK12(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fFalse = aa(X0,bool,X1,sK12(bool,X0,X2,X1)) ) )
| ~ spl14_24
| ~ spl14_94 ),
inference(superposition,[],[f1313,f714]) ).
tff(f4716,plain,
( spl14_241
| ~ spl14_58
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1138,f1128,f867,f4714]) ).
tff(f4714,plain,
( spl14_241
<=> ! [X2: bool,X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = filter(bool,aa(bool,fun(bool,bool),fconj,X0),cons(bool,X2,X1)) )
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_241])]) ).
tff(f867,plain,
( spl14_58
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_58])]) ).
tff(f1128,plain,
( spl14_79
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: list(X0)] :
( ( filter(X0,X3,X1) = filter(X0,X3,cons(X0,X2,X1)) )
| pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_79])]) ).
tff(f1138,plain,
( ! [X2: bool,X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = filter(bool,aa(bool,fun(bool,bool),fconj,X0),cons(bool,X2,X1)) )
| pp(X0) )
| ~ spl14_58
| ~ spl14_79 ),
inference(resolution,[],[f1129,f868]) ).
tff(f868,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X1) )
| ~ spl14_58 ),
inference(avatar_component_clause,[],[f867]) ).
tff(f1129,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( pp(aa(X0,bool,X3,X2))
| ( filter(X0,X3,X1) = filter(X0,X3,cons(X0,X2,X1)) ) )
| ~ spl14_79 ),
inference(avatar_component_clause,[],[f1128]) ).
tff(f4712,plain,
( spl14_240
| ~ spl14_59
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1137,f1128,f871,f4710]) ).
tff(f4710,plain,
( spl14_240
<=> ! [X2: bool,X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = filter(bool,aa(bool,fun(bool,bool),fconj,X0),cons(bool,X2,X1)) )
| pp(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_240])]) ).
tff(f871,plain,
( spl14_59
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_59])]) ).
tff(f1137,plain,
( ! [X2: bool,X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = filter(bool,aa(bool,fun(bool,bool),fconj,X0),cons(bool,X2,X1)) )
| pp(X2) )
| ~ spl14_59
| ~ spl14_79 ),
inference(resolution,[],[f1129,f872]) ).
tff(f872,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X0) )
| ~ spl14_59 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f4708,plain,
( spl14_239
| ~ spl14_68
| ~ spl14_76 ),
inference(avatar_split_clause,[],[f1107,f1077,f926,f4706]) ).
tff(f4706,plain,
( spl14_239
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = nil(bool) )
| pp(X0)
| pp(sK4(bool,X1,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_239])]) ).
tff(f926,plain,
( spl14_68
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_68])]) ).
tff(f1077,plain,
( spl14_76
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = filter(X0,X2,X1) )
| pp(aa(X0,bool,X2,sK4(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_76])]) ).
tff(f1107,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = nil(bool) )
| pp(X0)
| pp(sK4(bool,X1,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl14_68
| ~ spl14_76 ),
inference(resolution,[],[f1078,f927]) ).
tff(f927,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| pp(X1)
| pp(X0) )
| ~ spl14_68 ),
inference(avatar_component_clause,[],[f926]) ).
tff(f1078,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( pp(aa(X0,bool,X2,sK4(X0,X1,X2)))
| ( nil(X0) = filter(X0,X2,X1) ) )
| ~ spl14_76 ),
inference(avatar_component_clause,[],[f1077]) ).
tff(f4704,plain,
( spl14_238
| ~ spl14_68
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1090,f1073,f926,f4702]) ).
tff(f4702,plain,
( spl14_238
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = nil(bool) )
| pp(X0)
| pp(sK2(bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_238])]) ).
tff(f1073,plain,
( spl14_75
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,X1,sK2(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_75])]) ).
tff(f1090,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = nil(bool) )
| pp(X0)
| pp(sK2(bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) )
| ~ spl14_68
| ~ spl14_75 ),
inference(resolution,[],[f1074,f927]) ).
tff(f1074,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,sK2(X0,X1,X2)))
| ( nil(X0) = filter(X0,X1,X2) ) )
| ~ spl14_75 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f4642,plain,
( spl14_237
| ~ spl14_39
| ~ spl14_46
| ~ spl14_111 ),
inference(avatar_split_clause,[],[f1516,f1507,f810,f778,f4640]) ).
tff(f4640,plain,
( spl14_237
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),bot_bot(fun(X0,bool))))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_237])]) ).
tff(f778,plain,
( spl14_39
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = filter(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_39])]) ).
tff(f1507,plain,
( spl14_111
<=> ! [X0: $tType,X4: X0,X2: fun(X0,bool),X1: list(X0)] :
( ~ pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| ( nil(X0) != filter(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_111])]) ).
tff(f1516,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),bot_bot(fun(X0,bool))))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_46
| ~ spl14_111 ),
inference(forward_demodulation,[],[f1515,f811]) ).
tff(f1515,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),set(X0,nil(X0))))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_111 ),
inference(trivial_inequality_removal,[],[f1514]) ).
tff(f1514,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ( nil(X0) != nil(X0) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),set(X0,nil(X0))))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_111 ),
inference(superposition,[],[f1508,f779]) ).
tff(f779,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = filter(X0,X1,nil(X0)) )
| ~ spl14_39 ),
inference(avatar_component_clause,[],[f778]) ).
tff(f1508,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0),X4: X0] :
( ( nil(X0) != filter(X0,X2,X1) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| ~ pp(aa(X0,bool,X2,X4)) )
| ~ spl14_111 ),
inference(avatar_component_clause,[],[f1507]) ).
tff(f4638,plain,
( spl14_236
| ~ spl14_39
| ~ spl14_46
| ~ spl14_110 ),
inference(avatar_split_clause,[],[f1505,f1484,f810,f778,f4636]) ).
tff(f4636,plain,
( spl14_236
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),bot_bot(fun(X0,bool))))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_236])]) ).
tff(f1484,plain,
( spl14_110
<=> ! [X0: $tType,X4: X0,X2: fun(X0,bool),X1: list(X0)] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| ( filter(X0,X2,X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_110])]) ).
tff(f1505,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),bot_bot(fun(X0,bool))))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_46
| ~ spl14_110 ),
inference(forward_demodulation,[],[f1504,f811]) ).
tff(f1504,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),set(X0,nil(X0))))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_110 ),
inference(trivial_inequality_removal,[],[f1503]) ).
tff(f1503,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ( nil(X0) != nil(X0) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),set(X0,nil(X0))))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl14_39
| ~ spl14_110 ),
inference(superposition,[],[f1485,f779]) ).
tff(f1485,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0),X4: X0] :
( ( filter(X0,X2,X1) != X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| pp(aa(X0,bool,X2,X4)) )
| ~ spl14_110 ),
inference(avatar_component_clause,[],[f1484]) ).
tff(f4634,plain,
( spl14_235
| ~ spl14_67
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1042,f934,f922,f4632]) ).
tff(f4632,plain,
( spl14_235
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = X1 )
| ~ pp(sK3(bool,X1,aa(bool,fun(bool,bool),fconj,X0)))
| ~ pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_235])]) ).
tff(f922,plain,
( spl14_67
<=> ! [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,[spl14_67])]) ).
tff(f934,plain,
( spl14_70
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X2,X1) = X1 )
| ~ pp(aa(X0,bool,X2,sK3(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_70])]) ).
tff(f1042,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = X1 )
| ~ pp(sK3(bool,X1,aa(bool,fun(bool,bool),fconj,X0)))
| ~ pp(X0) )
| ~ spl14_67
| ~ spl14_70 ),
inference(resolution,[],[f935,f923]) ).
tff(f923,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl14_67 ),
inference(avatar_component_clause,[],[f922]) ).
tff(f935,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ~ pp(aa(X0,bool,X2,sK3(X0,X1,X2)))
| ( filter(X0,X2,X1) = X1 ) )
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f934]) ).
tff(f4538,plain,
( spl14_234
| ~ spl14_92
| ~ spl14_120 ),
inference(avatar_split_clause,[],[f1631,f1626,f1284,f4536]) ).
tff(f4536,plain,
( spl14_234
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X4: fun(X0,X1),X3: list(X0)] :
( ( map(X0,X1,X2,X3) = map(X0,X1,X4,X3) )
| pp(aa(X0,bool,set(X0,X3),sK13(X1,X0,X4,X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_234])]) ).
tff(f1284,plain,
( spl14_92
<=> ! [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,[spl14_92])]) ).
tff(f1626,plain,
( spl14_120
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: list(X1),X2: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),sK13(X0,X1,X2,X3,X4)),set(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_120])]) ).
tff(f1631,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: list(X0),X4: fun(X0,X1)] :
( ( map(X0,X1,X2,X3) = map(X0,X1,X4,X3) )
| pp(aa(X0,bool,set(X0,X3),sK13(X1,X0,X4,X3,X2))) )
| ~ spl14_92
| ~ spl14_120 ),
inference(resolution,[],[f1627,f1285]) ).
tff(f1285,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)) )
| ~ spl14_92 ),
inference(avatar_component_clause,[],[f1284]) ).
tff(f1627,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),sK13(X0,X1,X2,X3,X4)),set(X1,X3)))
| ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) ) )
| ~ spl14_120 ),
inference(avatar_component_clause,[],[f1626]) ).
tff(f4534,plain,
( spl14_233
| ~ spl14_24
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1268,f1241,f713,f4532]) ).
tff(f4532,plain,
( spl14_233
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: fun(X0,bool)] :
( ( map(X0,bool,X1,cons(X0,X2,X3)) = cons(bool,fTrue,map(X0,bool,X1,X3)) )
| ( fFalse = aa(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_233])]) ).
tff(f1241,plain,
( spl14_90
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_90])]) ).
tff(f1268,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,bool)] :
( ( map(X0,bool,X1,cons(X0,X2,X3)) = cons(bool,fTrue,map(X0,bool,X1,X3)) )
| ( fFalse = aa(X0,bool,X1,X2) ) )
| ~ spl14_24
| ~ spl14_90 ),
inference(superposition,[],[f1242,f714]) ).
tff(f1242,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) )
| ~ spl14_90 ),
inference(avatar_component_clause,[],[f1241]) ).
tff(f4530,plain,
( spl14_232
| ~ spl14_59
| ~ spl14_76 ),
inference(avatar_split_clause,[],[f1105,f1077,f871,f4528]) ).
tff(f4528,plain,
( spl14_232
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(sK4(bool,X1,aa(bool,fun(bool,bool),fconj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_232])]) ).
tff(f1105,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(sK4(bool,X1,aa(bool,fun(bool,bool),fconj,X0))) )
| ~ spl14_59
| ~ spl14_76 ),
inference(resolution,[],[f1078,f872]) ).
tff(f4526,plain,
( spl14_231
| ~ spl14_91
| ~ spl14_222 ),
inference(avatar_split_clause,[],[f4242,f4196,f1280,f4523]) ).
tff(f4523,plain,
( spl14_231
<=> ( plus_plus(int,zero_zero(int)) = combi(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_231])]) ).
tff(f1280,plain,
( spl14_91
<=> ! [X0: int] : ( aa(int,int,plus_plus(int,zero_zero(int)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_91])]) ).
tff(f4196,plain,
( spl14_222
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK12(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK12(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_222])]) ).
tff(f4242,plain,
( ( plus_plus(int,zero_zero(int)) = combi(int) )
| ~ spl14_91
| ~ spl14_222 ),
inference(trivial_inequality_removal,[],[f4241]) ).
tff(f4241,plain,
( ( sK12(int,int,plus_plus(int,zero_zero(int)),combi(int)) != sK12(int,int,plus_plus(int,zero_zero(int)),combi(int)) )
| ( plus_plus(int,zero_zero(int)) = combi(int) )
| ~ spl14_91
| ~ spl14_222 ),
inference(superposition,[],[f4197,f1281]) ).
tff(f1281,plain,
( ! [X0: int] : ( aa(int,int,plus_plus(int,zero_zero(int)),X0) = X0 )
| ~ spl14_91 ),
inference(avatar_component_clause,[],[f1280]) ).
tff(f4197,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK12(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK12(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl14_222 ),
inference(avatar_component_clause,[],[f4196]) ).
tff(f4521,plain,
( spl14_230
| ~ spl14_59
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1088,f1073,f871,f4519]) ).
tff(f4519,plain,
( spl14_230
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(sK2(bool,aa(bool,fun(bool,bool),fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_230])]) ).
tff(f1088,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(sK2(bool,aa(bool,fun(bool,bool),fconj,X0),X1)) )
| ~ spl14_59
| ~ spl14_75 ),
inference(resolution,[],[f1074,f872]) ).
tff(f4320,plain,
( spl14_229
| ~ spl14_13
| ~ spl14_99 ),
inference(avatar_split_clause,[],[f1366,f1362,f661,f4318]) ).
tff(f4318,plain,
( spl14_229
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,X0,X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_229])]) ).
tff(f1362,plain,
( spl14_99
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_99])]) ).
tff(f1366,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,div_mod(int,X0,X2)),X1),X2) )
| ~ spl14_13
| ~ spl14_99 ),
inference(resolution,[],[f1363,f663]) ).
tff(f1363,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X2)),X1),X2) ) )
| ~ spl14_99 ),
inference(avatar_component_clause,[],[f1362]) ).
tff(f4316,plain,
( spl14_228
| ~ spl14_13
| ~ spl14_98 ),
inference(avatar_split_clause,[],[f1365,f1358,f661,f4314]) ).
tff(f4314,plain,
( spl14_228
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,X0),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_228])]) ).
tff(f1358,plain,
( spl14_98
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_98])]) ).
tff(f1365,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,plus_plus(int,X0),X1),X2) = div_mod(int,aa(int,int,plus_plus(int,X0),div_mod(int,X1,X2)),X2) )
| ~ spl14_13
| ~ spl14_98 ),
inference(resolution,[],[f1359,f663]) ).
tff(f1359,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),div_mod(X0,X2,X1)),X1) ) )
| ~ spl14_98 ),
inference(avatar_component_clause,[],[f1358]) ).
tff(f4312,plain,
( spl14_227
| ~ spl14_45
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1263,f1241,f804,f4310]) ).
tff(f4310,plain,
( spl14_227
<=> ! [X1: $tType,X0: $tType,X4: list(X0),X3: X0,X2: X1] : ( map(X0,X1,combk(X1,X0,X2),cons(X0,X3,X4)) = cons(X1,X2,map(X0,X1,combk(X1,X0,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_227])]) ).
tff(f804,plain,
( spl14_45
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_45])]) ).
tff(f1263,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: list(X0)] : ( map(X0,X1,combk(X1,X0,X2),cons(X0,X3,X4)) = cons(X1,X2,map(X0,X1,combk(X1,X0,X2),X4)) )
| ~ spl14_45
| ~ spl14_90 ),
inference(superposition,[],[f1242,f805]) ).
tff(f805,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f804]) ).
tff(f4308,plain,
( spl14_226
| ~ spl14_45
| ~ spl14_89 ),
inference(avatar_split_clause,[],[f1261,f1237,f804,f4306]) ).
tff(f4306,plain,
( spl14_226
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: bool] :
( ~ pp(X1)
| ( filter(X0,combk(bool,X0,X1),cons(X0,X2,X3)) = cons(X0,X2,filter(X0,combk(bool,X0,X1),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_226])]) ).
tff(f1237,plain,
( spl14_89
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: list(X0)] :
( ( filter(X0,X3,cons(X0,X2,X1)) = cons(X0,X2,filter(X0,X3,X1)) )
| ~ pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_89])]) ).
tff(f1261,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: bool] :
( ~ pp(X1)
| ( filter(X0,combk(bool,X0,X1),cons(X0,X2,X3)) = cons(X0,X2,filter(X0,combk(bool,X0,X1),X3)) ) )
| ~ spl14_45
| ~ spl14_89 ),
inference(superposition,[],[f1238,f805]) ).
tff(f1238,plain,
( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( ~ pp(aa(X0,bool,X3,X2))
| ( filter(X0,X3,cons(X0,X2,X1)) = cons(X0,X2,filter(X0,X3,X1)) ) )
| ~ spl14_89 ),
inference(avatar_component_clause,[],[f1237]) ).
tff(f4300,plain,
( spl14_225
| ~ spl14_56
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1041,f934,f859,f4298]) ).
tff(f4298,plain,
( spl14_225
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = X1 )
| ~ pp(sK3(bool,X1,aa(bool,fun(bool,bool),fdisj,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_225])]) ).
tff(f859,plain,
( spl14_56
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_56])]) ).
tff(f1041,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = X1 )
| ~ pp(sK3(bool,X1,aa(bool,fun(bool,bool),fdisj,X0))) )
| ~ spl14_56
| ~ spl14_70 ),
inference(resolution,[],[f935,f860]) ).
tff(f860,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) )
| ~ spl14_56 ),
inference(avatar_component_clause,[],[f859]) ).
tff(f4206,plain,
( spl14_224
| ~ spl14_33
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1327,f1312,f752,f4204]) ).
tff(f4204,plain,
( spl14_224
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK12(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK12(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_224])]) ).
tff(f1327,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK12(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK12(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl14_33
| ~ spl14_94 ),
inference(superposition,[],[f1313,f753]) ).
tff(f4202,plain,
( spl14_223
| ~ spl14_24
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1326,f1312,f713,f4200]) ).
tff(f4200,plain,
( spl14_223
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fFalse = sK12(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_223])]) ).
