TSTP Solution File: LCL809_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL809_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:35 EDT 2024
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 345
% Syntax : Number of formulae : 967 ( 311 unt; 69 typ; 0 def)
% Number of atoms : 2039 ( 686 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1923 ( 782 ~; 781 |; 103 &)
% ( 206 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 61 ( 41 >; 20 *; 0 +; 0 <<)
% Number of predicates : 183 ( 181 usr; 174 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 15 con; 0-5 aty)
% Number of variables : 1562 (1473 !; 57 ?;1562 :)
% ( 32 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
char1: $tType ).
tff(type_def_10,type,
literal: $tType ).
tff(type_def_11,type,
nibble: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
bool_size: bool > nat ).
tff(func_def_8,type,
it: fun(dB,bool) ).
tff(func_def_9,type,
abs: dB > dB ).
tff(func_def_10,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_11,type,
var: nat > dB ).
tff(func_def_12,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_13,type,
dB_size: dB > nat ).
tff(func_def_14,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_15,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_16,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_17,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_18,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_19,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_20,type,
monoid_add_listsum:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_21,type,
suc: nat > nat ).
tff(func_def_22,type,
nat_size: nat > nat ).
tff(func_def_23,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_24,type,
char: ( nibble * nibble ) > char1 ).
tff(func_def_25,type,
char_case:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_26,type,
char_rec:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char1 ) > X0 ) ).
tff(func_def_27,type,
char_size: char1 > nat ).
tff(func_def_28,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_29,type,
fFalse: bool ).
tff(func_def_30,type,
fTrue: bool ).
tff(func_def_31,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
a: dB ).
tff(func_def_33,type,
b: dB ).
tff(func_def_34,type,
bs: list(dB) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
n: nat ).
tff(func_def_37,type,
t: dB ).
tff(func_def_38,type,
u: dB ).
tff(func_def_39,type,
ua: dB ).
tff(func_def_40,type,
sK2: nat > nat ).
tff(func_def_41,type,
sK3: nat > nat ).
tff(func_def_42,type,
sK4: dB > dB ).
tff(func_def_43,type,
sK5: dB > list(dB) ).
tff(func_def_44,type,
sK6: dB > nat ).
tff(func_def_45,type,
sK7: dB > dB ).
tff(func_def_46,type,
sK8: dB > dB ).
tff(func_def_47,type,
sK9: dB > list(dB) ).
tff(func_def_48,type,
sK10: char1 > nibble ).
tff(func_def_49,type,
sK11: char1 > nibble ).
tff(func_def_50,type,
sK12: fun(nat,bool) > nat ).
tff(func_def_51,type,
sK13: fun(nat,bool) > nat ).
tff(func_def_52,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_7,type,
sP0: dB > $o ).
tff(pred_def_8,type,
sP1: dB > $o ).
tff(f1714,plain,
$false,
inference(avatar_sat_refutation,[],[f516,f521,f526,f531,f536,f540,f544,f549,f555,f559,f563,f567,f573,f577,f582,f587,f592,f596,f601,f606,f611,f616,f621,f634,f638,f642,f646,f650,f654,f658,f662,f666,f671,f678,f682,f686,f690,f694,f698,f702,f706,f714,f731,f739,f746,f751,f755,f759,f763,f768,f773,f779,f794,f799,f803,f807,f812,f824,f828,f832,f837,f848,f853,f857,f862,f867,f873,f879,f889,f893,f897,f901,f934,f938,f942,f968,f972,f976,f980,f991,f995,f999,f1003,f1008,f1015,f1020,f1026,f1030,f1060,f1064,f1068,f1072,f1077,f1084,f1088,f1092,f1100,f1110,f1114,f1118,f1122,f1133,f1137,f1141,f1145,f1151,f1155,f1159,f1163,f1171,f1175,f1183,f1188,f1198,f1202,f1215,f1220,f1225,f1229,f1241,f1245,f1250,f1255,f1260,f1268,f1295,f1300,f1308,f1314,f1318,f1323,f1327,f1332,f1338,f1360,f1364,f1368,f1410,f1433,f1438,f1443,f1447,f1453,f1461,f1466,f1473,f1478,f1499,f1507,f1514,f1520,f1527,f1560,f1566,f1570,f1576,f1580,f1588,f1596,f1604,f1608,f1625,f1632,f1640,f1647,f1655,f1661,f1671,f1681,f1688,f1696,f1709,f1713]) ).
tff(f1713,plain,
( ~ spl15_135
| spl15_45
| ~ spl15_125 ),
inference(avatar_split_clause,[],[f1261,f1258,f736,f1335]) ).
tff(f1335,plain,
( spl15_135
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_135])]) ).
tff(f736,plain,
( spl15_45
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
tff(f1258,plain,
( spl15_125
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_125])]) ).
tff(f1261,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u)))
| spl15_45
| ~ spl15_125 ),
inference(resolution,[],[f1259,f738]) ).
tff(f738,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))))
| spl15_45 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f1259,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_125 ),
inference(avatar_component_clause,[],[f1258]) ).
tff(f1709,plain,
spl15_173,
inference(avatar_split_clause,[],[f431,f1707]) ).
tff(f1707,plain,
( spl15_173
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_173])]) ).
tff(f431,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X40: list(X2),X50: fun(X2,X1),X51: X0,X52: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X52,X51,map(X2,X1,X50,X40)) = foldl(X0,X2,combc(X0,fun(X2,X1),fun(X2,X0),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X52),X50),X51,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_foldl__map) ).
tff(f1696,plain,
( spl15_172
| ~ spl15_126
| ~ spl15_171 ),
inference(avatar_split_clause,[],[f1692,f1686,f1266,f1694]) ).
tff(f1694,plain,
( spl15_172
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_172])]) ).
tff(f1266,plain,
( spl15_126
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_126])]) ).
tff(f1686,plain,
( spl15_171
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_171])]) ).
tff(f1692,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl15_126
| ~ spl15_171 ),
inference(forward_demodulation,[],[f1691,f1267]) ).
tff(f1267,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl15_126 ),
inference(avatar_component_clause,[],[f1266]) ).
tff(f1691,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl15_126
| ~ spl15_171 ),
inference(forward_demodulation,[],[f1690,f1267]) ).
tff(f1690,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl15_126
| ~ spl15_171 ),
inference(forward_demodulation,[],[f1689,f1267]) ).
tff(f1689,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),X1)) )
| ~ spl15_126
| ~ spl15_171 ),
inference(forward_demodulation,[],[f1687,f1267]) ).
tff(f1687,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) )
| ~ spl15_171 ),
inference(avatar_component_clause,[],[f1686]) ).
tff(f1688,plain,
spl15_171,
inference(avatar_split_clause,[],[f408,f1686]) ).
tff(f408,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X7: nat,X6: dB,X18: dB,X5: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,X5),X18)),X6),X7) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X6),X7)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X18),X6),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_subst__App) ).
tff(f1681,plain,
( spl15_170
| ~ spl15_13
| ~ spl15_126
| ~ spl15_169 ),
inference(avatar_split_clause,[],[f1676,f1668,f1266,f570,f1678]) ).
tff(f1678,plain,
( spl15_170
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(bool_size(fFalse))),aa(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),u))),bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_170])]) ).
tff(f570,plain,
( spl15_13
<=> ( bool_size(fTrue) = bool_size(fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
tff(f1668,plain,
( spl15_169
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fTrue))),var(bool_size(fTrue)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)),bool_size(fTrue)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_169])]) ).
tff(f1676,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(bool_size(fFalse))),aa(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),u))),bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u))))
| ~ spl15_13
| ~ spl15_126
| ~ spl15_169 ),
inference(forward_demodulation,[],[f1675,f1267]) ).
tff(f1675,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(bool_size(fFalse))),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fFalse)))),bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u))))
| ~ spl15_13
| ~ spl15_126
| ~ spl15_169 ),
inference(forward_demodulation,[],[f1674,f1267]) ).
tff(f1674,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fFalse))),var(bool_size(fFalse)))),bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u))))
| ~ spl15_13
| ~ spl15_126
| ~ spl15_169 ),
inference(forward_demodulation,[],[f1673,f572]) ).
tff(f572,plain,
( ( bool_size(fTrue) = bool_size(fFalse) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f570]) ).
tff(f1673,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fTrue))),var(bool_size(fTrue)))),bool_size(fTrue)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u))))
| ~ spl15_126
| ~ spl15_169 ),
inference(forward_demodulation,[],[f1672,f1267]) ).
tff(f1672,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fTrue))),var(bool_size(fTrue)))),bool_size(fTrue)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n))))
| ~ spl15_126
| ~ spl15_169 ),
inference(forward_demodulation,[],[f1670,f1267]) ).
tff(f1670,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fTrue))),var(bool_size(fTrue)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)),bool_size(fTrue))))
| ~ spl15_169 ),
inference(avatar_component_clause,[],[f1668]) ).
tff(f1671,plain,
spl15_169,
inference(avatar_split_clause,[],[f468,f1668]) ).
tff(f468,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),bool_size(fTrue))),var(bool_size(fTrue)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)),bool_size(fTrue)))),
inference(forward_demodulation,[],[f436,f291]) ).
tff(f291,plain,
zero_zero(nat) = bool_size(fTrue),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
zero_zero(nat) = bool_size(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_bool_Osize_I1_J) ).
tff(f436,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)),zero_zero(nat)))),
inference(definition_unfolding,[],[f303,f290]) ).
tff(f290,plain,
i = n,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
i = n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True) ).
tff(f303,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f1661,plain,
( spl15_168
| ~ spl15_126
| ~ spl15_167 ),
inference(avatar_split_clause,[],[f1657,f1653,f1266,f1659]) ).
tff(f1659,plain,
( spl15_168
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_168])]) ).
tff(f1653,plain,
( spl15_167
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_167])]) ).
tff(f1657,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl15_126
| ~ spl15_167 ),
inference(forward_demodulation,[],[f1656,f1267]) ).
tff(f1656,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl15_126
| ~ spl15_167 ),
inference(forward_demodulation,[],[f1654,f1267]) ).
tff(f1654,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) )
| ~ spl15_167 ),
inference(avatar_component_clause,[],[f1653]) ).
tff(f1655,plain,
spl15_167,
inference(avatar_split_clause,[],[f407,f1653]) ).
tff(f407,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X43: nat,X45: dB,X22: list(dB),X44: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X44,X22)),X45),X43) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X44),X45),X43),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X45),X43),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_subst__map) ).
tff(f1647,plain,
( spl15_166
| ~ spl15_13
| ~ spl15_126
| ~ spl15_165 ),
inference(avatar_split_clause,[],[f1643,f1638,f1266,f570,f1645]) ).
tff(f1645,plain,
( spl15_166
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),bool_size(fFalse)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_166])]) ).
tff(f1638,plain,
( spl15_165
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),bool_size(fTrue)),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_165])]) ).
tff(f1643,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),bool_size(fFalse)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_13
| ~ spl15_126
| ~ spl15_165 ),
inference(forward_demodulation,[],[f1642,f1267]) ).
tff(f1642,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),bool_size(fFalse)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_13
| ~ spl15_126
| ~ spl15_165 ),
inference(forward_demodulation,[],[f1641,f572]) ).
tff(f1641,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),bool_size(fTrue)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_126
| ~ spl15_165 ),
inference(forward_demodulation,[],[f1639,f1267]) ).
tff(f1639,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),bool_size(fTrue)),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_165 ),
inference(avatar_component_clause,[],[f1638]) ).
tff(f1640,plain,
spl15_165,
inference(avatar_split_clause,[],[f508,f1638]) ).
tff(f508,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),bool_size(fTrue)),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(forward_demodulation,[],[f393,f291]) ).
tff(f393,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f232]) ).
tff(f232,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0)))
=> ( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X48: list(dB),X46: dB,X47: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X47),X46),zero_zero(nat)),X48)))
=> ( pp(aa(dB,bool,it,X46))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X47)),X46),X48))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Beta) ).
tff(f1632,plain,
( spl15_164
| ~ spl15_13
| ~ spl15_126
| ~ spl15_163 ),
inference(avatar_split_clause,[],[f1628,f1623,f1266,f570,f1630]) ).
