TSTP Solution File: COM069_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM069_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 : n021.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 10:47:40 EDT 2024
% Result : Theorem 1.63s 0.60s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 406
% Syntax : Number of formulae : 1143 ( 215 unt; 61 typ; 0 def)
% Number of atoms : 2734 ( 870 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2766 (1114 ~;1168 |; 19 &)
% ( 254 <=>; 211 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 28 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 28 ( 17 >; 11 *; 0 +; 0 <<)
% Number of predicates : 245 ( 243 usr; 224 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 9 con; 0-4 aty)
% Number of variables : 2355 (2297 !; 2 ?;2355 :)
% ( 56 !>; 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(func_def_0,type,
big_linorder_Min:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_1,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_2,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,X0)) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_5,type,
div_div:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
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,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_9,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_10,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_11,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_12,type,
iprod:
!>[X0: $tType] : fun(list(X0),fun(list(X0),X0)) ).
tff(func_def_13,type,
filter:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) ) > fun(list(X1),X0) ) ).
tff(func_def_15,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_16,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_17,type,
tl:
!>[X0: $tType] : fun(list(X0),list(X0)) ).
tff(func_def_18,type,
ord_less:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_19,type,
c_PresArith_Oatom_OLe: fun(int,fun(list(int),atom)) ).
tff(func_def_20,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_21,type,
divisor: fun(atom,int) ).
tff(func_def_22,type,
zlcms: list(int) > int ).
tff(func_def_23,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fFalse: bool ).
tff(func_def_27,type,
fTrue: bool ).
tff(func_def_28,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_31,type,
a: atom ).
tff(func_def_32,type,
as: list(atom) ).
tff(func_def_33,type,
n: int ).
tff(func_def_34,type,
xs: list(int) ).
tff(func_def_35,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_div:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
pp: bool > $o ).
tff(f4689,plain,
$false,
inference(avatar_sat_refutation,[],[f530,f535,f540,f545,f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f634,f641,f645,f649,f653,f657,f661,f665,f669,f674,f678,f682,f686,f700,f705,f709,f713,f717,f725,f731,f735,f739,f743,f747,f755,f760,f764,f768,f772,f782,f786,f790,f794,f798,f802,f806,f810,f814,f827,f836,f840,f844,f848,f853,f862,f866,f877,f881,f885,f901,f905,f911,f915,f932,f936,f940,f944,f948,f952,f961,f965,f969,f973,f984,f988,f1006,f1010,f1016,f1020,f1024,f1028,f1035,f1039,f1043,f1047,f1052,f1059,f1063,f1067,f1071,f1093,f1098,f1102,f1106,f1110,f1148,f1152,f1156,f1160,f1164,f1168,f1172,f1176,f1191,f1301,f1305,f1624,f1628,f1634,f1638,f1658,f1662,f1667,f1671,f1709,f1764,f1776,f1793,f1808,f1870,f1874,f1878,f1925,f1952,f2009,f2026,f2031,f2037,f2043,f2048,f2063,f2082,f2086,f2095,f2099,f2103,f2190,f2194,f2250,f2255,f2267,f2277,f2281,f2285,f2357,f2362,f2378,f2382,f2411,f2419,f2431,f2435,f2483,f2487,f2491,f2495,f2499,f2516,f2744,f2751,f2769,f2826,f2830,f2986,f2990,f2995,f3027,f3121,f3125,f3129,f3155,f3256,f3260,f3264,f3268,f3288,f3292,f3296,f3706,f3710,f3759,f3819,f3872,f3876,f3880,f3884,f3888,f4113,f4117,f4164,f4168,f4172,f4176,f4180,f4296,f4300,f4319,f4327,f4473,f4481,f4489,f4493,f4585]) ).
tff(f4585,plain,
( spl1_142
| ~ spl1_222 ),
inference(avatar_contradiction_clause,[],[f4584]) ).
tff(f4584,plain,
( $false
| spl1_142
| ~ spl1_222 ),
inference(trivial_inequality_removal,[],[f4573]) ).
tff(f4573,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) != 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)
| spl1_142
| ~ spl1_222 ),
inference(superposition,[],[f2047,f4488]) ).
tff(f4488,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl1_222 ),
inference(avatar_component_clause,[],[f4487]) ).
tff(f4487,plain,
( spl1_222
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_222])]) ).
tff(f2047,plain,
( ( 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)
| spl1_142 ),
inference(avatar_component_clause,[],[f2045]) ).
tff(f2045,plain,
( spl1_142
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_142])]) ).
tff(f4493,plain,
( spl1_223
| ~ spl1_59
| ~ spl1_131 ),
inference(avatar_split_clause,[],[f1853,f1806,f808,f4491]) ).
tff(f4491,plain,
( spl1_223
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_223])]) ).
tff(f808,plain,
( spl1_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,[spl1_59])]) ).
tff(f1806,plain,
( spl1_131
<=> ! [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,[spl1_131])]) ).
tff(f1853,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(aa(bool,bool,X1,X0)) )
| ~ spl1_59
| ~ spl1_131 ),
inference(superposition,[],[f809,f1807]) ).
tff(f1807,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)) )
| ~ spl1_131 ),
inference(avatar_component_clause,[],[f1806]) ).
tff(f809,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X0) )
| ~ spl1_59 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f4489,plain,
( spl1_222
| ~ spl1_17
| ~ spl1_123 ),
inference(avatar_split_clause,[],[f1663,f1656,f607,f4487]) ).
tff(f607,plain,
( spl1_17
<=> ring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f1656,plain,
( spl1_123
<=> ! [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,[spl1_123])]) ).
tff(f1663,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl1_17
| ~ spl1_123 ),
inference(resolution,[],[f1657,f609]) ).
tff(f609,plain,
( ring_div(int)
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f607]) ).
tff(f1657,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ring_div(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) ) )
| ~ spl1_123 ),
inference(avatar_component_clause,[],[f1656]) ).
tff(f4481,plain,
( ~ spl1_220
| spl1_221
| ~ spl1_22
| ~ spl1_110 ),
inference(avatar_split_clause,[],[f1205,f1154,f632,f4479,f4475]) ).
tff(f4475,plain,
( spl1_220
<=> ordere236663937imp_le(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_220])]) ).
tff(f4479,plain,
( spl1_221
<=> ! [X2: bool,X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),fFalse),plus_plus(bool,X0,X2)))
| ( fTrue = plus_plus(bool,X0,X1) )
| pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_221])]) ).
tff(f632,plain,
( spl1_22
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f1154,plain,
( spl1_110
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
tff(f1205,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),fFalse),plus_plus(bool,X0,X2)))
| pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),X1),X2))
| ~ ordere236663937imp_le(bool)
| ( fTrue = plus_plus(bool,X0,X1) ) )
| ~ spl1_22
| ~ spl1_110 ),
inference(superposition,[],[f1155,f633]) ).
tff(f633,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f1155,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordere236663937imp_le(X0) )
| ~ spl1_110 ),
inference(avatar_component_clause,[],[f1154]) ).
tff(f4473,plain,
( ~ spl1_218
| spl1_219
| ~ spl1_22
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f1179,f1146,f632,f4471,f4467]) ).
tff(f4467,plain,
( spl1_218
<=> ordere223160158up_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_218])]) ).
tff(f4471,plain,
( spl1_219
<=> ! [X2: bool,X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),fFalse),plus_plus(bool,X0,X2)))
| ( fTrue = plus_plus(bool,X0,X1) )
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_219])]) ).
tff(f1146,plain,
( spl1_108
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
tff(f1179,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),fFalse),plus_plus(bool,X0,X2)))
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),ord_less(bool),X1),X2))
| ~ ordere223160158up_add(bool)
| ( fTrue = plus_plus(bool,X0,X1) ) )
| ~ spl1_22
| ~ spl1_108 ),
inference(superposition,[],[f1147,f633]) ).
tff(f1147,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) )
| ~ spl1_108 ),
inference(avatar_component_clause,[],[f1146]) ).
tff(f4327,plain,
( spl1_216
| ~ spl1_217
| ~ spl1_81
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f1031,f1026,f950,f4324,f4321]) ).
tff(f4321,plain,
( spl1_216
<=> ! [X0: int,X1: list(int)] : ~ pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X0),X1)),set(atom,as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_216])]) ).
tff(f4324,plain,
( spl1_217
<=> ( zero_zero(int) = one_one(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_217])]) ).
tff(f950,plain,
( spl1_81
<=> ! [X0: list(int),X1: int] : ( one_one(int) = aa(atom,int,divisor,aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
tff(f1026,plain,
( spl1_93
<=> ! [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,[spl1_93])]) ).
tff(f1031,plain,
( ! [X0: int,X1: list(int)] :
( ( zero_zero(int) != one_one(int) )
| ~ pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X0),X1)),set(atom,as))) )
| ~ spl1_81
| ~ spl1_93 ),
inference(superposition,[],[f1027,f951]) ).
tff(f951,plain,
( ! [X0: list(int),X1: int] : ( one_one(int) = aa(atom,int,divisor,aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0)) )
| ~ spl1_81 ),
inference(avatar_component_clause,[],[f950]) ).
tff(f1027,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))) )
| ~ spl1_93 ),
inference(avatar_component_clause,[],[f1026]) ).
tff(f4319,plain,
( spl1_215
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f994,f982,f4317]) ).
tff(f4317,plain,
( spl1_215
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_215])]) ).
tff(f982,plain,
( spl1_86
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
tff(f994,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) )
| ~ spl1_86 ),
inference(forward_demodulation,[],[f990,f983]) ).
tff(f983,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) )
| ~ spl1_86 ),
inference(avatar_component_clause,[],[f982]) ).
tff(f990,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),div_mod(int,aa(int,int,times_times(int,X0),X1),X2)),X2) )
| ~ spl1_86 ),
inference(superposition,[],[f983,f983]) ).
tff(f4300,plain,
( spl1_214
| ~ spl1_64
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f1137,f1108,f842,f4298]) ).
tff(f4298,plain,
( spl1_214
<=> ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ linord219039673up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_214])]) ).
tff(f842,plain,
( spl1_64
<=> ! [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,[spl1_64])]) ).
tff(f1108,plain,
( spl1_107
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
tff(f1137,plain,
( ! [X0: $tType,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ linord219039673up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)))) )
| ~ spl1_64
| ~ spl1_107 ),
inference(resolution,[],[f1109,f843]) ).
tff(f843,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f842]) ).
tff(f1109,plain,
( ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ linord219039673up_add(X0) )
| ~ spl1_107 ),
inference(avatar_component_clause,[],[f1108]) ).
tff(f4296,plain,
( ~ spl1_16
| spl1_213
| ~ spl1_53
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f920,f788,f784,f4294,f602]) ).
tff(f602,plain,
( spl1_16
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f4294,plain,
( spl1_213
<=> ! [X0: int,X1: int] :
( ( plus_plus(int,X1,X0) != X0 )
| ( zero_zero(int) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_213])]) ).
tff(f784,plain,
( spl1_53
<=> ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f788,plain,
( spl1_54
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f920,plain,
( ! [X0: int,X1: int] :
( ( plus_plus(int,X1,X0) != X0 )
| ( zero_zero(int) = X1 )
| ~ cancel_semigroup_add(int) )
| ~ spl1_53
| ~ spl1_54 ),
inference(superposition,[],[f789,f785]) ).
tff(f785,plain,
( ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f784]) ).
tff(f789,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
| ( X1 = X3 )
| ~ cancel_semigroup_add(X0) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f788]) ).
tff(f4180,plain,
( spl1_212
| ~ spl1_65
| ~ spl1_131 ),
inference(avatar_split_clause,[],[f1834,f1806,f846,f4178]) ).
tff(f4178,plain,
( spl1_212
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: X1] : ( aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),combk(X1,X0)),X3),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_212])]) ).
tff(f846,plain,
( spl1_65
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
tff(f1834,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0)] : ( aa(X1,X1,aa(fun(X1,X0),fun(X1,X1),aa(fun(X1,fun(X0,X1)),fun(fun(X1,X0),fun(X1,X1)),combs(X1,X0,X1),combk(X1,X0)),X3),X2) = X2 )
| ~ spl1_65
| ~ spl1_131 ),
inference(superposition,[],[f1807,f847]) ).
tff(f847,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 )
| ~ spl1_65 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f4176,plain,
( spl1_211
| ~ spl1_64
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1242,f1166,f842,f4174]) ).
tff(f4174,plain,
( spl1_211
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere236663937imp_le(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_211])]) ).
tff(f1166,plain,
( spl1_113
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
tff(f1242,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere236663937imp_le(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)))) )
| ~ spl1_64
| ~ spl1_113 ),
inference(resolution,[],[f1167,f843]) ).
tff(f1167,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordere236663937imp_le(X0) )
| ~ spl1_113 ),
inference(avatar_component_clause,[],[f1166]) ).
tff(f4172,plain,
( spl1_210
| ~ spl1_64
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f1227,f1162,f842,f4170]) ).
tff(f4170,plain,
( spl1_210
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere236663937imp_le(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_210])]) ).
tff(f1162,plain,
( spl1_112
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
tff(f1227,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere236663937imp_le(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)))) )
| ~ spl1_64
| ~ spl1_112 ),
inference(resolution,[],[f1163,f843]) ).
tff(f1163,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ ordere236663937imp_le(X0) )
| ~ spl1_112 ),
inference(avatar_component_clause,[],[f1162]) ).
tff(f4168,plain,
( spl1_209
| ~ spl1_64
| ~ spl1_109 ),
inference(avatar_split_clause,[],[f1192,f1150,f842,f4166]) ).
tff(f4166,plain,
( spl1_209
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere223160158up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_209])]) ).
tff(f1150,plain,
( spl1_109
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
tff(f1192,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere223160158up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)))) )
| ~ spl1_64
| ~ spl1_109 ),
inference(resolution,[],[f1151,f843]) ).
tff(f1151,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) )
| ~ spl1_109 ),
inference(avatar_component_clause,[],[f1150]) ).
tff(f4164,plain,
( spl1_208
| ~ spl1_64
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f1177,f1146,f842,f4162]) ).
tff(f4162,plain,
( spl1_208
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere223160158up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_208])]) ).
tff(f1177,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ ordere223160158up_add(X0)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)))) )
| ~ spl1_64
| ~ spl1_108 ),
inference(resolution,[],[f1147,f843]) ).
tff(f4117,plain,
( spl1_207
| ~ spl1_60
| ~ spl1_131 ),
inference(avatar_split_clause,[],[f1852,f1806,f812,f4115]) ).
