TSTP Solution File: LCL840_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Fri Sep 1 18:56:35 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 466
% Syntax : Number of formulae : 1344 ( 258 unt; 75 typ; 0 def)
% Number of atoms : 3455 ( 736 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3782 (1596 ~;1589 |; 135 &)
% ( 294 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 81 ( 42 >; 39 *; 0 +; 0 <<)
% Number of predicates : 282 ( 280 usr; 272 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 25 con; 0-5 aty)
% Number of variables : 2828 (;2714 !; 90 ?;2828 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_15,type,
suc: nat > nat ).
tff(func_def_16,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_17,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_18,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_19,type,
fFalse: bool ).
tff(func_def_20,type,
fTrue: bool ).
tff(func_def_21,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_22,type,
t2: type ).
tff(func_def_23,type,
t: type ).
tff(func_def_24,type,
t_a: type ).
tff(func_def_25,type,
t1: type ).
tff(func_def_26,type,
ua1: type ).
tff(func_def_27,type,
a: dB ).
tff(func_def_28,type,
as: list(dB) ).
tff(func_def_29,type,
e: fun(nat,type) ).
tff(func_def_30,type,
ea: fun(nat,type) ).
tff(func_def_31,type,
i: nat ).
tff(func_def_32,type,
ia: nat ).
tff(func_def_33,type,
r: dB ).
tff(func_def_34,type,
t3: dB ).
tff(func_def_35,type,
u: dB ).
tff(func_def_36,type,
ua: dB ).
tff(func_def_37,type,
sK3: type ).
tff(func_def_38,type,
sK4: type ).
tff(func_def_39,type,
sK5: nat > nat ).
tff(func_def_40,type,
sK6: nat > nat ).
tff(func_def_41,type,
sK7: dB > dB ).
tff(func_def_42,type,
sK8: dB > list(dB) ).
tff(func_def_43,type,
sK9: dB > nat ).
tff(func_def_44,type,
sK10: dB > dB ).
tff(func_def_45,type,
sK11: dB > dB ).
tff(func_def_46,type,
sK12: dB > list(dB) ).
tff(func_def_47,type,
sK13: ( dB * dB ) > dB ).
tff(func_def_48,type,
sK14: fun(nat,bool) > nat ).
tff(func_def_49,type,
sK15: fun(nat,bool) > nat ).
tff(func_def_50,type,
sK16: ( dB * fun(nat,type) ) > type ).
tff(func_def_51,type,
sK17: ( dB * fun(nat,type) ) > type ).
tff(func_def_52,type,
sK18: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_53,type,
sK19: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_54,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_55,type,
sK21: ( dB * dB * dB ) > dB ).
tff(func_def_56,type,
sK22: ( dB * dB * dB ) > dB ).
tff(func_def_57,type,
sK23: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_58,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_59,type,
sK25: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
typing: ( fun(nat,type) * dB * type ) > $o ).
tff(pred_def_5,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $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(pred_def_9,type,
sP2: ( dB * dB * dB ) > $o ).
tff(f2495,plain,
$false,
inference(avatar_sat_refutation,[],[f480,f485,f490,f495,f500,f504,f508,f512,f516,f520,f525,f531,f536,f541,f546,f551,f555,f559,f564,f569,f573,f577,f581,f585,f589,f593,f597,f601,f605,f609,f624,f631,f635,f639,f643,f647,f660,f666,f672,f676,f684,f689,f693,f697,f703,f708,f712,f717,f722,f726,f731,f735,f739,f743,f748,f752,f757,f761,f766,f772,f776,f780,f784,f792,f796,f800,f804,f811,f817,f823,f829,f834,f838,f844,f848,f852,f856,f860,f864,f875,f879,f883,f888,f892,f897,f901,f906,f911,f917,f921,f928,f932,f936,f941,f946,f950,f970,f975,f980,f986,f991,f996,f1002,f1008,f1013,f1018,f1022,f1027,f1031,f1036,f1041,f1048,f1059,f1065,f1069,f1076,f1080,f1086,f1090,f1094,f1098,f1102,f1106,f1112,f1158,f1163,f1167,f1171,f1176,f1183,f1187,f1194,f1200,f1207,f1213,f1221,f1226,f1232,f1238,f1243,f1249,f1253,f1263,f1269,f1276,f1282,f1288,f1293,f1297,f1302,f1307,f1313,f1317,f1350,f1363,f1371,f1377,f1385,f1392,f1398,f1414,f1420,f1424,f1429,f1438,f1445,f1449,f1453,f1457,f1466,f1473,f1478,f1486,f1493,f1503,f1511,f1528,f1534,f1539,f1545,f1552,f1556,f1560,f1564,f1570,f1579,f1587,f1600,f1604,f1609,f1616,f1624,f1633,f1639,f1643,f1647,f1675,f1679,f1683,f1687,f1711,f1734,f1738,f1742,f1746,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1787,f1792,f1797,f1808,f1812,f1816,f1820,f1825,f1833,f1837,f1841,f1848,f1852,f1864,f1868,f1872,f1882,f1886,f1890,f1894,f1898,f1968,f1974,f1978,f1982,f1986,f1990,f1994,f1998,f2003,f2117,f2121,f2125,f2129,f2133,f2137,f2141,f2145,f2174,f2178,f2182,f2187,f2210,f2214,f2221,f2225,f2229,f2347,f2351,f2356,f2360,f2364,f2403,f2407,f2411,f2437,f2441,f2445,f2449,f2494]) ).