tff(f1630,plain,
( spl15_164
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),bool_size(fFalse)),X2),X3)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_164])]) ).
tff(f1623,plain,
( spl15_163
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),bool_size(fTrue)),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_163])]) ).
tff(f1628,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),bool_size(fFalse)),X2),X3)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_13
| ~ spl15_126
| ~ spl15_163 ),
inference(forward_demodulation,[],[f1627,f1267]) ).
tff(f1627,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),bool_size(fFalse)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_13
| ~ spl15_126
| ~ spl15_163 ),
inference(forward_demodulation,[],[f1626,f572]) ).
tff(f1626,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),bool_size(fTrue)),X2),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_126
| ~ spl15_163 ),
inference(forward_demodulation,[],[f1624,f1267]) ).
tff(f1624,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),bool_size(fTrue)),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_163 ),
inference(avatar_component_clause,[],[f1623]) ).
tff(f1625,plain,
spl15_163,
inference(avatar_split_clause,[],[f488,f1623]) ).
tff(f488,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),bool_size(fTrue)),X3)))
| sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(forward_demodulation,[],[f446,f291]) ).
tff(f446,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f345]) ).
tff(f345,plain,
! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f252,f253]) ).
tff(f253,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f252,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f251]) ).
tff(f251,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1608,plain,
( spl15_162
| ~ spl15_37
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f783,f757,f688,f1606]) ).
tff(f1606,plain,
( spl15_162
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_162])]) ).
tff(f688,plain,
( spl15_37
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
tff(f757,plain,
( spl15_49
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
tff(f783,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl15_37
| ~ spl15_49 ),
inference(resolution,[],[f758,f689]) ).
tff(f689,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl15_37 ),
inference(avatar_component_clause,[],[f688]) ).
tff(f758,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl15_49 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f1604,plain,
( spl15_161
| ~ spl15_126
| ~ spl15_160 ),
inference(avatar_split_clause,[],[f1600,f1594,f1266,f1602]) ).
tff(f1602,plain,
( spl15_161
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_161])]) ).
tff(f1594,plain,
( spl15_160
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_160])]) ).
tff(f1600,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) )
| ~ spl15_126
| ~ spl15_160 ),
inference(forward_demodulation,[],[f1599,f1267]) ).
tff(f1599,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )
| ~ spl15_126
| ~ spl15_160 ),
inference(forward_demodulation,[],[f1598,f1267]) ).
tff(f1598,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl15_126
| ~ spl15_160 ),
inference(forward_demodulation,[],[f1597,f1267]) ).
tff(f1597,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl15_126
| ~ spl15_160 ),
inference(forward_demodulation,[],[f1595,f1267]) ).
tff(f1595,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) )
| ~ spl15_160 ),
inference(avatar_component_clause,[],[f1594]) ).
tff(f1596,plain,
spl15_160,
inference(avatar_split_clause,[],[f391,f1594]) ).
tff(f391,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X7: nat,X5: dB,X6: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X6),X5)),X7) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X6),X7)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X5),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_lift_Osimps_I2_J) ).
tff(f1588,plain,
spl15_159,
inference(avatar_split_clause,[],[f424,f1586]) ).
tff(f1586,plain,
( spl15_159
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_159])]) ).
tff(f424,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ) ),
inference(flattening,[],[f280]) ).
tff(f280,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) )
& ( ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) )
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ) ),
inference(nnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X24: fun(X0,bool),X25: fun(X0,bool),X26: list(X0)] :
( listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X25),X24),X26)
<=> ( listsp(X0,X24,X26)
& listsp(X0,X25,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_listsp__conj__eq) ).
tff(f1580,plain,
spl15_158,
inference(avatar_split_clause,[],[f423,f1578]) ).
tff(f1578,plain,
( spl15_158
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_158])]) ).
tff(f423,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1576,plain,
spl15_157,
inference(avatar_split_clause,[],[f422,f1574]) ).
tff(f1574,plain,
( spl15_157
<=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_157])]) ).
tff(f422,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1570,plain,
( spl15_156
| ~ spl15_126
| ~ spl15_154 ),
inference(avatar_split_clause,[],[f1562,f1558,f1266,f1568]) ).
tff(f1568,plain,
( spl15_156
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_156])]) ).
tff(f1558,plain,
( spl15_154
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_154])]) ).
tff(f1562,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) = aa(dB,dB,combc(dB,nat,dB,lift,X0),foldl(dB,dB,app,X2,X1)) )
| ~ spl15_126
| ~ spl15_154 ),
inference(forward_demodulation,[],[f1561,f1267]) ).
tff(f1561,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl15_126
| ~ spl15_154 ),
inference(forward_demodulation,[],[f1559,f1267]) ).
tff(f1559,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl15_154 ),
inference(avatar_component_clause,[],[f1558]) ).
tff(f1566,plain,
( spl15_155
| ~ spl15_36
| ~ spl15_46 ),
inference(avatar_split_clause,[],[f781,f744,f684,f1564]) ).
tff(f1564,plain,
( spl15_155
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_155])]) ).
tff(f684,plain,
( spl15_36
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
tff(f744,plain,
( spl15_46
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).
tff(f781,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK8(X0)) )
| ~ spl15_36
| ~ spl15_46 ),
inference(resolution,[],[f745,f685]) ).
tff(f685,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl15_36 ),
inference(avatar_component_clause,[],[f684]) ).
tff(f745,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) )
| ~ spl15_46 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f1560,plain,
spl15_154,
inference(avatar_split_clause,[],[f390,f1558]) ).
tff(f390,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X43: nat,X22: list(dB),X44: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X44,X22)),X43) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X44),X43),map(dB,dB,combc(dB,nat,dB,lift,X43),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_lift__map) ).
tff(f1527,plain,
spl15_153,
inference(avatar_split_clause,[],[f430,f1525]) ).
tff(f1525,plain,
( spl15_153
<=> ! [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,[spl15_153])]) ).
tff(f430,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,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X75: X0,X76: fun(X0,X1),X77: 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),X77),X76),X75) = aa(X1,X2,X77,aa(X0,X1,X76,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1520,plain,
( spl15_152
| ~ spl15_13
| ~ spl15_126
| ~ spl15_151 ),
inference(avatar_split_clause,[],[f1516,f1512,f1266,f570,f1518]) ).
tff(f1518,plain,
( spl15_152
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),bool_size(fFalse)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_152])]) ).
tff(f1512,plain,
( spl15_151
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),bool_size(fTrue)),sK9(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_151])]) ).
tff(f1516,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),bool_size(fFalse)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl15_13
| ~ spl15_126
| ~ spl15_151 ),
inference(forward_demodulation,[],[f1515,f572]) ).
tff(f1515,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),bool_size(fTrue)),sK8(X0)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl15_126
| ~ spl15_151 ),
inference(forward_demodulation,[],[f1513,f1267]) ).
tff(f1513,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),bool_size(fTrue)),sK9(X0))))
| ~ sP0(X0) )
| ~ spl15_151 ),
inference(avatar_component_clause,[],[f1512]) ).
tff(f1514,plain,
spl15_151,
inference(avatar_split_clause,[],[f489,f1512]) ).
tff(f489,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),bool_size(fTrue)),sK9(X0))))
| ~ sP0(X0) ),
inference(forward_demodulation,[],[f343,f291]) ).
tff(f343,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f1507,plain,
( spl15_150
| ~ spl15_126
| ~ spl15_138
| ~ spl15_149 ),
inference(avatar_split_clause,[],[f1502,f1496,f1366,f1266,f1504]) ).
tff(f1504,plain,
( spl15_150
<=> pp(aa(dB,bool,it,aa(dB,dB,combs(dB,dB,dB,app,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_150])]) ).
tff(f1366,plain,
( spl15_138
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(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,[spl15_138])]) ).
tff(f1496,plain,
( spl15_149
<=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_149])]) ).
tff(f1502,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combs(dB,dB,dB,app,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n)),u)))
| ~ spl15_126
| ~ spl15_138
| ~ spl15_149 ),
inference(forward_demodulation,[],[f1501,f1391]) ).
tff(f1391,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2,X5: fun(X2,X0)] : ( aa(X2,X1,combs(X2,X0,X1,X3,X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) )
| ~ spl15_126
| ~ spl15_138 ),
inference(superposition,[],[f1367,f1267]) ).
tff(f1367,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl15_138 ),
inference(avatar_component_clause,[],[f1366]) ).
tff(f1501,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),n),u)),u)))
| ~ spl15_126
| ~ spl15_149 ),
inference(forward_demodulation,[],[f1500,f1267]) ).
tff(f1500,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)),u)))
| ~ spl15_126
| ~ spl15_149 ),
inference(forward_demodulation,[],[f1498,f1267]) ).
tff(f1498,plain,
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n))))
| ~ spl15_149 ),
inference(avatar_component_clause,[],[f1496]) ).
tff(f1499,plain,
spl15_149,
inference(avatar_split_clause,[],[f435,f1496]) ).
tff(f435,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),n)))),
inference(definition_unfolding,[],[f302,f290]) ).
tff(f302,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,u),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f1478,plain,
( spl15_148
| ~ spl15_126
| ~ spl15_147 ),
inference(avatar_split_clause,[],[f1474,f1471,f1266,f1476]) ).
tff(f1476,plain,
( spl15_148
<=> ! [X0: nat,X3: nat,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) = liftn(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_148])]) ).
tff(f1471,plain,
( spl15_147
<=> ! [X0: nat,X3: nat,X2: dB,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_147])]) ).
tff(f1474,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) = liftn(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0) )
| ~ spl15_126
| ~ spl15_147 ),
inference(forward_demodulation,[],[f1472,f1267]) ).
tff(f1472,plain,
( ! [X2: dB,X3: nat,X0: nat,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) )
| ~ spl15_147 ),
inference(avatar_component_clause,[],[f1471]) ).
tff(f1473,plain,
spl15_147,
inference(avatar_split_clause,[],[f406,f1471]) ).
tff(f406,plain,
! [X2: dB,X3: nat,X0: nat,X1: dB] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: nat,X1: dB,X2: dB,X3: nat] : ( liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X7: nat,X5: dB,X6: dB,X23: nat] : ( liftn(X23,aa(dB,dB,aa(dB,fun(dB,dB),app,X6),X5),X7) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X23,X6,X7)),liftn(X23,X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_liftn_Osimps_I2_J) ).
tff(f1466,plain,
( spl15_146
| ~ spl15_126
| ~ spl15_145 ),
inference(avatar_split_clause,[],[f1462,f1459,f1266,f1464]) ).
tff(f1464,plain,
( spl15_146
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_146])]) ).
tff(f1459,plain,
( spl15_145
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_145])]) ).
tff(f1462,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_126
| ~ spl15_145 ),
inference(forward_demodulation,[],[f1460,f1267]) ).
tff(f1460,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl15_145 ),
inference(avatar_component_clause,[],[f1459]) ).
tff(f1461,plain,
spl15_145,
inference(avatar_split_clause,[],[f392,f1459]) ).
tff(f392,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X9: nat,X4: nat,X10: dB] :
( pp(aa(dB,bool,it,X10))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X10),var(X4)),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_subst__Var__IT) ).
tff(f1453,plain,
( spl15_144
| ~ spl15_126
| ~ spl15_143 ),
inference(avatar_split_clause,[],[f1449,f1445,f1266,f1451]) ).
tff(f1451,plain,
( spl15_144
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_144])]) ).
tff(f1445,plain,
( spl15_143
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_143])]) ).
tff(f1449,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl15_126
| ~ spl15_143 ),
inference(forward_demodulation,[],[f1448,f1267]) ).
tff(f1448,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl15_126
| ~ spl15_143 ),
inference(forward_demodulation,[],[f1446,f1267]) ).
tff(f1446,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl15_143 ),
inference(avatar_component_clause,[],[f1445]) ).
tff(f1447,plain,
spl15_143,
inference(avatar_split_clause,[],[f389,f1445]) ).
tff(f389,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: dB,X7: nat,X5: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X5),X7)),X6),X7) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subst__lift) ).
tff(f1443,plain,
( spl15_142
| ~ spl15_13
| ~ spl15_140 ),
inference(avatar_split_clause,[],[f1434,f1430,f570,f1440]) ).