tff(f1326,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fFalse = sK12(X0,bool,X1,X2) ) )
| ~ spl14_24
| ~ spl14_94 ),
inference(superposition,[],[f1313,f714]) ).
tff(f4198,plain,
( spl14_222
| ~ spl14_33
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1315,f1312,f752,f4196]) ).
tff(f1315,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK12(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK12(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl14_33
| ~ spl14_94 ),
inference(superposition,[],[f1313,f753]) ).
tff(f4194,plain,
( ~ spl14_220
| spl14_221
| ~ spl14_189
| ~ spl14_24
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f1213,f1173,f713,f3614,f4192,f4188]) ).
tff(f4188,plain,
( spl14_220
<=> group_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_220])]) ).
tff(f4192,plain,
( spl14_221
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_221])]) ).
tff(f3614,plain,
( spl14_189
<=> ( fTrue = zero_zero(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_189])]) ).
tff(f1173,plain,
( spl14_83
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_83])]) ).
tff(f1213,plain,
( ! [X0: bool,X1: bool] :
( ( fTrue != zero_zero(bool) )
| ( X0 = X1 )
| ~ group_add(bool)
| ( fFalse = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) )
| ~ spl14_24
| ~ spl14_83 ),
inference(superposition,[],[f1174,f714]) ).
tff(f1174,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ( X1 = X2 )
| ~ group_add(X0) )
| ~ spl14_83 ),
inference(avatar_component_clause,[],[f1173]) ).
tff(f4186,plain,
( spl14_219
| ~ spl14_70
| ~ spl14_191 ),
inference(avatar_split_clause,[],[f3655,f3634,f934,f4184]) ).
tff(f4184,plain,
( spl14_219
<=> ! [X0: $tType,X1: list(X0)] : ( filter(X0,set(X0,X1),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_219])]) ).
tff(f3634,plain,
( spl14_191
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = X2 )
| pp(aa(X0,bool,set(X0,X2),sK3(X0,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_191])]) ).
tff(f3655,plain,
( ! [X0: $tType,X1: list(X0)] : ( filter(X0,set(X0,X1),X1) = X1 )
| ~ spl14_70
| ~ spl14_191 ),
inference(duplicate_literal_removal,[],[f3637]) ).
tff(f3637,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( filter(X0,set(X0,X1),X1) = X1 )
| ( filter(X0,set(X0,X1),X1) = X1 ) )
| ~ spl14_70
| ~ spl14_191 ),
inference(resolution,[],[f3635,f935]) ).
tff(f3635,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( pp(aa(X0,bool,set(X0,X2),sK3(X0,X2,X1)))
| ( filter(X0,X1,X2) = X2 ) )
| ~ spl14_191 ),
inference(avatar_component_clause,[],[f3634]) ).
tff(f4182,plain,
( ~ spl14_217
| spl14_218
| ~ spl14_24
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f1191,f1165,f713,f4180,f4176]) ).
tff(f4176,plain,
( spl14_217
<=> cancel_semigroup_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_217])]) ).
tff(f4180,plain,
( spl14_218
<=> ! [X2: bool,X0: bool,X1: bool] :
( ( fTrue != aa(bool,bool,plus_plus(bool,X2),X1) )
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X1) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_218])]) ).
tff(f1165,plain,
( spl14_81
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X1),X2) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_81])]) ).
tff(f1191,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( fTrue != aa(bool,bool,plus_plus(bool,X2),X1) )
| ( X0 = X2 )
| ~ cancel_semigroup_add(bool)
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X1) ) )
| ~ spl14_24
| ~ spl14_81 ),
inference(superposition,[],[f1166,f714]) ).
tff(f1166,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X1),X2) )
| ( X1 = X3 )
| ~ cancel_semigroup_add(X0) )
| ~ spl14_81 ),
inference(avatar_component_clause,[],[f1165]) ).
tff(f4174,plain,
( ~ spl14_215
| spl14_216
| ~ spl14_24
| ~ spl14_80 ),
inference(avatar_split_clause,[],[f1180,f1161,f713,f4172,f4168]) ).
tff(f4168,plain,
( spl14_215
<=> cancel146912293up_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_215])]) ).
tff(f4172,plain,
( spl14_216
<=> ! [X2: bool,X0: bool,X1: bool] :
( ( fTrue != aa(bool,bool,plus_plus(bool,X0),X2) )
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X1) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_216])]) ).
tff(f1161,plain,
( spl14_80
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) )
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_80])]) ).
tff(f1180,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( fTrue != aa(bool,bool,plus_plus(bool,X0),X2) )
| ( X1 = X2 )
| ~ cancel146912293up_add(bool)
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X1) ) )
| ~ spl14_24
| ~ spl14_80 ),
inference(superposition,[],[f1162,f714]) ).
tff(f1162,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) )
| ( X1 = X2 )
| ~ cancel146912293up_add(X0) )
| ~ spl14_80 ),
inference(avatar_component_clause,[],[f1161]) ).
tff(f4166,plain,
( spl14_214
| ~ spl14_70
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1142,f1128,f934,f4164]) ).
tff(f4164,plain,
( spl14_214
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = filter(X0,X1,cons(X0,sK3(X0,X3,X1),X2)) )
| ( filter(X0,X1,X3) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_214])]) ).
tff(f1142,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = filter(X0,X1,cons(X0,sK3(X0,X3,X1),X2)) )
| ( filter(X0,X1,X3) = X3 ) )
| ~ spl14_70
| ~ spl14_79 ),
inference(resolution,[],[f1129,f935]) ).
tff(f4092,plain,
( spl14_42
| ~ spl14_189
| ~ spl14_190 ),
inference(avatar_split_clause,[],[f3985,f3625,f3614,f791]) ).
tff(f791,plain,
( spl14_42
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_42])]) ).
tff(f3625,plain,
( spl14_190
<=> ( fFalse = zero_zero(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_190])]) ).
tff(f3985,plain,
( ( fFalse = fTrue )
| ~ spl14_189
| ~ spl14_190 ),
inference(superposition,[],[f3627,f3615]) ).
tff(f3615,plain,
( ( fTrue = zero_zero(bool) )
| ~ spl14_189 ),
inference(avatar_component_clause,[],[f3614]) ).
tff(f3627,plain,
( ( fFalse = zero_zero(bool) )
| ~ spl14_190 ),
inference(avatar_component_clause,[],[f3625]) ).
tff(f4091,plain,
( spl14_213
| ~ spl14_45
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1328,f1312,f804,f4089]) ).
tff(f4089,plain,
( spl14_213
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK12(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_213])]) ).
tff(f1328,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK12(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl14_45
| ~ spl14_94 ),
inference(superposition,[],[f1313,f805]) ).
tff(f4087,plain,
( spl14_212
| ~ spl14_45
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f1316,f1312,f804,f4085]) ).
tff(f4085,plain,
( spl14_212
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK12(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_212])]) ).
tff(f1316,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK12(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl14_45
| ~ spl14_94 ),
inference(superposition,[],[f1313,f805]) ).
tff(f4083,plain,
( spl14_211
| ~ spl14_61
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1271,f1241,f879,f4081]) ).
tff(f4081,plain,
( spl14_211
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: list(X1),X2: fun(X1,X0),X6: list(X0),X3: X1] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( map(X1,X0,X2,X4) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_211])]) ).
tff(f879,plain,
( spl14_61
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X1 = X3 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_61])]) ).
tff(f1271,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( map(X1,X0,X2,X4) = X6 ) )
| ~ spl14_61
| ~ spl14_90 ),
inference(superposition,[],[f880,f1242]) ).
tff(f880,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X1 = X3 ) )
| ~ spl14_61 ),
inference(avatar_component_clause,[],[f879]) ).
tff(f4079,plain,
( spl14_210
| ~ spl14_65
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1140,f1128,f906,f4077]) ).
tff(f4077,plain,
( spl14_210
<=> ! [X0: $tType,X3: X0,X2: list(X0),X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = filter(X0,X1,cons(X0,X3,X2)) )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_210])]) ).
tff(f906,plain,
( spl14_65
<=> ! [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,[spl14_65])]) ).
tff(f1140,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = filter(X0,X1,cons(X0,X3,X2)) )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) )
| ~ spl14_65
| ~ spl14_79 ),
inference(resolution,[],[f1129,f907]) ).
tff(f907,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl14_65 ),
inference(avatar_component_clause,[],[f906]) ).
tff(f4075,plain,
( spl14_209
| ~ spl14_65
| ~ spl14_78 ),
inference(avatar_split_clause,[],[f1131,f1123,f906,f4072]) ).
tff(f4072,plain,
( spl14_209
<=> pp(aa(fun(fun(atom,bool),bool),bool,fEx(fun(atom,bool)),aa(atom,fun(fun(atom,bool),bool),member(atom),a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_209])]) ).
tff(f1123,plain,
( spl14_78
<=> pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_78])]) ).
tff(f1131,plain,
( pp(aa(fun(fun(atom,bool),bool),bool,fEx(fun(atom,bool)),aa(atom,fun(fun(atom,bool),bool),member(atom),a)))
| ~ spl14_65
| ~ spl14_78 ),
inference(resolution,[],[f1125,f907]) ).
tff(f1125,plain,
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as)))
| ~ spl14_78 ),
inference(avatar_component_clause,[],[f1123]) ).
tff(f3999,plain,
( spl14_208
| ~ spl14_92
| ~ spl14_108 ),
inference(avatar_split_clause,[],[f1487,f1476,f1284,f3997]) ).
tff(f3997,plain,
( spl14_208
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| pp(aa(X0,bool,X1,big_linorder_Max(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_208])]) ).
tff(f1476,plain,
( spl14_108
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_108])]) ).
tff(f1487,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0)
| pp(aa(X0,bool,X1,big_linorder_Max(X0,X1))) )
| ~ spl14_92
| ~ spl14_108 ),
inference(resolution,[],[f1477,f1285]) ).
tff(f1477,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) )
| ~ spl14_108 ),
inference(avatar_component_clause,[],[f1476]) ).
tff(f3995,plain,
( spl14_207
| ~ spl14_53
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1273,f1241,f845,f3993]) ).
tff(f3993,plain,
( spl14_207
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: list(X1),X2: fun(X1,X0),X6: list(X0),X3: X1] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_207])]) ).
tff(f845,plain,
( spl14_53
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_53])]) ).
tff(f1273,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( aa(X1,X0,X2,X3) = X5 ) )
| ~ spl14_53
| ~ spl14_90 ),
inference(superposition,[],[f846,f1242]) ).
tff(f846,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X2 = X4 ) )
| ~ spl14_53 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f3984,plain,
( spl14_206
| ~ spl14_45
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1149,f1128,f804,f3982]) ).
tff(f3982,plain,
( spl14_206
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: bool] :
( pp(X1)
| ( filter(X0,combk(bool,X0,X1),X3) = filter(X0,combk(bool,X0,X1),cons(X0,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_206])]) ).
tff(f1149,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: bool] :
( pp(X1)
| ( filter(X0,combk(bool,X0,X1),X3) = filter(X0,combk(bool,X0,X1),cons(X0,X2,X3)) ) )
| ~ spl14_45
| ~ spl14_79 ),
inference(superposition,[],[f1129,f805]) ).
tff(f3797,plain,
( spl14_205
| ~ spl14_12
| ~ spl14_26
| ~ spl14_72
| ~ spl14_113 ),
inference(avatar_split_clause,[],[f1567,f1556,f1061,f724,f656,f3795]) ).
tff(f3795,plain,
( spl14_205
<=> ! [X0: int,X1: int] : ( div_mod(int,X1,X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X1),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_205])]) ).
tff(f656,plain,
( spl14_12
<=> group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).
tff(f724,plain,
( spl14_26
<=> ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_26])]) ).
tff(f1061,plain,
( spl14_72
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_72])]) ).
tff(f1556,plain,
( spl14_113
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),div_mod(int,X1,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_113])]) ).
tff(f1567,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X1,X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X1),X0),X0) )
| ~ spl14_12
| ~ spl14_26
| ~ spl14_72
| ~ spl14_113 ),
inference(forward_demodulation,[],[f1563,f1085]) ).
tff(f1085,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),zero_zero(int)) = X0 )
| ~ spl14_12
| ~ spl14_72 ),
inference(resolution,[],[f1062,f658]) ).
tff(f658,plain,
( group_add(int)
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f1062,plain,
( ! [X0: $tType,X1: X0] :
( ~ group_add(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 ) )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f1563,plain,
( ! [X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X1),X0),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X1),zero_zero(int)),X0) )
| ~ spl14_26
| ~ spl14_113 ),
inference(superposition,[],[f1557,f725]) ).
tff(f725,plain,
( ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) )
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f724]) ).
tff(f1557,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),div_mod(int,X1,X0)),X0) )
| ~ spl14_113 ),
inference(avatar_component_clause,[],[f1556]) ).
tff(f3793,plain,
( spl14_204
| ~ spl14_44
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1270,f1241,f800,f3791]) ).
tff(f3791,plain,
( spl14_204
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: fun(X0,X1)] : ( map(X0,X1,X2,cons(X0,X3,nil(X0))) = cons(X1,aa(X0,X1,X2,X3),nil(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_204])]) ).
tff(f800,plain,
( spl14_44
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_44])]) ).
tff(f1270,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: X0] : ( map(X0,X1,X2,cons(X0,X3,nil(X0))) = cons(X1,aa(X0,X1,X2,X3),nil(X1)) )
| ~ spl14_44
| ~ spl14_90 ),
inference(superposition,[],[f1242,f801]) ).
tff(f801,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) )
| ~ spl14_44 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f3788,plain,
( spl14_203
| ~ spl14_63
| spl14_190 ),
inference(avatar_split_clause,[],[f3697,f3625,f898,f3786]) ).
tff(f3786,plain,
( spl14_203
<=> ! [X0: bool] :
( ( zero_zero(bool) = X0 )
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_203])]) ).
tff(f898,plain,
( spl14_63
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_63])]) ).
tff(f3697,plain,
( ! [X0: bool] :
( ( zero_zero(bool) = X0 )
| ( fFalse = X0 ) )
| ~ spl14_63
| spl14_190 ),
inference(trivial_inequality_removal,[],[f3691]) ).
tff(f3691,plain,
( ! [X0: bool] :
( ( fFalse != fFalse )
| ( zero_zero(bool) = X0 )
| ( fFalse = X0 ) )
| ~ spl14_63
| spl14_190 ),
inference(superposition,[],[f3626,f899]) ).
tff(f899,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) )
| ~ spl14_63 ),
inference(avatar_component_clause,[],[f898]) ).
tff(f3626,plain,
( ( fFalse != zero_zero(bool) )
| spl14_190 ),
inference(avatar_component_clause,[],[f3625]) ).
tff(f3784,plain,
( spl14_202
| ~ spl14_33
| ~ spl14_89 ),
inference(avatar_split_clause,[],[f1260,f1237,f752,f3782]) ).
tff(f3782,plain,
( spl14_202
<=> ! [X0: bool,X1: list(bool)] :
( ~ pp(X0)
| ( filter(bool,combi(bool),cons(bool,X0,X1)) = cons(bool,X0,filter(bool,combi(bool),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_202])]) ).
tff(f1260,plain,
( ! [X0: bool,X1: list(bool)] :
( ~ pp(X0)
| ( filter(bool,combi(bool),cons(bool,X0,X1)) = cons(bool,X0,filter(bool,combi(bool),X1)) ) )
| ~ spl14_33
| ~ spl14_89 ),
inference(superposition,[],[f1238,f753]) ).
tff(f3780,plain,
( spl14_201
| ~ spl14_12
| ~ spl14_88 ),
inference(avatar_split_clause,[],[f1245,f1233,f656,f3778]) ).
tff(f3778,plain,
( spl14_201
<=> ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(int,int,plus_plus(int,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_201])]) ).
tff(f1233,plain,
( spl14_88
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X2),X1)),X1) = X2 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_88])]) ).
tff(f1245,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),aa(int,int,plus_plus(int,X0),X1)),X1) = X0 )
| ~ spl14_12
| ~ spl14_88 ),
inference(resolution,[],[f1234,f658]) ).
tff(f1234,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ group_add(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X2),X1)),X1) = X2 ) )
| ~ spl14_88 ),
inference(avatar_component_clause,[],[f1233]) ).
tff(f3776,plain,
( spl14_200
| ~ spl14_12
| ~ spl14_87 ),
inference(avatar_split_clause,[],[f1244,f1229,f656,f3774]) ).
tff(f3774,plain,
( spl14_200
<=> ! [X0: int,X1: int] : ( aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_200])]) ).
tff(f1229,plain,
( spl14_87
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_87])]) ).
tff(f1244,plain,
( ! [X0: int,X1: int] : ( aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1)),X1) = X0 )
| ~ spl14_12
| ~ spl14_87 ),
inference(resolution,[],[f1230,f658]) ).
tff(f1230,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ group_add(X0)
| ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2 ) )
| ~ spl14_87 ),
inference(avatar_component_clause,[],[f1229]) ).
tff(f3772,plain,
( spl14_199
| ~ spl14_24
| ~ spl14_76 ),
inference(avatar_split_clause,[],[f1114,f1077,f713,f3770]) ).
tff(f3770,plain,
( spl14_199
<=> ! [X0: list(bool),X1: fun(bool,bool)] :
( pp(aa(bool,bool,X1,fTrue))
| ( filter(bool,X1,X0) = nil(bool) )
| ( fFalse = sK4(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_199])]) ).