tff(f4115,plain,
( spl1_207
<=> ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_207])]) ).
tff(f812,plain,
( spl1_60
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f1852,plain,
( ! [X0: bool,X1: fun(bool,bool)] :
( ~ pp(aa(bool,bool,aa(fun(bool,bool),fun(bool,bool),aa(fun(bool,fun(bool,bool)),fun(fun(bool,bool),fun(bool,bool)),combs(bool,bool,bool),fconj),X1),X0))
| pp(X0) )
| ~ spl1_60
| ~ spl1_131 ),
inference(superposition,[],[f813,f1807]) ).
tff(f813,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| pp(X1) )
| ~ spl1_60 ),
inference(avatar_component_clause,[],[f812]) ).
tff(f4113,plain,
( spl1_206
| ~ spl1_64
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f1079,f1061,f842,f4111]) ).
tff(f4111,plain,
( spl1_206
<=> ! [X0: int,X1: int] :
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| pp(aa(fun(int,bool),bool,fEx(int),aa(int,fun(int,bool),ord_less(int),div_mod(int,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_206])]) ).
tff(f1061,plain,
( spl1_100
<=> ! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X0,X1)),X1))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
tff(f1079,plain,
( ! [X0: int,X1: int] :
( ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| pp(aa(fun(int,bool),bool,fEx(int),aa(int,fun(int,bool),ord_less(int),div_mod(int,X1,X0)))) )
| ~ spl1_64
| ~ spl1_100 ),
inference(resolution,[],[f1062,f843]) ).
tff(f1062,plain,
( ! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X0,X1)),X1))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) )
| ~ spl1_100 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f3888,plain,
( spl1_205
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1734,f1707,f3886]) ).
tff(f3886,plain,
( spl1_205
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,aa(X0,X0,times_times(X0,X4),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X4),X3),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_205])]) ).
tff(f1707,plain,
( spl1_127
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(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,[spl1_127])]) ).
tff(f1734,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,aa(X0,X0,times_times(X0,X4),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X4),X3),X2) )
| ~ semiring_div(X0) )
| ~ spl1_127 ),
inference(equality_resolution,[],[f1708]) ).
tff(f1708,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: 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,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ~ semiring_div(X0) )
| ~ spl1_127 ),
inference(avatar_component_clause,[],[f1707]) ).
tff(f3884,plain,
( spl1_204
| ~ spl1_23
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f1273,f1174,f639,f3882]) ).
tff(f3882,plain,
( spl1_204
<=> ! [X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),zero_zero(int)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_204])]) ).
tff(f639,plain,
( spl1_23
<=> ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f1174,plain,
( spl1_115
<=> ! [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,[spl1_115])]) ).
tff(f1273,plain,
( ! [X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X0) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),zero_zero(int)),X1),X0) )
| ~ spl1_23
| ~ spl1_115 ),
inference(superposition,[],[f1175,f640]) ).
tff(f640,plain,
( ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) )
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f1175,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) )
| ~ spl1_115 ),
inference(avatar_component_clause,[],[f1174]) ).
tff(f3880,plain,
( ~ spl1_16
| spl1_203
| ~ spl1_47
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f887,f792,f753,f3878,f602]) ).
tff(f3878,plain,
( spl1_203
<=> ! [X0: int,X1: int] :
( ( plus_plus(int,X0,X1) != X0 )
| ( zero_zero(int) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_203])]) ).
tff(f753,plain,
( spl1_47
<=> ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
tff(f792,plain,
( spl1_55
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f887,plain,
( ! [X0: int,X1: int] :
( ( plus_plus(int,X0,X1) != X0 )
| ( zero_zero(int) = X1 )
| ~ cancel_semigroup_add(int) )
| ~ spl1_47
| ~ spl1_55 ),
inference(superposition,[],[f793,f754]) ).
tff(f754,plain,
( ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 )
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f753]) ).
tff(f793,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ( X1 = X2 )
| ~ cancel_semigroup_add(X0) )
| ~ spl1_55 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f3876,plain,
( spl1_202
| ~ spl1_65
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f1000,f986,f846,f3874]) ).
tff(f3874,plain,
( spl1_202
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK0(X1,X0,aa(X1,fun(X0,X1),combk(X1,X0),X2),X3)) != X2 )
| ( aa(X1,fun(X0,X1),combk(X1,X0),X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_202])]) ).
tff(f986,plain,
( spl1_87
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK0(X0,X1,X2,X3)) != aa(X1,X0,X2,sK0(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
tff(f1000,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK0(X1,X0,aa(X1,fun(X0,X1),combk(X1,X0),X2),X3)) != X2 )
| ( aa(X1,fun(X0,X1),combk(X1,X0),X2) = X3 ) )
| ~ spl1_65
| ~ spl1_87 ),
inference(superposition,[],[f987,f847]) ).
tff(f987,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK0(X0,X1,X2,X3)) != aa(X1,X0,X2,sK0(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl1_87 ),
inference(avatar_component_clause,[],[f986]) ).
tff(f3872,plain,
( spl1_201
| ~ spl1_65
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f997,f986,f846,f3870]) ).
tff(f3870,plain,
( spl1_201
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK0(X1,X0,X3,aa(X1,fun(X0,X1),combk(X1,X0),X2))) != X2 )
| ( aa(X1,fun(X0,X1),combk(X1,X0),X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_201])]) ).
tff(f997,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK0(X1,X0,X3,aa(X1,fun(X0,X1),combk(X1,X0),X2))) != X2 )
| ( aa(X1,fun(X0,X1),combk(X1,X0),X2) = X3 ) )
| ~ spl1_65
| ~ spl1_87 ),
inference(superposition,[],[f987,f847]) ).
tff(f3819,plain,
( ~ spl1_20
| spl1_200
| ~ spl1_20
| ~ spl1_23
| ~ spl1_62
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1735,f1707,f834,f639,f622,f3817,f622]) ).
tff(f3817,plain,
( spl1_200
<=> ! [X0: int,X3: int,X2: int,X1: int] :
( ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X1),X3),X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ( zero_zero(int) != div_mod(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_200])]) ).
tff(f622,plain,
( spl1_20
<=> semiring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f834,plain,
( spl1_62
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
tff(f1735,plain,
( ! [X2: int,X3: int,X0: int,X1: int] :
( ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X1),X3),X0) )
| ( zero_zero(int) != div_mod(int,X1,X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ~ semiring_div(int) )
| ~ spl1_20
| ~ spl1_23
| ~ spl1_62
| ~ spl1_127 ),
inference(forward_demodulation,[],[f1715,f849]) ).
tff(f849,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X0) )
| ~ spl1_20
| ~ spl1_62 ),
inference(resolution,[],[f835,f624]) ).
tff(f624,plain,
( semiring_div(int)
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f622]) ).
tff(f835,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X2) ) )
| ~ spl1_62 ),
inference(avatar_component_clause,[],[f834]) ).
tff(f1715,plain,
( ! [X2: int,X3: int,X0: int,X1: int] :
( ( zero_zero(int) != div_mod(int,X1,X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ( div_mod(int,aa(int,int,times_times(int,X0),X2),X0) = div_mod(int,aa(int,int,times_times(int,X1),X3),X0) )
| ~ semiring_div(int) )
| ~ spl1_23
| ~ spl1_127 ),
inference(superposition,[],[f1708,f640]) ).
tff(f3759,plain,
( ~ spl1_20
| spl1_199
| ~ spl1_20
| ~ spl1_23
| ~ spl1_57
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f1323,f1299,f800,f639,f622,f3757,f622]) ).
tff(f3757,plain,
( spl1_199
<=> ! [X0: int,X3: int,X2: int,X1: int] :
( ( div_mod(int,X2,X0) = div_mod(int,plus_plus(int,X1,X3),X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ( zero_zero(int) != div_mod(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_199])]) ).
tff(f800,plain,
( spl1_57
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,plus_plus(X0,X2,X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f1299,plain,
( spl1_117
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X5,X2),X4) = div_mod(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,[spl1_117])]) ).
tff(f1323,plain,
( ! [X2: int,X3: int,X0: int,X1: int] :
( ( div_mod(int,X2,X0) = div_mod(int,plus_plus(int,X1,X3),X0) )
| ( zero_zero(int) != div_mod(int,X1,X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ~ semiring_div(int) )
| ~ spl1_20
| ~ spl1_23
| ~ spl1_57
| ~ spl1_117 ),
inference(forward_demodulation,[],[f1307,f829]) ).
tff(f829,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X1,X0),X1) )
| ~ spl1_20
| ~ spl1_57 ),
inference(resolution,[],[f801,f624]) ).
tff(f801,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,X2) = div_mod(X0,plus_plus(X0,X2,X1),X2) ) )
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f1307,plain,
( ! [X2: int,X3: int,X0: int,X1: int] :
( ( zero_zero(int) != div_mod(int,X1,X0) )
| ( div_mod(int,X2,X0) != div_mod(int,X3,X0) )
| ( div_mod(int,plus_plus(int,X0,X2),X0) = div_mod(int,plus_plus(int,X1,X3),X0) )
| ~ semiring_div(int) )
| ~ spl1_23
| ~ spl1_117 ),
inference(superposition,[],[f1300,f640]) ).
tff(f1300,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: 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,plus_plus(X0,X5,X2),X4) = div_mod(X0,plus_plus(X0,X3,X1),X4) )
| ~ semiring_div(X0) )
| ~ spl1_117 ),
inference(avatar_component_clause,[],[f1299]) ).
tff(f3710,plain,
( spl1_198
| ~ spl1_110
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f1237,f1162,f1154,f3708]) ).
tff(f3708,plain,
( spl1_198
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ ordere236663937imp_le(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_198])]) ).
tff(f1237,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ ordere236663937imp_le(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X2)) )
| ~ spl1_110
| ~ spl1_112 ),
inference(duplicate_literal_removal,[],[f1225]) ).
tff(f1225,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ ordere236663937imp_le(X0)
| pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X2))
| ~ ordere236663937imp_le(X0) )
| ~ spl1_110
| ~ spl1_112 ),
inference(resolution,[],[f1163,f1155]) ).
tff(f3706,plain,
( spl1_197
| ~ spl1_64
| ~ spl1_84 ),
inference(avatar_split_clause,[],[f977,f967,f842,f3704]) ).
tff(f3704,plain,
( spl1_197
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_197])]) ).
tff(f967,plain,
( spl1_84
<=> ! [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,[spl1_84])]) ).
tff(f977,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| pp(aa(fun(fun(X0,bool),bool),bool,fEx(fun(X0,bool)),aa(X0,fun(fun(X0,bool),bool),member(X0),X2))) )
| ~ spl1_64
| ~ spl1_84 ),
inference(resolution,[],[f968,f843]) ).
tff(f968,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)) )
| ~ spl1_84 ),
inference(avatar_component_clause,[],[f967]) ).
tff(f3296,plain,
( spl1_196
| ~ spl1_64
| ~ spl1_118 ),
inference(avatar_split_clause,[],[f1620,f1303,f842,f3294]) ).
tff(f3294,plain,
( spl1_196
<=> ! [X4: list(int),X0: fun(int,fun(list(int),bool)),X3: int,X2: fun(int,fun(int,fun(list(int),bool))),X1: fun(int,fun(int,fun(list(int),bool)))] :
( ~ pp(aa(list(int),bool,aa(int,fun(list(int),bool),X0,X3),X4))
| pp(aa(fun(atom,bool),bool,fEx(atom),atom_case(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_196])]) ).
tff(f1303,plain,
( spl1_118
<=> ! [X0: $tType,X3: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0)),X2: int,X1: list(int)] : ( aa(atom,X0,atom_case(X0,X5,X4,X3),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X2),X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
tff(f1620,plain,
( ! [X2: fun(int,fun(int,fun(list(int),bool))),X3: int,X0: fun(int,fun(list(int),bool)),X1: fun(int,fun(int,fun(list(int),bool))),X4: list(int)] :
( ~ pp(aa(list(int),bool,aa(int,fun(list(int),bool),X0,X3),X4))
| pp(aa(fun(atom,bool),bool,fEx(atom),atom_case(bool,X0,X1,X2))) )
| ~ spl1_64
| ~ spl1_118 ),
inference(superposition,[],[f843,f1304]) ).
tff(f1304,plain,
( ! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(atom,X0,atom_case(X0,X5,X4,X3),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X2),X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) )
| ~ spl1_118 ),
inference(avatar_component_clause,[],[f1303]) ).
tff(f3292,plain,
( spl1_195
| ~ spl1_20
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1055,f1045,f622,f3290]) ).
tff(f3290,plain,
( spl1_195
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,div_mod(int,X0,X1)),X2) = div_mod(int,aa(int,int,times_times(int,X0),X2),aa(int,int,times_times(int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_195])]) ).
tff(f1045,plain,
( spl1_97
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
tff(f1055,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,div_mod(int,X0,X1)),X2) = div_mod(int,aa(int,int,times_times(int,X0),X2),aa(int,int,times_times(int,X1),X2)) )
| ~ spl1_20
| ~ spl1_97 ),
inference(resolution,[],[f1046,f624]) ).
tff(f1046,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) ) )
| ~ spl1_97 ),
inference(avatar_component_clause,[],[f1045]) ).
tff(f3288,plain,
( spl1_194
| ~ spl1_20
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1054,f1041,f622,f3286]) ).
tff(f3286,plain,
( spl1_194
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),div_mod(int,X1,X2)) = div_mod(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_194])]) ).
tff(f1041,plain,
( spl1_96
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
tff(f1054,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),div_mod(int,X1,X2)) = div_mod(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) )
| ~ spl1_20
| ~ spl1_96 ),
inference(resolution,[],[f1042,f624]) ).
tff(f1042,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) ) )
| ~ spl1_96 ),
inference(avatar_component_clause,[],[f1041]) ).
tff(f3268,plain,
( spl1_193
| ~ spl1_20
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f1053,f1037,f622,f3266]) ).
tff(f3266,plain,
( spl1_193
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_193])]) ).
tff(f1037,plain,
( spl1_95
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
tff(f1053,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl1_20
| ~ spl1_95 ),
inference(resolution,[],[f1038,f624]) ).
tff(f1038,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) )
| ~ spl1_95 ),
inference(avatar_component_clause,[],[f1037]) ).
tff(f3264,plain,
( spl1_192
| ~ spl1_4
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1048,f1033,f542,f3262]) ).
tff(f3262,plain,
( spl1_192
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_192])]) ).
tff(f542,plain,
( spl1_4
<=> ab_semigroup_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f1033,plain,
( spl1_94
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
tff(f1048,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) )
| ~ spl1_4
| ~ spl1_94 ),
inference(resolution,[],[f1034,f544]) ).