tff(f1440,plain,
( spl15_142
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_142])]) ).
tff(f1430,plain,
( spl15_140
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_140])]) ).
tff(f1434,plain,
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs)))
| ~ spl15_13
| ~ spl15_140 ),
inference(forward_demodulation,[],[f1432,f572]) ).
tff(f1432,plain,
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs)))
| ~ spl15_140 ),
inference(avatar_component_clause,[],[f1430]) ).
tff(f1438,plain,
( spl15_141
| ~ spl15_30
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f784,f757,f656,f1436]) ).
tff(f1436,plain,
( spl15_141
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_141])]) ).
tff(f656,plain,
( spl15_30
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
tff(f784,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl15_30
| ~ spl15_49 ),
inference(resolution,[],[f758,f657]) ).
tff(f657,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f1433,plain,
spl15_140,
inference(avatar_split_clause,[],[f467,f1430]) ).
tff(f467,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs))),
inference(forward_demodulation,[],[f434,f291]) ).
tff(f434,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),n),bs))),
inference(definition_unfolding,[],[f301,f290]) ).
tff(f301,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),bs))),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),bs))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Cons_I3_J) ).
tff(f1410,plain,
spl15_139,
inference(avatar_split_clause,[],[f511,f1408]) ).
tff(f1408,plain,
( spl15_139
<=> ! [X0: $tType,X5: fun(nat,X0),X4: fun(dB,fun(dB,X0)),X3: fun(dB,X0),X2: dB,X1: dB] : ( aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1) = dB_case(X0,X5,X4,X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_139])]) ).
tff(f511,plain,
! [X0: $tType,X2: dB,X3: fun(dB,X0),X1: dB,X4: fun(dB,fun(dB,X0)),X5: fun(nat,X0)] : ( aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1) = dB_case(X0,X5,X4,X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)) ),
inference(forward_demodulation,[],[f429,f427]) ).
tff(f427,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X75: X0,X76: X1,X77: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X77,X76),X75) = aa(X1,X2,aa(X0,fun(X1,X2),X77,X75),X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f429,plain,
! [X0: $tType,X2: dB,X3: fun(dB,X0),X1: dB,X4: fun(dB,fun(dB,X0)),X5: fun(nat,X0)] : ( dB_case(X0,X5,X4,X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) = aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: dB,X2: dB,X3: fun(dB,X0),X4: fun(dB,fun(dB,X0)),X5: fun(nat,X0)] : ( dB_case(X0,X5,X4,X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) = aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X14: dB,X15: dB,X28: fun(dB,X0),X29: fun(dB,fun(dB,X0)),X30: fun(nat,X0)] : ( dB_case(X0,X30,X29,X28,aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X14)) = aa(dB,X0,aa(dB,fun(dB,X0),X29,X15),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dB_Osimps_I11_J) ).
tff(f1368,plain,
spl15_138,
inference(avatar_split_clause,[],[f428,f1366]) ).
tff(f428,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(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,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X75: X0,X76: fun(X0,X1),X77: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X77,X76),X75) = aa(X1,X2,aa(X0,fun(X1,X2),X77,X75),aa(X0,X1,X76,X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1364,plain,
spl15_137,
inference(avatar_split_clause,[],[f420,f1362]) ).
tff(f1362,plain,
( spl15_137
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_137])]) ).
tff(f420,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X12: dB,X13: dB,X14: dB,X15: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X14) = aa(dB,dB,aa(dB,fun(dB,dB),app,X13),X12) )
<=> ( ( X12 = X14 )
& ( X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dB_Osimps_I2_J) ).
tff(f1360,plain,
spl15_136,
inference(avatar_split_clause,[],[f419,f1358]) ).
tff(f1358,plain,
( spl15_136
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_136])]) ).
tff(f419,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f279]) ).
tff(f1338,plain,
( spl15_135
| ~ spl15_126
| ~ spl15_134 ),
inference(avatar_split_clause,[],[f1333,f1329,f1266,f1335]) ).
tff(f1329,plain,
( spl15_134
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_134])]) ).
tff(f1333,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u)))
| ~ spl15_126
| ~ spl15_134 ),
inference(forward_demodulation,[],[f1331,f1267]) ).
tff(f1331,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)))
| ~ spl15_134 ),
inference(avatar_component_clause,[],[f1329]) ).
tff(f1332,plain,
spl15_134,
inference(avatar_split_clause,[],[f433,f1329]) ).
tff(f433,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))),
inference(definition_unfolding,[],[f300,f290]) ).
tff(f300,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096IT_A_Ib_091u_Pi_093_J_096) ).
tff(f1327,plain,
spl15_133,
inference(avatar_split_clause,[],[f409,f1325]) ).
tff(f1325,plain,
( spl15_133
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK14(X0,X1,X2,X3)) != aa(X1,X0,X2,sK14(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_133])]) ).
tff(f409,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK14(X0,X1,X2,X3)) != aa(X1,X0,X2,sK14(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK14(X0,X1,X2,X3)) != aa(X1,X0,X2,sK14(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f234,f270]) ).
tff(f270,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,sK14(X0,X1,X2,X3)) != aa(X1,X0,X2,sK14(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f234,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,[],[f200]) ).
tff(f200,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,X52: fun(X0,X1),X50: fun(X0,X1)] :
( ! [X59: X0] : ( aa(X0,X1,X50,X59) = aa(X0,X1,X52,X59) )
=> ( X50 = X52 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ext) ).
tff(f1323,plain,
( spl15_132
| ~ spl15_126
| ~ spl15_131 ),
inference(avatar_split_clause,[],[f1319,f1316,f1266,f1321]) ).
tff(f1321,plain,
( spl15_132
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_132])]) ).
tff(f1316,plain,
( spl15_131
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_131])]) ).
tff(f1319,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK8(X0)),abs(sK7(X0))),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl15_126
| ~ spl15_131 ),
inference(forward_demodulation,[],[f1317,f1267]) ).
tff(f1317,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl15_131 ),
inference(avatar_component_clause,[],[f1316]) ).
tff(f1318,plain,
spl15_131,
inference(avatar_split_clause,[],[f342,f1316]) ).
tff(f342,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f1314,plain,
( spl15_130
| ~ spl15_69
| ~ spl15_126
| ~ spl15_129 ),
inference(avatar_split_clause,[],[f1310,f1306,f1266,f877,f1312]) ).
tff(f1312,plain,
( spl15_130
<=> ! [X0: dB,X1: dB] : ( plus_plus(nat,size_size(dB,X1),suc(size_size(dB,X0))) = size_size(dB,aa(dB,dB,combc(dB,dB,dB,app,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_130])]) ).
tff(f877,plain,
( spl15_69
<=> ! [X0: nat,X1: nat] : ( plus_plus(nat,suc(X1),X0) = plus_plus(nat,X1,suc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_69])]) ).
tff(f1306,plain,
( spl15_129
<=> ! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(size_size(dB,X1)),size_size(dB,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_129])]) ).
tff(f1310,plain,
( ! [X0: dB,X1: dB] : ( plus_plus(nat,size_size(dB,X1),suc(size_size(dB,X0))) = size_size(dB,aa(dB,dB,combc(dB,dB,dB,app,X0),X1)) )
| ~ spl15_69
| ~ spl15_126
| ~ spl15_129 ),
inference(forward_demodulation,[],[f1309,f1267]) ).
tff(f1309,plain,
( ! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,size_size(dB,X1),suc(size_size(dB,X0))) )
| ~ spl15_69
| ~ spl15_129 ),
inference(forward_demodulation,[],[f1307,f878]) ).
tff(f878,plain,
( ! [X0: nat,X1: nat] : ( plus_plus(nat,suc(X1),X0) = plus_plus(nat,X1,suc(X0)) )
| ~ spl15_69 ),
inference(avatar_component_clause,[],[f877]) ).
tff(f1307,plain,
( ! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(size_size(dB,X1)),size_size(dB,X0)) )
| ~ spl15_129 ),
inference(avatar_component_clause,[],[f1306]) ).
tff(f1308,plain,
spl15_129,
inference(avatar_split_clause,[],[f498,f1306]) ).
tff(f498,plain,
! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(size_size(dB,X1)),size_size(dB,X0)) ),
inference(forward_demodulation,[],[f497,f356]) ).
tff(f356,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X23: nat,X60: nat] : ( suc(plus_plus(nat,X60,X23)) = plus_plus(nat,suc(X60),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__Suc) ).
tff(f497,plain,
! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = suc(plus_plus(nat,size_size(dB,X1),size_size(dB,X0))) ),
inference(forward_demodulation,[],[f496,f484]) ).
tff(f484,plain,
! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f483,f313]) ).
tff(f313,plain,
! [X0: nat] : ( size_size(nat,X0) = X0 ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: nat] : ( size_size(nat,X0) = X0 ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X23: nat] : ( size_size(nat,X23) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat__size) ).
tff(f483,plain,
! [X0: nat] : ( size_size(nat,suc(X0)) = plus_plus(nat,X0,suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f482,f313]) ).
tff(f482,plain,
! [X0: nat] : ( size_size(nat,suc(X0)) = plus_plus(nat,size_size(nat,X0),suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f322,f291]) ).
tff(f322,plain,
! [X0: nat] : ( size_size(nat,suc(X0)) = plus_plus(nat,size_size(nat,X0),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat] : ( size_size(nat,suc(X0)) = plus_plus(nat,size_size(nat,X0),suc(zero_zero(nat))) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X21: nat] : ( size_size(nat,suc(X21)) = plus_plus(nat,size_size(nat,X21),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_nat_Osize_I4_J) ).
tff(f496,plain,
! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,size_size(dB,X1),size_size(dB,X0)),suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f361,f291]) ).
tff(f361,plain,
! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,size_size(dB,X1),size_size(dB,X0)),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: dB,X1: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,size_size(dB,X1),size_size(dB,X0)),suc(zero_zero(nat))) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X55: dB,X56: dB] : ( size_size(dB,aa(dB,dB,aa(dB,fun(dB,dB),app,X56),X55)) = plus_plus(nat,plus_plus(nat,size_size(dB,X56),size_size(dB,X55)),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_dB_Osize_I5_J) ).
tff(f1300,plain,
( spl15_128
| ~ spl15_126
| ~ spl15_127 ),
inference(avatar_split_clause,[],[f1296,f1293,f1266,f1298]) ).
tff(f1298,plain,
( spl15_128
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_128])]) ).
tff(f1293,plain,
( spl15_127
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_127])]) ).
tff(f1296,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_126
| ~ spl15_127 ),
inference(forward_demodulation,[],[f1294,f1267]) ).
tff(f1294,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_127 ),
inference(avatar_component_clause,[],[f1293]) ).
tff(f1295,plain,
spl15_127,
inference(avatar_split_clause,[],[f369,f1293]) ).
tff(f369,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X4: nat,X5: dB] :
( pp(aa(dB,bool,it,X5))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X5),var(X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_app__Var__IT) ).
tff(f1268,plain,
spl15_126,
inference(avatar_split_clause,[],[f427,f1266]) ).
tff(f1260,plain,
( spl15_125
| ~ spl15_124 ),
inference(avatar_split_clause,[],[f1256,f1253,f1258]) ).
tff(f1253,plain,
( spl15_124
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_124])]) ).
tff(f1256,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_124 ),
inference(forward_demodulation,[],[f1254,f427]) ).
tff(f1254,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl15_124 ),
inference(avatar_component_clause,[],[f1253]) ).
tff(f1255,plain,
spl15_124,
inference(avatar_split_clause,[],[f368,f1253]) ).
tff(f368,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X4: nat,X5: dB] :
( pp(aa(dB,bool,it,X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X5),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lift__IT) ).
tff(f1250,plain,
( spl15_123
| ~ spl15_122 ),
inference(avatar_split_clause,[],[f1246,f1243,f1248]) ).
tff(f1248,plain,
( spl15_123
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_123])]) ).
tff(f1243,plain,
( spl15_122
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_122])]) ).
tff(f1246,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),combc(dB,dB,fun(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl15_122 ),
inference(forward_demodulation,[],[f1244,f427]) ).
tff(f1244,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl15_122 ),
inference(avatar_component_clause,[],[f1243]) ).