tff(f1114,plain,
( ! [X0: list(bool),X1: fun(bool,bool)] :
( pp(aa(bool,bool,X1,fTrue))
| ( filter(bool,X1,X0) = nil(bool) )
| ( fFalse = sK4(bool,X0,X1) ) )
| ~ spl14_24
| ~ spl14_76 ),
inference(superposition,[],[f1078,f714]) ).
tff(f3768,plain,
( spl14_198
| ~ spl14_24
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1097,f1073,f713,f3766]) ).
tff(f3766,plain,
( spl14_198
<=> ! [X0: fun(bool,bool),X1: list(bool)] :
( pp(aa(bool,bool,X0,fTrue))
| ( filter(bool,X0,X1) = nil(bool) )
| ( fFalse = sK2(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_198])]) ).
tff(f1097,plain,
( ! [X0: fun(bool,bool),X1: list(bool)] :
( pp(aa(bool,bool,X0,fTrue))
| ( filter(bool,X0,X1) = nil(bool) )
| ( fFalse = sK2(bool,X0,X1) ) )
| ~ spl14_24
| ~ spl14_75 ),
inference(superposition,[],[f1074,f714]) ).
tff(f3689,plain,
( spl14_197
| ~ spl14_92
| ~ spl14_106 ),
inference(avatar_split_clause,[],[f1439,f1417,f1284,f3687]) ).
tff(f3687,plain,
( spl14_197
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,set(X0,X2),sK4(X0,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_197])]) ).
tff(f1417,plain,
( spl14_106
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = filter(X0,X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1,X2)),set(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_106])]) ).
tff(f1439,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,set(X0,X2),sK4(X0,X2,X1))) )
| ~ spl14_92
| ~ spl14_106 ),
inference(resolution,[],[f1418,f1285]) ).
tff(f1418,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1,X2)),set(X0,X1)))
| ( nil(X0) = filter(X0,X2,X1) ) )
| ~ spl14_106 ),
inference(avatar_component_clause,[],[f1417]) ).
tff(f3685,plain,
( spl14_196
| ~ spl14_92
| ~ spl14_105 ),
inference(avatar_split_clause,[],[f1424,f1413,f1284,f3683]) ).
tff(f3683,plain,
( spl14_196
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,set(X0,X2),sK2(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_196])]) ).
tff(f1413,plain,
( spl14_105
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),set(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_105])]) ).
tff(f1424,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,set(X0,X2),sK2(X0,X1,X2))) )
| ~ spl14_92
| ~ spl14_105 ),
inference(resolution,[],[f1414,f1285]) ).
tff(f1414,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),set(X0,X2)))
| ( nil(X0) = filter(X0,X1,X2) ) )
| ~ spl14_105 ),
inference(avatar_component_clause,[],[f1413]) ).
tff(f3681,plain,
( spl14_195
| ~ spl14_7
| ~ spl14_85 ),
inference(avatar_split_clause,[],[f1227,f1219,f631,f3679]) ).
tff(f3679,plain,
( spl14_195
<=> ! [X0: list(int)] : ( zero_zero(int) = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),nil(int)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_195])]) ).
tff(f631,plain,
( spl14_7
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
tff(f1219,plain,
( spl14_85
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X1) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_85])]) ).
tff(f1227,plain,
( ! [X0: list(int)] : ( zero_zero(int) = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),nil(int)),X0) )
| ~ spl14_7
| ~ spl14_85 ),
inference(resolution,[],[f1220,f633]) ).
tff(f633,plain,
( ring(int)
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f631]) ).
tff(f1220,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X1) ) )
| ~ spl14_85 ),
inference(avatar_component_clause,[],[f1219]) ).
tff(f3677,plain,
( spl14_194
| ~ spl14_7
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f1226,f1215,f631,f3675]) ).
tff(f3675,plain,
( spl14_194
<=> ! [X0: list(int)] : ( zero_zero(int) = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X0),nil(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_194])]) ).
tff(f1215,plain,
( spl14_84
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X1),nil(X0)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_84])]) ).
tff(f1226,plain,
( ! [X0: list(int)] : ( zero_zero(int) = aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X0),nil(int)) )
| ~ spl14_7
| ~ spl14_84 ),
inference(resolution,[],[f1216,f633]) ).
tff(f1216,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X1),nil(X0)) ) )
| ~ spl14_84 ),
inference(avatar_component_clause,[],[f1215]) ).
tff(f3673,plain,
( spl14_193
| ~ spl14_24
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1048,f934,f713,f3671]) ).
tff(f3671,plain,
( spl14_193
<=> ! [X0: list(bool),X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,X1,fTrue))
| ( filter(bool,X1,X0) = X0 )
| ( fFalse = sK3(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_193])]) ).
tff(f1048,plain,
( ! [X0: list(bool),X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,X1,fTrue))
| ( filter(bool,X1,X0) = X0 )
| ( fFalse = sK3(bool,X0,X1) ) )
| ~ spl14_24
| ~ spl14_70 ),
inference(superposition,[],[f935,f714]) ).
tff(f3659,plain,
( spl14_192
| spl14_147
| ~ spl14_65
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f1019,f922,f906,f2087,f3657]) ).
tff(f3657,plain,
( spl14_192
<=> ! [X1: bool] :
( ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_192])]) ).
tff(f2087,plain,
( spl14_147
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_147])]) ).
tff(f1019,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) )
| ~ spl14_65
| ~ spl14_67 ),
inference(resolution,[],[f923,f907]) ).
tff(f3636,plain,
( spl14_191
| ~ spl14_92
| ~ spl14_104 ),
inference(avatar_split_clause,[],[f1397,f1384,f1284,f3634]) ).
tff(f1384,plain,
( spl14_104
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X2,X1) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1,X2)),set(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_104])]) ).
tff(f1397,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( filter(X0,X1,X2) = X2 )
| pp(aa(X0,bool,set(X0,X2),sK3(X0,X2,X1))) )
| ~ spl14_92
| ~ spl14_104 ),
inference(resolution,[],[f1385,f1285]) ).
tff(f1385,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1,X2)),set(X0,X1)))
| ( filter(X0,X2,X1) = X1 ) )
| ~ spl14_104 ),
inference(avatar_component_clause,[],[f1384]) ).
tff(f3628,plain,
( spl14_190
| ~ spl14_24
| spl14_189 ),
inference(avatar_split_clause,[],[f3623,f3614,f713,f3625]) ).
tff(f3623,plain,
( ( fFalse = zero_zero(bool) )
| ~ spl14_24
| spl14_189 ),
inference(trivial_inequality_removal,[],[f3622]) ).
tff(f3622,plain,
( ( fTrue != fTrue )
| ( fFalse = zero_zero(bool) )
| ~ spl14_24
| spl14_189 ),
inference(superposition,[],[f3616,f714]) ).
tff(f3616,plain,
( ( fTrue != zero_zero(bool) )
| spl14_189 ),
inference(avatar_component_clause,[],[f3614]) ).
tff(f3617,plain,
( ~ spl14_187
| spl14_188
| ~ spl14_189
| ~ spl14_24
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f938,f918,f713,f3614,f3611,f3607]) ).
tff(f3607,plain,
( spl14_187
<=> linord219039673up_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_187])]) ).
tff(f3611,plain,
( spl14_188
<=> ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_188])]) ).
tff(f918,plain,
( spl14_66
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,plus_plus(X0,X1),X1) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_66])]) ).
tff(f938,plain,
( ! [X0: bool] :
( ( fTrue != zero_zero(bool) )
| ( fTrue = X0 )
| ~ linord219039673up_add(bool)
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X0) ) )
| ~ spl14_24
| ~ spl14_66 ),
inference(inner_rewriting,[],[f937]) ).
tff(f937,plain,
( ! [X0: bool] :
( ( fTrue != zero_zero(bool) )
| ( zero_zero(bool) = X0 )
| ~ linord219039673up_add(bool)
| ( fFalse = aa(bool,bool,plus_plus(bool,X0),X0) ) )
| ~ spl14_24
| ~ spl14_66 ),
inference(superposition,[],[f919,f714]) ).
tff(f919,plain,
( ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != aa(X0,X0,plus_plus(X0,X1),X1) )
| ( zero_zero(X0) = X1 )
| ~ linord219039673up_add(X0) )
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f918]) ).
tff(f3574,plain,
( spl14_186
| ~ spl14_33
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f1148,f1128,f752,f3572]) ).
tff(f3572,plain,
( spl14_186
<=> ! [X0: bool,X1: list(bool)] :
( pp(X0)
| ( filter(bool,combi(bool),X1) = filter(bool,combi(bool),cons(bool,X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_186])]) ).
tff(f1148,plain,
( ! [X0: bool,X1: list(bool)] :
( pp(X0)
| ( filter(bool,combi(bool),X1) = filter(bool,combi(bool),cons(bool,X0,X1)) ) )
| ~ spl14_33
| ~ spl14_79 ),
inference(superposition,[],[f1129,f753]) ).
tff(f3570,plain,
( spl14_185
| ~ spl14_65
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1091,f1073,f906,f3568]) ).
tff(f3568,plain,
( spl14_185
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_185])]) ).
tff(f1091,plain,
( ! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(fun(X0,bool),bool,fEx(X0),X1)) )
| ~ spl14_65
| ~ spl14_75 ),
inference(resolution,[],[f1074,f907]) ).
tff(f2632,plain,
( ~ spl14_97
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2604]) ).
tff(f2604,plain,
( $false
| ~ spl14_97
| ~ spl14_147 ),
inference(resolution,[],[f2088,f1355]) ).
tff(f1355,plain,
( pp(aa(atom,bool,set(atom,as),a))
| ~ spl14_97 ),
inference(avatar_component_clause,[],[f1353]) ).
tff(f1353,plain,
( spl14_97
<=> pp(aa(atom,bool,set(atom,as),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_97])]) ).
tff(f2088,plain,
( ! [X0: bool] : ~ pp(X0)
| ~ spl14_147 ),
inference(avatar_component_clause,[],[f2087]) ).
tff(f2631,plain,
( ~ spl14_136
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2605]) ).
tff(f2605,plain,
( $false
| ~ spl14_136
| ~ spl14_147 ),
inference(resolution,[],[f2088,f1994]) ).
tff(f1994,plain,
( pp(aa(atom,bool,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),a))
| ~ spl14_136 ),
inference(avatar_component_clause,[],[f1992]) ).
tff(f1992,plain,
( spl14_136
<=> pp(aa(atom,bool,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_136])]) ).
tff(f2630,plain,
( ~ spl14_54
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2606]) ).
tff(f2606,plain,
( $false
| ~ spl14_54
| ~ spl14_147 ),
inference(resolution,[],[f2088,f850]) ).
tff(f850,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl14_54 ),
inference(avatar_component_clause,[],[f849]) ).
tff(f849,plain,
( spl14_54
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_54])]) ).
tff(f2629,plain,
( ~ spl14_78
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2608]) ).
tff(f2608,plain,
( $false
| ~ spl14_78
| ~ spl14_147 ),
inference(resolution,[],[f2088,f1125]) ).
tff(f2628,plain,
( ~ spl14_137
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2613]) ).
tff(f2613,plain,
( $false
| ~ spl14_137
| ~ spl14_147 ),
inference(resolution,[],[f2088,f1999]) ).
tff(f1999,plain,
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as))))
| ~ spl14_137 ),
inference(avatar_component_clause,[],[f1997]) ).
tff(f1997,plain,
( spl14_137
<=> pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_137])]) ).
tff(f2627,plain,
( ~ spl14_138
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2614]) ).
tff(f2614,plain,
( $false
| ~ spl14_138
| ~ spl14_147 ),
inference(resolution,[],[f2088,f2004]) ).
tff(f2004,plain,
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as))))
| ~ spl14_138 ),
inference(avatar_component_clause,[],[f2002]) ).
tff(f2002,plain,
( spl14_138
<=> pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_138])]) ).
tff(f2626,plain,
( ~ spl14_147
| ~ spl14_163 ),
inference(avatar_contradiction_clause,[],[f2615]) ).
tff(f2615,plain,
( $false
| ~ spl14_147
| ~ spl14_163 ),
inference(resolution,[],[f2088,f2233]) ).
tff(f2233,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl14_163 ),
inference(avatar_component_clause,[],[f2231]) ).
tff(f2231,plain,
( spl14_163
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_163])]) ).
tff(f2625,plain,
( ~ spl14_146
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2616]) ).
tff(f2616,plain,
( $false
| ~ spl14_146
| ~ spl14_147 ),
inference(resolution,[],[f2088,f2085]) ).
tff(f2085,plain,
( pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool)))
| ~ spl14_146 ),
inference(avatar_component_clause,[],[f2083]) ).
tff(f2083,plain,
( spl14_146
<=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_146])]) ).
tff(f2624,plain,
( ~ spl14_130
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2617]) ).
tff(f2617,plain,
( $false
| ~ spl14_130
| ~ spl14_147 ),
inference(resolution,[],[f2088,f1789]) ).
tff(f1789,plain,
( pp(aa(fun(atom,bool),bool,fEx(atom),set(atom,as)))
| ~ spl14_130 ),
inference(avatar_component_clause,[],[f1787]) ).
tff(f1787,plain,
( spl14_130
<=> pp(aa(fun(atom,bool),bool,fEx(atom),set(atom,as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_130])]) ).
tff(f2623,plain,
( ~ spl14_147
| ~ spl14_181 ),
inference(avatar_contradiction_clause,[],[f2618]) ).
tff(f2618,plain,
( $false
| ~ spl14_147
| ~ spl14_181 ),
inference(resolution,[],[f2088,f2553]) ).
tff(f2553,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl14_181 ),
inference(avatar_component_clause,[],[f2552]) ).
tff(f2552,plain,
( spl14_181
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_181])]) ).
tff(f2622,plain,
( ~ spl14_20
| ~ spl14_147 ),
inference(avatar_contradiction_clause,[],[f2619]) ).
tff(f2619,plain,
( $false
| ~ spl14_20
| ~ spl14_147 ),
inference(resolution,[],[f2088,f698]) ).
tff(f698,plain,
( pp(fTrue)
| ~ spl14_20 ),
inference(avatar_component_clause,[],[f696]) ).
tff(f696,plain,
( spl14_20
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
tff(f2596,plain,
( spl14_147
| spl14_184
| ~ spl14_56
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f912,f906,f859,f2594,f2087]) ).
tff(f2594,plain,
( spl14_184
<=> ! [X0: bool] : pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fdisj,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_184])]) ).
tff(f912,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fdisj,X0)))
| ~ pp(X1) )
| ~ spl14_56
| ~ spl14_65 ),
inference(resolution,[],[f907,f860]) ).
tff(f2562,plain,
( spl14_183
| spl14_1
| ~ spl14_168 ),
inference(avatar_split_clause,[],[f2350,f2323,f601,f2560]) ).
tff(f2560,plain,
( spl14_183
<=> ! [X0: $tType,X1: list(X0)] : ( nil(X0) = filter(X0,combk(bool,X0,fFalse),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_183])]) ).
tff(f601,plain,
( spl14_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
tff(f2323,plain,
( spl14_168
<=> ! [X0: $tType,X2: list(X0),X1: bool] :
( pp(X1)
| ( nil(X0) = filter(X0,combk(bool,X0,X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_168])]) ).
tff(f2350,plain,
( ! [X0: $tType,X1: list(X0)] : ( nil(X0) = filter(X0,combk(bool,X0,fFalse),X1) )
| spl14_1
| ~ spl14_168 ),
inference(resolution,[],[f2324,f603]) ).
tff(f603,plain,
( ~ pp(fFalse)
| spl14_1 ),
inference(avatar_component_clause,[],[f601]) ).
tff(f2324,plain,
( ! [X0: $tType,X2: list(X0),X1: bool] :
( pp(X1)
| ( nil(X0) = filter(X0,combk(bool,X0,X1),X2) ) )
| ~ spl14_168 ),
inference(avatar_component_clause,[],[f2323]) ).
tff(f2558,plain,
( spl14_182
| ~ spl14_58
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1089,f1073,f867,f2556]) ).
tff(f2556,plain,
( spl14_182
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_182])]) ).
tff(f1089,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fconj,X0),X1) = nil(bool) )
| pp(X0) )
| ~ spl14_58
| ~ spl14_75 ),
inference(resolution,[],[f1074,f868]) ).
tff(f2554,plain,
( spl14_181
| ~ spl14_54
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f910,f906,f849,f2552]) ).
tff(f910,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl14_54
| ~ spl14_65 ),
inference(resolution,[],[f907,f850]) ).
tff(f2439,plain,
( spl14_180
| ~ spl14_30
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1276,f1241,f740,f2437]) ).
tff(f2437,plain,
( spl14_180
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_180])]) ).
tff(f740,plain,
( spl14_30
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_30])]) ).
tff(f1276,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) )
| ~ spl14_30
| ~ spl14_90 ),
inference(superposition,[],[f741,f1242]) ).
tff(f741,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 )
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f2435,plain,
( spl14_179
| ~ spl14_33
| ~ spl14_76 ),
inference(avatar_split_clause,[],[f1120,f1077,f752,f2433]) ).
tff(f2433,plain,
( spl14_179
<=> ! [X0: list(bool)] :
( pp(sK4(bool,X0,combi(bool)))
| ( filter(bool,combi(bool),X0) = nil(bool) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_179])]) ).
tff(f1120,plain,
( ! [X0: list(bool)] :
( pp(sK4(bool,X0,combi(bool)))
| ( filter(bool,combi(bool),X0) = nil(bool) ) )
| ~ spl14_33
| ~ spl14_76 ),
inference(superposition,[],[f1078,f753]) ).