tff(f544,plain,
( ab_semigroup_mult(int)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f542]) ).
tff(f1034,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_mult(X0)
| ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) ) )
| ~ spl1_94 ),
inference(avatar_component_clause,[],[f1033]) ).
tff(f3260,plain,
( spl1_191
| ~ spl1_22
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f1001,f986,f632,f3258]) ).
tff(f3258,plain,
( spl1_191
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK0(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK0(bool,X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_191])]) ).
tff(f1001,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK0(bool,X0,X1,X2)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK0(bool,X0,X1,X2)) ) )
| ~ spl1_22
| ~ spl1_87 ),
inference(superposition,[],[f987,f633]) ).
tff(f3256,plain,
( spl1_190
| ~ spl1_22
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f998,f986,f632,f3254]) ).
tff(f3254,plain,
( spl1_190
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK0(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK0(bool,X0,X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_190])]) ).
tff(f998,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( fFalse != aa(X0,bool,X2,sK0(bool,X0,X2,X1)) )
| ( X1 = X2 )
| ( fTrue = aa(X0,bool,X1,sK0(bool,X0,X2,X1)) ) )
| ~ spl1_22
| ~ spl1_87 ),
inference(superposition,[],[f987,f633]) ).
tff(f3155,plain,
( spl1_189
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f1322,f1299,f3153]) ).
tff(f3153,plain,
( spl1_189
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,plus_plus(X0,X4,X1),X2) = div_mod(X0,plus_plus(X0,X4,X3),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_189])]) ).
tff(f1322,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,plus_plus(X0,X4,X1),X2) = div_mod(X0,plus_plus(X0,X4,X3),X2) )
| ~ semiring_div(X0) )
| ~ spl1_117 ),
inference(equality_resolution,[],[f1300]) ).
tff(f3129,plain,
( spl1_188
| ~ spl1_20
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1030,f1022,f622,f3127]) ).
tff(f3127,plain,
( spl1_188
<=> ! [X2: int,X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,X1,X2) = div_div(int,aa(int,int,times_times(int,X1),X0),aa(int,int,times_times(int,X2),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_188])]) ).
tff(f1022,plain,
( spl1_92
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_div(X0,X2,X1) = div_div(X0,aa(X0,X0,times_times(X0,X2),X3),aa(X0,X0,times_times(X0,X1),X3)) )
| ( zero_zero(X0) = X3 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
tff(f1030,plain,
( ! [X2: int,X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,X1,X2) = div_div(int,aa(int,int,times_times(int,X1),X0),aa(int,int,times_times(int,X2),X0)) ) )
| ~ spl1_20
| ~ spl1_92 ),
inference(resolution,[],[f1023,f624]) ).
tff(f1023,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = X3 )
| ( div_div(X0,X2,X1) = div_div(X0,aa(X0,X0,times_times(X0,X2),X3),aa(X0,X0,times_times(X0,X1),X3)) ) )
| ~ spl1_92 ),
inference(avatar_component_clause,[],[f1022]) ).
tff(f3125,plain,
( spl1_187
| ~ spl1_20
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1029,f1014,f622,f3123]) ).
tff(f3123,plain,
( spl1_187
<=> ! [X2: int,X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) = div_div(int,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_187])]) ).
tff(f1014,plain,
( spl1_90
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) = div_div(X0,X2,X1) )
| ( zero_zero(X0) = X3 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
tff(f1029,plain,
( ! [X2: int,X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) = div_div(int,X1,X2) ) )
| ~ spl1_20
| ~ spl1_90 ),
inference(resolution,[],[f1015,f624]) ).
tff(f1015,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = X3 )
| ( div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) = div_div(X0,X2,X1) ) )
| ~ spl1_90 ),
inference(avatar_component_clause,[],[f1014]) ).
tff(f3121,plain,
( spl1_186
| ~ spl1_66
| ~ spl1_150 ),
inference(avatar_split_clause,[],[f2224,f2192,f851,f3119]) ).
tff(f3119,plain,
( spl1_186
<=> ! [X0: int] : ( zero_zero(int) = aa(int,int,times_times(int,X0),zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_186])]) ).
tff(f851,plain,
( spl1_66
<=> ! [X0: int] : ( div_mod(int,X0,zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
tff(f2192,plain,
( spl1_150
<=> ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
tff(f2224,plain,
( ! [X0: int] : ( zero_zero(int) = aa(int,int,times_times(int,X0),zero_zero(int)) )
| ~ spl1_66
| ~ spl1_150 ),
inference(superposition,[],[f2193,f852]) ).
tff(f852,plain,
( ! [X0: int] : ( div_mod(int,X0,zero_zero(int)) = X0 )
| ~ spl1_66 ),
inference(avatar_component_clause,[],[f851]) ).
tff(f2193,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X1) )
| ~ spl1_150 ),
inference(avatar_component_clause,[],[f2192]) ).
tff(f3027,plain,
( spl1_185
| ~ spl1_20
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f1012,f1008,f622,f3025]) ).
tff(f3025,plain,
( spl1_185
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_185])]) ).
tff(f1008,plain,
( spl1_89
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
tff(f1012,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),X1),X2) )
| ~ spl1_20
| ~ spl1_89 ),
inference(resolution,[],[f1009,f624]) ).
tff(f1009,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) ) )
| ~ spl1_89 ),
inference(avatar_component_clause,[],[f1008]) ).
tff(f2995,plain,
( spl1_184
| ~ spl1_155
| ~ spl1_160
| ~ spl1_183 ),
inference(avatar_split_clause,[],[f2991,f2988,f2359,f2264,f2993]) ).
tff(f2993,plain,
( spl1_184
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fTrue = sK0(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_184])]) ).
tff(f2264,plain,
( spl1_155
<=> ( fFalse = zero_zero(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
tff(f2359,plain,
( spl1_160
<=> ( fTrue = zero_zero(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
tff(f2988,plain,
( spl1_183
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK0(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_183])]) ).
tff(f2991,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fTrue = sK0(X0,bool,X1,X2) ) )
| ~ spl1_155
| ~ spl1_160
| ~ spl1_183 ),
inference(forward_demodulation,[],[f2989,f2808]) ).
tff(f2808,plain,
( ( fFalse = fTrue )
| ~ spl1_155
| ~ spl1_160 ),
inference(superposition,[],[f2361,f2265]) ).
tff(f2265,plain,
( ( fFalse = zero_zero(bool) )
| ~ spl1_155 ),
inference(avatar_component_clause,[],[f2264]) ).
tff(f2361,plain,
( ( fTrue = zero_zero(bool) )
| ~ spl1_160 ),
inference(avatar_component_clause,[],[f2359]) ).
tff(f2989,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK0(X0,bool,X1,X2) ) )
| ~ spl1_183 ),
inference(avatar_component_clause,[],[f2988]) ).
tff(f2990,plain,
( spl1_183
| ~ spl1_22
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f999,f986,f632,f2988]) ).
tff(f999,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
| ( X1 = X2 )
| ( fTrue = sK0(X0,bool,X1,X2) ) )
| ~ spl1_22
| ~ spl1_87 ),
inference(superposition,[],[f987,f633]) ).
tff(f2986,plain,
( ~ spl1_181
| spl1_182
| ~ spl1_155
| ~ spl1_22
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f953,f930,f632,f2264,f2984,f2980]) ).
tff(f2980,plain,
( spl1_181
<=> group_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_181])]) ).
tff(f2984,plain,
( spl1_182
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_182])]) ).
tff(f930,plain,
( spl1_76
<=> ! [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,[spl1_76])]) ).
tff(f953,plain,
( ! [X0: bool,X1: bool] :
( ( fFalse != zero_zero(bool) )
| ( X0 = X1 )
| ~ group_add(bool)
| ( fTrue = aa(bool,bool,aa(bool,fun(bool,bool),minus_minus(bool),X0),X1) ) )
| ~ spl1_22
| ~ spl1_76 ),
inference(superposition,[],[f931,f633]) ).
tff(f931,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) )
| ~ spl1_76 ),
inference(avatar_component_clause,[],[f930]) ).
tff(f2830,plain,
( spl1_180
| ~ spl1_20
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f980,f971,f622,f2828]) ).
tff(f2828,plain,
( spl1_180
<=> ! [X0: int,X1: int] : ( zero_zero(int) = div_div(int,aa(int,int,times_times(int,zero_zero(int)),X0),aa(int,int,times_times(int,zero_zero(int)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_180])]) ).
tff(f971,plain,
( spl1_85
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,zero_zero(X0)),X2),aa(X0,X0,times_times(X0,zero_zero(X0)),X1)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
tff(f980,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_div(int,aa(int,int,times_times(int,zero_zero(int)),X0),aa(int,int,times_times(int,zero_zero(int)),X1)) )
| ~ spl1_20
| ~ spl1_85 ),
inference(resolution,[],[f972,f624]) ).
tff(f972,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,zero_zero(X0)),X2),aa(X0,X0,times_times(X0,zero_zero(X0)),X1)) ) )
| ~ spl1_85 ),
inference(avatar_component_clause,[],[f971]) ).
tff(f2826,plain,
( spl1_179
| ~ spl1_20
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f974,f959,f622,f2824]) ).
tff(f2824,plain,
( spl1_179
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,div_mod(int,X0,X2),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_179])]) ).
tff(f959,plain,
( spl1_82
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X1),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
tff(f974,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,div_mod(int,X0,X2),div_mod(int,X1,X2)),X2) )
| ~ spl1_20
| ~ spl1_82 ),
inference(resolution,[],[f960,f624]) ).
tff(f960,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X1),div_mod(X0,X2,X1)),X1) ) )
| ~ spl1_82 ),
inference(avatar_component_clause,[],[f959]) ).
tff(f2769,plain,
( spl1_178
| ~ spl1_19
| ~ spl1_23
| ~ spl1_71
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f1266,f1170,f883,f639,f617,f2767]) ).
tff(f2767,plain,
( spl1_178
<=> ! [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,[spl1_178])]) ).
tff(f617,plain,
( spl1_19
<=> group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f883,plain,
( spl1_71
<=> ! [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,[spl1_71])]) ).
tff(f1170,plain,
( spl1_114
<=> ! [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,[spl1_114])]) ).
tff(f1266,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) )
| ~ spl1_19
| ~ spl1_23
| ~ spl1_71
| ~ spl1_114 ),
inference(forward_demodulation,[],[f1255,f897]) ).
tff(f897,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),zero_zero(int)) = X0 )
| ~ spl1_19
| ~ spl1_71 ),
inference(resolution,[],[f884,f619]) ).
tff(f619,plain,
( group_add(int)
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f617]) ).
tff(f884,plain,
( ! [X0: $tType,X1: X0] :
( ~ group_add(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),zero_zero(X0)) = X1 ) )
| ~ spl1_71 ),
inference(avatar_component_clause,[],[f883]) ).
tff(f1255,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) )
| ~ spl1_23
| ~ spl1_114 ),
inference(superposition,[],[f1171,f640]) ).
tff(f1171,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) )
| ~ spl1_114 ),
inference(avatar_component_clause,[],[f1170]) ).
tff(f2751,plain,
( spl1_176
| spl1_177
| ~ spl1_64
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f869,f860,f842,f2749,f2746]) ).
tff(f2746,plain,
( spl1_176
<=> ! [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,[spl1_176])]) ).
tff(f2749,plain,
( spl1_177
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_177])]) ).
tff(f860,plain,
( spl1_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,[spl1_67])]) ).
tff(f869,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ~ pp(X1)
| pp(aa(fun(bool,bool),bool,fEx(bool),aa(bool,fun(bool,bool),fconj,X1))) )
| ~ spl1_64
| ~ spl1_67 ),
inference(resolution,[],[f861,f843]) ).
tff(f861,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl1_67 ),
inference(avatar_component_clause,[],[f860]) ).
tff(f2744,plain,
( spl1_175
| ~ spl1_64
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f858,f846,f842,f2742]) ).
tff(f2742,plain,
( spl1_175
<=> ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(bool,fun(X0,bool),combk(bool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_175])]) ).
tff(f858,plain,
( ! [X0: $tType,X1: bool] :
( ~ pp(X1)
| pp(aa(fun(X0,bool),bool,fEx(X0),aa(bool,fun(X0,bool),combk(bool,X0),X1))) )
| ~ spl1_64
| ~ spl1_65 ),
inference(superposition,[],[f843,f847]) ).
tff(f2516,plain,
( spl1_174
| ~ spl1_116
| spl1_160 ),
inference(avatar_split_clause,[],[f2427,f2359,f1189,f2514]) ).
tff(f2514,plain,
( spl1_174
<=> ! [X0: bool] :
( ( zero_zero(bool) = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_174])]) ).
tff(f1189,plain,
( spl1_116
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
tff(f2427,plain,
( ! [X0: bool] :
( ( zero_zero(bool) = X0 )
| ( fTrue = X0 ) )
| ~ spl1_116
| spl1_160 ),
inference(trivial_inequality_removal,[],[f2421]) ).
tff(f2421,plain,
( ! [X0: bool] :
( ( fTrue != fTrue )
| ( zero_zero(bool) = X0 )
| ( fTrue = X0 ) )
| ~ spl1_116
| spl1_160 ),
inference(superposition,[],[f2360,f1190]) ).
tff(f1190,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl1_116 ),
inference(avatar_component_clause,[],[f1189]) ).
tff(f2360,plain,
( ( fTrue != zero_zero(bool) )
| spl1_160 ),
inference(avatar_component_clause,[],[f2359]) ).
tff(f2499,plain,
( spl1_173
| ~ spl1_20
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f957,f946,f622,f2497]) ).
tff(f2497,plain,
( spl1_173
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,div_mod(int,X0,X2),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_173])]) ).
tff(f946,plain,
( spl1_80
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X1),X2) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X2),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
tff(f957,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,div_mod(int,X0,X2),X1),X2) )
| ~ spl1_20
| ~ spl1_80 ),
inference(resolution,[],[f947,f624]) ).
tff(f947,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,plus_plus(X0,X3,X1),X2) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X2),X1),X2) ) )
| ~ spl1_80 ),
inference(avatar_component_clause,[],[f946]) ).
tff(f2495,plain,
( spl1_172
| ~ spl1_20
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f956,f942,f622,f2493]) ).
tff(f2493,plain,
( spl1_172
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,X0,div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_172])]) ).
tff(f942,plain,
( spl1_79
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,X3,div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
tff(f956,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,plus_plus(int,X0,X1),X2) = div_mod(int,plus_plus(int,X0,div_mod(int,X1,X2)),X2) )
| ~ spl1_20
| ~ spl1_79 ),
inference(resolution,[],[f943,f624]) ).