tff(f1245,plain,
spl15_122,
inference(avatar_split_clause,[],[f358,f1243]) ).
tff(f358,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X18: dB,X7: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X7)),X18),X7) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_subst__eq) ).
tff(f1241,plain,
spl15_121,
inference(avatar_split_clause,[],[f337,f1239]) ).
tff(f1239,plain,
( spl15_121
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_121])]) ).
tff(f337,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) )
| ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f247,f249,f248]) ).
tff(f248,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f249,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f247,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f246]) ).
tff(f246,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1229,plain,
( spl15_120
| ~ spl15_13
| ~ spl15_118 ),
inference(avatar_split_clause,[],[f1221,f1218,f570,f1227]) ).
tff(f1227,plain,
( spl15_120
<=> ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_120])]) ).
tff(f1218,plain,
( spl15_118
<=> ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_118])]) ).
tff(f1221,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1)))) )
| ~ spl15_13
| ~ spl15_118 ),
inference(forward_demodulation,[],[f1219,f572]) ).
tff(f1219,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1)))) )
| ~ spl15_118 ),
inference(avatar_component_clause,[],[f1218]) ).
tff(f1225,plain,
( spl15_119
| ~ spl15_13
| ~ spl15_117 ),
inference(avatar_split_clause,[],[f1216,f1213,f570,f1223]) ).
tff(f1223,plain,
( spl15_119
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_119])]) ).
tff(f1213,plain,
( spl15_117
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_117])]) ).
tff(f1216,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) )
| ~ spl15_13
| ~ spl15_117 ),
inference(forward_demodulation,[],[f1214,f572]) ).
tff(f1214,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) )
| ~ spl15_117 ),
inference(avatar_component_clause,[],[f1213]) ).
tff(f1220,plain,
spl15_118,
inference(avatar_split_clause,[],[f501,f1218]) ).
tff(f501,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1)))) ),
inference(forward_demodulation,[],[f373,f291]) ).
tff(f373,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK13(X1))))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ( ~ pp(aa(nat,bool,X1,suc(sK13(X1))))
& pp(aa(nat,bool,X1,sK13(X1))) )
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f230,f260]) ).
tff(f260,plain,
! [X1: fun(nat,bool)] :
( ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,suc(X2)))
& pp(aa(nat,bool,X1,X2)) )
=> ( ~ pp(aa(nat,bool,X1,suc(sK13(X1))))
& pp(aa(nat,bool,X1,sK13(X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,suc(X2)))
& pp(aa(nat,bool,X1,X2)) )
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(flattening,[],[f229]) ).
tff(f229,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,suc(X2)))
& pp(aa(nat,bool,X1,X2)) )
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
=> ( ! [X2: nat] :
( pp(aa(nat,bool,X1,X2))
=> pp(aa(nat,bool,X1,suc(X2))) )
=> pp(aa(nat,bool,X1,X0)) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X41: nat,X70: fun(nat,bool)] :
( pp(aa(nat,bool,X70,zero_zero(nat)))
=> ( ! [X71: nat] :
( pp(aa(nat,bool,X70,X71))
=> pp(aa(nat,bool,X70,suc(X71))) )
=> pp(aa(nat,bool,X70,X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__induct) ).
tff(f1215,plain,
spl15_117,
inference(avatar_split_clause,[],[f500,f1213]) ).
tff(f500,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(forward_demodulation,[],[f370,f291]) ).
tff(f370,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| pp(aa(nat,bool,X1,suc(sK12(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ( ~ pp(aa(nat,bool,X1,sK12(X1)))
& pp(aa(nat,bool,X1,suc(sK12(X1)))) )
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f228,f258]) ).
tff(f258,plain,
! [X1: fun(nat,bool)] :
( ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,X2))
& pp(aa(nat,bool,X1,suc(X2))) )
=> ( ~ pp(aa(nat,bool,X1,sK12(X1)))
& pp(aa(nat,bool,X1,suc(sK12(X1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f228,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,X2))
& pp(aa(nat,bool,X1,suc(X2))) )
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(flattening,[],[f227]) ).
tff(f227,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ? [X2: nat] :
( ~ pp(aa(nat,bool,X1,X2))
& pp(aa(nat,bool,X1,suc(X2))) )
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
=> ( ! [X2: nat] :
( pp(aa(nat,bool,X1,suc(X2)))
=> pp(aa(nat,bool,X1,X2)) )
=> pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X69: nat,X70: fun(nat,bool)] :
( pp(aa(nat,bool,X70,X69))
=> ( ! [X71: nat] :
( pp(aa(nat,bool,X70,suc(X71)))
=> pp(aa(nat,bool,X70,X71)) )
=> pp(aa(nat,bool,X70,zero_zero(nat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__induct) ).
tff(f1202,plain,
( spl15_116
| ~ spl15_13
| ~ spl15_114 ),
inference(avatar_split_clause,[],[f1189,f1186,f570,f1200]) ).
tff(f1200,plain,
( spl15_116
<=> ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_116])]) ).
tff(f1186,plain,
( spl15_114
<=> ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_114])]) ).
tff(f1189,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fFalse)))
| pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1))) )
| ~ spl15_13
| ~ spl15_114 ),
inference(forward_demodulation,[],[f1187,f572]) ).
tff(f1187,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1))) )
| ~ spl15_114 ),
inference(avatar_component_clause,[],[f1186]) ).
tff(f1198,plain,
( spl15_115
| ~ spl15_13
| ~ spl15_113 ),
inference(avatar_split_clause,[],[f1184,f1181,f570,f1196]) ).
tff(f1196,plain,
( spl15_115
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fFalse)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_115])]) ).
tff(f1181,plain,
( spl15_113
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_113])]) ).
tff(f1184,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fFalse)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) )
| ~ spl15_13
| ~ spl15_113 ),
inference(forward_demodulation,[],[f1182,f572]) ).
tff(f1182,plain,
( ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) )
| ~ spl15_113 ),
inference(avatar_component_clause,[],[f1181]) ).
tff(f1188,plain,
spl15_114,
inference(avatar_split_clause,[],[f502,f1186]) ).
tff(f502,plain,
! [X0: nat,X1: fun(nat,bool)] :
( ~ pp(aa(nat,bool,X1,bool_size(fTrue)))
| pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1))) ),
inference(forward_demodulation,[],[f372,f291]) ).
tff(f372,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK13(X1)))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f261]) ).
tff(f1183,plain,
spl15_113,
inference(avatar_split_clause,[],[f499,f1181]) ).
tff(f499,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,bool_size(fTrue)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(forward_demodulation,[],[f371,f291]) ).
tff(f371,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ~ pp(aa(nat,bool,X1,sK12(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(cnf_transformation,[],[f259]) ).
tff(f1175,plain,
( spl15_112
| ~ spl15_54
| ~ spl15_69
| ~ spl15_71
| ~ spl15_110 ),
inference(avatar_split_clause,[],[f1166,f1161,f891,f877,f792,f1173]) ).
tff(f1173,plain,
( spl15_112
<=> ! [X0: dB,X1: dB] : ( plus_plus(nat,dB_size(X1),dB_size(abs(X0))) = dB_size(aa(dB,dB,combc(dB,dB,dB,app,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_112])]) ).
tff(f792,plain,
( spl15_54
<=> ! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fFalse))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).
tff(f891,plain,
( spl15_71
<=> ! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fFalse))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_71])]) ).
tff(f1161,plain,
( spl15_110
<=> ! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(dB_size(X1)),dB_size(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_110])]) ).
tff(f1166,plain,
( ! [X0: dB,X1: dB] : ( plus_plus(nat,dB_size(X1),dB_size(abs(X0))) = dB_size(aa(dB,dB,combc(dB,dB,dB,app,X0),X1)) )
| ~ spl15_54
| ~ spl15_69
| ~ spl15_71
| ~ spl15_110 ),
inference(forward_demodulation,[],[f1165,f427]) ).
tff(f1165,plain,
( ! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,dB_size(X1),dB_size(abs(X0))) )
| ~ spl15_54
| ~ spl15_69
| ~ spl15_71
| ~ spl15_110 ),
inference(forward_demodulation,[],[f1164,f916]) ).
tff(f916,plain,
( ! [X0: dB] : ( dB_size(abs(X0)) = suc(dB_size(X0)) )
| ~ spl15_54
| ~ spl15_71 ),
inference(superposition,[],[f892,f793]) ).
tff(f793,plain,
( ! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fFalse))) )
| ~ spl15_54 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f892,plain,
( ! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fFalse))) )
| ~ spl15_71 ),
inference(avatar_component_clause,[],[f891]) ).
tff(f1164,plain,
( ! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,dB_size(X1),suc(dB_size(X0))) )
| ~ spl15_69
| ~ spl15_110 ),
inference(forward_demodulation,[],[f1162,f878]) ).
tff(f1162,plain,
( ! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(dB_size(X1)),dB_size(X0)) )
| ~ spl15_110 ),
inference(avatar_component_clause,[],[f1161]) ).
tff(f1171,plain,
( spl15_111
| ~ spl15_16
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f787,f757,f584,f1168]) ).
tff(f1168,plain,
( spl15_111
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_111])]) ).
tff(f584,plain,
( spl15_16
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
tff(f787,plain,
( sP1(abs(ua))
| ~ spl15_16
| ~ spl15_49 ),
inference(resolution,[],[f758,f586]) ).
tff(f586,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f1163,plain,
spl15_110,
inference(avatar_split_clause,[],[f494,f1161]) ).
tff(f494,plain,
! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,suc(dB_size(X1)),dB_size(X0)) ),
inference(forward_demodulation,[],[f493,f356]) ).
tff(f493,plain,
! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = suc(plus_plus(nat,dB_size(X1),dB_size(X0))) ),
inference(forward_demodulation,[],[f492,f484]) ).
tff(f492,plain,
! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,dB_size(X1),dB_size(X0)),suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f359,f291]) ).
tff(f359,plain,
! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,dB_size(X1),dB_size(X0)),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: dB,X1: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) = plus_plus(nat,plus_plus(nat,dB_size(X1),dB_size(X0)),suc(zero_zero(nat))) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X55: dB,X56: dB] : ( dB_size(aa(dB,dB,aa(dB,fun(dB,dB),app,X56),X55)) = plus_plus(nat,plus_plus(nat,dB_size(X56),dB_size(X55)),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_dB_Osize_I2_J) ).
tff(f1159,plain,
spl15_109,
inference(avatar_split_clause,[],[f404,f1157]) ).
tff(f1157,plain,
( spl15_109
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_109])]) ).
tff(f404,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X48: list(dB),X41: nat,X44: dB,X46: dB] : ( foldl(dB,dB,app,var(X41),X48) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X46)),X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Abs__App__neq__Var__apps) ).
tff(f1155,plain,
spl15_108,
inference(avatar_split_clause,[],[f387,f1153]) ).
tff(f1153,plain,
( spl15_108
<=> ! [X2: nat,X0: nat,X1: dB] : ( liftn(suc(X2),X1,X0) = aa(nat,dB,aa(dB,fun(nat,dB),lift,liftn(X2,X1,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_108])]) ).
tff(f387,plain,
! [X2: nat,X0: nat,X1: dB] : ( liftn(suc(X2),X1,X0) = aa(nat,dB,aa(dB,fun(nat,dB),lift,liftn(X2,X1,X0)),X0) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: nat,X1: dB,X2: nat] : ( liftn(suc(X2),X1,X0) = aa(nat,dB,aa(dB,fun(nat,dB),lift,liftn(X2,X1,X0)),X0) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X7: nat,X5: dB,X23: nat] : ( liftn(suc(X23),X5,X7) = aa(nat,dB,aa(dB,fun(nat,dB),lift,liftn(X23,X5,X7)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_liftn__lift) ).
tff(f1151,plain,
spl15_107,
inference(avatar_split_clause,[],[f335,f1149]) ).
tff(f1149,plain,
( spl15_107
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_107])]) ).
tff(f335,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f1145,plain,
spl15_106,
inference(avatar_split_clause,[],[f417,f1143]) ).
tff(f1143,plain,
( spl15_106
<=> ! [X2: list(dB),X0: list(dB),X1: nat,X3: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_106])]) ).