tff(f2431,plain,
( spl14_178
| ~ spl14_33
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1103,f1073,f752,f2429]) ).
tff(f2429,plain,
( spl14_178
<=> ! [X0: list(bool)] :
( pp(sK2(bool,combi(bool),X0))
| ( filter(bool,combi(bool),X0) = nil(bool) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_178])]) ).
tff(f1103,plain,
( ! [X0: list(bool)] :
( pp(sK2(bool,combi(bool),X0))
| ( filter(bool,combi(bool),X0) = nil(bool) ) )
| ~ spl14_33
| ~ spl14_75 ),
inference(superposition,[],[f1074,f753]) ).
tff(f2427,plain,
( spl14_177
| ~ spl14_13
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f1087,f1069,f661,f2425]) ).
tff(f2425,plain,
( spl14_177
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,plus_plus(int,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_177])]) ).
tff(f1069,plain,
( spl14_74
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_74])]) ).
tff(f1087,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,plus_plus(int,X0),X1),X1) )
| ~ spl14_13
| ~ spl14_74 ),
inference(resolution,[],[f1070,f663]) ).
tff(f1070,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X1) ) )
| ~ spl14_74 ),
inference(avatar_component_clause,[],[f1069]) ).
tff(f2423,plain,
( spl14_176
| ~ spl14_13
| ~ spl14_73 ),
inference(avatar_split_clause,[],[f1086,f1065,f661,f2421]) ).
tff(f2421,plain,
( spl14_176
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,plus_plus(int,X1),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_176])]) ).
tff(f1065,plain,
( spl14_73
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_73])]) ).
tff(f1086,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,plus_plus(int,X1),X0),X1) )
| ~ spl14_13
| ~ spl14_73 ),
inference(resolution,[],[f1066,f663]) ).
tff(f1066,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X2) ) )
| ~ spl14_73 ),
inference(avatar_component_clause,[],[f1065]) ).
tff(f2419,plain,
( spl14_175
| ~ spl14_12
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f1085,f1061,f656,f2417]) ).
tff(f2417,plain,
( spl14_175
<=> ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_175])]) ).
tff(f2415,plain,
( spl14_174
| ~ spl14_12
| ~ spl14_71 ),
inference(avatar_split_clause,[],[f1084,f1057,f656,f2413]) ).
tff(f2413,plain,
( spl14_174
<=> ! [X0: int] : ( zero_zero(int) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_174])]) ).
tff(f1057,plain,
( spl14_71
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_71])]) ).
tff(f1084,plain,
( ! [X0: int] : ( zero_zero(int) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) )
| ~ spl14_12
| ~ spl14_71 ),
inference(resolution,[],[f1058,f658]) ).
tff(f1058,plain,
( ! [X0: $tType,X1: X0] :
( ~ group_add(X0)
| ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) ) )
| ~ spl14_71 ),
inference(avatar_component_clause,[],[f1057]) ).
tff(f2411,plain,
( spl14_173
| ~ spl14_57
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1040,f934,f863,f2409]) ).
tff(f2409,plain,
( spl14_173
<=> ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = X1 )
| ~ pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_173])]) ).
tff(f863,plain,
( spl14_57
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_57])]) ).
tff(f1040,plain,
( ! [X0: bool,X1: list(bool)] :
( ( filter(bool,aa(bool,fun(bool,bool),fdisj,X0),X1) = X1 )
| ~ pp(X0) )
| ~ spl14_57
| ~ spl14_70 ),
inference(resolution,[],[f935,f864]) ).
tff(f864,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) )
| ~ spl14_57 ),
inference(avatar_component_clause,[],[f863]) ).
tff(f2391,plain,
( spl14_172
| ~ spl14_20
| ~ spl14_159 ),
inference(avatar_split_clause,[],[f2292,f2209,f696,f2389]) ).
tff(f2389,plain,
( spl14_172
<=> ! [X0: $tType,X1: list(X0)] : ( filter(X0,combk(bool,X0,fTrue),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_172])]) ).
tff(f2209,plain,
( spl14_159
<=> ! [X0: $tType,X2: list(X0),X1: bool] :
( ~ pp(X1)
| ( filter(X0,combk(bool,X0,X1),X2) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_159])]) ).
tff(f2292,plain,
( ! [X0: $tType,X1: list(X0)] : ( filter(X0,combk(bool,X0,fTrue),X1) = X1 )
| ~ spl14_20
| ~ spl14_159 ),
inference(resolution,[],[f2210,f698]) ).
tff(f2210,plain,
( ! [X0: $tType,X2: list(X0),X1: bool] :
( ~ pp(X1)
| ( filter(X0,combk(bool,X0,X1),X2) = X2 ) )
| ~ spl14_159 ),
inference(avatar_component_clause,[],[f2209]) ).
tff(f2378,plain,
( spl14_171
| ~ spl14_93
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f1343,f1340,f1288,f2376]) ).
tff(f2376,plain,
( spl14_171
<=> ! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ pp(aa(int,bool,set(int,X0),zero_zero(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_171])]) ).
tff(f1343,plain,
( ! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ pp(aa(int,bool,set(int,X0),zero_zero(int))) )
| ~ spl14_93
| ~ spl14_96 ),
inference(resolution,[],[f1341,f1289]) ).
tff(f2374,plain,
( spl14_170
| ~ spl14_33
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1054,f934,f752,f2372]) ).
tff(f2372,plain,
( spl14_170
<=> ! [X0: list(bool)] :
( ~ pp(sK3(bool,X0,combi(bool)))
| ( filter(bool,combi(bool),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_170])]) ).
tff(f1054,plain,
( ! [X0: list(bool)] :
( ~ pp(sK3(bool,X0,combi(bool)))
| ( filter(bool,combi(bool),X0) = X0 ) )
| ~ spl14_33
| ~ spl14_70 ),
inference(superposition,[],[f935,f753]) ).
tff(f2370,plain,
( spl14_169
| ~ spl14_45
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f916,f906,f804,f2368]) ).
tff(f2368,plain,
( spl14_169
<=> ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),combk(bool,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_169])]) ).
tff(f916,plain,
( ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),combk(bool,X0,X1))) )
| ~ spl14_45
| ~ spl14_65 ),
inference(superposition,[],[f907,f805]) ).
tff(f2325,plain,
( spl14_168
| ~ spl14_45
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1104,f1073,f804,f2323]) ).
tff(f1104,plain,
( ! [X0: $tType,X2: list(X0),X1: bool] :
( pp(X1)
| ( nil(X0) = filter(X0,combk(bool,X0,X1),X2) ) )
| ~ spl14_45
| ~ spl14_75 ),
inference(superposition,[],[f1074,f805]) ).
tff(f2321,plain,
( spl14_167
| ~ spl14_24
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f808,f804,f713,f2319]) ).
tff(f2319,plain,
( spl14_167
<=> ! [X0: $tType,X2: X0,X1: bool] :
( ( fTrue = X1 )
| ( fFalse = aa(X0,bool,combk(bool,X0,X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_167])]) ).
tff(f808,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fTrue = X1 )
| ( fFalse = aa(X0,bool,combk(bool,X0,X1),X2) ) )
| ~ spl14_24
| ~ spl14_45 ),
inference(superposition,[],[f805,f714]) ).
tff(f2277,plain,
( spl14_166
| ~ spl14_36
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1275,f1241,f764,f2275]) ).
tff(f2275,plain,
( spl14_166
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( nil(X0) != map(X1,X0,X2,cons(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_166])]) ).
tff(f764,plain,
( spl14_36
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( nil(X0) != cons(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_36])]) ).
tff(f1275,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( nil(X0) != map(X1,X0,X2,cons(X1,X3,X4)) )
| ~ spl14_36
| ~ spl14_90 ),
inference(superposition,[],[f765,f1242]) ).
tff(f765,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( nil(X0) != cons(X0,X2,X1) )
| ~ spl14_36 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f2264,plain,
( ~ spl14_165
| ~ spl14_29
| ~ spl14_161
| spl14_164 ),
inference(avatar_split_clause,[],[f2259,f2254,f2219,f736,f2261]) ).
tff(f736,plain,
( spl14_29
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_29])]) ).
tff(f2219,plain,
( spl14_161
<=> ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_161])]) ).
tff(f2254,plain,
( spl14_164
<=> ( div_mod(int,aa(int,int,plus_plus(int,big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(i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= 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,aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_164])]) ).
tff(f2259,plain,
( ( div_mod(int,aa(int,int,plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as))))),aa(atom,int,divisor,a)) != div_mod(int,aa(int,int,plus_plus(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)),aa(atom,int,divisor,a))),div_mod(int,div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),x),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) )
| ~ spl14_29
| ~ spl14_161
| spl14_164 ),
inference(forward_demodulation,[],[f2258,f2221]) ).
tff(f2221,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) )
| ~ spl14_161 ),
inference(avatar_component_clause,[],[f2219]) ).
tff(f2258,plain,
( ( div_mod(int,aa(int,int,plus_plus(int,big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)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!= div_mod(int,aa(int,int,plus_plus(int,div_mod(int,big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(i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n(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) )
| ~ spl14_29
| spl14_164 ),
inference(forward_demodulation,[],[f2256,f737]) ).
tff(f737,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f2256,plain,
( ( 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)
| spl14_164 ),
inference(avatar_component_clause,[],[f2254]) ).
tff(f2257,plain,
~ spl14_164,
inference(avatar_split_clause,[],[f385,f2254]) ).
tff(f385,plain,
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inference(cnf_transformation,[],[f145]) ).
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inference(flattening,[],[f144]) ).
tff(f144,negated_conjecture,
( ~ 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,aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) ),
inference(negated_conjecture,[],[f143]) ).
tff(f143,conjecture,
div_mod(int,aa(int,int,plus_plus(int,big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(i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= 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,aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f2234,plain,
( spl14_163
| ~ spl14_29
| ~ spl14_162 ),
inference(avatar_split_clause,[],[f2229,f2225,f736,f2231]) ).
tff(f2225,plain,
( spl14_162
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_162])]) ).
tff(f2229,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl14_29
| ~ spl14_162 ),
inference(forward_demodulation,[],[f2227,f737]) ).
tff(f2227,plain,
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))))
| ~ spl14_162 ),
inference(avatar_component_clause,[],[f2225]) ).
tff(f2228,plain,
spl14_162,
inference(avatar_split_clause,[],[f577,f2225]) ).
tff(f577,plain,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs))),collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),
inference(forward_demodulation,[],[f415,f414]) ).
tff(f414,plain,
big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lm) ).
tff(f415,plain,
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inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool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n(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096Max_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_058_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f2222,plain,
( spl14_161
| ~ spl14_29
| ~ spl14_160 ),
inference(avatar_split_clause,[],[f2217,f2213,f736,f2219]) ).
tff(f2213,plain,
( spl14_160
<=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_160])]) ).
tff(f2217,plain,
( ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = big_linorder_Max(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) )
| ~ spl14_29
| ~ spl14_160 ),
inference(forward_demodulation,[],[f2215,f737]) ).
tff(f2215,plain,
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) )
| ~ spl14_160 ),
inference(avatar_component_clause,[],[f2213]) ).
tff(f2216,plain,
spl14_160,
inference(avatar_split_clause,[],[f414,f2213]) ).
tff(f2211,plain,
( spl14_159
| ~ spl14_45
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f1055,f934,f804,f2209]) ).
tff(f1055,plain,
( ! [X0: $tType,X2: list(X0),X1: bool] :
( ~ pp(X1)
| ( filter(X0,combk(bool,X0,X1),X2) = X2 ) )
| ~ spl14_45
| ~ spl14_70 ),
inference(superposition,[],[f935,f805]) ).
tff(f2206,plain,
~ spl14_158,
inference(avatar_split_clause,[],[f413,f2203]) ).
tff(f2203,plain,
( spl14_158
<=> ( collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) = bot_bot(fun(int,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_158])]) ).
tff(f413,plain,
collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != bot_bot(fun(int,bool)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) != bot_bot(fun(int,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__096_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_126_061_A_123_125_096) ).
tff(f2200,plain,
( spl14_157
| ~ spl14_29
| ~ spl14_156 ),
inference(avatar_split_clause,[],[f2195,f2191,f736,f2197]) ).
tff(f2197,plain,
( spl14_157
<=> finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_157])]) ).
tff(f2191,plain,
( spl14_156
<=> finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_156])]) ).
tff(f2195,plain,
( finite_finite1(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))
| ~ spl14_29
| ~ spl14_156 ),
inference(forward_demodulation,[],[f2193,f737]) ).
tff(f2193,plain,
( finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as))))))))
| ~ spl14_156 ),
inference(avatar_component_clause,[],[f2191]) ).
tff(f2194,plain,
spl14_156,
inference(avatar_split_clause,[],[f412,f2191]) ).
tff(f412,plain,
finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
finite_finite1(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
tff(f2180,plain,
( spl14_155
| ~ spl14_29
| ~ spl14_154 ),
inference(avatar_split_clause,[],[f2176,f2173,f736,f2178]) ).
tff(f2178,plain,
( spl14_155
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2)
| ~ linord2061991079up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_155])]) ).
tff(f2173,plain,
( spl14_154
<=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2)
| ~ linord2061991079up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_154])]) ).
tff(f2176,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2)
| ~ linord2061991079up_add(X0) )
| ~ spl14_29
| ~ spl14_154 ),
inference(forward_demodulation,[],[f2174,f737]) ).
tff(f2174,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2)
| ~ linord2061991079up_add(X0) )
| ~ spl14_154 ),
inference(avatar_component_clause,[],[f2173]) ).
tff(f2175,plain,
spl14_154,
inference(avatar_split_clause,[],[f426,f2173]) ).
tff(f426,plain,
! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2)
| ~ linord2061991079up_add(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2) )
| ~ linord2061991079up_add(X0) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0,X2: fun(X0,bool)] :
( ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) )
| ( bot_bot(fun(X0,bool)) = X2 )
| ~ finite_finite1(X0,X2) )
| ~ linord2061991079up_add(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( linord2061991079up_add(X0)
=> ! [X1: X0,X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( ( bot_bot(fun(X0,bool)) != X2 )
=> ( aa(X0,X0,plus_plus(X0,X1),big_linorder_Max(X0,X2)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X1))))),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))))) ) ) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( linord2061991079up_add(X0)
=> ! [X30: X0,X31: fun(X0,bool)] :
( finite_finite1(X0,X31)
=> ( ( bot_bot(fun(X0,bool)) != X31 )
=> ( aa(X0,X0,plus_plus(X0,X30),big_linorder_Max(X0,X31)) = big_linorder_Max(X0,collect(X0,aa(fun(X0,fun(X0,bool)),fun(X0,bool),aa(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),fEx(X0)),aa(fun(X0,bool),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),aa(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,fun(bool,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X0),combs(X0,bool,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X0),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,X0),fun(X0,fun(X0,bool)),aa(fun(X0,fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,X0),fun(X0,fun(X0,bool))),combc(X0,fun(X0,X0),fun(X0,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool))),aa(fun(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,X0),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,X0),fun(X0,bool)),X0),combb(X0,bool,X0)),fequal(X0))),plus_plus(X0,X30))))),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)),X31))))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__Max__commute) ).
tff(f2169,plain,
spl14_153,
inference(avatar_split_clause,[],[f591,f2167]) ).
tff(f2167,plain,
( spl14_153
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X1,X0)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_153])]) ).
tff(f591,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))) ),
inference(forward_demodulation,[],[f590,f480]) ).
tff(f480,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X7: fun(X0,bool)] : ( collect(X0,X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f590,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f534,f480]) ).
tff(f534,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(ennf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,bool)] :
( finite_finite1(X1,collect(X1,X3))
=> finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X1,bool),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,bool),fun(X1,bool))),fun(fun(X1,bool),fun(X0,fun(X1,bool))),combc(X0,fun(X1,bool),fun(X1,bool)),aa(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool))),aa(fun(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool))),fun(fun(X0,fun(X1,fun(bool,bool))),fun(X0,fun(fun(X1,bool),fun(X1,bool)))),combb(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),X0),combs(X1,bool,bool)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool))),aa(fun(fun(X1,bool),fun(X1,fun(bool,bool))),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,fun(bool,bool)))),combb(fun(X1,bool),fun(X1,fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj)),aa(fun(X1,X0),fun(X0,fun(X1,bool)),aa(fun(X0,fun(fun(X1,X0),fun(X1,bool))),fun(fun(X1,X0),fun(X0,fun(X1,bool))),combc(X0,fun(X1,X0),fun(X1,bool)),aa(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool))),aa(fun(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X1,X0),fun(X1,bool)))),combb(fun(X0,bool),fun(fun(X1,X0),fun(X1,bool)),X0),combb(X0,bool,X1)),fequal(X0))),X2)))),X3)))) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X1: $tType,X0: $tType,X9: fun(X0,X1),X7: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X7))
=> finite_finite1(X1,collect(X1,aa(fun(X1,fun(X0,bool)),fun(X1,bool),aa(fun(fun(X0,bool),bool),fun(fun(X1,fun(X0,bool)),fun(X1,bool)),combb(fun(X0,bool),bool,X1),fEx(X0)),aa(fun(X0,bool),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X1,fun(X0,bool))),combc(X1,fun(X0,bool),fun(X0,bool)),aa(fun(X1,fun(X0,fun(bool,bool))),fun(X1,fun(fun(X0,bool),fun(X0,bool))),aa(fun(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X1,fun(X0,fun(bool,bool))),fun(X1,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),X1),combs(X0,bool,bool)),aa(fun(X1,fun(X0,bool)),fun(X1,fun(X0,fun(bool,bool))),aa(fun(fun(X0,bool),fun(X0,fun(bool,bool))),fun(fun(X1,fun(X0,bool)),fun(X1,fun(X0,fun(bool,bool)))),combb(fun(X0,bool),fun(X0,fun(bool,bool)),X1),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj)),aa(fun(X0,X1),fun(X1,fun(X0,bool)),aa(fun(X1,fun(fun(X0,X1),fun(X0,bool))),fun(fun(X0,X1),fun(X1,fun(X0,bool))),combc(X1,fun(X0,X1),fun(X0,bool)),aa(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X0,X1),fun(X0,bool))),aa(fun(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool))),fun(fun(X1,fun(X1,bool)),fun(X1,fun(fun(X0,X1),fun(X0,bool)))),combb(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),X1),combb(X1,bool,X0)),fequal(X1))),X9)))),X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__image__set) ).