tff(f943,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,X3,div_mod(X0,X2,X1)),X1) ) )
| ~ spl1_79 ),
inference(avatar_component_clause,[],[f942]) ).
tff(f2491,plain,
( spl1_171
| ~ spl1_20
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f955,f938,f622,f2489]) ).
tff(f2489,plain,
( spl1_171
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,aa(int,int,times_times(int,X2),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_171])]) ).
tff(f938,plain,
( spl1_78
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X3,X1) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
tff(f955,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,aa(int,int,times_times(int,X2),X1)),X1) )
| ~ spl1_20
| ~ spl1_78 ),
inference(resolution,[],[f939,f624]) ).
tff(f939,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X3,X1) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X1) ) )
| ~ spl1_78 ),
inference(avatar_component_clause,[],[f938]) ).
tff(f2487,plain,
( spl1_170
| ~ spl1_20
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f954,f934,f622,f2485]) ).
tff(f2485,plain,
( spl1_170
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,aa(int,int,times_times(int,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_170])]) ).
tff(f934,plain,
( spl1_77
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X3,X2) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
tff(f954,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,aa(int,int,times_times(int,X1),X2)),X1) )
| ~ spl1_20
| ~ spl1_77 ),
inference(resolution,[],[f935,f624]) ).
tff(f935,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X3,X2) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X2) ) )
| ~ spl1_77 ),
inference(avatar_component_clause,[],[f934]) ).
tff(f2483,plain,
( spl1_169
| ~ spl1_22
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f857,f846,f632,f2481]) ).
tff(f2481,plain,
( spl1_169
<=> ! [X0: $tType,X2: X0,X1: bool] :
( ( fFalse = X1 )
| ( fTrue = aa(X0,bool,aa(bool,fun(X0,bool),combk(bool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_169])]) ).
tff(f857,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fFalse = X1 )
| ( fTrue = aa(X0,bool,aa(bool,fun(X0,bool),combk(bool,X0),X1),X2) ) )
| ~ spl1_22
| ~ spl1_65 ),
inference(superposition,[],[f847,f633]) ).
tff(f2435,plain,
( spl1_168
| ~ spl1_19
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f928,f913,f617,f2433]) ).
tff(f2433,plain,
( spl1_168
<=> ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),plus_plus(int,X0,X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_168])]) ).
tff(f913,plain,
( spl1_75
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X2,X1)),X1) = X2 )
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
tff(f928,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),plus_plus(int,X0,X1)),X1) = X0 )
| ~ spl1_19
| ~ spl1_75 ),
inference(resolution,[],[f914,f619]) ).
tff(f914,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ group_add(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X2,X1)),X1) = X2 ) )
| ~ spl1_75 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f2431,plain,
( spl1_167
| ~ spl1_19
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f916,f909,f617,f2429]) ).
tff(f2429,plain,
( spl1_167
<=> ! [X0: int,X1: 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,[spl1_167])]) ).
tff(f909,plain,
( spl1_74
<=> ! [X0: $tType,X2: X0,X1: 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,[spl1_74])]) ).
tff(f916,plain,
( ! [X0: int,X1: int] : ( plus_plus(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X1),X1) = X0 )
| ~ spl1_19
| ~ spl1_74 ),
inference(resolution,[],[f910,f619]) ).
tff(f910,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ group_add(X0)
| ( plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1),X1) = X2 ) )
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f2419,plain,
( ~ spl1_165
| spl1_166
| ~ spl1_22
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f818,f788,f632,f2417,f2413]) ).
tff(f2413,plain,
( spl1_165
<=> cancel_semigroup_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
tff(f2417,plain,
( spl1_166
<=> ! [X2: bool,X0: bool,X1: bool] :
( ( fFalse != plus_plus(bool,X2,X1) )
| ( fTrue = plus_plus(bool,X0,X1) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
tff(f818,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( fFalse != plus_plus(bool,X2,X1) )
| ( X0 = X2 )
| ~ cancel_semigroup_add(bool)
| ( fTrue = plus_plus(bool,X0,X1) ) )
| ~ spl1_22
| ~ spl1_54 ),
inference(superposition,[],[f789,f633]) ).
tff(f2411,plain,
( ~ spl1_163
| spl1_164
| ~ spl1_22
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f815,f780,f632,f2409,f2405]) ).
tff(f2405,plain,
( spl1_163
<=> cancel146912293up_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
tff(f2409,plain,
( spl1_164
<=> ! [X2: bool,X0: bool,X1: bool] :
( ( fFalse != plus_plus(bool,X0,X2) )
| ( fTrue = plus_plus(bool,X0,X1) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_164])]) ).
tff(f780,plain,
( spl1_52
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f815,plain,
( ! [X2: bool,X0: bool,X1: bool] :
( ( fFalse != plus_plus(bool,X0,X2) )
| ( X1 = X2 )
| ~ cancel146912293up_add(bool)
| ( fTrue = plus_plus(bool,X0,X1) ) )
| ~ spl1_22
| ~ spl1_52 ),
inference(superposition,[],[f781,f633]) ).
tff(f781,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ( X1 = X2 )
| ~ cancel146912293up_add(X0) )
| ~ spl1_52 ),
inference(avatar_component_clause,[],[f780]) ).
tff(f2382,plain,
( spl1_162
| ~ spl1_20
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f907,f903,f622,f2380]) ).
tff(f2380,plain,
( spl1_162
<=> ! [X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X1),X0),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
tff(f903,plain,
( spl1_73
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X1),X2),X2) = X1 )
| ( zero_zero(X0) = X2 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
tff(f907,plain,
( ! [X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X1),X0),X0) = X1 ) )
| ~ spl1_20
| ~ spl1_73 ),
inference(resolution,[],[f904,f624]) ).
tff(f904,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = X2 )
| ( div_div(X0,aa(X0,X0,times_times(X0,X1),X2),X2) = X1 ) )
| ~ spl1_73 ),
inference(avatar_component_clause,[],[f903]) ).
tff(f2378,plain,
( spl1_161
| ~ spl1_20
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f906,f899,f622,f2376]) ).
tff(f2376,plain,
( spl1_161
<=> ! [X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X0),X1),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_161])]) ).
tff(f899,plain,
( spl1_72
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X2),X1),X2) = X1 )
| ( zero_zero(X0) = X2 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
tff(f906,plain,
( ! [X0: int,X1: int] :
( ( zero_zero(int) = X0 )
| ( div_div(int,aa(int,int,times_times(int,X0),X1),X0) = X1 ) )
| ~ spl1_20
| ~ spl1_72 ),
inference(resolution,[],[f900,f624]) ).
tff(f900,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = X2 )
| ( div_div(X0,aa(X0,X0,times_times(X0,X2),X1),X2) = X1 ) )
| ~ spl1_72 ),
inference(avatar_component_clause,[],[f899]) ).
tff(f2362,plain,
( spl1_160
| ~ spl1_22
| spl1_155 ),
inference(avatar_split_clause,[],[f2273,f2264,f632,f2359]) ).
tff(f2273,plain,
( ( fTrue = zero_zero(bool) )
| ~ spl1_22
| spl1_155 ),
inference(trivial_inequality_removal,[],[f2272]) ).
tff(f2272,plain,
( ( fFalse != fFalse )
| ( fTrue = zero_zero(bool) )
| ~ spl1_22
| spl1_155 ),
inference(superposition,[],[f2266,f633]) ).
tff(f2266,plain,
( ( fFalse != zero_zero(bool) )
| spl1_155 ),
inference(avatar_component_clause,[],[f2264]) ).
tff(f2357,plain,
( spl1_159
| ~ spl1_51
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f855,f842,f770,f2355]) ).
tff(f2355,plain,
( spl1_159
<=> ! [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,[spl1_159])]) ).
tff(f770,plain,
( spl1_51
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f855,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,fEx(X0),aa(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl1_51
| ~ spl1_64 ),
inference(resolution,[],[f843,f771]) ).
tff(f771,plain,
( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
| ~ spl1_51 ),
inference(avatar_component_clause,[],[f770]) ).
tff(f2285,plain,
( spl1_158
| ~ spl1_19
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f897,f883,f617,f2283]) ).
tff(f2283,plain,
( spl1_158
<=> ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
tff(f2281,plain,
( spl1_157
| ~ spl1_19
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f896,f879,f617,f2279]) ).
tff(f2279,plain,
( spl1_157
<=> ! [X0: int] : ( zero_zero(int) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
tff(f879,plain,
( spl1_70
<=> ! [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,[spl1_70])]) ).
tff(f896,plain,
( ! [X0: int] : ( zero_zero(int) = aa(int,int,aa(int,fun(int,int),minus_minus(int),X0),X0) )
| ~ spl1_19
| ~ spl1_70 ),
inference(resolution,[],[f880,f619]) ).
tff(f880,plain,
( ! [X0: $tType,X1: X0] :
( ~ group_add(X0)
| ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X1),X1) ) )
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f879]) ).
tff(f2277,plain,
( spl1_156
| ~ spl1_3
| ~ spl1_69 ),
inference(avatar_split_clause,[],[f895,f875,f537,f2275]) ).
tff(f2275,plain,
( spl1_156
<=> ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
tff(f537,plain,
( spl1_3
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f875,plain,
( spl1_69
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
tff(f895,plain,
( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) )
| ~ spl1_3
| ~ spl1_69 ),
inference(resolution,[],[f876,f539]) ).
tff(f539,plain,
( ab_semigroup_add(int)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f537]) ).
tff(f876,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_add(X0)
| ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) )
| ~ spl1_69 ),
inference(avatar_component_clause,[],[f875]) ).
tff(f2267,plain,
( ~ spl1_153
| spl1_154
| ~ spl1_155
| ~ spl1_22
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f775,f762,f632,f2264,f2261,f2257]) ).
tff(f2257,plain,
( spl1_153
<=> linord219039673up_add(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
tff(f2261,plain,
( spl1_154
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = plus_plus(bool,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
tff(f762,plain,
( spl1_49
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f775,plain,
( ! [X0: bool] :
( ( fFalse != zero_zero(bool) )
| ( fFalse = X0 )
| ~ linord219039673up_add(bool)
| ( fTrue = plus_plus(bool,X0,X0) ) )
| ~ spl1_22
| ~ spl1_49 ),
inference(inner_rewriting,[],[f774]) ).
tff(f774,plain,
( ! [X0: bool] :
( ( fFalse != zero_zero(bool) )
| ( zero_zero(bool) = X0 )
| ~ linord219039673up_add(bool)
| ( fTrue = plus_plus(bool,X0,X0) ) )
| ~ spl1_22
| ~ spl1_49 ),
inference(superposition,[],[f763,f633]) ).
tff(f763,plain,
( ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ( zero_zero(X0) = X1 )
| ~ linord219039673up_add(X0) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f762]) ).
tff(f2255,plain,
( spl1_152
| ~ spl1_66
| ~ spl1_149 ),
inference(avatar_split_clause,[],[f2198,f2188,f851,f2253]) ).
tff(f2253,plain,
( spl1_152
<=> ! [X0: int] : ( zero_zero(int) = aa(int,int,times_times(int,zero_zero(int)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_152])]) ).
tff(f2188,plain,
( spl1_149
<=> ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
tff(f2198,plain,
( ! [X0: int] : ( zero_zero(int) = aa(int,int,times_times(int,zero_zero(int)),X0) )
| ~ spl1_66
| ~ spl1_149 ),
inference(superposition,[],[f2189,f852]) ).
tff(f2189,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X0) )
| ~ spl1_149 ),
inference(avatar_component_clause,[],[f2188]) ).
tff(f2250,plain,
( spl1_151
| ~ spl1_20
| ~ spl1_23
| ~ spl1_63
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f993,f982,f838,f639,f622,f2248]) ).
tff(f2248,plain,
( spl1_151
<=> ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X1),zero_zero(int)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
tff(f838,plain,
( spl1_63
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f993,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X1),zero_zero(int)),X0) )
| ~ spl1_20
| ~ spl1_23
| ~ spl1_63
| ~ spl1_86 ),
inference(forward_demodulation,[],[f989,f854]) ).
tff(f854,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_mod(int,aa(int,int,times_times(int,X0),X1),X1) )
| ~ spl1_20
| ~ spl1_63 ),
inference(resolution,[],[f839,f624]) ).
tff(f839,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X1) ) )
| ~ spl1_63 ),
inference(avatar_component_clause,[],[f838]) ).
tff(f989,plain,
( ! [X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X1),X0),X0) = div_mod(int,aa(int,int,times_times(int,X1),zero_zero(int)),X0) )
| ~ spl1_23
| ~ spl1_86 ),
inference(superposition,[],[f983,f640]) ).
tff(f2194,plain,
( spl1_150
| ~ spl1_20
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f854,f838,f622,f2192]) ).
tff(f2190,plain,
( spl1_149
| ~ spl1_20
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f849,f834,f622,f2188]) ).
tff(f2103,plain,
( spl1_148
| ~ spl1_20
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f830,f804,f622,f2101]) ).
tff(f2101,plain,
( spl1_148
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
tff(f804,plain,
( spl1_58
<=> ! [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,[spl1_58])]) ).
tff(f830,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) )
| ~ spl1_20
| ~ spl1_58 ),
inference(resolution,[],[f805,f624]) ).
tff(f805,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) ) )
| ~ spl1_58 ),
inference(avatar_component_clause,[],[f804]) ).
tff(f2099,plain,
( spl1_147
| ~ spl1_20
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f829,f800,f622,f2097]) ).
tff(f2097,plain,
( spl1_147
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
tff(f2095,plain,
( spl1_146
| ~ spl1_20
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f828,f796,f622,f2093]) ).
tff(f2093,plain,
( spl1_146
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
tff(f796,plain,
( spl1_56
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,plus_plus(X0,X2,X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f828,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,plus_plus(int,X0,X1),X1) )
| ~ spl1_20
| ~ spl1_56 ),
inference(resolution,[],[f797,f624]) ).
tff(f797,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,plus_plus(X0,X2,X1),X1) ) )
| ~ spl1_56 ),
inference(avatar_component_clause,[],[f796]) ).
tff(f2086,plain,
( spl1_145
| ~ spl1_20
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f776,f766,f622,f2084]) ).