tff(f417,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(flattening,[],[f276]) ).
tff(f276,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
inference(nnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X48: list(dB),X41: nat,X42: list(dB),X49: nat] :
( ( foldl(dB,dB,app,var(X49),X42) = foldl(dB,dB,app,var(X41),X48) )
<=> ( ( X42 = X48 )
& ( X41 = X49 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Var__apps__eq__Var__apps__conv) ).
tff(f1141,plain,
spl15_105,
inference(avatar_split_clause,[],[f414,f1139]) ).
tff(f1139,plain,
( spl15_105
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_105])]) ).
tff(f414,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(flattening,[],[f274]) ).
tff(f274,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X48: list(dB),X46: dB,X42: list(dB),X47: dB] :
( ( foldl(dB,dB,app,abs(X47),X42) = foldl(dB,dB,app,abs(X46),X48) )
<=> ( ( X42 = X48 )
& ( X46 = X47 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Abs__apps__eq__Abs__apps__conv) ).
tff(f1137,plain,
( spl15_104
| ~ spl15_13
| ~ spl15_102 ),
inference(avatar_split_clause,[],[f1123,f1120,f570,f1135]) ).
tff(f1135,plain,
( spl15_104
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_104])]) ).
tff(f1120,plain,
( spl15_102
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_102])]) ).
tff(f1123,plain,
( ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),X0))
| ~ listsp(dB,it,X0) )
| ~ spl15_13
| ~ spl15_102 ),
inference(forward_demodulation,[],[f1121,f572]) ).
tff(f1121,plain,
( ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),X0))
| ~ listsp(dB,it,X0) )
| ~ spl15_102 ),
inference(avatar_component_clause,[],[f1120]) ).
tff(f1133,plain,
( spl15_103
| ~ spl15_17
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f786,f757,f589,f1130]) ).
tff(f1130,plain,
( spl15_103
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_103])]) ).
tff(f589,plain,
( spl15_17
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
tff(f786,plain,
( sP1(abs(u))
| ~ spl15_17
| ~ spl15_49 ),
inference(resolution,[],[f758,f591]) ).
tff(f591,plain,
( pp(aa(dB,bool,it,u))
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f589]) ).
tff(f1122,plain,
spl15_102,
inference(avatar_split_clause,[],[f487,f1120]) ).
tff(f487,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,bool_size(fTrue)),X0))
| ~ listsp(dB,it,X0) ),
inference(forward_demodulation,[],[f333,f291]) ).
tff(f333,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: list(dB)] :
( listsp(dB,it,X0)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X22: list(dB)] :
( listsp(dB,it,X22)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_lifts__IT) ).
tff(f1118,plain,
spl15_101,
inference(avatar_split_clause,[],[f416,f1116]) ).
tff(f1116,plain,
( spl15_101
<=> ! [X0: list(dB),X3: nat,X2: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_101])]) ).
tff(f416,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f1114,plain,
spl15_100,
inference(avatar_split_clause,[],[f413,f1112]) ).
tff(f1112,plain,
( spl15_100
<=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_100])]) ).
tff(f413,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1110,plain,
spl15_99,
inference(avatar_split_clause,[],[f402,f1108]) ).
tff(f1108,plain,
( spl15_99
<=> ! [X0: $tType,X3: fun(nibble,fun(nibble,X0)),X2: nibble,X1: nibble] : ( char_case(X0,X3,char(X2,X1)) = aa(nibble,X0,aa(nibble,fun(nibble,X0),X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_99])]) ).
tff(f402,plain,
! [X0: $tType,X2: nibble,X3: fun(nibble,fun(nibble,X0)),X1: nibble] : ( char_case(X0,X3,char(X2,X1)) = aa(nibble,X0,aa(nibble,fun(nibble,X0),X3,X2),X1) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: nibble,X2: nibble,X3: fun(nibble,fun(nibble,X0))] : ( char_case(X0,X3,char(X2,X1)) = aa(nibble,X0,aa(nibble,fun(nibble,X0),X3,X2),X1) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType,X35: nibble,X36: nibble,X30: fun(nibble,fun(nibble,X0))] : ( char_case(X0,X30,char(X36,X35)) = aa(nibble,X0,aa(nibble,fun(nibble,X0),X30,X36),X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_char_Osimps_I2_J) ).
tff(f1100,plain,
( spl15_98
| ~ spl15_15
| ~ spl15_49 ),
inference(avatar_split_clause,[],[f785,f757,f579,f1097]) ).
tff(f1097,plain,
( spl15_98
<=> sP1(abs(t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_98])]) ).
tff(f579,plain,
( spl15_15
<=> pp(aa(dB,bool,it,t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
tff(f785,plain,
( sP1(abs(t))
| ~ spl15_15
| ~ spl15_49 ),
inference(resolution,[],[f758,f581]) ).
tff(f581,plain,
( pp(aa(dB,bool,it,t))
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f579]) ).
tff(f1092,plain,
spl15_97,
inference(avatar_split_clause,[],[f398,f1090]) ).
tff(f1090,plain,
( spl15_97
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_97])]) ).
tff(f398,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X46: dB,X22: list(dB),X47: dB] :
( ( foldl(dB,dB,app,X47,X22) = foldl(dB,dB,app,X46,X22) )
<=> ( X46 = X47 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_apps__eq__tail__conv) ).
tff(f1088,plain,
spl15_96,
inference(avatar_split_clause,[],[f366,f1086]) ).
tff(f1086,plain,
( spl15_96
<=> ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_96])]) ).
tff(f366,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X41: nat,X42: list(dB)] :
( listsp(dB,it,X42)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X41),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_IT_OVar) ).
tff(f1084,plain,
spl15_95,
inference(avatar_split_clause,[],[f365,f1082]) ).
tff(f1082,plain,
( spl15_95
<=> ! [X1: $tType,X0: $tType,X2: list(X0)] :
( ( zero_zero(X1) = monoid_add_listsum(X1,map(X0,X1,combk(X1,X0,zero_zero(X1)),X2)) )
| ~ monoid_add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_95])]) ).
tff(f365,plain,
! [X1: $tType,X0: $tType,X2: list(X0)] :
( ( zero_zero(X1) = monoid_add_listsum(X1,map(X0,X1,combk(X1,X0,zero_zero(X1)),X2)) )
| ~ monoid_add(X1) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: list(X0)] : ( zero_zero(X1) = monoid_add_listsum(X1,map(X0,X1,combk(X1,X0,zero_zero(X1)),X2)) )
| ~ monoid_add(X1) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: $tType] :
( monoid_add(X1)
=> ! [X2: list(X0)] : ( zero_zero(X1) = monoid_add_listsum(X1,map(X0,X1,combk(X1,X0,zero_zero(X1)),X2)) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X1: $tType,X0: $tType] :
( monoid_add(X0)
=> ! [X40: list(X1)] : ( zero_zero(X0) = monoid_add_listsum(X0,map(X1,X0,combk(X0,X1,zero_zero(X0)),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_listsum__0) ).
tff(f1077,plain,
( spl15_94
| ~ spl15_93 ),
inference(avatar_split_clause,[],[f1073,f1070,f1075]) ).
tff(f1075,plain,
( spl15_94
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_94])]) ).
tff(f1070,plain,
( spl15_93
<=> ! [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,[spl15_93])]) ).
tff(f1073,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl15_93 ),
inference(forward_demodulation,[],[f1071,f427]) ).
tff(f1071,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl15_93 ),
inference(avatar_component_clause,[],[f1070]) ).
tff(f1072,plain,
spl15_93,
inference(avatar_split_clause,[],[f362,f1070]) ).
tff(f362,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X76: bool,X77: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X77),X76))
| ~ pp(X76)
| ~ pp(X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f1068,plain,
spl15_92,
inference(avatar_split_clause,[],[f338,f1066]) ).
tff(f1066,plain,
( spl15_92
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_92])]) ).
tff(f338,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK4(X0)))
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f1064,plain,
spl15_91,
inference(avatar_split_clause,[],[f401,f1062]) ).
tff(f1062,plain,
( spl15_91
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_91])]) ).
tff(f401,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X48: list(dB),X47: dB,X22: list(dB),X41: nat] : ( foldl(dB,dB,app,var(X41),X22) != foldl(dB,dB,app,abs(X47),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Var__apps__neq__Abs__apps) ).
tff(f1060,plain,
( spl15_90
| ~ spl15_30
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f715,f684,f656,f1058]) ).
tff(f1058,plain,
( spl15_90
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_90])]) ).
tff(f715,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl15_30
| ~ spl15_36 ),
inference(resolution,[],[f685,f657]) ).
tff(f1030,plain,
spl15_89,
inference(avatar_split_clause,[],[f385,f1028]) ).
tff(f1028,plain,
( spl15_89
<=> ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_89])]) ).
tff(f385,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X21: nat,X19: dB,X20: dB] : ( var(X21) != aa(dB,dB,aa(dB,fun(dB,dB),app,X20),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_dB_Osimps_I5_J) ).
tff(f1026,plain,
spl15_88,
inference(avatar_split_clause,[],[f383,f1024]) ).
tff(f1024,plain,
( spl15_88
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_88])]) ).
tff(f383,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X57: dB,X55: dB,X56: dB] : ( abs(X57) != aa(dB,dB,aa(dB,fun(dB,dB),app,X56),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_dB_Osimps_I8_J) ).
tff(f1020,plain,
( spl15_87
| ~ spl15_86 ),
inference(avatar_split_clause,[],[f1016,f1013,f1018]) ).
tff(f1018,plain,
( spl15_87
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_87])]) ).
tff(f1013,plain,
( spl15_86
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_86])]) ).
tff(f1016,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl15_86 ),
inference(forward_demodulation,[],[f1014,f427]) ).
tff(f1014,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl15_86 ),
inference(avatar_component_clause,[],[f1013]) ).
tff(f1015,plain,
spl15_86,
inference(avatar_split_clause,[],[f364,f1013]) ).
tff(f364,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X76: bool,X77: bool] :
( pp(X77)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X77),X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f1008,plain,
( spl15_85
| ~ spl15_84 ),
inference(avatar_split_clause,[],[f1004,f1001,f1006]) ).
tff(f1006,plain,
( spl15_85
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_85])]) ).
tff(f1001,plain,
( spl15_84
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_84])]) ).
tff(f1004,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl15_84 ),
inference(forward_demodulation,[],[f1002,f427]) ).
tff(f1002,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl15_84 ),
inference(avatar_component_clause,[],[f1001]) ).
tff(f1003,plain,
spl15_84,
inference(avatar_split_clause,[],[f363,f1001]) ).
tff(f363,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X76: bool,X77: bool] :
( pp(X76)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X77),X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f999,plain,
spl15_83,
inference(avatar_split_clause,[],[f336,f997]) ).
tff(f997,plain,
( spl15_83
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_83])]) ).
tff(f336,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f995,plain,
spl15_82,
inference(avatar_split_clause,[],[f329,f993]) ).
tff(f993,plain,
( spl15_82
<=> ! [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,[spl15_82])]) ).
tff(f329,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,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
<=> ( X1 = X2 ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,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,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X74: X0,X27: X0,X51: X0] :
( ( plus_plus(X0,X51,X27) = plus_plus(X0,X51,X74) )
<=> ( X27 = X74 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__left__cancel) ).
tff(f991,plain,
spl15_81,
inference(avatar_split_clause,[],[f327,f989]) ).
tff(f989,plain,
( spl15_81
<=> ! [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,[spl15_81])]) ).
tff(f327,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,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
| ( X1 != X3 ) )
& ( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
<=> ( X1 = X3 ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,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,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X74: X0,X51: X0,X27: X0] :
( ( plus_plus(X0,X27,X51) = plus_plus(X0,X74,X51) )
<=> ( X27 = X74 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__right__cancel) ).
tff(f980,plain,
spl15_80,
inference(avatar_split_clause,[],[f509,f978]) ).
tff(f978,plain,
( spl15_80
<=> ! [X0: $tType,X3: fun(nibble,fun(nibble,X0)),X2: nibble,X1: nibble] : ( char_case(X0,X3,char(X2,X1)) = char_rec(X0,X3,char(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_80])]) ).