tff(f2153,plain,
spl14_152,
inference(avatar_split_clause,[],[f599,f2151]) ).
tff(f2151,plain,
( spl14_152
<=> ! [X1: $tType,X0: $tType,X5: X1,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_152])]) ).
tff(f599,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5)) ),
inference(forward_demodulation,[],[f598,f480]) ).
tff(f598,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( ~ finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f597,f480]) ).
tff(f597,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f535,f480]) ).
tff(f535,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool),X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f372]) ).
tff(f372,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3))))
& pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3))) ) )
& ( ! [X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f370,f371]) ).
tff(f371,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) )
=> ( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3))))
& pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f370,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) ) )
& ( ! [X5: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X5)))
| ~ pp(aa(X1,bool,X3,X5)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(rectify,[],[f369]) ).
tff(f369,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ? [X4: X1] :
( ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
& pp(aa(X1,bool,X3,X4)) ) )
& ( ! [X4: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
| ~ pp(aa(X1,bool,X3,X4)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(nnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
<=> ! [X4: X1] :
( finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4)))
| ~ pp(aa(X1,bool,X3,X4)) ) )
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(ennf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X1,collect(X1,X3))
=> ( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
<=> ! [X4: X1] :
( pp(aa(X1,bool,X3,X4))
=> finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),X4))) ) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X1: $tType,X0: $tType,X13: fun(X1,fun(X0,bool)),X7: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X7))
=> ( finite_finite1(X1,collect(X1,aa(fun(X1,fun(X0,bool)),fun(X1,bool),aa(fun(fun(X0,bool),bool),fun(fun(X1,fun(X0,bool)),fun(X1,bool)),combb(fun(X0,bool),bool,X1),fEx(X0)),aa(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool)),aa(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X1,fun(X0,bool)),fun(X1,fun(X0,bool))),combb(fun(X0,bool),fun(X0,bool),X1),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X7))),X13))))
<=> ! [X42: X0] :
( pp(aa(X0,bool,X7,X42))
=> finite_finite1(X1,collect(X1,aa(X0,fun(X1,bool),aa(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),X13),X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite__Collect__bounded__ex) ).
tff(f2143,plain,
spl14_151,
inference(avatar_split_clause,[],[f594,f2141]) ).
tff(f2141,plain,
( spl14_151
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_151])]) ).
tff(f594,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))) ),
inference(forward_demodulation,[],[f593,f480]) ).
tff(f593,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3)))
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f592,f480]) ).
tff(f592,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f537,f480]) ).
tff(f537,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| ~ finite_finite1(X0,collect(X0,aa(X1,fun(X0,bool),aa(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),X2),sK11(X0,X1,X2,X3))))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f372]) ).
tff(f2114,plain,
spl14_150,
inference(avatar_split_clause,[],[f596,f2112]) ).
tff(f2112,plain,
( spl14_150
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X2: fun(X0,fun(X1,bool))] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_150])]) ).
tff(f596,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( ~ finite_finite1(X1,X3)
| finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3))) ),
inference(forward_demodulation,[],[f595,f480]) ).
tff(f595,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2)))
| pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(forward_demodulation,[],[f536,f480]) ).
tff(f536,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: fun(X1,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,fun(X1,bool)),fun(X0,bool),aa(fun(fun(X1,bool),bool),fun(fun(X0,fun(X1,bool)),fun(X0,bool)),combb(fun(X1,bool),bool,X0),fEx(X1)),aa(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool)),aa(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X0,fun(X1,bool)),fun(X0,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X0),aa(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),aa(fun(X1,bool),fun(X1,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X3))),X2))))
| pp(aa(X1,bool,X3,sK11(X0,X1,X2,X3)))
| ~ finite_finite1(X1,collect(X1,X3)) ),
inference(cnf_transformation,[],[f372]) ).
tff(f2104,plain,
spl14_149,
inference(avatar_split_clause,[],[f504,f2102]) ).
tff(f2102,plain,
( spl14_149
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] : ( set(X0,filter(X0,X2,X1)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),set(X0,X1)))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_149])]) ).
tff(f504,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] : ( set(X0,filter(X0,X2,X1)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),set(X0,X1)))),X2)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] : ( set(X0,filter(X0,X2,X1)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),set(X0,X1)))),X2)) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X6: list(X0),X7: fun(X0,bool)] : ( set(X0,filter(X0,X7,X6)) = collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),set(X0,X6)))),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_set__filter) ).
tff(f2093,plain,
spl14_148,
inference(avatar_split_clause,[],[f531,f2091]) ).
tff(f2091,plain,
( spl14_148
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: list(X0)] : ( filter(X0,X3,filter(X0,X2,X1)) = filter(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)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_148])]) ).
tff(f531,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: list(X0)] : ( filter(X0,X3,filter(X0,X2,X1)) = filter(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)),X3),X1) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool),X3: fun(X0,bool)] : ( filter(X0,X3,filter(X0,X2,X1)) = filter(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)),X3),X1) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X6: list(X0),X13: fun(X0,bool),X7: fun(X0,bool)] : ( filter(X0,X7,filter(X0,X13,X6)) = filter(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),X13)),X7),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_filter__filter) ).
tff(f2089,plain,
( spl14_146
| spl14_147
| ~ spl14_33
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f915,f906,f752,f2087,f2083]) ).
tff(f915,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl14_33
| ~ spl14_65 ),
inference(superposition,[],[f907,f753]) ).
tff(f2078,plain,
spl14_145,
inference(avatar_split_clause,[],[f585,f2076]) ).
tff(f2076,plain,
( spl14_145
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| ~ finite_finite1(X0,X1)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_145])]) ).
tff(f585,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| ~ finite_finite1(X0,X1)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)) ),
inference(forward_demodulation,[],[f584,f480]) ).
tff(f584,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f583,f480]) ).
tff(f583,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f525,f480]) ).
tff(f525,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(cnf_transformation,[],[f358]) ).
tff(f358,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) )
& ( ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ) ),
inference(flattening,[],[f357]) ).
tff(f357,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,X2)) )
& ( ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) )
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ) ),
inference(nnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1)))
<=> ( finite_finite1(X0,collect(X0,X1))
& finite_finite1(X0,collect(X0,X2)) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType,X13: fun(X0,bool),X7: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X7)),X13)))
<=> ( finite_finite1(X0,collect(X0,X13))
& finite_finite1(X0,collect(X0,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_finite__Collect__disjI) ).
tff(f2064,plain,
spl14_144,
inference(avatar_split_clause,[],[f589,f2062]) ).
tff(f2062,plain,
( spl14_144
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_144])]) ).
tff(f589,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| finite_finite1(X0,X2) ),
inference(forward_demodulation,[],[f588,f480]) ).
tff(f588,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X2)
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ),
inference(forward_demodulation,[],[f523,f480]) ).
tff(f523,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X2))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ),
inference(cnf_transformation,[],[f358]) ).
tff(f2060,plain,
spl14_143,
inference(avatar_split_clause,[],[f587,f2058]) ).
tff(f2058,plain,
( spl14_143
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| finite_finite1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_143])]) ).
tff(f587,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))
| finite_finite1(X0,X1) ),
inference(forward_demodulation,[],[f586,f480]) ).
tff(f586,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ),
inference(forward_demodulation,[],[f524,f480]) ).
tff(f524,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,X1))
| ~ finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X2)),X1))) ),
inference(cnf_transformation,[],[f358]) ).
tff(f2056,plain,
spl14_142,
inference(avatar_split_clause,[],[f582,f2054]) ).
tff(f2054,plain,
( spl14_142
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_142])]) ).
tff(f582,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X2)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)) ),
inference(forward_demodulation,[],[f581,f480]) ).
tff(f581,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(forward_demodulation,[],[f511,f480]) ).
tff(f511,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X2)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))
| ( ~ finite_finite1(X0,collect(X0,X1))
& ~ finite_finite1(X0,collect(X0,X2)) ) ),
inference(ennf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,X1))
| finite_finite1(X0,collect(X0,X2)) )
=> finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X13: fun(X0,bool),X7: fun(X0,bool)] :
( ( finite_finite1(X0,collect(X0,X13))
| finite_finite1(X0,collect(X0,X7)) )
=> finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X7)),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_finite__Collect__conjI) ).
tff(f2052,plain,
( spl14_141
| ~ spl14_13
| ~ spl14_55 ),
inference(avatar_split_clause,[],[f886,f855,f661,f2050]) ).
tff(f2050,plain,
( spl14_141
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_141])]) ).
tff(f855,plain,
( spl14_55
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_55])]) ).
tff(f886,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) )
| ~ spl14_13
| ~ spl14_55 ),
inference(resolution,[],[f856,f663]) ).
tff(f856,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) ) )
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f855]) ).
tff(f2048,plain,
spl14_140,
inference(avatar_split_clause,[],[f580,f2046]) ).
tff(f2046,plain,
( spl14_140
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_140])]) ).
tff(f580,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ~ finite_finite1(X0,X1)
| finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)) ),
inference(forward_demodulation,[],[f579,f480]) ).
tff(f579,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))
| ~ finite_finite1(X0,collect(X0,X1)) ),
inference(forward_demodulation,[],[f512,f480]) ).
tff(f512,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,collect(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))
| ~ finite_finite1(X0,collect(X0,X1)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f2044,plain,
spl14_139,
inference(avatar_split_clause,[],[f476,f2042]) ).
tff(f2042,plain,
( spl14_139
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_139])]) ).
tff(f476,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Ominus(X0) )
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X1)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Ominus(X0) )
=> ! [X43: list(X0),X27: X0,X39: list(X0),X29: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),cons(X0,X29,X39)),cons(X0,X27,X43)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X29),X27),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X39),X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_list__diff__Cons__Cons) ).
tff(f2005,plain,
spl14_138,
inference(avatar_split_clause,[],[f416,f2002]) ).
tff(f416,plain,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f259,f333]) ).
tff(f333,plain,
( ? [X0: int,X1: list(int)] :
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as)))) )
=> ( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),sK0),sK1)),set(product_prod(int,list(int)),lbounds(as)))) ) ),
introduced(choice_axiom,[]) ).
tff(f259,plain,
? [X0: int,X1: list(int)] :
( ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) )
& pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as)))) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
~ ! [X0: int,X1: list(int)] :
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X0),X1)),set(product_prod(int,list(int)),lbounds(as))))
=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X1),xs)) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
~ ! [X4: int,X5: list(int)] :
( pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),X4),X5)),set(product_prod(int,list(int)),lbounds(as))))
=> ( big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) != aa(int,int,aa(int,fun(int,int),minus_minus(int),X4),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),X5),xs)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096_B_Bthesis_O_A_I_B_Bli_Alks_O_A_091_124_A_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_059_AMax_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_061_Ali_A_N_A_092_060langle_062lks_Mxs_092_060rangle_062_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f2000,plain,
spl14_137,
inference(avatar_split_clause,[],[f411,f1997]) ).
tff(f411,plain,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(fun(product_prod(int,list(int)),bool),bool,aa(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),member(product_prod(int,list(int))),aa(list(int),product_prod(int,list(int)),aa(int,fun(list(int),product_prod(int,list(int))),product_Pair(int,list(int)),li),lks)),set(product_prod(int,list(int)),lbounds(as)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_096) ).
tff(f1995,plain,
spl14_136,
inference(avatar_split_clause,[],[f410,f1992]) ).
tff(f410,plain,
pp(aa(atom,bool,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),a)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(atom,bool,atom_case(bool,combk(fun(list(int),bool),int,combk(bool,list(int),fFalse)),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue))),combk(fun(int,fun(list(int),bool)),int,combk(fun(list(int),bool),int,combk(bool,list(int),fTrue)))),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096is__dvd_Aa_096) ).
tff(f1986,plain,
spl14_135,
inference(avatar_split_clause,[],[f578,f1983]) ).
tff(f1983,plain,
( spl14_135
<=> ( aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_135])]) ).
tff(f578,plain,
aa(int,int,aa(int,fun(int,int),minus_minus(int),li),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),lks),xs)) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)),
inference(forward_demodulation,[],[f417,f414]) ).
tff(f417,plain,
big_linorder_Max(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) = aa(int,int,aa(int,fun(int,int),minus_minus(int),sK0),aa(list(int),int,aa(list(int),fun(list(int),int),iprod(int),sK1),xs)),
inference(cnf_transformation,[],[f334]) ).
tff(f1938,plain,
spl14_134,
inference(avatar_split_clause,[],[f444,f1936]) ).
tff(f1936,plain,
( spl14_134
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ ring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_134])]) ).
tff(f444,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ ring_div(X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ ring_div(X0) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ ring_div(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( ring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,X5,X4) = div_mod(X0,X3,X4) )
=> ( ( div_mod(X0,X2,X4) = div_mod(X0,X1,X4) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X1),X4) ) ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X23: X0,X11: X0,X24: X0,X25: X0,X12: X0] :
( ( div_mod(X0,X12,X25) = div_mod(X0,X24,X25) )
=> ( ( div_mod(X0,X11,X25) = div_mod(X0,X23,X25) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X11),X25) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X24),X23),X25) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mod__diff__cong) ).
tff(f1865,plain,
spl14_133,
inference(avatar_split_clause,[],[f553,f1863]) ).
tff(f1863,plain,
( spl14_133
<=> ! [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,[spl14_133])]) ).
tff(f553,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,[],[f251]) ).
tff(f251,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,[],[f130]) ).
tff(f130,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X48: X0,X49: fun(X0,X1),X47: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X47),X49),X48) = aa(X1,X2,aa(X0,fun(X1,X2),X47,X48),aa(X0,X1,X49,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1847,plain,
spl14_132,
inference(avatar_split_clause,[],[f538,f1845]) ).
tff(f1845,plain,
( spl14_132
<=> ! [X0: $tType,X3: X0,X2: X0,X1: list(X0)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
| ( X2 = X3 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,cons(X0,X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_132])]) ).
tff(f538,plain,
! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
| ( X2 = X3 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,cons(X0,X2,X1)))) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
| ( X2 = X3 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,cons(X0,X2,X1)))) ),
inference(flattening,[],[f328]) ).
tff(f328,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
| ( X2 = X3 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,cons(X0,X2,X1)))) ),
inference(ennf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,cons(X0,X2,X1))))
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
| ( X2 = X3 ) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X6: list(X0),X38: X0,X40: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X40),set(X0,cons(X0,X38,X6))))
=> ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X40),set(X0,X6)))
| ( X38 = X40 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_set__ConsD) ).
tff(f1830,plain,
spl14_131,
inference(avatar_split_clause,[],[f548,f1828]) ).
tff(f1828,plain,
( spl14_131
<=> ! [X1: $tType,X0: $tType,X3: list(X1),X4: fun(X1,X0),X6: X1,X2: fun(X1,X0)] :
( ( aa(X1,X0,X4,X6) = aa(X1,X0,X2,X6) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X6),set(X1,X3)))
| ( map(X1,X0,X4,X3) != map(X1,X0,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_131])]) ).
tff(f548,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X6: X1,X4: fun(X1,X0)] :
( ( aa(X1,X0,X4,X6) = aa(X1,X0,X2,X6) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X6),set(X1,X3)))
| ( map(X1,X0,X4,X3) != map(X1,X0,X2,X3) ) ),
inference(cnf_transformation,[],[f382]) ).
tff(f382,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| ( ( aa(X1,X0,X4,sK13(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3,X4)) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),sK13(X0,X1,X2,X3,X4)),set(X1,X3))) ) )
& ( ! [X6: X1] :
( ( aa(X1,X0,X4,X6) = aa(X1,X0,X2,X6) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X6),set(X1,X3))) )
| ( map(X1,X0,X4,X3) != map(X1,X0,X2,X3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f380,f381]) ).
tff(f381,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ? [X5: X1] :
( ( aa(X1,X0,X4,X5) != aa(X1,X0,X2,X5) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3))) )
=> ( ( aa(X1,X0,X4,sK13(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3,X4)) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),sK13(X0,X1,X2,X3,X4)),set(X1,X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f380,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| ? [X5: X1] :
( ( aa(X1,X0,X4,X5) != aa(X1,X0,X2,X5) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3))) ) )
& ( ! [X6: X1] :
( ( aa(X1,X0,X4,X6) = aa(X1,X0,X2,X6) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X6),set(X1,X3))) )
| ( map(X1,X0,X4,X3) != map(X1,X0,X2,X3) ) ) ),
inference(rectify,[],[f379]) ).