tff(f2084,plain,
( spl1_145
<=> ! [X0: int] :
( ( zero_zero(int) = X0 )
| ( one_one(int) = div_div(int,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
tff(f766,plain,
( spl1_50
<=> ! [X0: $tType,X1: X0] :
( ( one_one(X0) = div_div(X0,X1,X1) )
| ( zero_zero(X0) = X1 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f776,plain,
( ! [X0: int] :
( ( zero_zero(int) = X0 )
| ( one_one(int) = div_div(int,X0,X0) ) )
| ~ spl1_20
| ~ spl1_50 ),
inference(resolution,[],[f767,f624]) ).
tff(f767,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = X1 )
| ( one_one(X0) = div_div(X0,X1,X1) ) )
| ~ spl1_50 ),
inference(avatar_component_clause,[],[f766]) ).
tff(f2082,plain,
( spl1_144
| ~ spl1_13
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f773,f758,f587,f2080]) ).
tff(f2080,plain,
( spl1_144
<=> ! [X0: list(int)] : ( map(int,int,times_times(int,one_one(int)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_144])]) ).
tff(f587,plain,
( spl1_13
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f758,plain,
( spl1_48
<=> ! [X0: $tType,X1: list(X0)] :
( ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f773,plain,
( ! [X0: list(int)] : ( map(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl1_13
| ~ spl1_48 ),
inference(resolution,[],[f759,f589]) ).
tff(f589,plain,
( monoid_mult(int)
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f759,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ monoid_mult(X0)
| ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f758]) ).
tff(f2063,plain,
( spl1_143
| ~ spl1_20
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f756,f745,f622,f2061]) ).
tff(f2061,plain,
( spl1_143
<=> ! [X0: int,X1: int] : ( zero_zero(int) = div_div(int,div_mod(int,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_143])]) ).
tff(f745,plain,
( spl1_46
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_div(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f756,plain,
( ! [X0: int,X1: int] : ( zero_zero(int) = div_div(int,div_mod(int,X0,X1),X1) )
| ~ spl1_20
| ~ spl1_46 ),
inference(resolution,[],[f746,f624]) ).
tff(f746,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_div(X0,div_mod(X0,X2,X1),X1) ) )
| ~ spl1_46 ),
inference(avatar_component_clause,[],[f745]) ).
tff(f2048,plain,
( ~ spl1_142
| ~ spl1_25
| spl1_140 ),
inference(avatar_split_clause,[],[f2039,f2034,f647,f2045]) ).
tff(f647,plain,
( spl1_25
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f2034,plain,
( spl1_140
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) = 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introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
tff(f2039,plain,
( ( 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!= 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)
| ~ spl1_25
| spl1_140 ),
inference(forward_demodulation,[],[f2038,f648]) ).
tff(f648,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f647]) ).
tff(f2038,plain,
( ( 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!= div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))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)
| ~ spl1_25
| spl1_140 ),
inference(forward_demodulation,[],[f2036,f648]) ).
tff(f2036,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) != div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),aa(atom,int,divisor,a))),aa(atom,int,divisor,a)) )
| spl1_140 ),
inference(avatar_component_clause,[],[f2034]) ).
tff(f2043,plain,
( spl1_141
| ~ spl1_7
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f749,f733,f557,f2041]) ).
tff(f2041,plain,
( spl1_141
<=> ! [X0: int] : ( aa(int,int,times_times(int,one_one(int)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
tff(f557,plain,
( spl1_7
<=> comm_monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f733,plain,
( spl1_43
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f749,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl1_7
| ~ spl1_43 ),
inference(resolution,[],[f734,f559]) ).
tff(f559,plain,
( comm_monoid_mult(int)
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f557]) ).
tff(f734,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl1_43 ),
inference(avatar_component_clause,[],[f733]) ).
tff(f2037,plain,
~ spl1_140,
inference(avatar_split_clause,[],[f359,f2034]) ).
tff(f359,plain,
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!= 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inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) != div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fu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inference(flattening,[],[f135]) ).
tff(f135,negated_conjecture,
( ~ div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fu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),
inference(negated_conjecture,[],[f134]) ).
tff(f134,conjecture,
div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as))))),aa(atom,int,divisor,a)) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,n,aa(atom,int,divisor,a))),div_mod(int,aa(int,int,times_times(int,plus_plus(int,div_div(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),n),big_linorder_Min(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)),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),aa(fun(list(int),list(int)),fun(list(int),fun(list(int),int)),aa(fun(list(int),fun(list(int),int)),fun(fun(list(int),list(int)),fun(list(int),fun(list(int),int))),combb(list(int),fun(list(int),int),list(int)),iprod(int)),tl(int))),xs))))))),aa(fun(atom,bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(atom,bool),fun(int,bool))),fun(fun(atom,bool),fun(list(int),fun(int,bool))),combc(list(int),fun(atom,bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool))),aa(fun(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(atom,bool),bool))),fun(list(int),fun(fun(atom,bool),fun(int,bool)))),combb(fun(int,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(int,bool)),list(int)),combc(int,fun(atom,bool),bool)),aa(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool))),aa(fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),fun(fun(list(int),fun(int,atom)),fun(list(int),fun(int,fun(fun(atom,bool),bool)))),combb(fun(int,atom),fun(int,fun(fun(atom,bool),bool)),list(int)),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(int,atom),fun(int,fun(fun(atom,bool),bool))),combb(atom,fun(fun(atom,bool),bool),int),member(atom))),aa(fun(int,fun(list(int),atom)),fun(list(int),fun(int,atom)),combc(int,list(int),atom),c_PresArith_Oatom_OLe)))),collect(atom,aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(bool,bool)),fun(fun(atom,bool),fun(atom,bool)),combs(atom,bool,bool),aa(fun(atom,bool),fun(atom,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(atom,bool),fun(atom,fun(bool,bool))),combb(bool,fun(bool,bool),atom),fconj),aa(fun(atom,bool),fun(atom,bool),aa(fun(atom,fun(fun(atom,bool),bool)),fun(fun(atom,bool),fun(atom,bool)),combc(atom,fun(atom,bool),bool),member(atom)),set(atom,as)))),atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),list_case(bool,int,fFalse,aa(fun(int,bool),fun(int,fun(list(int),bool)),aa(fun(bool,fun(list(int),bool)),fun(fun(int,bool),fun(int,fun(list(int),bool))),combb(bool,fun(list(int),bool),int),combk(bool,list(int))),aa(int,fun(int,bool),aa(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),zero_zero(int))))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse))))))))))))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue)))),as)))),one_one(int))),zlcms(map(atom,int,divisor,filter(atom,atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),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(f2031,plain,
spl1_139,
inference(avatar_split_clause,[],[f418,f2029]) ).
tff(f2029,plain,
( spl1_139
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
tff(f418,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X32: list(X0),X33: list(X0),X34: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),minus_minus(list(X0)),X34),X33)),X32) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X34),X32)),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X33),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_iprod__left__diff__distrib) ).
tff(f2026,plain,
spl1_138,
inference(avatar_split_clause,[],[f417,f2024]) ).
tff(f2024,plain,
( spl1_138
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),plus_plus(list(X0),X3,X2)),X1) = plus_plus(X0,aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
tff(f417,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),plus_plus(list(X0),X3,X2)),X1) = plus_plus(X0,aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),plus_plus(list(X0),X3,X2)),X1) = plus_plus(X0,aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),plus_plus(list(X0),X3,X2)),X1) = plus_plus(X0,aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X3),X1),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X32: list(X0),X33: list(X0),X34: list(X0)] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),plus_plus(list(X0),X34,X33)),X32) = plus_plus(X0,aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X34),X32),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X33),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_iprod__left__add__distrib) ).
tff(f2009,plain,
spl1_137,
inference(avatar_split_clause,[],[f406,f2007]) ).
tff(f2007,plain,
( spl1_137
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ( 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) )
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
tff(f406,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ( 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) )
| ~ ordered_ab_group_add(X0) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3)) ) )
| ( 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) ) )
| ~ ordered_ab_group_add(X0) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
| ( 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) ) )
| ~ ordered_ab_group_add(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X4),X3) )
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X20: X0,X14: X0,X15: X0,X13: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X13),X15) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X14),X20) )
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X13),X15))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X14),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_diff__eq__diff__less) ).
tff(f1952,plain,
spl1_136,
inference(avatar_split_clause,[],[f437,f1950]) ).
tff(f1950,plain,
( spl1_136
<=> ! [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,[spl1_136])]) ).
tff(f437,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,[],[f289]) ).
tff(f289,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,[],[f288]) ).
tff(f288,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,[],[f180]) ).
tff(f180,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,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X22: X0,X10: X0,X23: X0,X12: X0,X11: X0] :
( ( div_mod(X0,X11,X12) = div_mod(X0,X23,X12) )
=> ( ( div_mod(X0,X10,X12) = div_mod(X0,X22,X12) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X10),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X23),X22),X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mod__diff__cong) ).
tff(f1925,plain,
( spl1_135
| ~ spl1_7
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f748,f729,f557,f1923]) ).
tff(f1923,plain,
( spl1_135
<=> ! [X0: int] : ( aa(int,int,times_times(int,X0),one_one(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
tff(f729,plain,
( spl1_42
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
tff(f748,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),one_one(int)) = X0 )
| ~ spl1_7
| ~ spl1_42 ),
inference(resolution,[],[f730,f559]) ).
tff(f730,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f729]) ).
tff(f1878,plain,
spl1_134,
inference(avatar_split_clause,[],[f421,f1876]) ).
tff(f1876,plain,
( spl1_134
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
tff(f421,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3)) )
| ~ ordere223160158up_add(X0) ),
inference(flattening,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1))) ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X21: X0,X12: X0,X10: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),X10))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X12),X21))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X11,X12)),plus_plus(X0,X10,X21))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__strict__mono) ).
tff(f1874,plain,
spl1_133,
inference(avatar_split_clause,[],[f402,f1872]) ).
tff(f1872,plain,
( spl1_133
<=> ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
tff(f402,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X2,X1))) ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X10: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X11))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X10))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X11,X10))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__pos__pos) ).
tff(f1870,plain,
spl1_132,
inference(avatar_split_clause,[],[f401,f1868]) ).
tff(f1868,plain,
( spl1_132
<=> ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X2,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0)))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
tff(f401,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X2,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0)))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X2,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0))) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X2,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0))) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0)))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X2,X1)),zero_zero(X0))) ) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X10: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),zero_zero(X0)))
=> ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X10),zero_zero(X0)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X11,X10)),zero_zero(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__neg__neg) ).
tff(f1808,plain,
spl1_131,
inference(avatar_split_clause,[],[f510,f1806]) ).
tff(f510,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,[],[f246]) ).
tff(f246,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,[],[f124]) ).
tff(f124,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X39: X0,X40: fun(X0,X1),X38: 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),X38),X40),X39) = aa(X1,X2,aa(X0,fun(X1,X2),X38,X39),aa(X0,X1,X40,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1793,plain,
spl1_130,
inference(avatar_split_clause,[],[f490,f1791]) ).
tff(f1791,plain,
( spl1_130
<=> ! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X1,X0)),zero_zero(int)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
tff(f490,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X1,X0)),zero_zero(int)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(cnf_transformation,[],[f336]) ).
tff(f336,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X1,X0)),zero_zero(int)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(flattening,[],[f335]) ).
tff(f335,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X1,X0)),zero_zero(int)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(ennf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
=> ( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X0))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X1,X0)),zero_zero(int))) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X10: int,X11: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X11),zero_zero(int)))
=> ( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X10))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_div(int,X11,X10)),zero_zero(int))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_div__neg__pos__less0) ).
tff(f1776,plain,
spl1_129,
inference(avatar_split_clause,[],[f416,f1774]) ).
tff(f1774,plain,
( spl1_129
<=> ! [X0: $tType,X3: X0,X2: list(X0),X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),map(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
tff(f416,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: list(X0)] :
( ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),map(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: X0] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),map(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: X0] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),map(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X2),X1)) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X7: list(X0),X8: list(X0),X9: X0] : ( aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),map(X0,X0,times_times(X0,X9),X8)),X7) = aa(X0,X0,times_times(X0,X9),aa(list(X0),X0,aa(list(X0),fun(list(X0),X0),iprod(X0),X8),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_iprod__assoc) ).
tff(f1764,plain,
spl1_128,
inference(avatar_split_clause,[],[f499,f1762]) ).
tff(f1762,plain,
( spl1_128
<=> ! [X2: int,X0: int,X1: int] :
( ( div_mod(int,X1,aa(int,int,times_times(int,X0),X2)) = plus_plus(int,aa(int,int,times_times(int,X0),div_mod(int,div_div(int,X1,X0),X2)),div_mod(int,X1,X0)) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
tff(f499,plain,
! [X2: int,X0: int,X1: int] :
( ( div_mod(int,X1,aa(int,int,times_times(int,X0),X2)) = plus_plus(int,aa(int,int,times_times(int,X0),div_mod(int,div_div(int,X1,X0),X2)),div_mod(int,X1,X0)) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X2)) ),
inference(cnf_transformation,[],[f338]) ).
tff(f338,plain,
! [X0: int,X1: int,X2: int] :
( ( div_mod(int,X1,aa(int,int,times_times(int,X0),X2)) = plus_plus(int,aa(int,int,times_times(int,X0),div_mod(int,div_div(int,X1,X0),X2)),div_mod(int,X1,X0)) )
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X2)) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: int,X1: int,X2: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X2))
=> ( div_mod(int,X1,aa(int,int,times_times(int,X0),X2)) = plus_plus(int,aa(int,int,times_times(int,X0),div_mod(int,div_div(int,X1,X0),X2)),div_mod(int,X1,X0)) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X10: int,X11: int,X12: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X12))
=> ( div_mod(int,X11,aa(int,int,times_times(int,X10),X12)) = plus_plus(int,aa(int,int,times_times(int,X10),div_mod(int,div_div(int,X11,X10),X12)),div_mod(int,X11,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_zmod__zmult2__eq) ).
tff(f1709,plain,
spl1_127,
inference(avatar_split_clause,[],[f482,f1707]) ).
tff(f482,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(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,[],[f332]) ).
tff(f332,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(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,[],[f331]) ).
tff(f331,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(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,[],[f221]) ).
tff(f221,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,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) ) ) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X22: X0,X10: X0,X23: X0,X12: X0,X11: X0] :
( ( div_mod(X0,X11,X12) = div_mod(X0,X23,X12) )
=> ( ( div_mod(X0,X10,X12) = div_mod(X0,X22,X12) )
=> ( div_mod(X0,aa(X0,X0,times_times(X0,X11),X10),X12) = div_mod(X0,aa(X0,X0,times_times(X0,X23),X22),X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mod__mult__cong) ).
tff(f1671,plain,
spl1_126,
inference(avatar_split_clause,[],[f404,f1669]) ).