tff(f509,plain,
! [X0: $tType,X2: nibble,X3: fun(nibble,fun(nibble,X0)),X1: nibble] : ( char_case(X0,X3,char(X2,X1)) = char_rec(X0,X3,char(X2,X1)) ),
inference(forward_demodulation,[],[f403,f402]) ).
tff(f403,plain,
! [X0: $tType,X2: nibble,X3: fun(nibble,fun(nibble,X0)),X1: nibble] : ( aa(nibble,X0,aa(nibble,fun(nibble,X0),X3,X2),X1) = char_rec(X0,X3,char(X2,X1)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: nibble,X2: nibble,X3: fun(nibble,fun(nibble,X0))] : ( aa(nibble,X0,aa(nibble,fun(nibble,X0),X3,X2),X1) = char_rec(X0,X3,char(X2,X1)) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X35: nibble,X36: nibble,X30: fun(nibble,fun(nibble,X0))] : ( aa(nibble,X0,aa(nibble,fun(nibble,X0),X30,X36),X35) = char_rec(X0,X30,char(X36,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_char_Orecs) ).
tff(f976,plain,
spl15_79,
inference(avatar_split_clause,[],[f426,f974]) ).
tff(f974,plain,
( spl15_79
<=> ! [X0: $tType,X2: fun(dB,X0),X4: fun(nat,X0),X3: fun(dB,fun(dB,X0)),X1: nat] : ( dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_79])]) ).
tff(f426,plain,
! [X0: $tType,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X1: nat,X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: nat,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X17: nat,X28: fun(dB,X0),X29: fun(dB,fun(dB,X0)),X30: fun(nat,X0)] : ( dB_case(X0,X30,X29,X28,var(X17)) = aa(nat,X0,X30,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dB_Osimps_I10_J) ).
tff(f972,plain,
spl15_78,
inference(avatar_split_clause,[],[f425,f970]) ).
tff(f970,plain,
( spl15_78
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(dB,fun(dB,X0)),X2: fun(dB,X0),X1: dB] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_78])]) ).
tff(f425,plain,
! [X0: $tType,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X1: dB,X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: dB,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X54: dB,X28: fun(dB,X0),X29: fun(dB,fun(dB,X0)),X30: fun(nat,X0)] : ( dB_case(X0,X30,X29,X28,abs(X54)) = aa(dB,X0,X28,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_dB_Osimps_I12_J) ).
tff(f968,plain,
spl15_77,
inference(avatar_split_clause,[],[f334,f966]) ).
tff(f966,plain,
( spl15_77
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_77])]) ).
tff(f334,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X10: dB] :
( pp(aa(dB,bool,it,X10))
=> pp(aa(dB,bool,it,abs(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Lambda) ).
tff(f942,plain,
spl15_76,
inference(avatar_split_clause,[],[f445,f940]) ).
tff(f940,plain,
( spl15_76
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_76])]) ).
tff(f445,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f339]) ).
tff(f339,plain,
! [X2: list(dB),X3: nat,X0: dB] :
( sP1(X0)
| ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f938,plain,
spl15_75,
inference(avatar_split_clause,[],[f396,f936]) ).
tff(f936,plain,
( spl15_75
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_75])]) ).
tff(f396,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X41: nat,X49: nat,X69: nat] :
( ( plus_plus(nat,X69,X49) = plus_plus(nat,X69,X41) )
<=> ( X41 = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__add__left__cancel) ).
tff(f934,plain,
spl15_74,
inference(avatar_split_clause,[],[f394,f932]) ).
tff(f932,plain,
( spl15_74
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_74])]) ).
tff(f394,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ) ),
inference(nnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X41: nat,X69: nat,X49: nat] :
( ( plus_plus(nat,X49,X69) = plus_plus(nat,X41,X69) )
<=> ( X41 = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__add__right__cancel) ).
tff(f901,plain,
( spl15_73
| ~ spl15_13
| ~ spl15_68 ),
inference(avatar_split_clause,[],[f875,f871,f570,f899]) ).
tff(f899,plain,
( spl15_73
<=> ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) = X1 )
| ( bool_size(fFalse) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_73])]) ).
tff(f871,plain,
( spl15_68
<=> ! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_68])]) ).
tff(f875,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) = X1 )
| ( bool_size(fFalse) != plus_plus(nat,X1,X0) ) )
| ~ spl15_13
| ~ spl15_68 ),
inference(forward_demodulation,[],[f874,f572]) ).
tff(f874,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X1 ) )
| ~ spl15_13
| ~ spl15_68 ),
inference(forward_demodulation,[],[f872,f572]) ).
tff(f872,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X1 ) )
| ~ spl15_68 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f897,plain,
( spl15_72
| ~ spl15_13
| ~ spl15_67 ),
inference(avatar_split_clause,[],[f869,f865,f570,f895]) ).
tff(f895,plain,
( spl15_72
<=> ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) = X0 )
| ( bool_size(fFalse) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_72])]) ).
tff(f865,plain,
( spl15_67
<=> ! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_67])]) ).
tff(f869,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) = X0 )
| ( bool_size(fFalse) != plus_plus(nat,X1,X0) ) )
| ~ spl15_13
| ~ spl15_67 ),
inference(forward_demodulation,[],[f868,f572]) ).
tff(f868,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fFalse) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X0 ) )
| ~ spl15_13
| ~ spl15_67 ),
inference(forward_demodulation,[],[f866,f572]) ).
tff(f866,plain,
( ! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X0 ) )
| ~ spl15_67 ),
inference(avatar_component_clause,[],[f865]) ).
tff(f893,plain,
( spl15_71
| ~ spl15_13
| ~ spl15_66 ),
inference(avatar_split_clause,[],[f863,f860,f570,f891]) ).
tff(f860,plain,
( spl15_66
<=> ! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fTrue))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_66])]) ).
tff(f863,plain,
( ! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fFalse))) )
| ~ spl15_13
| ~ spl15_66 ),
inference(forward_demodulation,[],[f861,f572]) ).
tff(f861,plain,
( ! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fTrue))) )
| ~ spl15_66 ),
inference(avatar_component_clause,[],[f860]) ).
tff(f889,plain,
( spl15_70
| ~ spl15_13
| ~ spl15_65 ),
inference(avatar_split_clause,[],[f858,f855,f570,f887]) ).
tff(f887,plain,
( spl15_70
<=> ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(bool_size(fFalse))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_70])]) ).
tff(f855,plain,
( spl15_65
<=> ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(bool_size(fTrue))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_65])]) ).
tff(f858,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(bool_size(fFalse))) )
| ~ spl15_13
| ~ spl15_65 ),
inference(forward_demodulation,[],[f856,f572]) ).
tff(f856,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(bool_size(fTrue))) )
| ~ spl15_65 ),
inference(avatar_component_clause,[],[f855]) ).
tff(f879,plain,
( spl15_69
| ~ spl15_63 ),
inference(avatar_split_clause,[],[f849,f846,f877]) ).
tff(f846,plain,
( spl15_63
<=> ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_63])]) ).
tff(f849,plain,
( ! [X0: nat,X1: nat] : ( plus_plus(nat,suc(X1),X0) = plus_plus(nat,X1,suc(X0)) )
| ~ spl15_63 ),
inference(forward_demodulation,[],[f847,f357]) ).
tff(f357,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X23: nat,X60: nat] : ( plus_plus(nat,X60,suc(X23)) = suc(plus_plus(nat,X60,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__Suc__right) ).
tff(f847,plain,
( ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) )
| ~ spl15_63 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f873,plain,
spl15_68,
inference(avatar_split_clause,[],[f507,f871]) ).
tff(f507,plain,
! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X1 ) ),
inference(forward_demodulation,[],[f506,f291]) ).
tff(f506,plain,
! [X0: nat,X1: nat] :
( ( bool_size(fTrue) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(forward_demodulation,[],[f380,f291]) ).
tff(f380,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
inference(flattening,[],[f265]) ).
tff(f265,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X41: nat,X49: nat] :
( ( zero_zero(nat) = plus_plus(nat,X49,X41) )
<=> ( ( zero_zero(nat) = X41 )
& ( zero_zero(nat) = X49 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__is__0) ).
tff(f867,plain,
spl15_67,
inference(avatar_split_clause,[],[f505,f865]) ).
tff(f505,plain,
! [X0: nat,X1: nat] :
( ( bool_size(fTrue) != plus_plus(nat,X1,X0) )
| ( bool_size(fTrue) = X0 ) ),
inference(forward_demodulation,[],[f504,f291]) ).
tff(f504,plain,
! [X0: nat,X1: nat] :
( ( bool_size(fTrue) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(forward_demodulation,[],[f381,f291]) ).
tff(f381,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f862,plain,
spl15_66,
inference(avatar_split_clause,[],[f481,f860]) ).
tff(f481,plain,
! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f321,f291]) ).
tff(f321,plain,
! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB] : ( dB_size(abs(X0)) = plus_plus(nat,dB_size(X0),suc(zero_zero(nat))) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X73: dB] : ( dB_size(abs(X73)) = plus_plus(nat,dB_size(X73),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_dB_Osize_I3_J) ).
tff(f857,plain,
spl15_65,
inference(avatar_split_clause,[],[f480,f855]) ).
tff(f480,plain,
! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(bool_size(fTrue))) ),
inference(forward_demodulation,[],[f320,f291]) ).
tff(f320,plain,
! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X21: nat] : ( nat_size(suc(X21)) = plus_plus(nat,nat_size(X21),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat_Osize_I2_J) ).
tff(f853,plain,
spl15_64,
inference(avatar_split_clause,[],[f357,f851]) ).
tff(f851,plain,
( spl15_64
<=> ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_64])]) ).
tff(f848,plain,
spl15_63,
inference(avatar_split_clause,[],[f356,f846]) ).
tff(f837,plain,
( spl15_62
| ~ spl15_16
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f718,f684,f584,f834]) ).
tff(f834,plain,
( spl15_62
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_62])]) ).
tff(f718,plain,
( sP1(ua)
| ~ spl15_16
| ~ spl15_36 ),
inference(resolution,[],[f685,f586]) ).
tff(f832,plain,
spl15_61,
inference(avatar_split_clause,[],[f411,f830]) ).
tff(f830,plain,
( spl15_61
<=> ! [X2: nibble,X0: nibble,X1: nibble,X3: nibble] :
( ( X0 = X2 )
| ( char(X1,X0) != char(X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_61])]) ).
tff(f411,plain,
! [X2: nibble,X3: nibble,X0: nibble,X1: nibble] :
( ( X0 = X2 )
| ( char(X1,X0) != char(X3,X2) ) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: nibble,X1: nibble,X2: nibble,X3: nibble] :
( ( ( char(X1,X0) = char(X3,X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( char(X1,X0) != char(X3,X2) ) ) ),
inference(flattening,[],[f272]) ).
tff(f272,plain,
! [X0: nibble,X1: nibble,X2: nibble,X3: nibble] :
( ( ( char(X1,X0) = char(X3,X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( char(X1,X0) != char(X3,X2) ) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: nibble,X1: nibble,X2: nibble,X3: nibble] :
( ( char(X1,X0) = char(X3,X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X33: nibble,X34: nibble,X35: nibble,X36: nibble] :
( ( char(X36,X35) = char(X34,X33) )
<=> ( ( X33 = X35 )
& ( X34 = X36 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_char_Oinject) ).
tff(f828,plain,
spl15_60,
inference(avatar_split_clause,[],[f410,f826]) ).
tff(f826,plain,
( spl15_60
<=> ! [X0: nibble,X3: nibble,X2: nibble,X1: nibble] :
( ( X1 = X3 )
| ( char(X1,X0) != char(X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_60])]) ).
tff(f410,plain,
! [X2: nibble,X3: nibble,X0: nibble,X1: nibble] :
( ( X1 = X3 )
| ( char(X1,X0) != char(X3,X2) ) ),
inference(cnf_transformation,[],[f273]) ).
tff(f824,plain,
spl15_59,
inference(avatar_split_clause,[],[f400,f822]) ).
tff(f822,plain,
( spl15_59
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_59])]) ).
tff(f400,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X1: $tType,X0: $tType,X76: X1,X77: X0] : ( aa(X1,X0,combk(X0,X1,X77),X76) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f812,plain,
( spl15_58
| ~ spl15_13
| ~ spl15_53 ),
inference(avatar_split_clause,[],[f780,f776,f570,f809]) ).