tff(f379,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| ? [X5: X1] :
( ( aa(X1,X0,X4,X5) != aa(X1,X0,X2,X5) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3))) ) )
& ( ! [X5: X1] :
( ( aa(X1,X0,X4,X5) = aa(X1,X0,X2,X5) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3))) )
| ( map(X1,X0,X4,X3) != map(X1,X0,X2,X3) ) ) ),
inference(nnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
<=> ! [X5: X1] :
( ( aa(X1,X0,X4,X5) = aa(X1,X0,X2,X5) )
| ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3))) ) ),
inference(ennf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
<=> ! [X5: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X5),set(X1,X3)))
=> ( aa(X1,X0,X4,X5) = aa(X1,X0,X2,X5) ) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType,X1: $tType,X8: fun(X1,X0),X6: list(X1),X9: fun(X1,X0)] :
( ( map(X1,X0,X9,X6) = map(X1,X0,X8,X6) )
<=> ! [X10: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X10),set(X1,X6)))
=> ( aa(X1,X0,X9,X10) = aa(X1,X0,X8,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_map__eq__conv) ).
tff(f1790,plain,
( spl14_130
| ~ spl14_65
| ~ spl14_97 ),
inference(avatar_split_clause,[],[f1388,f1353,f906,f1787]) ).
tff(f1388,plain,
( pp(aa(fun(atom,bool),bool,fEx(atom),set(atom,as)))
| ~ spl14_65
| ~ spl14_97 ),
inference(resolution,[],[f1355,f907]) ).
tff(f1785,plain,
spl14_129,
inference(avatar_split_clause,[],[f475,f1783]) ).
tff(f1783,plain,
( spl14_129
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,plus_plus(X0,X4),X2),aa(list(X0),list(X0),plus_plus(list(X0),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_129])]) ).
tff(f475,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,plus_plus(X0,X4),X2),aa(list(X0),list(X0),plus_plus(list(X0),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,plus_plus(X0,X4),X2),aa(list(X0),list(X0),plus_plus(list(X0),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f310]) ).
tff(f310,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,plus_plus(X0,X4),X2),aa(list(X0),list(X0),plus_plus(list(X0),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,plus_plus(X0,X4),X2),aa(list(X0),list(X0),plus_plus(list(X0),X3),X1)) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X43: list(X0),X27: X0,X39: list(X0),X29: X0] : ( aa(list(X0),list(X0),plus_plus(list(X0),cons(X0,X29,X39)),cons(X0,X27,X43)) = cons(X0,aa(X0,X0,plus_plus(X0,X29),X27),aa(list(X0),list(X0),plus_plus(list(X0),X39),X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_list__add__Cons) ).
tff(f1781,plain,
spl14_128,
inference(avatar_split_clause,[],[f468,f1779]) ).
tff(f1779,plain,
( spl14_128
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_128])]) ).
tff(f468,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(flattening,[],[f299]) ).
tff(f299,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,X5,X4) = div_mod(X0,X3,X4) )
=> ( ( div_mod(X0,X2,X4) = div_mod(X0,X1,X4) )
=> ( div_mod(X0,aa(X0,X0,plus_plus(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X4) ) ) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X23: X0,X11: X0,X24: X0,X25: X0,X12: X0] :
( ( div_mod(X0,X12,X25) = div_mod(X0,X24,X25) )
=> ( ( div_mod(X0,X11,X25) = div_mod(X0,X23,X25) )
=> ( div_mod(X0,aa(X0,X0,plus_plus(X0,X12),X11),X25) = div_mod(X0,aa(X0,X0,plus_plus(X0,X24),X23),X25) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_mod__add__cong) ).
tff(f1775,plain,
spl14_127,
inference(avatar_split_clause,[],[f555,f1773]) ).
tff(f1773,plain,
( spl14_127
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: X0,X2: X1] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_127])]) ).
tff(f555,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( ( X2 = X4 )
& ( X3 = X5 ) )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(ennf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) )
=> ~ ( ( X3 = X5 )
=> ( X2 != X4 ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X1: $tType,X23: X1,X24: X0,X11: X1,X12: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X12),X11) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X24),X23) )
=> ~ ( ( X12 = X24 )
=> ( X11 != X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Pair__inject) ).
tff(f1771,plain,
spl14_126,
inference(avatar_split_clause,[],[f554,f1769]) ).
tff(f1769,plain,
( spl14_126
<=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_126])]) ).
tff(f554,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) ) ),
inference(cnf_transformation,[],[f332]) ).
tff(f1766,plain,
spl14_125,
inference(avatar_split_clause,[],[f437,f1764]) ).
tff(f1764,plain,
( spl14_125
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_125])]) ).
tff(f437,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( ring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X11),X25) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X12,X25)),div_mod(X0,X11,X25)),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mod__diff__eq) ).
tff(f1662,plain,
spl14_124,
inference(avatar_split_clause,[],[f552,f1660]) ).
tff(f1660,plain,
( spl14_124
<=> ! [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,[spl14_124])]) ).
tff(f552,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,[],[f250]) ).
tff(f250,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,[],[f126]) ).
tff(f126,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X48: X0,X49: fun(X0,X1),X47: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X47),X49),X48) = aa(X1,X2,X47,aa(X0,X1,X49,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1658,plain,
spl14_123,
inference(avatar_split_clause,[],[f551,f1656]) ).
tff(f1656,plain,
( spl14_123
<=> ! [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,[spl14_123])]) ).
tff(f551,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,[],[f249]) ).
tff(f249,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,[],[f127]) ).
tff(f127,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X48: X0,X49: X1,X47: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X47),X49),X48) = aa(X1,X2,aa(X0,fun(X1,X2),X47,X48),X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1654,plain,
spl14_122,
inference(avatar_split_clause,[],[f528,f1652]) ).
tff(f1652,plain,
( spl14_122
<=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_122])]) ).
tff(f528,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
inference(cnf_transformation,[],[f368]) ).
tff(f368,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2))))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f365,f367,f366]) ).
tff(f366,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
=> pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f367,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
=> pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK9(X0,X1,X2)),sK10(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f365,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(rectify,[],[f364]) ).
tff(f364,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
| ! [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
inference(nnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
<=> ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType,X1: $tType,X7: fun(product_prod(X0,X1),bool)] :
( ? [X18: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X7,X18))
<=> ? [X19: X0,X20: X1] : pp(aa(product_prod(X0,X1),bool,X7,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X19),X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).
tff(f1650,plain,
spl14_121,
inference(avatar_split_clause,[],[f527,f1648]) ).
tff(f1648,plain,
( spl14_121
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK5(X0,X1,X2)),sK6(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_121])]) ).
tff(f527,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK5(X0,X1,X2)),sK6(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f363]) ).
tff(f363,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK5(X0,X1,X2)),sK6(X0,X1,X2)))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f360,f362,f361]) ).
tff(f361,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK5(X0,X1,X2)),sK6(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f362,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f360,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(rectify,[],[f359]) ).
tff(f359,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
| ? [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
inference(nnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
<=> ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X1: $tType,X7: fun(product_prod(X0,X1),bool)] :
( ! [X18: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X7,X18))
<=> ! [X19: X0,X20: X1] : pp(aa(product_prod(X0,X1),bool,X7,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X19),X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_split__paired__All) ).
tff(f1628,plain,
spl14_120,
inference(avatar_split_clause,[],[f549,f1626]) ).
tff(f549,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),sK13(X0,X1,X2,X3,X4)),set(X1,X3))) ),
inference(cnf_transformation,[],[f382]) ).
tff(f1624,plain,
( spl14_119
| ~ spl14_24
| ~ spl14_33 ),
inference(avatar_split_clause,[],[f768,f752,f713,f1622]) ).
tff(f1622,plain,
( spl14_119
<=> ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_119])]) ).
tff(f768,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = aa(bool,bool,combi(bool),X0) ) )
| ~ spl14_24
| ~ spl14_33 ),
inference(superposition,[],[f753,f714]) ).
tff(f1620,plain,
spl14_118,
inference(avatar_split_clause,[],[f436,f1618]) ).
tff(f1618,plain,
( spl14_118
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),X2),X1) )
| ~ ring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_118])]) ).
tff(f436,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),X2),X1) )
| ~ ring_div(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),X2),X1) )
| ~ ring_div(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( ring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X3,X1)),X2),X1) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X11),X25) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X12,X25)),X11),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mod__diff__left__eq) ).
tff(f1616,plain,
spl14_117,
inference(avatar_split_clause,[],[f435,f1614]) ).
tff(f1614,plain,
( spl14_117
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_117])]) ).
tff(f435,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ ring_div(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( ring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X3),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X11),X25) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),div_mod(X0,X11,X25)),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mod__diff__right__eq) ).
tff(f1593,plain,
spl14_116,
inference(avatar_split_clause,[],[f529,f1591]) ).
tff(f1591,plain,
( spl14_116
<=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_116])]) ).
tff(f529,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(cnf_transformation,[],[f368]) ).
tff(f1589,plain,
spl14_115,
inference(avatar_split_clause,[],[f526,f1587]) ).
tff(f1587,plain,
( spl14_115
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_115])]) ).
tff(f526,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ),
inference(cnf_transformation,[],[f363]) ).
tff(f1562,plain,
spl14_114,
inference(avatar_split_clause,[],[f503,f1560]) ).
tff(f1560,plain,
( spl14_114
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X2,X1)),X0),X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_114])]) ).
tff(f503,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X2,X1)),X0),X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X0),X1) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: int,X1: int,X2: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X2,X1)),X0),X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X0),X1) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X27: int,X28: int,X29: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X29,X28)),X27),X28) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X29),X27),X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_zdiff__zmod__left) ).
tff(f1558,plain,
spl14_113,
inference(avatar_split_clause,[],[f502,f1556]) ).
tff(f502,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),div_mod(int,X1,X0)),X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: int,X1: int,X2: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X2),div_mod(int,X1,X0)),X0) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X28: int,X27: int,X29: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X29),X27),X28) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X29),div_mod(int,X27,X28)),X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zdiff__zmod__right) ).
tff(f1513,plain,
spl14_112,
inference(avatar_split_clause,[],[f550,f1511]) ).
tff(f550,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( map(X1,X0,X4,X3) = map(X1,X0,X2,X3) )
| ( aa(X1,X0,X4,sK13(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK13(X0,X1,X2,X3,X4)) ) ),
inference(cnf_transformation,[],[f382]) ).
tff(f1509,plain,
spl14_111,
inference(avatar_split_clause,[],[f518,f1507]) ).
tff(f518,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0),X4: X0] :
( ~ pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| ( nil(X0) != filter(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f355]) ).
tff(f355,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = filter(X0,X2,X1) )
| ( pp(aa(X0,bool,X2,sK4(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1,X2)),set(X0,X1))) ) )
& ( ! [X4: X0] :
( ~ pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( nil(X0) != filter(X0,X2,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f353,f354]) ).
tff(f354,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ? [X3: X0] :
( pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
=> ( pp(aa(X0,bool,X2,sK4(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1,X2)),set(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f353,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = filter(X0,X2,X1) )
| ? [X3: X0] :
( pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X4: X0] :
( ~ pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( nil(X0) != filter(X0,X2,X1) ) ) ),
inference(rectify,[],[f352]) ).
tff(f352,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = filter(X0,X2,X1) )
| ? [X3: X0] :
( pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
| ( nil(X0) != filter(X0,X2,X1) ) ) ),
inference(nnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X2,X1) )
<=> ! [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) ),
inference(ennf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X2,X1) )
<=> ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
=> ~ pp(aa(X0,bool,X2,X3)) ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X6: list(X0),X7: fun(X0,bool)] :
( ( filter(X0,X7,X6) = nil(X0) )
<=> ! [X10: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X10),set(X0,X6)))
=> ~ pp(aa(X0,bool,X7,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_filter__empty__conv) ).
tff(f1486,plain,
spl14_110,
inference(avatar_split_clause,[],[f515,f1484]) ).
tff(f515,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0),X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1)))
| ( filter(X0,X2,X1) != X1 ) ),
inference(cnf_transformation,[],[f351]) ).
tff(f351,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( filter(X0,X2,X1) = X1 )
| ( ~ pp(aa(X0,bool,X2,sK3(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1,X2)),set(X0,X1))) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( filter(X0,X2,X1) != X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f349,f350]) ).
tff(f350,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
=> ( ~ pp(aa(X0,bool,X2,sK3(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1,X2)),set(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f349,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( filter(X0,X2,X1) = X1 )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( filter(X0,X2,X1) != X1 ) ) ),
inference(rectify,[],[f348]) ).
tff(f348,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( filter(X0,X2,X1) = X1 )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
| ( filter(X0,X2,X1) != X1 ) ) ),
inference(nnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( filter(X0,X2,X1) = X1 )
<=> ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) ),
inference(ennf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( filter(X0,X2,X1) = X1 )
<=> ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
=> pp(aa(X0,bool,X2,X3)) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType,X6: list(X0),X7: fun(X0,bool)] :
( ( filter(X0,X7,X6) = X6 )
<=> ! [X10: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X10),set(X0,X6)))
=> pp(aa(X0,bool,X7,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_filter__id__conv) ).
tff(f1482,plain,
spl14_109,
inference(avatar_split_clause,[],[f509,f1480]) ).
tff(f1480,plain,
( spl14_109
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_109])]) ).
tff(f509,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X2) ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ finite_finite1(X0,X1) )
& ( finite_finite1(X0,X1)
| ~ finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) ) )
| ~ finite_finite1(X0,X2) ),
inference(nnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
<=> finite_finite1(X0,X1) )
| ~ finite_finite1(X0,X2) ),
inference(ennf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
<=> finite_finite1(X0,X1) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType,X33: fun(X0,bool),X34: fun(X0,bool)] :
( finite_finite1(X0,X34)
=> ( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X33),X34))
<=> finite_finite1(X0,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Diff2) ).
tff(f1478,plain,
spl14_108,
inference(avatar_split_clause,[],[f469,f1476]) ).
tff(f469,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1) )
| ~ linorder(X0) ),
inference(flattening,[],[f301]) ).
tff(f301,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 )
| ~ finite_finite1(X0,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
=> ( ( bot_bot(fun(X0,bool)) != X1 )
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X1)),X1)) ) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X33: fun(X0,bool)] :
( finite_finite1(X0,X33)
=> ( ( bot_bot(fun(X0,bool)) != X33 )
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),big_linorder_Max(X0,X33)),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Max__in) ).
tff(f1423,plain,
spl14_107,
inference(avatar_split_clause,[],[f566,f1421]) ).
tff(f1421,plain,
( spl14_107
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0] :
( ( X3 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X2) )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_107])]) ).
tff(f566,plain,
! [X0: $tType,X2: X0,X3: X0,X4: X0] :
( ( X3 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X2) )
| ~ group_add(X0) ),
inference(equality_resolution,[],[f456]) ).
tff(f456,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( X3 = X4 )
| ( X1 != X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( ( X3 = X4 )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( X3 != X4 ) ) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) ) )
| ~ group_add(X0) ),
inference(nnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( X3 = X4 )
<=> ( X1 = X2 ) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) ) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) )
=> ( ( X3 = X4 )
<=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X26: X0,X15: X0,X16: X0,X17: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X17),X16) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X15),X26) )
=> ( ( X16 = X17 )
<=> ( X15 = X26 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_diff__eq__diff__eq) ).
tff(f1419,plain,
spl14_106,
inference(avatar_split_clause,[],[f519,f1417]) ).
tff(f519,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = filter(X0,X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1,X2)),set(X0,X1))) ),
inference(cnf_transformation,[],[f355]) ).
tff(f1415,plain,
spl14_105,
inference(avatar_split_clause,[],[f513,f1413]) ).
tff(f513,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),set(X0,X2))) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $tType,X1: fun(X0,bool),X2: list(X0)] :
( ( nil(X0) = filter(X0,X1,X2) )
| ( pp(aa(X0,bool,X1,sK2(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),set(X0,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f322,f346]) ).
tff(f346,plain,
! [X0: $tType,X1: fun(X0,bool),X2: list(X0)] :
( ? [X3: X0] :
( pp(aa(X0,bool,X1,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X2))) )
=> ( pp(aa(X0,bool,X1,sK2(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1,X2)),set(X0,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f322,plain,
! [X0: $tType,X1: fun(X0,bool),X2: list(X0)] :
( ( nil(X0) = filter(X0,X1,X2) )
| ? [X3: X0] :
( pp(aa(X0,bool,X1,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X2))) ) ),
inference(ennf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: fun(X0,bool),X2: list(X0)] :
( ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X2)))
=> ~ pp(aa(X0,bool,X1,X3)) )
=> ( nil(X0) = filter(X0,X1,X2) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X7: fun(X0,bool),X6: list(X0)] :
( ! [X32: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X32),set(X0,X6)))
=> ~ pp(aa(X0,bool,X7,X32)) )
=> ( filter(X0,X7,X6) = nil(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_filter__False) ).
tff(f1386,plain,
spl14_104,
inference(avatar_split_clause,[],[f516,f1384]) ).
tff(f516,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X2,X1) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1,X2)),set(X0,X1))) ),
inference(cnf_transformation,[],[f351]) ).
tff(f1382,plain,
spl14_103,
inference(avatar_split_clause,[],[f508,f1380]) ).
tff(f1380,plain,
( spl14_103
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_103])]) ).
tff(f508,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))
| ~ finite_finite1(X0,X2) ),
inference(ennf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( finite_finite1(X0,X2)
=> finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType,X34: fun(X0,bool),X33: fun(X0,bool)] :
( finite_finite1(X0,X33)
=> finite_finite1(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X33),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_finite__Diff) ).