tff(f1669,plain,
( spl1_126
<=> ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0)))
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
tff(f404,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0)))
| ~ ordered_ab_group_add(X0) ),
inference(cnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0))) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) )
| ~ ordered_ab_group_add(X0) ),
inference(nnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0))) )
| ~ ordered_ab_group_add(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0))) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( ordered_ab_group_add(X0)
=> ! [X15: X0,X13: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X13),X15))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X13),X15)),zero_zero(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__iff__diff__less__0) ).
tff(f1667,plain,
spl1_125,
inference(avatar_split_clause,[],[f403,f1665]) ).
tff(f1665,plain,
( spl1_125
<=> ! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordered_ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
tff(f403,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordered_ab_group_add(X0) ),
inference(cnf_transformation,[],[f342]) ).
tff(f1662,plain,
( spl1_124
| ~ spl1_21
| ~ spl1_116 ),
inference(avatar_split_clause,[],[f1477,f1189,f627,f1660]) ).
tff(f1660,plain,
( spl1_124
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
tff(f627,plain,
( spl1_21
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f1477,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ( X0 = X1 )
| ( fTrue = X1 ) )
| ~ spl1_21
| ~ spl1_116 ),
inference(superposition,[],[f629,f1190]) ).
tff(f629,plain,
( pp(fTrue)
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f627]) ).
tff(f1658,plain,
spl1_123,
inference(avatar_split_clause,[],[f424,f1656]) ).
tff(f424,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,[],[f279]) ).
tff(f279,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,[],[f171]) ).
tff(f171,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,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X10),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X11,X12)),div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mod__diff__eq) ).
tff(f1638,plain,
spl1_122,
inference(avatar_split_clause,[],[f509,f1636]) ).
tff(f1636,plain,
( spl1_122
<=> ! [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,[spl1_122])]) ).
tff(f509,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,[],[f245]) ).
tff(f245,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,[],[f121]) ).
tff(f121,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X39: X0,X40: fun(X0,X1),X38: 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),X38),X40),X39) = aa(X1,X2,X38,aa(X0,X1,X40,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1634,plain,
spl1_121,
inference(avatar_split_clause,[],[f508,f1632]) ).
tff(f1632,plain,
( spl1_121
<=> ! [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,[spl1_121])]) ).
tff(f508,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,[],[f244]) ).
tff(f244,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,[],[f122]) ).
tff(f122,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X39: X0,X40: X1,X38: 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),X38),X40),X39) = aa(X1,X2,aa(X0,fun(X1,X2),X38,X39),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1628,plain,
spl1_120,
inference(avatar_split_clause,[],[f423,f1626]) ).
tff(f1626,plain,
( spl1_120
<=> ! [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,[spl1_120])]) ).
tff(f423,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,[],[f278]) ).
tff(f278,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,[],[f170]) ).
tff(f170,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,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X10),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),div_mod(X0,X11,X12)),X10),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mod__diff__left__eq) ).
tff(f1624,plain,
spl1_119,
inference(avatar_split_clause,[],[f422,f1622]) ).
tff(f1622,plain,
( spl1_119
<=> ! [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,[spl1_119])]) ).
tff(f422,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,[],[f277]) ).
tff(f277,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,[],[f169]) ).
tff(f169,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,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( ring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X10),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mod__diff__right__eq) ).
tff(f1305,plain,
spl1_118,
inference(avatar_split_clause,[],[f507,f1303]) ).
tff(f507,plain,
! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(atom,X0,atom_case(X0,X5,X4,X3),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X2),X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType,X1: list(int),X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(atom,X0,atom_case(X0,X5,X4,X3),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X2),X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType,X18: list(int),X19: int,X35: fun(int,fun(int,fun(list(int),X0))),X36: fun(int,fun(int,fun(list(int),X0))),X37: fun(int,fun(list(int),X0))] : ( aa(atom,X0,atom_case(X0,X37,X36,X35),aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X19),X18)) = aa(list(int),X0,aa(int,fun(list(int),X0),X37,X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_atom_Osimps_I10_J) ).
tff(f1301,plain,
spl1_117,
inference(avatar_split_clause,[],[f481,f1299]) ).
tff(f481,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,plus_plus(X0,X5,X2),X4) = div_mod(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,[],[f330]) ).
tff(f330,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,plus_plus(X0,X5,X2),X4) = div_mod(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,[],[f329]) ).
tff(f329,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,plus_plus(X0,X5,X2),X4) = div_mod(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,[],[f220]) ).
tff(f220,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,plus_plus(X0,X5,X2),X4) = div_mod(X0,plus_plus(X0,X3,X1),X4) ) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X22: X0,X10: X0,X23: X0,X12: X0,X11: X0] :
( ( div_mod(X0,X11,X12) = div_mod(X0,X23,X12) )
=> ( ( div_mod(X0,X10,X12) = div_mod(X0,X22,X12) )
=> ( div_mod(X0,plus_plus(X0,X11,X10),X12) = div_mod(X0,plus_plus(X0,X23,X22),X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mod__add__cong) ).
tff(f1191,plain,
( spl1_116
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f635,f632,f1189]) ).
tff(f635,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl1_22 ),
inference(superposition,[],[f633,f633]) ).
tff(f1176,plain,
spl1_115,
inference(avatar_split_clause,[],[f495,f1174]) ).
tff(f495,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,[],[f234]) ).
tff(f234,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,[],[f82]) ).
tff(f82,axiom,
! [X29: int,X30: int,X31: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),div_mod(int,X31,X30)),X29),X30) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X31),X29),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_zdiff__zmod__left) ).
tff(f1172,plain,
spl1_114,
inference(avatar_split_clause,[],[f494,f1170]) ).
tff(f494,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,[],[f233]) ).
tff(f233,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,[],[f83]) ).
tff(f83,axiom,
! [X30: int,X29: int,X31: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X31),X29),X30) = div_mod(int,aa(int,int,aa(int,fun(int,int),minus_minus(int),X31),div_mod(int,X29,X30)),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zdiff__zmod__right) ).
tff(f1168,plain,
spl1_113,
inference(avatar_split_clause,[],[f436,f1166]) ).
tff(f436,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f350]) ).
tff(f350,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X15: X0,X13: X0,X14: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X14,X13)),plus_plus(X0,X14,X15)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X13),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__less__cancel__left) ).
tff(f1164,plain,
spl1_112,
inference(avatar_split_clause,[],[f434,f1162]) ).
tff(f434,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X15: X0,X14: X0,X13: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X13,X14)),plus_plus(X0,X15,X14)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X13),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_add__less__cancel__right) ).
tff(f1160,plain,
spl1_111,
inference(avatar_split_clause,[],[f428,f1158]) ).
tff(f1158,plain,
( spl1_111
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
tff(f428,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X10: X0,X12: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X11,X12)),plus_plus(X0,X10,X12)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__less__imp__less__right) ).
tff(f1156,plain,
spl1_110,
inference(avatar_split_clause,[],[f427,f1154]) ).
tff(f427,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X10: X0,X11: X0,X12: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X12,X11)),plus_plus(X0,X12,X10)))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__less__imp__less__left) ).
tff(f1152,plain,
spl1_109,
inference(avatar_split_clause,[],[f420,f1150]) ).
tff(f420,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1))) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X12: X0,X10: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),X10))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X11,X12)),plus_plus(X0,X10,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__strict__right__mono) ).
tff(f1148,plain,
spl1_108,
inference(avatar_split_clause,[],[f419,f1146]) ).
tff(f419,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2))) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X12: X0,X10: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X11),X10))
=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X12,X11)),plus_plus(X0,X12,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__strict__left__mono) ).
tff(f1110,plain,
spl1_107,
inference(avatar_split_clause,[],[f415,f1108]) ).
tff(f415,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f346]) ).
tff(f346,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0))) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X13: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X13,X13)),zero_zero(X0)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X13),zero_zero(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_double__add__less__zero__iff__single__add__less__zero) ).
tff(f1106,plain,
spl1_106,
inference(avatar_split_clause,[],[f414,f1104]) ).
tff(f1104,plain,
( spl1_106
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
tff(f414,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X1)),zero_zero(X0)))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f346]) ).
tff(f1102,plain,
spl1_105,
inference(avatar_split_clause,[],[f413,f1100]) ).
tff(f1100,plain,
( spl1_105
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
tff(f413,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) )
& ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1))) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X13: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X13,X13)))
<=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zero__less__double__add__iff__zero__less__single__add) ).
tff(f1098,plain,
spl1_104,
inference(avatar_split_clause,[],[f412,f1096]) ).
tff(f1096,plain,
( spl1_104
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
tff(f412,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),plus_plus(X0,X1,X1)))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f345]) ).
tff(f1093,plain,
spl1_103,
inference(avatar_split_clause,[],[f505,f1091]) ).
tff(f1091,plain,
( spl1_103
<=> ! [X2: list(int),X0: list(int),X1: int,X3: int] :
( ( X0 = X2 )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
tff(f505,plain,
! [X2: list(int),X3: int,X0: list(int),X1: int] :
( ( X0 = X2 )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ),
inference(cnf_transformation,[],[f358]) ).
tff(f358,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) = aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ) ),
inference(flattening,[],[f357]) ).
tff(f357,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) = aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ) ),
inference(nnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) = aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X16: list(int),X17: int,X18: list(int),X19: int] :
( ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X19),X18) = aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X17),X16) )
<=> ( ( X16 = X18 )
& ( X17 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_atom_Osimps_I1_J) ).
tff(f1071,plain,
spl1_102,
inference(avatar_split_clause,[],[f520,f1069]) ).
tff(f1069,plain,
( spl1_102
<=> ! [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,[spl1_102])]) ).
tff(f520,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,[],[f447]) ).
tff(f447,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,[],[f353]) ).
tff(f353,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,[],[f296]) ).
tff(f296,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,[],[f187]) ).
tff(f187,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,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X20: X0,X14: X0,X15: X0,X13: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X13),X15) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X14),X20) )
=> ( ( X13 = X15 )
<=> ( X14 = X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_diff__eq__diff__eq) ).
tff(f1067,plain,
spl1_101,
inference(avatar_split_clause,[],[f504,f1065]) ).
tff(f1065,plain,
( spl1_101
<=> ! [X0: list(int),X3: int,X2: list(int),X1: int] :
( ( X1 = X3 )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
tff(f504,plain,
! [X2: list(int),X3: int,X0: list(int),X1: int] :
( ( X1 = X3 )
| ( aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0) != aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X3),X2) ) ),
inference(cnf_transformation,[],[f358]) ).
tff(f1063,plain,
spl1_100,
inference(avatar_split_clause,[],[f491,f1061]) ).
tff(f491,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X0,X1)),X1))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(cnf_transformation,[],[f337]) ).
tff(f337,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X0,X1)),X1))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(ennf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X0,X1)),X1)) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X11: int,X10: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),zero_zero(int)),X10))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),div_mod(int,X11,X10)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_pos__mod__bound) ).
tff(f1059,plain,
spl1_99,
inference(avatar_split_clause,[],[f489,f1057]) ).
tff(f1057,plain,
( spl1_99
<=> ! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),div_mod(int,X0,X1)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
tff(f489,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),div_mod(int,X0,X1)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),div_mod(int,X0,X1)))
| ~ pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(ennf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: int,X1: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X1),div_mod(int,X0,X1))) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X11: int,X10: int] :
( pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X10),zero_zero(int)))
=> pp(aa(int,bool,aa(int,fun(int,bool),ord_less(int),X10),div_mod(int,X11,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neg__mod__bound) ).
tff(f1052,plain,
( spl1_98
| ~ spl1_20
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f720,f711,f622,f1050]) ).
tff(f1050,plain,
( spl1_98
<=> ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
tff(f711,plain,
( spl1_39
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,one_one(X0)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
tff(f720,plain,
( ! [X0: int] : ( zero_zero(int) = div_mod(int,X0,one_one(int)) )
| ~ spl1_20
| ~ spl1_39 ),
inference(resolution,[],[f712,f624]) ).
tff(f712,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_mod(X0,X1,one_one(X0)) ) )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f1047,plain,
spl1_97,
inference(avatar_split_clause,[],[f476,f1045]) ).
tff(f476,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X12: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X11),X12),aa(X0,X0,times_times(X0,X10),X12)) = aa(X0,X0,times_times(X0,div_mod(X0,X11,X10)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mod__mult__mult2) ).
tff(f1043,plain,
spl1_96,
inference(avatar_split_clause,[],[f475,f1041]) ).
tff(f475,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X12),X11),aa(X0,X0,times_times(X0,X12),X10)) = aa(X0,X0,times_times(X0,X12),div_mod(X0,X11,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mod__mult__mult1) ).
tff(f1039,plain,
spl1_95,
inference(avatar_split_clause,[],[f474,f1037]) ).
tff(f474,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X11),X10),X12) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X11,X12)),div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mod__mult__eq) ).
tff(f1035,plain,
spl1_94,
inference(avatar_split_clause,[],[f393,f1033]) ).
tff(f393,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( ab_semigroup_mult(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType] :
( ab_semigroup_mult(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X11),X10)),X12) = aa(X0,X0,times_times(X0,X11),aa(X0,X0,times_times(X0,X10),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ab__semigroup__mult__class_Omult__ac_I1_J) ).
tff(f1028,plain,
spl1_93,
inference(avatar_split_clause,[],[f483,f1026]) ).
tff(f483,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,[],[f333]) ).
tff(f333,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,[],[f222]) ).
tff(f222,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,[],[f1]) ).
tff(f1,axiom,
! [X4: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X4),set(atom,as)))
=> ( aa(atom,int,divisor,X4) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_norm) ).
tff(f1024,plain,
spl1_92,
inference(avatar_split_clause,[],[f479,f1022]) ).
tff(f479,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_div(X0,X2,X1) = div_div(X0,aa(X0,X0,times_times(X0,X2),X3),aa(X0,X0,times_times(X0,X1),X3)) )
| ( zero_zero(X0) = X3 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( div_div(X0,X2,X1) = div_div(X0,aa(X0,X0,times_times(X0,X2),X3),aa(X0,X0,times_times(X0,X1),X3)) )
| ( zero_zero(X0) = X3 ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( zero_zero(X0) != X3 )
=> ( div_div(X0,X2,X1) = div_div(X0,aa(X0,X0,times_times(X0,X2),X3),aa(X0,X0,times_times(X0,X1),X3)) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0,X12: X0] :
( ( zero_zero(X0) != X12 )
=> ( div_div(X0,X11,X10) = div_div(X0,aa(X0,X0,times_times(X0,X11),X12),aa(X0,X0,times_times(X0,X10),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_div__mult__mult2) ).