tff(f809,plain,
( spl15_58
<=> ( bool_size(fFalse) = plus_plus(nat,bool_size(fFalse),bool_size(fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_58])]) ).
tff(f776,plain,
( spl15_53
<=> ( bool_size(fTrue) = plus_plus(nat,bool_size(fTrue),bool_size(fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).
tff(f780,plain,
( ( bool_size(fFalse) = plus_plus(nat,bool_size(fFalse),bool_size(fFalse)) )
| ~ spl15_13
| ~ spl15_53 ),
inference(forward_demodulation,[],[f778,f572]) ).
tff(f778,plain,
( ( bool_size(fTrue) = plus_plus(nat,bool_size(fTrue),bool_size(fTrue)) )
| ~ spl15_53 ),
inference(avatar_component_clause,[],[f776]) ).
tff(f807,plain,
( spl15_57
| ~ spl15_13
| ~ spl15_52 ),
inference(avatar_split_clause,[],[f774,f771,f570,f805]) ).
tff(f805,plain,
( spl15_57
<=> ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( suc(sK3(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_57])]) ).
tff(f771,plain,
( spl15_52
<=> ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK3(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).
tff(f774,plain,
( ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( suc(sK3(X0)) = X0 ) )
| ~ spl15_13
| ~ spl15_52 ),
inference(forward_demodulation,[],[f772,f572]) ).
tff(f772,plain,
( ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK3(X0)) = X0 ) )
| ~ spl15_52 ),
inference(avatar_component_clause,[],[f771]) ).
tff(f803,plain,
( spl15_56
| ~ spl15_13
| ~ spl15_51 ),
inference(avatar_split_clause,[],[f769,f766,f570,f801]) ).
tff(f801,plain,
( spl15_56
<=> ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( suc(sK2(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).
tff(f766,plain,
( spl15_51
<=> ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK2(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
tff(f769,plain,
( ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( suc(sK2(X0)) = X0 ) )
| ~ spl15_13
| ~ spl15_51 ),
inference(forward_demodulation,[],[f767,f572]) ).
tff(f767,plain,
( ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK2(X0)) = X0 ) )
| ~ spl15_51 ),
inference(avatar_component_clause,[],[f766]) ).
tff(f799,plain,
( spl15_55
| ~ spl15_17
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f717,f684,f589,f796]) ).
tff(f796,plain,
( spl15_55
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).
tff(f717,plain,
( sP1(u)
| ~ spl15_17
| ~ spl15_36 ),
inference(resolution,[],[f685,f591]) ).
tff(f794,plain,
( spl15_54
| ~ spl15_13
| ~ spl15_50 ),
inference(avatar_split_clause,[],[f764,f761,f570,f792]) ).
tff(f761,plain,
( spl15_50
<=> ! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fTrue))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
tff(f764,plain,
( ! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fFalse))) )
| ~ spl15_13
| ~ spl15_50 ),
inference(forward_demodulation,[],[f762,f572]) ).
tff(f762,plain,
( ! [X0: nat] : ( suc(X0) = plus_plus(nat,X0,suc(bool_size(fTrue))) )
| ~ spl15_50 ),
inference(avatar_component_clause,[],[f761]) ).
tff(f779,plain,
spl15_53,
inference(avatar_split_clause,[],[f503,f776]) ).
tff(f503,plain,
bool_size(fTrue) = plus_plus(nat,bool_size(fTrue),bool_size(fTrue)),
inference(forward_demodulation,[],[f451,f291]) ).
tff(f451,plain,
zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)),
inference(equality_resolution,[],[f450]) ).
tff(f450,plain,
! [X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,zero_zero(nat)) )
| ( zero_zero(nat) != X1 ) ),
inference(equality_resolution,[],[f382]) ).
tff(f382,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f773,plain,
spl15_52,
inference(avatar_split_clause,[],[f486,f771]) ).
tff(f486,plain,
! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK3(X0)) = X0 ) ),
inference(forward_demodulation,[],[f332,f291]) ).
tff(f332,plain,
! [X0: nat] :
( ( suc(sK3(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: nat] :
( ( suc(sK3(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f218,f243]) ).
tff(f243,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK3(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ? [X1: nat] : ( suc(X1) = X0 ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X23: nat] :
( ( zero_zero(nat) != X23 )
=> ? [X72: nat] : ( suc(X72) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_not0__implies__Suc) ).
tff(f768,plain,
spl15_51,
inference(avatar_split_clause,[],[f485,f766]) ).
tff(f485,plain,
! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( suc(sK2(X0)) = X0 ) ),
inference(forward_demodulation,[],[f331,f291]) ).
tff(f331,plain,
! [X0: nat] :
( ( suc(sK2(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: nat] :
( ( suc(sK2(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f217,f241]) ).
tff(f241,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK2(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f217,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ~ ! [X1: nat] : ( suc(X1) != X0 ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X37: nat] :
( ( zero_zero(nat) != X37 )
=> ~ ! [X68: nat] : ( suc(X68) != X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_nat_Oexhaust) ).
tff(f763,plain,
spl15_50,
inference(avatar_split_clause,[],[f484,f761]) ).
tff(f759,plain,
spl15_49,
inference(avatar_split_clause,[],[f444,f757]) ).
tff(f444,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f340]) ).
tff(f340,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f755,plain,
spl15_48,
inference(avatar_split_clause,[],[f355,f753]) ).
tff(f753,plain,
( spl15_48
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).
tff(f355,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X26: list(X0)] : ( map(X0,X0,combi(X0),X26) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_map__ident) ).
tff(f751,plain,
( spl15_47
| ~ spl15_15
| ~ spl15_36 ),
inference(avatar_split_clause,[],[f716,f684,f579,f748]) ).
tff(f748,plain,
( spl15_47
<=> sP1(t) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).
tff(f716,plain,
( sP1(t)
| ~ spl15_15
| ~ spl15_36 ),
inference(resolution,[],[f685,f581]) ).
tff(f746,plain,
spl15_46,
inference(avatar_split_clause,[],[f344,f744]) ).
tff(f344,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f739,plain,
( ~ spl15_45
| ~ spl15_9
| spl15_44 ),
inference(avatar_split_clause,[],[f734,f728,f552,f736]) ).
tff(f552,plain,
( spl15_9
<=> ( zero_zero(nat) = bool_size(fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
tff(f728,plain,
( spl15_44
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
tff(f734,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,bool_size(fFalse)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))))
| ~ spl15_9
| spl15_44 ),
inference(forward_demodulation,[],[f733,f554]) ).
tff(f554,plain,
( ( zero_zero(nat) = bool_size(fFalse) )
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f733,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,b),n),u))))
| spl15_44 ),
inference(forward_demodulation,[],[f732,f427]) ).
tff(f732,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n))))
| spl15_44 ),
inference(forward_demodulation,[],[f730,f427]) ).
tff(f730,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat))))
| spl15_44 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f731,plain,
~ spl15_44,
inference(avatar_split_clause,[],[f432,f728]) ).
tff(f432,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),n)),zero_zero(nat)))),
inference(definition_unfolding,[],[f282,f290]) ).
tff(f282,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(flattening,[],[f117]) ).
tff(f117,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
inference(negated_conjecture,[],[f116]) ).
tff(f116,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f714,plain,
( spl15_42
| ~ spl15_43
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f629,f594,f711,f708]) ).
tff(f708,plain,
( spl15_42
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
tff(f711,plain,
( spl15_43
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
tff(f594,plain,
( spl15_18
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
tff(f629,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl15_18 ),
inference(equality_factoring,[],[f595]) ).
tff(f595,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f594]) ).
tff(f706,plain,
spl15_41,
inference(avatar_split_clause,[],[f376,f704]) ).
tff(f704,plain,
( spl15_41
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
tff(f376,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X16: nat,X17: nat] :
( ( var(X17) = var(X16) )
<=> ( X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dB_Osimps_I1_J) ).
tff(f702,plain,
spl15_40,
inference(avatar_split_clause,[],[f374,f700]) ).
tff(f700,plain,
( spl15_40
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
tff(f374,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X53: dB,X54: dB] :
( ( abs(X54) = abs(X53) )
<=> ( X53 = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_dB_Osimps_I3_J) ).
tff(f698,plain,
spl15_39,
inference(avatar_split_clause,[],[f367,f696]) ).
tff(f696,plain,
( spl15_39
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
tff(f367,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X37: nat,X58: nat] :
( ( suc(X58) = suc(X37) )
=> ( X37 = X58 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Suc__inject) ).
tff(f694,plain,
spl15_38,
inference(avatar_split_clause,[],[f354,f692]) ).
tff(f692,plain,
( spl15_38
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
tff(f354,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X77: X0] : ( aa(X0,X0,combi(X0),X77) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f690,plain,
spl15_37,
inference(avatar_split_clause,[],[f347,f688]) ).
tff(f347,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f148,f236,f235]) ).
tff(f148,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X51: dB] :
( pp(aa(dB,bool,it,X51))
<=> ( ? [X65: dB,X66: dB,X67: list(dB)] :
( pp(aa(dB,bool,it,X66))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X65),X66),zero_zero(nat)),X67)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X65)),X66),X67) = X51 ) )
| ? [X65: dB] :
( pp(aa(dB,bool,it,X65))
& ( abs(X65) = X51 ) )
| ? [X63: list(dB),X64: nat] :
( listsp(dB,it,X63)
& ( foldl(dB,dB,app,var(X64),X63) = X51 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_IT_Osimps) ).
tff(f686,plain,
spl15_36,
inference(avatar_split_clause,[],[f346,f684]) ).
tff(f346,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f255]) ).
tff(f682,plain,
( spl15_35
| ~ spl15_13
| ~ spl15_33 ),
inference(avatar_split_clause,[],[f672,f669,f570,f680]) ).
tff(f680,plain,
( spl15_35
<=> ! [X0: nat,X1: dB] : ( liftn(bool_size(fFalse),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
tff(f669,plain,
( spl15_33
<=> ! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
tff(f672,plain,
( ! [X0: nat,X1: dB] : ( liftn(bool_size(fFalse),X1,X0) = X1 )
| ~ spl15_13
| ~ spl15_33 ),
inference(forward_demodulation,[],[f670,f572]) ).
tff(f670,plain,
( ! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 )
| ~ spl15_33 ),
inference(avatar_component_clause,[],[f669]) ).
tff(f678,plain,
( spl15_34
| ~ spl15_13
| ~ spl15_32 ),
inference(avatar_split_clause,[],[f667,f664,f570,f676]) ).
tff(f676,plain,
( spl15_34
<=> ! [X0: nat] : ( bool_size(fFalse) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
tff(f664,plain,
( spl15_32
<=> ! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
tff(f667,plain,
( ! [X0: nat] : ( bool_size(fFalse) = size_size(dB,var(X0)) )
| ~ spl15_13
| ~ spl15_32 ),
inference(forward_demodulation,[],[f665,f572]) ).
tff(f665,plain,
( ! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) )
| ~ spl15_32 ),
inference(avatar_component_clause,[],[f664]) ).
tff(f671,plain,
spl15_33,
inference(avatar_split_clause,[],[f490,f669]) ).
tff(f490,plain,
! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 ),
inference(forward_demodulation,[],[f352,f291]) ).
tff(f352,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X7: nat,X5: dB] : ( liftn(zero_zero(nat),X5,X7) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_liftn__0) ).
tff(f666,plain,
spl15_32,
inference(avatar_split_clause,[],[f479,f664]) ).
tff(f479,plain,
! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) ),
inference(forward_demodulation,[],[f318,f291]) ).
tff(f318,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X21: nat] : ( zero_zero(nat) = size_size(dB,var(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_dB_Osize_I4_J) ).
tff(f662,plain,
spl15_31,
inference(avatar_split_clause,[],[f348,f660]) ).
tff(f660,plain,
( spl15_31
<=> ! [X0: char1] : ( char(sK10(X0),sK11(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
tff(f348,plain,
! [X0: char1] : ( char(sK10(X0),sK11(X0)) = X0 ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: char1] : ( char(sK10(X0),sK11(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f221,f256]) ).