tff(f1378,plain,
spl14_102,
inference(avatar_split_clause,[],[f467,f1376]) ).
tff(f467,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X12),X11),X25) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X12,X25)),div_mod(X0,X11,X25)),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mod__add__eq) ).
tff(f1374,plain,
spl14_101,
inference(avatar_split_clause,[],[f427,f1372]) ).
tff(f427,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X3),X2)),X1) = aa(X0,X0,plus_plus(X0,X3),aa(X0,X0,plus_plus(X0,X2),X1)) )
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X3),X2)),X1) = aa(X0,X0,plus_plus(X0,X3),aa(X0,X0,plus_plus(X0,X2),X1)) )
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X3),X2)),X1) = aa(X0,X0,plus_plus(X0,X3),aa(X0,X0,plus_plus(X0,X2),X1)) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,plus_plus(X0,X12),X11)),X25) = aa(X0,X0,plus_plus(X0,X12),aa(X0,X0,plus_plus(X0,X11),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1370,plain,
spl14_100,
inference(avatar_split_clause,[],[f472,f1368]) ).
tff(f1368,plain,
( spl14_100
<=> ! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,divisor,X0) )
| ~ pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X0),set(atom,as))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_100])]) ).
tff(f472,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,divisor,X0) )
| ~ pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X0),set(atom,as))) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,divisor,X0) )
| ~ pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X0),set(atom,as))) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X0),set(atom,as)))
=> ( zero_zero(int) != aa(atom,int,divisor,X0) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X14: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X14),set(atom,as)))
=> ( aa(atom,int,divisor,X14) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_norm) ).
tff(f1364,plain,
spl14_99,
inference(avatar_split_clause,[],[f465,f1362]) ).
tff(f465,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X3,X2)),X1),X2) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X25: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X12),X11),X25) = div_mod(X0,aa(X0,X0,plus_plus(X0,div_mod(X0,X12,X25)),X11),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zmod__simps_I1_J) ).
tff(f1360,plain,
spl14_98,
inference(avatar_split_clause,[],[f463,f1358]) ).
tff(f463,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X3),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X25: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X12),X11),X25) = div_mod(X0,aa(X0,X0,plus_plus(X0,X12),div_mod(X0,X11,X25)),X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mod__add__right__eq) ).
tff(f1356,plain,
( spl14_97
| ~ spl14_78
| ~ spl14_92 ),
inference(avatar_split_clause,[],[f1291,f1284,f1123,f1353]) ).
tff(f1291,plain,
( pp(aa(atom,bool,set(atom,as),a))
| ~ spl14_78
| ~ spl14_92 ),
inference(resolution,[],[f1285,f1125]) ).
tff(f1342,plain,
spl14_96,
inference(avatar_split_clause,[],[f478,f1340]) ).
tff(f478,plain,
! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0))) ),
inference(cnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: list(int)] :
( ( ( zero_zero(int) = zlcms(X0) )
| ~ pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0))) )
& ( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0)))
| ( zero_zero(int) != zlcms(X0) ) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X44: list(int)] :
( ( zero_zero(int) = zlcms(X44) )
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zlcms0__iff) ).
tff(f1338,plain,
spl14_95,
inference(avatar_split_clause,[],[f477,f1336]) ).
tff(f1336,plain,
( spl14_95
<=> ! [X0: list(int)] :
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0)))
| ( zero_zero(int) != zlcms(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_95])]) ).
tff(f477,plain,
! [X0: list(int)] :
( pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,X0)))
| ( zero_zero(int) != zlcms(X0) ) ),
inference(cnf_transformation,[],[f342]) ).
tff(f1314,plain,
spl14_94,
inference(avatar_split_clause,[],[f539,f1312]) ).
tff(f539,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK12(X0,X1,X2,X3)) != aa(X1,X0,X2,sK12(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f374]) ).
tff(f374,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK12(X0,X1,X2,X3)) != aa(X1,X0,X2,sK12(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f330,f373]) ).
tff(f373,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,sK12(X0,X1,X2,X3)) != aa(X1,X0,X2,sK12(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f330,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,[],[f243]) ).
tff(f243,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X8: fun(X0,X1),X9: fun(X0,X1)] :
( ! [X32: X0] : ( aa(X0,X1,X9,X32) = aa(X0,X1,X8,X32) )
=> ( X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1290,plain,
spl14_93,
inference(avatar_split_clause,[],[f522,f1288]) ).
tff(f522,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,[],[f356]) ).
tff(f356,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,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X33: fun(X0,bool),X38: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X38),X33))
<=> pp(aa(X0,bool,X33,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f1286,plain,
spl14_92,
inference(avatar_split_clause,[],[f521,f1284]) ).
tff(f521,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,[],[f356]) ).
tff(f1282,plain,
( spl14_91
| ~ spl14_6
| ~ spl14_50 ),
inference(avatar_split_clause,[],[f838,f829,f626,f1280]) ).
tff(f626,plain,
( spl14_6
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
tff(f829,plain,
( spl14_50
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_50])]) ).
tff(f838,plain,
( ! [X0: int] : ( aa(int,int,plus_plus(int,zero_zero(int)),X0) = X0 )
| ~ spl14_6
| ~ spl14_50 ),
inference(resolution,[],[f830,f628]) ).
tff(f628,plain,
( monoid_add(int)
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f830,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_add(X0)
| ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 ) )
| ~ spl14_50 ),
inference(avatar_component_clause,[],[f829]) ).
tff(f1243,plain,
spl14_90,
inference(avatar_split_clause,[],[f544,f1241]) ).
tff(f544,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X1: $tType,X6: list(X1),X38: X1,X9: fun(X1,X0)] : ( map(X1,X0,X9,cons(X1,X38,X6)) = cons(X0,aa(X1,X0,X9,X38),map(X1,X0,X9,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_map_Osimps_I2_J) ).
tff(f1239,plain,
spl14_89,
inference(avatar_split_clause,[],[f532,f1237]) ).
tff(f532,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X3,cons(X0,X2,X1)) = cons(X0,X2,filter(X0,X3,X1)) )
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: fun(X0,bool)] :
( ( ( filter(X0,X3,X1) = filter(X0,X3,cons(X0,X2,X1)) )
| pp(aa(X0,bool,X3,X2)) )
& ( ( filter(X0,X3,cons(X0,X2,X1)) = cons(X0,X2,filter(X0,X3,X1)) )
| ~ pp(aa(X0,bool,X3,X2)) ) ),
inference(ennf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: fun(X0,bool)] :
( ( ~ pp(aa(X0,bool,X3,X2))
=> ( filter(X0,X3,X1) = filter(X0,X3,cons(X0,X2,X1)) ) )
& ( pp(aa(X0,bool,X3,X2))
=> ( filter(X0,X3,cons(X0,X2,X1)) = cons(X0,X2,filter(X0,X3,X1)) ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType,X6: list(X0),X38: X0,X7: fun(X0,bool)] :
( ( ~ pp(aa(X0,bool,X7,X38))
=> ( filter(X0,X7,X6) = filter(X0,X7,cons(X0,X38,X6)) ) )
& ( pp(aa(X0,bool,X7,X38))
=> ( filter(X0,X7,cons(X0,X38,X6)) = cons(X0,X38,filter(X0,X7,X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_filter_Osimps_I2_J) ).
tff(f1235,plain,
spl14_88,
inference(avatar_split_clause,[],[f450,f1233]) ).
tff(f450,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X2),X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X2),X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X2),X1)),X1) = X2 ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X11: X0,X12: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(X0,X0,plus_plus(X0,X12),X11)),X11) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__diff__cancel) ).
tff(f1231,plain,
spl14_87,
inference(avatar_split_clause,[],[f449,f1229]) ).
tff(f449,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),X1) = X2 ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X11: X0,X12: X0] : ( aa(X0,X0,plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X11)),X11) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_diff__add__cancel) ).
tff(f1225,plain,
( spl14_86
| ~ spl14_6
| ~ spl14_48 ),
inference(avatar_split_clause,[],[f836,f821,f626,f1223]) ).
tff(f1223,plain,
( spl14_86
<=> ! [X0: int] : ( aa(int,int,plus_plus(int,X0),zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_86])]) ).
tff(f821,plain,
( spl14_48
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_48])]) ).
tff(f836,plain,
( ! [X0: int] : ( aa(int,int,plus_plus(int,X0),zero_zero(int)) = X0 )
| ~ spl14_6
| ~ spl14_48 ),
inference(resolution,[],[f822,f628]) ).
tff(f822,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_add(X0)
| ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 ) )
| ~ spl14_48 ),
inference(avatar_component_clause,[],[f821]) ).
tff(f1221,plain,
spl14_85,
inference(avatar_split_clause,[],[f434,f1219]) ).
tff(f434,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X1) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X1) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X1) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X43: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),nil(X0)),X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_iprod__Nil) ).
tff(f1217,plain,
spl14_84,
inference(avatar_split_clause,[],[f433,f1215]) ).
tff(f433,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X1),nil(X0)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X1),nil(X0)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X1),nil(X0)) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X39: list(X0)] : ( zero_zero(X0) = aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X39),nil(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_iprod__Nil2) ).
tff(f1175,plain,
spl14_83,
inference(avatar_split_clause,[],[f452,f1173]) ).
tff(f452,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f339]) ).
tff(f339,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
& ( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) )
| ( X1 != X2 ) ) )
| ~ group_add(X0) ),
inference(nnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 = X2 )
<=> ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X16: X0,X17: X0] :
( ( X16 = X17 )
<=> ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X17),X16) = zero_zero(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_eq__iff__diff__eq__0) ).
tff(f1171,plain,
spl14_82,
inference(avatar_split_clause,[],[f439,f1169]) ).
tff(f1169,plain,
( spl14_82
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_82])]) ).
tff(f439,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,plus_plus(X0,X3),X2) = aa(X0,X0,plus_plus(X0,X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X25: X0,X11: X0,X12: X0] :
( ( aa(X0,X0,plus_plus(X0,X12),X11) = aa(X0,X0,plus_plus(X0,X12),X25) )
=> ( X11 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__left__imp__eq) ).
tff(f1167,plain,
spl14_81,
inference(avatar_split_clause,[],[f438,f1165]) ).
tff(f438,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X1),X2) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X1),X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,plus_plus(X0,X3),X2) = aa(X0,X0,plus_plus(X0,X1),X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X25: X0,X12: X0,X11: X0] :
( ( aa(X0,X0,plus_plus(X0,X11),X12) = aa(X0,X0,plus_plus(X0,X25),X12) )
=> ( X11 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__right__imp__eq) ).
tff(f1163,plain,
spl14_80,
inference(avatar_split_clause,[],[f428,f1161]) ).
tff(f428,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) )
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,plus_plus(X0,X3),X2) != aa(X0,X0,plus_plus(X0,X3),X1) ) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,plus_plus(X0,X3),X2) = aa(X0,X0,plus_plus(X0,X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X25: X0,X11: X0,X12: X0] :
( ( aa(X0,X0,plus_plus(X0,X12),X11) = aa(X0,X0,plus_plus(X0,X12),X25) )
=> ( X11 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__imp__eq) ).
tff(f1130,plain,
spl14_79,
inference(avatar_split_clause,[],[f533,f1128]) ).
tff(f533,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X3,X1) = filter(X0,X3,cons(X0,X2,X1)) )
| pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1126,plain,
spl14_78,
inference(avatar_split_clause,[],[f409,f1123]) ).
tff(f409,plain,
pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),a),set(atom,as))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096a_A_058_Aset_Aas_096) ).
tff(f1083,plain,
( spl14_77
| spl14_1
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f973,f898,f601,f1081]) ).
tff(f1081,plain,
( spl14_77
<=> ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ( X0 = X1 )
| ( fFalse = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_77])]) ).
tff(f973,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ( X0 = X1 )
| ( fFalse = X1 ) )
| spl14_1
| ~ spl14_63 ),
inference(superposition,[],[f603,f899]) ).
tff(f1079,plain,
spl14_76,
inference(avatar_split_clause,[],[f520,f1077]) ).
tff(f520,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = filter(X0,X2,X1) )
| pp(aa(X0,bool,X2,sK4(X0,X1,X2))) ),
inference(cnf_transformation,[],[f355]) ).
tff(f1075,plain,
spl14_75,
inference(avatar_split_clause,[],[f514,f1073]) ).
tff(f514,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,bool)] :
( ( nil(X0) = filter(X0,X1,X2) )
| pp(aa(X0,bool,X1,sK2(X0,X1,X2))) ),
inference(cnf_transformation,[],[f347]) ).
tff(f1071,plain,
spl14_74,
inference(avatar_split_clause,[],[f462,f1069]) ).
tff(f462,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,plus_plus(X0,X12),X11),X11) = div_mod(X0,X12,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mod__add__self2) ).
tff(f1067,plain,
spl14_73,
inference(avatar_split_clause,[],[f461,f1065]) ).
tff(f461,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,plus_plus(X0,X2),X1),X2) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X11: X0] : ( div_mod(X0,X12,X11) = div_mod(X0,aa(X0,X0,plus_plus(X0,X11),X12),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_mod__add__self1) ).
tff(f1063,plain,
spl14_72,
inference(avatar_split_clause,[],[f448,f1061]) ).
tff(f448,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X12: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),zero_zero(X0)) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_diff__0__right) ).
tff(f1059,plain,
spl14_71,
inference(avatar_split_clause,[],[f447,f1057]) ).
tff(f447,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X12: X0] : ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X12),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_diff__self) ).
tff(f936,plain,
spl14_70,
inference(avatar_split_clause,[],[f517,f934]) ).
tff(f517,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( filter(X0,X2,X1) = X1 )
| ~ pp(aa(X0,bool,X2,sK3(X0,X1,X2))) ),
inference(cnf_transformation,[],[f351]) ).
tff(f932,plain,
spl14_69,
inference(avatar_split_clause,[],[f507,f930]) ).
tff(f930,plain,
( spl14_69
<=> ! [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,[spl14_69])]) ).
tff(f507,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,[],[f226]) ).
tff(f226,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f141]) ).
tff(f141,axiom,
! [X0: $tType,X27: X0,X29: X0] :
( ( X27 = X29 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X29),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f928,plain,
spl14_68,
inference(avatar_split_clause,[],[f487,f926]) ).
tff(f487,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) ),
inference(rectify,[],[f138]) ).
tff(f138,axiom,
! [X49: bool,X47: bool] :
( pp(X49)
| pp(X47)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
tff(f924,plain,
spl14_67,
inference(avatar_split_clause,[],[f484,f922]) ).
tff(f484,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X49: bool,X47: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49))
| ~ pp(X49)
| ~ pp(X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f920,plain,
spl14_66,
inference(avatar_split_clause,[],[f424,f918]) ).
tff(f424,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,plus_plus(X0,X1),X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,X1),X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,plus_plus(X0,X1),X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,X1),X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,X1),X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X17: X0] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,X17),X17) )
<=> ( zero_zero(X0) = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_double__zero__sym) ).
tff(f908,plain,
spl14_65,
inference(avatar_split_clause,[],[f506,f906]) ).
tff(f506,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,[],[f225]) ).
tff(f225,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,[],[f125]) ).
tff(f125,axiom,
! [X0: $tType,X29: X0,X47: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X47))
| ~ pp(aa(X0,bool,X47,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f904,plain,
spl14_64,
inference(avatar_split_clause,[],[f493,f902]) ).
tff(f902,plain,
( spl14_64
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_64])]) ).
tff(f493,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
inference(nnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: list(X0)] :
( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X6: list(X0)] :
( ( set(X0,X6) = bot_bot(fun(X0,bool)) )
<=> ( nil(X0) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_set__empty2) ).
tff(f900,plain,
( spl14_63
| ~ spl14_24 ),
inference(avatar_split_clause,[],[f720,f713,f898]) ).
tff(f720,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) )
| ~ spl14_24 ),
inference(superposition,[],[f714,f714]) ).
tff(f885,plain,
spl14_62,
inference(avatar_split_clause,[],[f559,f883]) ).
tff(f883,plain,
( spl14_62
<=> ! [X0: $tType] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,zero_zero(X0)),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_62])]) ).
tff(f559,plain,
! [X0: $tType] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,zero_zero(X0)),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f425]) ).
tff(f425,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,plus_plus(X0,X1),X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f335]) ).
tff(f881,plain,
spl14_61,
inference(avatar_split_clause,[],[f546,f879]) ).
tff(f546,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f378]) ).
tff(f378,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
inference(flattening,[],[f377]) ).
tff(f377,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType,X35: list(X0),X22: X0,X36: list(X0),X17: X0] :
( ( cons(X0,X17,X36) = cons(X0,X22,X35) )
<=> ( ( X35 = X36 )
& ( X17 = X22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_list_Oinject) ).
tff(f877,plain,
spl14_60,
inference(avatar_split_clause,[],[f540,f875]) ).
tff(f875,plain,
( spl14_60
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(X1)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_60])]) ).
tff(f540,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f375]) ).
tff(f375,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( ( nil(X0) = map(X1,X0,X3,X2) )
| ( nil(X1) != X2 ) )
& ( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X0) = map(X1,X0,X3,X2) )
<=> ( nil(X1) = X2 ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType,X1: $tType,X6: list(X1),X9: fun(X1,X0)] :
( ( map(X1,X0,X9,X6) = nil(X0) )
<=> ( nil(X1) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_map__is__Nil__conv) ).
tff(f873,plain,
spl14_59,
inference(avatar_split_clause,[],[f489,f871]) ).
tff(f489,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f135]) ).