tff(f1020,plain,
( spl1_91
| ~ spl1_20
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f718,f703,f622,f1018]) ).
tff(f1018,plain,
( spl1_91
<=> ! [X0: int] : ( zero_zero(int) = div_div(int,X0,zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
tff(f703,plain,
( spl1_37
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_div(X0,X1,zero_zero(X0)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
tff(f718,plain,
( ! [X0: int] : ( zero_zero(int) = div_div(int,X0,zero_zero(int)) )
| ~ spl1_20
| ~ spl1_37 ),
inference(resolution,[],[f704,f624]) ).
tff(f704,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( zero_zero(X0) = div_div(X0,X1,zero_zero(X0)) ) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f703]) ).
tff(f1016,plain,
spl1_90,
inference(avatar_split_clause,[],[f478,f1014]) ).
tff(f478,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) = div_div(X0,X2,X1) )
| ( zero_zero(X0) = X3 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ( div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) = div_div(X0,X2,X1) )
| ( zero_zero(X0) = X3 ) )
& ( ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ( zero_zero(X0) != X3 ) ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( ( zero_zero(X0) != X3 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) = div_div(X0,X2,X1) ) )
& ( ( zero_zero(X0) = X3 )
=> ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0,X12: X0] :
( ( ( zero_zero(X0) != X12 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X12),X11),aa(X0,X0,times_times(X0,X12),X10)) = div_div(X0,X11,X10) ) )
& ( ( zero_zero(X0) = X12 )
=> ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,X12),X11),aa(X0,X0,times_times(X0,X12),X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_div__mult__mult1__if) ).
tff(f1010,plain,
spl1_89,
inference(avatar_split_clause,[],[f472,f1008]) ).
tff(f472,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X11),X10),X12) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X11,X12)),X10),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mod__mult__left__eq) ).
tff(f1006,plain,
spl1_88,
inference(avatar_split_clause,[],[f471,f1004]) ).
tff(f1004,plain,
( spl1_88
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
tff(f471,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X11),X10),X12) = div_mod(X0,aa(X0,X0,times_times(X0,X11),div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mod__mult__right__eq) ).
tff(f988,plain,
spl1_87,
inference(avatar_split_clause,[],[f503,f986]) ).
tff(f503,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK0(X0,X1,X2,X3)) != aa(X1,X0,X2,sK0(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f356]) ).
tff(f356,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK0(X0,X1,X2,X3)) != aa(X1,X0,X2,sK0(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f339,f355]) ).
tff(f355,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,sK0(X0,X1,X2,X3)) != aa(X1,X0,X2,sK0(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f339,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,[],[f241]) ).
tff(f241,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,[],[f74]) ).
tff(f74,axiom,
! [X1: $tType,X0: $tType,X24: fun(X0,X1),X25: fun(X0,X1)] :
( ! [X26: X0] : ( aa(X0,X1,X25,X26) = aa(X0,X1,X24,X26) )
=> ( X24 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
tff(f984,plain,
spl1_86,
inference(avatar_split_clause,[],[f492,f982]) ).
tff(f492,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: int,X1: int,X2: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X12: int,X10: int,X11: int] : ( div_mod(int,aa(int,int,times_times(int,X11),div_mod(int,X10,X12)),X12) = div_mod(int,aa(int,int,times_times(int,X11),X10),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zmod__simps_I3_J) ).
tff(f973,plain,
spl1_85,
inference(avatar_split_clause,[],[f522,f971]) ).
tff(f522,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,zero_zero(X0)),X2),aa(X0,X0,times_times(X0,zero_zero(X0)),X1)) )
| ~ semiring_div(X0) ),
inference(equality_resolution,[],[f477]) ).
tff(f477,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( zero_zero(X0) = div_div(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ( zero_zero(X0) != X3 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f326]) ).
tff(f969,plain,
spl1_84,
inference(avatar_split_clause,[],[f501,f967]) ).
tff(f501,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,[],[f354]) ).
tff(f354,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,[],[f239]) ).
tff(f239,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,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X27: fun(X0,bool),X9: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X9),X27))
<=> pp(aa(X0,bool,X27,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
tff(f965,plain,
spl1_83,
inference(avatar_split_clause,[],[f500,f963]) ).
tff(f963,plain,
( spl1_83
<=> ! [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,[spl1_83])]) ).
tff(f500,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,[],[f354]) ).
tff(f961,plain,
spl1_82,
inference(avatar_split_clause,[],[f470,f959]) ).
tff(f470,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X1),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X1),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X1),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,plus_plus(X0,X11,X10),X12) = div_mod(X0,plus_plus(X0,div_mod(X0,X11,X12),div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mod__add__eq) ).
tff(f952,plain,
spl1_81,
inference(avatar_split_clause,[],[f485,f950]) ).
tff(f485,plain,
! [X0: list(int),X1: int] : ( one_one(int) = aa(atom,int,divisor,aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0)) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: list(int),X1: int] : ( one_one(int) = aa(atom,int,divisor,aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X1),X0)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X5: list(int),X6: int] : ( aa(atom,int,divisor,aa(list(int),atom,aa(int,fun(list(int),atom),c_PresArith_Oatom_OLe,X6),X5)) = one_one(int) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_divisor_Osimps_I1_J) ).
tff(f948,plain,
spl1_80,
inference(avatar_split_clause,[],[f468,f946]) ).
tff(f468,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X1),X2) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X1),X2) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X1),X2) = div_mod(X0,plus_plus(X0,div_mod(X0,X3,X2),X1),X2) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X12: X0,X11: X0] : ( div_mod(X0,plus_plus(X0,X11,X10),X12) = div_mod(X0,plus_plus(X0,div_mod(X0,X11,X12),X10),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmod__simps_I1_J) ).
tff(f944,plain,
spl1_79,
inference(avatar_split_clause,[],[f466,f942]) ).
tff(f466,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,X3,div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,X3,div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,plus_plus(X0,X3,X2),X1) = div_mod(X0,plus_plus(X0,X3,div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,plus_plus(X0,X11,X10),X12) = div_mod(X0,plus_plus(X0,X11,div_mod(X0,X10,X12)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mod__add__right__eq) ).
tff(f940,plain,
spl1_78,
inference(avatar_split_clause,[],[f465,f938]) ).
tff(f465,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,X3,X1) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X1) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X1) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X1) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X12: X0,X11: X0] : ( div_mod(X0,X11,X10) = div_mod(X0,plus_plus(X0,X11,aa(X0,X0,times_times(X0,X12),X10)),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_mod__mult__self1) ).
tff(f936,plain,
spl1_77,
inference(avatar_split_clause,[],[f464,f934]) ).
tff(f464,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,X3,X2) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X2) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X2) = div_mod(X0,plus_plus(X0,X3,aa(X0,X0,times_times(X0,X2),X1)),X2) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( div_mod(X0,X11,X10) = div_mod(X0,plus_plus(X0,X11,aa(X0,X0,times_times(X0,X10),X12)),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_mod__mult__self2) ).
tff(f932,plain,
spl1_76,
inference(avatar_split_clause,[],[f443,f930]) ).
tff(f443,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,[],[f351]) ).
tff(f351,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,[],[f294]) ).
tff(f294,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,[],[f185]) ).
tff(f185,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,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X15: X0,X13: X0] :
( ( X13 = X15 )
<=> ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X13),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_eq__iff__diff__eq__0) ).
tff(f915,plain,
spl1_75,
inference(avatar_split_clause,[],[f441,f913]) ).
tff(f441,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X2,X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X2,X1)),X1) = X2 )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X2,X1)),X1) = X2 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X10: X0,X11: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),plus_plus(X0,X11,X10)),X10) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__diff__cancel) ).
tff(f911,plain,
spl1_74,
inference(avatar_split_clause,[],[f440,f909]) ).
tff(f440,plain,
! [X0: $tType,X2: X0,X1: 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,[],[f292]) ).
tff(f292,plain,
! [X0: $tType] :
( ! [X1: X0,X2: 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,[],[f183]) ).
tff(f183,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] : ( plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X2),X1),X1) = X2 ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X10: X0,X11: X0] : ( plus_plus(X0,aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X10),X10) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_diff__add__cancel) ).
tff(f905,plain,
spl1_73,
inference(avatar_split_clause,[],[f463,f903]) ).
tff(f463,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X1),X2),X2) = X1 )
| ( zero_zero(X0) = X2 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X1),X2),X2) = X1 )
| ( zero_zero(X0) = X2 ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] :
( ( zero_zero(X0) != X2 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X1),X2),X2) = X1 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X10: X0] :
( ( zero_zero(X0) != X10 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X11),X10),X10) = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_div__mult__self2__is__id) ).
tff(f901,plain,
spl1_72,
inference(avatar_split_clause,[],[f462,f899]) ).
tff(f462,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X2),X1),X2) = X1 )
| ( zero_zero(X0) = X2 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( div_div(X0,aa(X0,X0,times_times(X0,X2),X1),X2) = X1 )
| ( zero_zero(X0) = X2 ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] :
( ( zero_zero(X0) != X2 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X2),X1),X2) = X1 ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X10: X0] :
( ( zero_zero(X0) != X10 )
=> ( div_div(X0,aa(X0,X0,times_times(X0,X10),X11),X10) = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_div__mult__self1__is__id) ).
tff(f885,plain,
spl1_71,
inference(avatar_split_clause,[],[f439,f883]) ).
tff(f439,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,[],[f291]) ).
tff(f291,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,[],[f182]) ).
tff(f182,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,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X11: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_diff__0__right) ).
tff(f881,plain,
spl1_70,
inference(avatar_split_clause,[],[f438,f879]) ).
tff(f438,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,[],[f290]) ).
tff(f290,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,[],[f181]) ).
tff(f181,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,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X11: X0] : ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),minus_minus(X0),X11),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_diff__self) ).
tff(f877,plain,
spl1_69,
inference(avatar_split_clause,[],[f392,f875]) ).
tff(f392,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X12: X0,X10: X0,X11: X0] : ( plus_plus(X0,plus_plus(X0,X11,X10),X12) = plus_plus(X0,X11,plus_plus(X0,X10,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f866,plain,
spl1_68,
inference(avatar_split_clause,[],[f498,f864]) ).
tff(f864,plain,
( spl1_68
<=> ! [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,[spl1_68])]) ).
tff(f498,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,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X0: $tType,X29: X0,X31: X0] :
( ( X29 = X31 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X31),X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f862,plain,
spl1_67,
inference(avatar_split_clause,[],[f486,f860]) ).
tff(f486,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f127]) ).
tff(f127,axiom,
! [X40: bool,X38: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X38),X40))
| ~ pp(X40)
| ~ pp(X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f853,plain,
( spl1_66
| ~ spl1_20
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f701,f684,f622,f851]) ).
tff(f684,plain,
( spl1_34
<=> ! [X0: $tType,X1: X0] :
( ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f701,plain,
( ! [X0: int] : ( div_mod(int,X0,zero_zero(int)) = X0 )
| ~ spl1_20
| ~ spl1_34 ),
inference(resolution,[],[f685,f624]) ).
tff(f685,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,zero_zero(X0)) = X1 ) )
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f684]) ).
tff(f848,plain,
spl1_65,
inference(avatar_split_clause,[],[f502,f846]) ).
tff(f502,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X1: $tType,X0: $tType,X40: X1,X38: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),combk(X0,X1),X38),X40) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f844,plain,
spl1_64,
inference(avatar_split_clause,[],[f497,f842]) ).
tff(f497,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,[],[f236]) ).
tff(f236,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,[],[f120]) ).
tff(f120,axiom,
! [X0: $tType,X31: X0,X38: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,fEx(X0),X38))
| ~ pp(aa(X0,bool,X38,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f840,plain,
spl1_63,
inference(avatar_split_clause,[],[f461,f838]) ).
tff(f461,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X1) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X11),X10),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_mod__mult__self2__is__0) ).
tff(f836,plain,
spl1_62,
inference(avatar_split_clause,[],[f460,f834]) ).
tff(f460,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X2),X1),X2) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X10: X0] : ( zero_zero(X0) = div_mod(X0,aa(X0,X0,times_times(X0,X10),X11),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mod__mult__self1__is__0) ).
tff(f827,plain,
( spl1_61
| ~ spl1_20
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f692,f680,f622,f825]) ).
tff(f825,plain,
( spl1_61
<=> ! [X0: int] : ( div_div(int,X0,one_one(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
tff(f680,plain,
( spl1_33
<=> ! [X0: $tType,X1: X0] :
( ( div_div(X0,X1,one_one(X0)) = X1 )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f692,plain,
( ! [X0: int] : ( div_div(int,X0,one_one(int)) = X0 )
| ~ spl1_20
| ~ spl1_33 ),
inference(resolution,[],[f681,f624]) ).
tff(f681,plain,
( ! [X0: $tType,X1: X0] :
( ~ semiring_div(X0)
| ( div_div(X0,X1,one_one(X0)) = X1 ) )
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f680]) ).
tff(f814,plain,
spl1_60,
inference(avatar_split_clause,[],[f488,f812]) ).
tff(f488,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X40: bool,X38: bool] :
( pp(X38)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X38),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f810,plain,
spl1_59,
inference(avatar_split_clause,[],[f487,f808]) ).
tff(f487,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X40: bool,X38: bool] :
( pp(X40)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X38),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f806,plain,
spl1_58,
inference(avatar_split_clause,[],[f459,f804]) ).
tff(f459,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,[],[f308]) ).
tff(f308,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,[],[f199]) ).
tff(f199,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)
=> ! [X10: X0,X11: X0] : ( div_mod(X0,X11,X10) = div_mod(X0,div_mod(X0,X11,X10),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mod__mod__trivial) ).
tff(f802,plain,
spl1_57,
inference(avatar_split_clause,[],[f458,f800]) ).
tff(f458,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,plus_plus(X0,X2,X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,plus_plus(X0,X2,X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,plus_plus(X0,X2,X1),X2) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0,X10: X0] : ( div_mod(X0,X11,X10) = div_mod(X0,plus_plus(X0,X10,X11),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_mod__add__self1) ).
tff(f798,plain,
spl1_56,
inference(avatar_split_clause,[],[f457,f796]) ).
tff(f457,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,plus_plus(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,plus_plus(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,plus_plus(X0,X2,X1),X1) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0] : ( div_mod(X0,X11,X10) = div_mod(X0,plus_plus(X0,X11,X10),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_mod__add__self2) ).
tff(f794,plain,
spl1_55,
inference(avatar_split_clause,[],[f426,f792]) ).