tff(f256,plain,
! [X0: char1] :
( ? [X1: nibble,X2: nibble] : ( char(X1,X2) = X0 )
=> ( char(sK10(X0),sK11(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f221,plain,
! [X0: char1] :
? [X1: nibble,X2: nibble] : ( char(X1,X2) = X0 ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: char1] :
~ ! [X1: nibble,X2: nibble] : ( char(X1,X2) != X0 ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X37: char1] :
~ ! [X38: nibble,X39: nibble] : ( char(X38,X39) != X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_char_Oexhaust) ).
tff(f658,plain,
spl15_30,
inference(avatar_split_clause,[],[f319,f656]) ).
tff(f319,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X23: nat] : pp(aa(dB,bool,it,var(X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Var__IT) ).
tff(f654,plain,
( spl15_29
| ~ spl15_5
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f625,f594,f533,f652]) ).
tff(f652,plain,
( spl15_29
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
tff(f533,plain,
( spl15_5
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
tff(f625,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl15_5
| ~ spl15_18 ),
inference(superposition,[],[f535,f595]) ).
tff(f535,plain,
( pp(fTrue)
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f533]) ).
tff(f650,plain,
( spl15_28
| ~ spl15_13
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f622,f619,f570,f648]) ).
tff(f648,plain,
( spl15_28
<=> ! [X0: bool] : ( bool_size(fFalse) = size_size(bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
tff(f619,plain,
( spl15_23
<=> ! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
tff(f622,plain,
( ! [X0: bool] : ( bool_size(fFalse) = size_size(bool,X0) )
| ~ spl15_13
| ~ spl15_23 ),
inference(forward_demodulation,[],[f620,f572]) ).
tff(f620,plain,
( ! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) )
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f619]) ).
tff(f646,plain,
( spl15_27
| ~ spl15_13
| ~ spl15_22 ),
inference(avatar_split_clause,[],[f617,f614,f570,f644]) ).
tff(f644,plain,
( spl15_27
<=> ! [X0: char1] : ( bool_size(fFalse) = size_size(char1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
tff(f614,plain,
( spl15_22
<=> ! [X0: char1] : ( bool_size(fTrue) = size_size(char1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
tff(f617,plain,
( ! [X0: char1] : ( bool_size(fFalse) = size_size(char1,X0) )
| ~ spl15_13
| ~ spl15_22 ),
inference(forward_demodulation,[],[f615,f572]) ).
tff(f615,plain,
( ! [X0: char1] : ( bool_size(fTrue) = size_size(char1,X0) )
| ~ spl15_22 ),
inference(avatar_component_clause,[],[f614]) ).
tff(f642,plain,
( spl15_26
| ~ spl15_13
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f612,f609,f570,f640]) ).
tff(f640,plain,
( spl15_26
<=> ! [X0: literal] : ( bool_size(fFalse) = size_size(literal,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
tff(f609,plain,
( spl15_21
<=> ! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
tff(f612,plain,
( ! [X0: literal] : ( bool_size(fFalse) = size_size(literal,X0) )
| ~ spl15_13
| ~ spl15_21 ),
inference(forward_demodulation,[],[f610,f572]) ).
tff(f610,plain,
( ! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) )
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f609]) ).
tff(f638,plain,
( spl15_25
| ~ spl15_13
| ~ spl15_20 ),
inference(avatar_split_clause,[],[f607,f604,f570,f636]) ).
tff(f636,plain,
( spl15_25
<=> ! [X0: nat] : ( bool_size(fFalse) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
tff(f604,plain,
( spl15_20
<=> ! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
tff(f607,plain,
( ! [X0: nat] : ( bool_size(fFalse) = dB_size(var(X0)) )
| ~ spl15_13
| ~ spl15_20 ),
inference(forward_demodulation,[],[f605,f572]) ).
tff(f605,plain,
( ! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) )
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f604]) ).
tff(f634,plain,
( spl15_24
| ~ spl15_13
| ~ spl15_19 ),
inference(avatar_split_clause,[],[f602,f598,f570,f631]) ).
tff(f631,plain,
( spl15_24
<=> ( bool_size(fFalse) = nat_size(bool_size(fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
tff(f598,plain,
( spl15_19
<=> ( bool_size(fTrue) = nat_size(bool_size(fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
tff(f602,plain,
( ( bool_size(fFalse) = nat_size(bool_size(fFalse)) )
| ~ spl15_13
| ~ spl15_19 ),
inference(forward_demodulation,[],[f600,f572]) ).
tff(f600,plain,
( ( bool_size(fTrue) = nat_size(bool_size(fTrue)) )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f598]) ).
tff(f621,plain,
spl15_23,
inference(avatar_split_clause,[],[f478,f619]) ).
tff(f478,plain,
! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) ),
inference(forward_demodulation,[],[f317,f291]) ).
tff(f317,plain,
! [X0: bool] : ( zero_zero(nat) = size_size(bool,X0) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: bool] : ( zero_zero(nat) = size_size(bool,X0) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X27: bool] : ( zero_zero(nat) = size_size(bool,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_size__bool) ).
tff(f616,plain,
spl15_22,
inference(avatar_split_clause,[],[f477,f614]) ).
tff(f477,plain,
! [X0: char1] : ( bool_size(fTrue) = size_size(char1,X0) ),
inference(forward_demodulation,[],[f316,f291]) ).
tff(f316,plain,
! [X0: char1] : ( zero_zero(nat) = size_size(char1,X0) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: char1] : ( zero_zero(nat) = size_size(char1,X0) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X11: char1] : ( zero_zero(nat) = size_size(char1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_size__char) ).
tff(f611,plain,
spl15_21,
inference(avatar_split_clause,[],[f476,f609]) ).
tff(f476,plain,
! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) ),
inference(forward_demodulation,[],[f315,f291]) ).
tff(f315,plain,
! [X0: literal] : ( zero_zero(nat) = size_size(literal,X0) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: literal] : ( zero_zero(nat) = size_size(literal,X0) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X6: literal] : ( zero_zero(nat) = size_size(literal,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_size__literal__def) ).
tff(f606,plain,
spl15_20,
inference(avatar_split_clause,[],[f475,f604]) ).
tff(f475,plain,
! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) ),
inference(forward_demodulation,[],[f314,f291]) ).
tff(f314,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X21: nat] : ( zero_zero(nat) = dB_size(var(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_dB_Osize_I1_J) ).
tff(f601,plain,
spl15_19,
inference(avatar_split_clause,[],[f463,f598]) ).
tff(f463,plain,
bool_size(fTrue) = nat_size(bool_size(fTrue)),
inference(forward_demodulation,[],[f293,f291]) ).
tff(f293,plain,
zero_zero(nat) = nat_size(zero_zero(nat)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
zero_zero(nat) = nat_size(zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nat_Osize_I1_J) ).
tff(f596,plain,
spl15_18,
inference(avatar_split_clause,[],[f323,f594]) ).
tff(f323,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X77: bool] :
( ( fFalse = X77 )
| ( fTrue = X77 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f592,plain,
spl15_17,
inference(avatar_split_clause,[],[f298,f589]) ).
tff(f298,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uIT) ).
tff(f587,plain,
spl15_16,
inference(avatar_split_clause,[],[f297,f584]) ).
tff(f297,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
tff(f582,plain,
spl15_15,
inference(avatar_split_clause,[],[f296,f579]) ).
tff(f296,plain,
pp(aa(dB,bool,it,t)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
tff(f577,plain,
( spl15_14
| ~ spl15_8
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f568,f565,f546,f575]) ).
tff(f575,plain,
( spl15_14
<=> ! [X0: nat] : ( bool_size(fFalse) != suc(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
tff(f546,plain,
( spl15_8
<=> ( zero_zero(nat) = bool_size(fTrue) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
tff(f565,plain,
( spl15_12
<=> ! [X0: nat] : ( bool_size(fTrue) != suc(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
tff(f568,plain,
( ! [X0: nat] : ( bool_size(fFalse) != suc(X0) )
| ~ spl15_8
| ~ spl15_12 ),
inference(forward_demodulation,[],[f566,f550]) ).
tff(f550,plain,
( ( bool_size(fTrue) = bool_size(fFalse) )
| ~ spl15_8 ),
inference(forward_demodulation,[],[f548,f292]) ).
tff(f292,plain,
zero_zero(nat) = bool_size(fFalse),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
zero_zero(nat) = bool_size(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_bool_Osize_I2_J) ).
tff(f548,plain,
( ( zero_zero(nat) = bool_size(fTrue) )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f546]) ).
tff(f566,plain,
( ! [X0: nat] : ( bool_size(fTrue) != suc(X0) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f565]) ).
tff(f573,plain,
( spl15_13
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f550,f546,f570]) ).
tff(f567,plain,
spl15_12,
inference(avatar_split_clause,[],[f469,f565]) ).
tff(f469,plain,
! [X0: nat] : ( bool_size(fTrue) != suc(X0) ),
inference(forward_demodulation,[],[f306,f291]) ).
tff(f306,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X61: nat] : ( zero_zero(nat) != suc(X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat_Osimps_I3_J) ).
tff(f563,plain,
spl15_11,
inference(avatar_split_clause,[],[f349,f561]) ).
tff(f561,plain,
( spl15_11
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
tff(f349,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X57: dB,X21: nat] : ( var(X21) != abs(X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_dB_Osimps_I6_J) ).
tff(f559,plain,
spl15_10,
inference(avatar_split_clause,[],[f313,f557]) ).
tff(f557,plain,
( spl15_10
<=> ! [X0: nat] : ( size_size(nat,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
tff(f555,plain,
spl15_9,
inference(avatar_split_clause,[],[f292,f552]) ).
tff(f549,plain,
spl15_8,
inference(avatar_split_clause,[],[f291,f546]) ).
tff(f544,plain,
spl15_7,
inference(avatar_split_clause,[],[f341,f542]) ).
tff(f542,plain,
( spl15_7
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
tff(f341,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f540,plain,
spl15_6,
inference(avatar_split_clause,[],[f304,f538]) ).
tff(f538,plain,
( spl15_6
<=> ! [X0: nat] : ( suc(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
tff(f304,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X23: nat] : ( suc(X23) != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_n__not__Suc__n) ).
tff(f536,plain,
spl15_5,
inference(avatar_split_clause,[],[f288,f533]) ).
tff(f288,plain,
pp(fTrue),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
tff(f531,plain,
spl15_4,
inference(avatar_split_clause,[],[f287,f528]) ).
tff(f528,plain,
( spl15_4
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
tff(f287,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
tff(f526,plain,
spl15_3,
inference(avatar_split_clause,[],[f286,f523]) ).
tff(f523,plain,
( spl15_3
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
tff(f286,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
tff(f521,plain,
spl15_2,
inference(avatar_split_clause,[],[f285,f518]) ).
tff(f518,plain,
( spl15_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
tff(f285,plain,
zero(nat),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f516,plain,
~ spl15_1,
inference(avatar_split_clause,[],[f283,f513]) ).
tff(f513,plain,
( spl15_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
tff(f283,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL809_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 14:09:12 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (2217)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (2220)WARNING: value z3 for option sas not known
% 0.19/0.37 % (2221)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.37 % (2219)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37 % (2222)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)
% 0.19/0.37 % (2223)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)
% 0.19/0.37 % (2220)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)
% 0.19/0.37 % (2218)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.37 % (2224)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)
% 0.19/0.38 % (2224)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.39 % (2225)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.40 % (2226)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)
% 0.19/0.40 % (2227)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)
% 0.19/0.40 % (2225)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % (2226)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % Exception at run slice level
% 0.19/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.42 % (2228)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)
% 0.19/0.43 % (2222)First to succeed.
% 0.19/0.45 % (2222)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2217"
% 0.19/0.45 % (2222)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46 % (2222)------------------------------
% 0.19/0.46 % (2222)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.46 % (2222)Termination reason: Refutation
% 0.19/0.46
% 0.19/0.46 % (2222)Memory used [KB]: 1788
% 0.19/0.46 % (2222)Time elapsed: 0.078 s
% 0.19/0.46 % (2222)Instructions burned: 132 (million)
% 0.19/0.46 % (2217)Success in time 0.094 s
%------------------------------------------------------------------------------