tff(f135,axiom,
! [X49: bool,X47: bool] :
( pp(X49)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f869,plain,
spl14_58,
inference(avatar_split_clause,[],[f488,f867]) ).
tff(f488,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f134]) ).
tff(f134,axiom,
! [X49: bool,X47: bool] :
( pp(X47)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X47),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f865,plain,
spl14_57,
inference(avatar_split_clause,[],[f486,f863]) ).
tff(f486,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))
| ~ pp(X1) ),
inference(rectify,[],[f136]) ).
tff(f136,axiom,
! [X49: bool,X47: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49))
| ~ pp(X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
tff(f861,plain,
spl14_56,
inference(avatar_split_clause,[],[f485,f859]) ).
tff(f485,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1))
| ~ pp(X1) ),
inference(rectify,[],[f137]) ).
tff(f137,axiom,
! [X47: bool,X49: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X47),X49))
| ~ pp(X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
tff(f857,plain,
spl14_55,
inference(avatar_split_clause,[],[f460,f855]) ).
tff(f460,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X12: X0] : ( div_mod(X0,X12,X11) = div_mod(X0,div_mod(X0,X12,X11),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mod__mod__trivial) ).
tff(f851,plain,
spl14_54,
inference(avatar_split_clause,[],[f570,f849]) ).
tff(f570,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f505]) ).
tff(f505,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,[],[f224]) ).
tff(f224,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f142]) ).
tff(f142,axiom,
! [X0: $tType,X27: X0,X29: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X29),X27))
| ( X27 != X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f847,plain,
spl14_53,
inference(avatar_split_clause,[],[f545,f845]) ).
tff(f545,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f378]) ).
tff(f843,plain,
( spl14_52
| ~ spl14_13
| ~ spl14_38 ),
inference(avatar_split_clause,[],[f786,f774,f661,f841]) ).
tff(f841,plain,
( spl14_52
<=> ! [X0: int] : ( div_mod(int,X0,zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_52])]) ).
tff(f774,plain,
( spl14_38
<=> ! [X0: $tType,X1: X0] :
( ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_38])]) ).
tff(f786,plain,
( ! [X0: int] : ( div_mod(int,X0,zero_zero(int)) = X0 )
| ~ spl14_13
| ~ spl14_38 ),
inference(resolution,[],[f775,f663]) ).
tff(f775,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,zero_zero(X0)) = X1 ) )
| ~ spl14_38 ),
inference(avatar_component_clause,[],[f774]) ).
tff(f835,plain,
spl14_51,
inference(avatar_split_clause,[],[f432,f833]) ).
tff(f833,plain,
( spl14_51
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_51])]) ).
tff(f432,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X12: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X12) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__0) ).
tff(f831,plain,
spl14_50,
inference(avatar_split_clause,[],[f431,f829]) ).
tff(f431,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X12: X0] : ( aa(X0,X0,plus_plus(X0,zero_zero(X0)),X12) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__0__left) ).
tff(f827,plain,
spl14_49,
inference(avatar_split_clause,[],[f430,f825]) ).
tff(f825,plain,
( spl14_49
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_49])]) ).
tff(f430,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X12: X0] : ( aa(X0,X0,plus_plus(X0,X12),zero_zero(X0)) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add_Ocomm__neutral) ).
tff(f823,plain,
spl14_48,
inference(avatar_split_clause,[],[f429,f821]) ).
tff(f429,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,plus_plus(X0,X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X12: X0] : ( aa(X0,X0,plus_plus(X0,X12),zero_zero(X0)) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__0__right) ).
tff(f819,plain,
~ spl14_47,
inference(avatar_split_clause,[],[f408,f816]) ).
tff(f816,plain,
( spl14_47
<=> ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_47])]) ).
tff(f408,plain,
lbounds(as) != nil(product_prod(int,list(int))),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
lbounds(as) != nil(product_prod(int,list(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096lbounds_Aas_A_126_061_A_091_093_096) ).
tff(f812,plain,
spl14_46,
inference(avatar_split_clause,[],[f421,f810]) ).
tff(f421,plain,
! [X0: $tType] : ( set(X0,nil(X0)) = bot_bot(fun(X0,bool)) ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] : ( set(X0,nil(X0)) = bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_List_Oset_Osimps_I1_J) ).
tff(f806,plain,
spl14_45,
inference(avatar_split_clause,[],[f530,f804]) ).
tff(f530,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X1: $tType,X0: $tType,X49: X1,X47: X0] : ( aa(X1,X0,combk(X0,X1,X47),X49) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f802,plain,
spl14_44,
inference(avatar_split_clause,[],[f501,f800]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X1: $tType,X0: $tType,X9: fun(X1,X0)] : ( nil(X0) = map(X1,X0,X9,nil(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_map_Osimps_I1_J) ).
tff(f798,plain,
spl14_43,
inference(avatar_split_clause,[],[f459,f796]) ).
tff(f796,plain,
( spl14_43
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_43])]) ).
tff(f459,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mod__0) ).
tff(f794,plain,
( spl14_41
| ~ spl14_42
| ~ spl14_24 ),
inference(avatar_split_clause,[],[f722,f713,f791,f788]) ).
tff(f788,plain,
( spl14_41
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_41])]) ).
tff(f722,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fFalse = X0 ) )
| ~ spl14_24 ),
inference(equality_factoring,[],[f714]) ).
tff(f784,plain,
spl14_40,
inference(avatar_split_clause,[],[f483,f782]) ).
tff(f483,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X14: list(X0)] : ( map(X0,X0,combi(X0),X14) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_map__ident) ).
tff(f780,plain,
spl14_39,
inference(avatar_split_clause,[],[f482,f778]) ).
tff(f482,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = filter(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = filter(X0,X1,nil(X0)) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X7: fun(X0,bool)] : ( nil(X0) = filter(X0,X7,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_filter_Osimps_I1_J) ).
tff(f776,plain,
spl14_38,
inference(avatar_split_clause,[],[f458,f774]) ).
tff(f458,plain,
! [X0: $tType,X1: X0] :
( ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $tType] :
( ! [X1: X0] : ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( div_mod(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0] : ( div_mod(X0,X12,zero_zero(X0)) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mod__by__0) ).
tff(f772,plain,
spl14_37,
inference(avatar_split_clause,[],[f457,f770]) ).
tff(f770,plain,
( spl14_37
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_37])]) ).
tff(f457,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,X1) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0] : ( zero_zero(X0) = div_mod(X0,X12,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mod__self) ).
tff(f766,plain,
spl14_36,
inference(avatar_split_clause,[],[f499,f764]) ).
tff(f499,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( nil(X0) != cons(X0,X2,X1) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( nil(X0) != cons(X0,X2,X1) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType,X41: list(X0),X24: X0] : ( nil(X0) != cons(X0,X24,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_list_Osimps_I2_J) ).
tff(f762,plain,
spl14_35,
inference(avatar_split_clause,[],[f492,f760]) ).
tff(f760,plain,
( spl14_35
<=> ! [X1: $tType,X0: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_35])]) ).
tff(f492,plain,
! [X1: $tType,X0: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(cnf_transformation,[],[f318]) ).
tff(f318,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(flattening,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(fun(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(ennf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: $tType] :
( ( finite_finite(X0)
& finite_finite(X1) )
=> finite_finite(fun(X0,X1)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X45: $tType,X46: $tType] :
( ( finite_finite(X45)
& finite_finite(X46) )
=> finite_finite(fun(X45,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
tff(f758,plain,
spl14_34,
inference(avatar_split_clause,[],[f491,f756]) ).
tff(f756,plain,
( spl14_34
<=> ! [X1: $tType,X0: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_34])]) ).
tff(f491,plain,
! [X1: $tType,X0: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(flattening,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: $tType] :
( finite_finite(product_prod(X0,X1))
| ~ finite_finite(X0)
| ~ finite_finite(X1) ),
inference(ennf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: $tType] :
( ( finite_finite(X0)
& finite_finite(X1) )
=> finite_finite(product_prod(X0,X1)) ),
inference(rectify,[],[f122]) ).
tff(f122,axiom,
! [X45: $tType,X46: $tType] :
( ( finite_finite(X45)
& finite_finite(X46) )
=> finite_finite(product_prod(X45,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
tff(f754,plain,
spl14_33,
inference(avatar_split_clause,[],[f481,f752]) ).
tff(f481,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X0: $tType,X47: X0] : ( aa(X0,X0,combi(X0),X47) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f750,plain,
spl14_32,
inference(avatar_split_clause,[],[f420,f748]) ).
tff(f748,plain,
( spl14_32
<=> ! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_32])]) ).
tff(f420,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X11: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zmod__zero) ).
tff(f746,plain,
( spl14_31
| ~ spl14_20
| ~ spl14_24 ),
inference(avatar_split_clause,[],[f721,f713,f696,f744]) ).
tff(f744,plain,
( spl14_31
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_31])]) ).
tff(f721,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl14_20
| ~ spl14_24 ),
inference(superposition,[],[f698,f714]) ).
tff(f742,plain,
spl14_30,
inference(avatar_split_clause,[],[f497,f740]) ).
tff(f497,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X39: list(X0),X29: X0] : ( cons(X0,X29,X39) != X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_not__Cons__self2) ).
tff(f738,plain,
spl14_29,
inference(avatar_split_clause,[],[f480,f736]) ).
tff(f734,plain,
spl14_28,
inference(avatar_split_clause,[],[f474,f732]) ).
tff(f732,plain,
( spl14_28
<=> ! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_28])]) ).
tff(f474,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f308]) ).
tff(f308,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType] :
( ( cl_Groups_Ominus(X0)
& zero(X0) )
=> cl_Groups_Ominus(list(X0)) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X45: $tType] :
( ( cl_Groups_Ominus(X45)
& zero(X45) )
=> cl_Groups_Ominus(list(X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
tff(f730,plain,
spl14_27,
inference(avatar_split_clause,[],[f473,f728]) ).
tff(f728,plain,
( spl14_27
<=> ! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
tff(f473,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f306]) ).
tff(f306,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType] :
( ( cl_Groups_Oplus(X0)
& zero(X0) )
=> cl_Groups_Oplus(list(X0)) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X45: $tType] :
( ( cl_Groups_Oplus(X45)
& zero(X45) )
=> cl_Groups_Oplus(list(X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
tff(f726,plain,
spl14_26,
inference(avatar_split_clause,[],[f419,f724]) ).
tff(f419,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X12: int] : ( zero_zero(int) = div_mod(int,X12,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zmod__self) ).
tff(f719,plain,
spl14_25,
inference(avatar_split_clause,[],[f490,f717]) ).
tff(f717,plain,
( spl14_25
<=> ! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
tff(f490,plain,
! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X1)
=> cl_Groups_Ominus(fun(X0,X1)) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X45: $tType,X46: $tType] :
( cl_Groups_Ominus(X46)
=> cl_Groups_Ominus(fun(X45,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
tff(f715,plain,
spl14_24,
inference(avatar_split_clause,[],[f422,f713]) ).
tff(f422,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X47: bool] :
( ( fFalse = X47 )
| ( fTrue = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
tff(f711,plain,
spl14_23,
inference(avatar_split_clause,[],[f418,f709]) ).
tff(f709,plain,
( spl14_23
<=> ! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
tff(f418,plain,
! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] : finite_finite1(X0,bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite_OemptyI) ).
tff(f707,plain,
spl14_22,
inference(avatar_split_clause,[],[f479,f705]) ).
tff(f705,plain,
( spl14_22
<=> ! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
tff(f479,plain,
! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: list(X0)] : finite_finite1(X0,set(X0,X1)),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X6: list(X0)] : finite_finite1(X0,set(X0,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__set) ).
tff(f703,plain,
spl14_21,
inference(avatar_split_clause,[],[f470,f701]) ).
tff(f701,plain,
( spl14_21
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
tff(f470,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( finite_finite1(X0,X1)
| ~ finite_finite(X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $tType] :
( ! [X1: fun(X0,bool)] : finite_finite1(X0,X1)
| ~ finite_finite(X0) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType] :
( finite_finite(X0)
=> ! [X1: fun(X0,bool)] : finite_finite1(X0,X1) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( finite_finite(X0)
=> ! [X33: fun(X0,bool)] : finite_finite1(X0,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_finite__code) ).
tff(f699,plain,
spl14_20,
inference(avatar_split_clause,[],[f406,f696]) ).
tff(f406,plain,
pp(fTrue),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f694,plain,
spl14_19,
inference(avatar_split_clause,[],[f405,f691]) ).
tff(f691,plain,
( spl14_19
<=> cl_Groups_Ominus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
tff(f405,plain,
cl_Groups_Ominus(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
cl_Groups_Ominus(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
tff(f689,plain,
spl14_18,
inference(avatar_split_clause,[],[f404,f686]) ).
tff(f686,plain,
( spl14_18
<=> cl_Groups_Ominus(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
tff(f404,plain,
cl_Groups_Ominus(bool),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
cl_Groups_Ominus(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
tff(f684,plain,
spl14_17,
inference(avatar_split_clause,[],[f403,f681]) ).
tff(f681,plain,
( spl14_17
<=> finite_finite(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
tff(f403,plain,
finite_finite(bool),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
finite_finite(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
tff(f679,plain,
spl14_16,
inference(avatar_split_clause,[],[f402,f676]) ).
tff(f676,plain,
( spl14_16
<=> cl_Groups_Oplus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
tff(f402,plain,
cl_Groups_Oplus(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
cl_Groups_Oplus(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
tff(f674,plain,
spl14_15,
inference(avatar_split_clause,[],[f401,f671]) ).
tff(f671,plain,
( spl14_15
<=> linorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
tff(f401,plain,
linorder(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f669,plain,
spl14_14,
inference(avatar_split_clause,[],[f400,f666]) ).
tff(f666,plain,
( spl14_14
<=> linorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
tff(f400,plain,
linorder(bool),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
linorder(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
tff(f664,plain,
spl14_13,
inference(avatar_split_clause,[],[f399,f661]) ).
tff(f399,plain,
semiring_div(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
semiring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f659,plain,
spl14_12,
inference(avatar_split_clause,[],[f398,f656]) ).
tff(f398,plain,
group_add(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
tff(f654,plain,
spl14_11,
inference(avatar_split_clause,[],[f397,f651]) ).
tff(f651,plain,
( spl14_11
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
tff(f397,plain,
zero(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f649,plain,
spl14_10,
inference(avatar_split_clause,[],[f396,f646]) ).
tff(f646,plain,
( spl14_10
<=> ring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
tff(f396,plain,
ring_div(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
ring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
tff(f644,plain,
spl14_9,
inference(avatar_split_clause,[],[f395,f641]) ).
tff(f641,plain,
( spl14_9
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
tff(f395,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f639,plain,
spl14_8,
inference(avatar_split_clause,[],[f394,f636]) ).
tff(f636,plain,
( spl14_8
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
tff(f394,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f634,plain,
spl14_7,
inference(avatar_split_clause,[],[f393,f631]) ).
tff(f393,plain,
ring(int),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f629,plain,
spl14_6,
inference(avatar_split_clause,[],[f392,f626]) ).
tff(f392,plain,
monoid_add(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f624,plain,
spl14_5,
inference(avatar_split_clause,[],[f391,f621]) ).
tff(f391,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f619,plain,
spl14_4,
inference(avatar_split_clause,[],[f390,f616]) ).
tff(f616,plain,
( spl14_4
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
tff(f390,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f614,plain,
spl14_3,
inference(avatar_split_clause,[],[f389,f611]) ).
tff(f611,plain,
( spl14_3
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
tff(f389,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f609,plain,
spl14_2,
inference(avatar_split_clause,[],[f388,f606]) ).
tff(f606,plain,
( spl14_2
<=> linord2061991079up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
tff(f388,plain,
linord2061991079up_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
linord2061991079up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__semigroup__add) ).
tff(f604,plain,
~ spl14_1,
inference(avatar_split_clause,[],[f386,f601]) ).
tff(f386,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f139]) ).
tff(f139,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : COM111_5 : TPTP v8.1.2. Released v6.0.0.
% 0.04/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Apr 30 05:13:21 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.28 % (432)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.32 % (433)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.32 % (435)WARNING: value z3 for option sas not known
% 0.12/0.32 % Exception at run slice level
% 0.12/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.32 % (436)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.32 % (434)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.32 % (435)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)
% 0.12/0.32 % (438)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)
% 0.12/0.32 % (439)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)
% 0.12/0.32 % (437)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)
% 0.12/0.33 % (439)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.33 % (440)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.33 % Exception at run slice level
% 0.12/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.33 % Exception at run slice level
% 0.12/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.34 % (440)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.34 % Exception at run slice level
% 0.12/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35 % (443)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.12/0.35 % (441)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)
% 0.12/0.35 % (442)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)
% 0.12/0.36 % (441)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.73/0.61 % (437)First to succeed.
% 2.57/0.68 % (437)Refutation found. Thanks to Tanya!
% 2.57/0.68 % SZS status Theorem for theBenchmark
% 2.57/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/0.69 % (437)------------------------------
% 2.57/0.69 % (437)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.57/0.69 % (437)Termination reason: Refutation
% 2.57/0.69
% 2.57/0.69 % (437)Memory used [KB]: 3990
% 2.57/0.69 % (437)Time elapsed: 0.353 s
% 2.57/0.69 % (437)Instructions burned: 779 (million)
% 2.57/0.69 % (437)------------------------------
% 2.57/0.69 % (437)------------------------------
% 2.57/0.69 % (432)Success in time 0.401 s
%------------------------------------------------------------------------------