tff(f426,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X10: X0,X11: X0] :
( ( plus_plus(X0,X11,X10) = plus_plus(X0,X11,X12) )
=> ( X10 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__left__imp__eq) ).
tff(f790,plain,
spl1_54,
inference(avatar_split_clause,[],[f425,f788]) ).
tff(f425,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X11: X0,X10: X0] :
( ( plus_plus(X0,X10,X11) = plus_plus(X0,X12,X11) )
=> ( X10 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__right__imp__eq) ).
tff(f786,plain,
( spl1_53
| ~ spl1_8
| ~ spl1_30 ),
inference(avatar_split_clause,[],[f689,f667,f562,f784]) ).
tff(f562,plain,
( spl1_8
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f667,plain,
( spl1_30
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f689,plain,
( ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 )
| ~ spl1_8
| ~ spl1_30 ),
inference(resolution,[],[f668,f564]) ).
tff(f564,plain,
( comm_monoid_add(int)
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f668,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_add(X0)
| ( plus_plus(X0,zero_zero(X0),X1) = X1 ) )
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f667]) ).
tff(f782,plain,
spl1_52,
inference(avatar_split_clause,[],[f394,f780]) ).
tff(f394,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X12: X0,X10: X0,X11: X0] :
( ( plus_plus(X0,X11,X10) = plus_plus(X0,X11,X12) )
=> ( X10 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__imp__eq) ).
tff(f772,plain,
spl1_51,
inference(avatar_split_clause,[],[f523,f770]) ).
tff(f523,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f496]) ).
tff(f496,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,[],[f235]) ).
tff(f235,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X0: $tType,X29: X0,X31: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X31),X29))
| ( X29 != X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f768,plain,
spl1_50,
inference(avatar_split_clause,[],[f455,f766]) ).
tff(f455,plain,
! [X0: $tType,X1: X0] :
( ( one_one(X0) = div_div(X0,X1,X1) )
| ( zero_zero(X0) = X1 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( one_one(X0) = div_div(X0,X1,X1) )
| ( zero_zero(X0) = X1 ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) != X1 )
=> ( one_one(X0) = div_div(X0,X1,X1) ) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] :
( ( zero_zero(X0) != X11 )
=> ( one_one(X0) = div_div(X0,X11,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_div__self) ).
tff(f764,plain,
spl1_49,
inference(avatar_split_clause,[],[f410,f762]) ).
tff(f410,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X13: X0] :
( ( zero_zero(X0) = plus_plus(X0,X13,X13) )
<=> ( zero_zero(X0) = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_double__zero__sym) ).
tff(f760,plain,
spl1_48,
inference(avatar_split_clause,[],[f409,f758]) ).
tff(f409,plain,
! [X0: $tType,X1: list(X0)] :
( ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X8: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X8) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_scale1) ).
tff(f755,plain,
( spl1_47
| ~ spl1_9
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f687,f659,f567,f753]) ).
tff(f567,plain,
( spl1_9
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f659,plain,
( spl1_28
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f687,plain,
( ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 )
| ~ spl1_9
| ~ spl1_28 ),
inference(resolution,[],[f660,f569]) ).
tff(f569,plain,
( monoid_add(int)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f660,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_add(X0)
| ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f659]) ).
tff(f747,plain,
spl1_46,
inference(avatar_split_clause,[],[f456,f745]) ).
tff(f456,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = div_div(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_div(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( zero_zero(X0) = div_div(X0,div_mod(X0,X2,X1),X1) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X10: X0,X11: X0] : ( div_div(X0,div_mod(X0,X11,X10),X10) = zero_zero(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_mod__div__trivial) ).
tff(f743,plain,
spl1_45,
inference(avatar_split_clause,[],[f408,f741]) ).
tff(f741,plain,
( spl1_45
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f408,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X11: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_mult__1__left) ).
tff(f739,plain,
spl1_44,
inference(avatar_split_clause,[],[f407,f737]) ).
tff(f737,plain,
( spl1_44
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f407,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X11: X0] : ( aa(X0,X0,times_times(X0,X11),one_one(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mult__1__right) ).
tff(f735,plain,
spl1_43,
inference(avatar_split_clause,[],[f400,f733]) ).
tff(f400,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X11: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_mult__1) ).
tff(f731,plain,
spl1_42,
inference(avatar_split_clause,[],[f399,f729]) ).
tff(f399,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X11: X0] : ( aa(X0,X0,times_times(X0,X11),one_one(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mult_Ocomm__neutral) ).
tff(f725,plain,
spl1_41,
inference(avatar_split_clause,[],[f515,f723]) ).
tff(f723,plain,
( spl1_41
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
tff(f515,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f411]) ).
tff(f411,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f344]) ).
tff(f717,plain,
spl1_40,
inference(avatar_split_clause,[],[f454,f715]) ).
tff(f715,plain,
( spl1_40
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
tff(f454,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( zero_zero(X0) = div_mod(X0,zero_zero(X0),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mod__0) ).
tff(f713,plain,
spl1_39,
inference(avatar_split_clause,[],[f453,f711]) ).
tff(f453,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,one_one(X0)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,one_one(X0)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,one_one(X0)) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( zero_zero(X0) = div_mod(X0,X11,one_one(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_mod__by__1) ).
tff(f709,plain,
spl1_38,
inference(avatar_split_clause,[],[f452,f707]) ).
tff(f707,plain,
( spl1_38
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_div(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
tff(f452,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_div(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_div(X0,zero_zero(X0),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_div(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( zero_zero(X0) = div_div(X0,zero_zero(X0),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_div__0) ).
tff(f705,plain,
spl1_37,
inference(avatar_split_clause,[],[f451,f703]) ).
tff(f451,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_div(X0,X1,zero_zero(X0)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_div(X0,X1,zero_zero(X0)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_div(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( zero_zero(X0) = div_div(X0,X11,zero_zero(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_div__by__0) ).
tff(f700,plain,
( spl1_35
| ~ spl1_36
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f637,f632,f697,f694]) ).
tff(f694,plain,
( spl1_35
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f697,plain,
( spl1_36
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f637,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl1_22 ),
inference(equality_factoring,[],[f633]) ).
tff(f686,plain,
spl1_34,
inference(avatar_split_clause,[],[f450,f684]) ).
tff(f450,plain,
! [X0: $tType,X1: X0] :
( ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: $tType] :
( ! [X1: X0] : ( div_mod(X0,X1,zero_zero(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( div_mod(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( div_mod(X0,X11,zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_mod__by__0) ).
tff(f682,plain,
spl1_33,
inference(avatar_split_clause,[],[f449,f680]) ).
tff(f449,plain,
! [X0: $tType,X1: X0] :
( ( div_div(X0,X1,one_one(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType] :
( ! [X1: X0] : ( div_div(X0,X1,one_one(X0)) = X1 )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( div_div(X0,X1,one_one(X0)) = X1 ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( div_div(X0,X11,one_one(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_div__by__1) ).
tff(f678,plain,
spl1_32,
inference(avatar_split_clause,[],[f448,f676]) ).
tff(f676,plain,
( spl1_32
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f448,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0] : ( zero_zero(X0) = div_mod(X0,X1,X1) ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X11: X0] : ( zero_zero(X0) = div_mod(X0,X11,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mod__self) ).
tff(f674,plain,
spl1_31,
inference(avatar_split_clause,[],[f398,f672]) ).
tff(f672,plain,
( spl1_31
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f398,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X11: X0] : ( plus_plus(X0,zero_zero(X0),X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__0__left) ).
tff(f669,plain,
spl1_30,
inference(avatar_split_clause,[],[f397,f667]) ).
tff(f397,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X11: X0] : ( plus_plus(X0,zero_zero(X0),X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__0) ).
tff(f665,plain,
spl1_29,
inference(avatar_split_clause,[],[f396,f663]) ).
tff(f663,plain,
( spl1_29
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f396,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X11: X0] : ( plus_plus(X0,X11,zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Ocomm__neutral) ).
tff(f661,plain,
spl1_28,
inference(avatar_split_clause,[],[f395,f659]) ).
tff(f395,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X11: X0] : ( plus_plus(X0,X11,zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__0__right) ).
tff(f657,plain,
spl1_27,
inference(avatar_split_clause,[],[f385,f655]) ).
tff(f655,plain,
( spl1_27
<=> ! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f385,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X0) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X10: int] : ( zero_zero(int) = div_mod(int,zero_zero(int),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zmod__zero) ).
tff(f653,plain,
spl1_26,
inference(avatar_split_clause,[],[f384,f651]) ).
tff(f651,plain,
( spl1_26
<=> ! [X0: int] : ( zero_zero(int) = div_div(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f384,plain,
! [X0: int] : ( zero_zero(int) = div_div(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: int] : ( zero_zero(int) = div_div(int,zero_zero(int),X0) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X10: int] : ( zero_zero(int) = div_div(int,zero_zero(int),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zdiv__zero) ).
tff(f649,plain,
spl1_25,
inference(avatar_split_clause,[],[f484,f647]) ).
tff(f484,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X28: fun(X0,bool)] : ( collect(X0,X28) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Collect__def) ).
tff(f645,plain,
( spl1_24
| spl1_1
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f636,f632,f527,f643]) ).
tff(f643,plain,
( spl1_24
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f527,plain,
( spl1_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f636,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl1_1
| ~ spl1_22 ),
inference(superposition,[],[f529,f633]) ).
tff(f529,plain,
( ~ pp(fFalse)
| spl1_1 ),
inference(avatar_component_clause,[],[f527]) ).
tff(f641,plain,
spl1_23,
inference(avatar_split_clause,[],[f383,f639]) ).
tff(f383,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: int] : ( zero_zero(int) = div_mod(int,X0,X0) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X11: int] : ( zero_zero(int) = div_mod(int,X11,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zmod__self) ).
tff(f634,plain,
spl1_22,
inference(avatar_split_clause,[],[f386,f632]) ).
tff(f386,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f126]) ).
tff(f126,axiom,
! [X38: bool] :
( ( fFalse = X38 )
| ( fTrue = X38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
tff(f630,plain,
spl1_21,
inference(avatar_split_clause,[],[f381,f627]) ).
tff(f381,plain,
pp(fTrue),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f625,plain,
spl1_20,
inference(avatar_split_clause,[],[f380,f622]) ).
tff(f380,plain,
semiring_div(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
semiring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f620,plain,
spl1_19,
inference(avatar_split_clause,[],[f379,f617]) ).
tff(f379,plain,
group_add(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
tff(f615,plain,
spl1_18,
inference(avatar_split_clause,[],[f378,f612]) ).
tff(f612,plain,
( spl1_18
<=> ordere236663937imp_le(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f378,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f610,plain,
spl1_17,
inference(avatar_split_clause,[],[f377,f607]) ).
tff(f377,plain,
ring_div(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
tff(f605,plain,
spl1_16,
inference(avatar_split_clause,[],[f376,f602]) ).
tff(f376,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(f600,plain,
spl1_15,
inference(avatar_split_clause,[],[f375,f597]) ).
tff(f597,plain,
( spl1_15
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f375,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f595,plain,
spl1_14,
inference(avatar_split_clause,[],[f374,f592]) ).
tff(f592,plain,
( spl1_14
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f374,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(f590,plain,
spl1_13,
inference(avatar_split_clause,[],[f373,f587]) ).
tff(f373,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f585,plain,
spl1_12,
inference(avatar_split_clause,[],[f372,f582]) ).
tff(f582,plain,
( spl1_12
<=> ordere223160158up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f372,plain,
ordere223160158up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
ordere223160158up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
tff(f580,plain,
spl1_11,
inference(avatar_split_clause,[],[f371,f577]) ).
tff(f577,plain,
( spl1_11
<=> ordered_ab_group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f371,plain,
ordered_ab_group_add(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
ordered_ab_group_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
tff(f575,plain,
spl1_10,
inference(avatar_split_clause,[],[f370,f572]) ).
tff(f572,plain,
( spl1_10
<=> ordere216010020id_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f370,plain,
ordere216010020id_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
ordere216010020id_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
tff(f570,plain,
spl1_9,
inference(avatar_split_clause,[],[f369,f567]) ).
tff(f369,plain,
monoid_add(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f565,plain,
spl1_8,
inference(avatar_split_clause,[],[f368,f562]) ).
tff(f368,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f560,plain,
spl1_7,
inference(avatar_split_clause,[],[f367,f557]) ).
tff(f367,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
tff(f555,plain,
spl1_6,
inference(avatar_split_clause,[],[f366,f552]) ).
tff(f552,plain,
( spl1_6
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f366,plain,
zero(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f550,plain,
spl1_5,
inference(avatar_split_clause,[],[f365,f547]) ).
tff(f547,plain,
( spl1_5
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f365,plain,
one(int),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f545,plain,
spl1_4,
inference(avatar_split_clause,[],[f364,f542]) ).
tff(f364,plain,
ab_semigroup_mult(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
tff(f540,plain,
spl1_3,
inference(avatar_split_clause,[],[f363,f537]) ).
tff(f363,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f535,plain,
spl1_2,
inference(avatar_split_clause,[],[f362,f532]) ).
tff(f532,plain,
( spl1_2
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f362,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f530,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f360,f527]) ).
tff(f360,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f130]) ).
tff(f130,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM069_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:10:55 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (21824)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (21827)WARNING: value z3 for option sas not known
% 0.14/0.39 % (21828)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (21826)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (21827)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)
% 0.14/0.39 % (21829)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)
% 0.14/0.39 % (21825)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (21830)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)
% 0.14/0.39 % (21831)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)
% 0.14/0.40 % (21831)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % Exception at run slice level% Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41 % (21832)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.41 % (21833)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)
% 0.20/0.42 % (21834)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)
% 0.20/0.42 % (21833)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % (21832)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44 % (21835)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)
% 0.20/0.58 % (21829)First to succeed.
% 1.63/0.60 % (21829)Refutation found. Thanks to Tanya!
% 1.63/0.60 % SZS status Theorem for theBenchmark
% 1.63/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.63/0.61 % (21829)------------------------------
% 1.63/0.61 % (21829)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.63/0.61 % (21829)Termination reason: Refutation
% 1.63/0.61
% 1.63/0.61 % (21829)Memory used [KB]: 3727
% 1.63/0.61 % (21829)Time elapsed: 0.207 s
% 1.63/0.61 % (21829)Instructions burned: 527 (million)
% 1.63/0.61 % (21829)------------------------------
% 1.63/0.61 % (21829)------------------------------
% 1.63/0.61 % (21824)Success in time 0.232 s
%------------------------------------------------------------------------------