tff(f2494,plain,
( ~ spl26_5
| ~ spl26_15
| spl26_12
| ~ spl26_270 ),
inference(avatar_split_clause,[],[f2488,f2443,f528,f543,f497]) ).
tff(f497,plain,
( spl26_5
<=> typing(e,u,t1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
tff(f543,plain,
( spl26_15
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_15])]) ).
tff(f528,plain,
( spl26_12
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
tff(f2443,plain,
( spl26_270
<=> ! [X5: dB] :
( ~ typing(e,X5,t1)
| ~ pp(aa(dB,bool,it,X5))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_270])]) ).
tff(f2488,plain,
( ~ pp(aa(dB,bool,it,u))
| ~ typing(e,u,t1)
| spl26_12
| ~ spl26_270 ),
inference(resolution,[],[f2444,f530]) ).
tff(f530,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| spl26_12 ),
inference(avatar_component_clause,[],[f528]) ).
tff(f2444,plain,
( ! [X5: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X5)))
| ~ pp(aa(dB,bool,it,X5))
| ~ typing(e,X5,t1) )
| ~ spl26_270 ),
inference(avatar_component_clause,[],[f2443]) ).
tff(f2449,plain,
( spl26_271
| ~ spl26_150
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1547,f1543,f1300,f2447]) ).
tff(f2447,plain,
( spl26_271
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK11(X0)),abs(sK10(X0))),sK12(X0))))
| ~ pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_271])]) ).
tff(f1300,plain,
( spl26_150
<=> ! [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,sK10(X0)),zero_zero(nat)),sK11(X0)),sK12(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_150])]) ).
tff(f1543,plain,
( spl26_180
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_180])]) ).
tff(f1547,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK11(X0)),abs(sK10(X0))),sK12(X0))))
| ~ pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) )
| ~ spl26_150
| ~ spl26_180 ),
inference(resolution,[],[f1544,f1301]) ).
tff(f1301,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,sK10(X0)),zero_zero(nat)),sK11(X0)),sK12(X0))))
| ~ sP0(X0) )
| ~ spl26_150 ),
inference(avatar_component_clause,[],[f1300]) ).
tff(f1544,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_180 ),
inference(avatar_component_clause,[],[f1543]) ).
tff(f2445,plain,
( spl26_270
| ~ spl26_19
| ~ spl26_164 ),
inference(avatar_split_clause,[],[f1431,f1427,f561,f2443]) ).
tff(f561,plain,
( spl26_19
<=> typing(shift(type,e,i,t1),a,t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_19])]) ).
tff(f1427,plain,
( spl26_164
<=> ! [X0: dB,X3: fun(nat,type),X2: nat,X1: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_164])]) ).
tff(f1431,plain,
( ! [X5: dB] :
( ~ typing(e,X5,t1)
| ~ pp(aa(dB,bool,it,X5))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),X5))) )
| ~ spl26_19
| ~ spl26_164 ),
inference(resolution,[],[f1428,f563]) ).
tff(f563,plain,
( typing(shift(type,e,i,t1),a,t2)
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f561]) ).
tff(f1428,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( ~ typing(shift(type,X3,X2,t1),a,X1)
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X0))) )
| ~ spl26_164 ),
inference(avatar_component_clause,[],[f1427]) ).
tff(f2441,plain,
( spl26_269
| ~ spl26_153 ),
inference(avatar_split_clause,[],[f1346,f1315,f2439]) ).
tff(f2439,plain,
( spl26_269
<=> ! [X5: type,X4: type,X0: fun(nat,type),X3: dB,X2: nat,X1: dB] :
( typing(X0,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),X3),X4)
| ~ typing(X0,X3,X5)
| ~ typing(shift(type,X0,X2,X5),X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_269])]) ).
tff(f1315,plain,
( spl26_153
<=> ! [X3: fun(nat,type),X4: type,X0: nat,X6: fun(nat,type),X5: dB,X2: dB,X1: type] :
( typing(X3,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2),X4)
| ( shift(type,X3,X0,X1) != X6 )
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_153])]) ).
tff(f1346,plain,
( ! [X2: nat,X3: dB,X0: fun(nat,type),X1: dB,X4: type,X5: type] :
( typing(X0,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),X3),X4)
| ~ typing(X0,X3,X5)
| ~ typing(shift(type,X0,X2,X5),X1,X4) )
| ~ spl26_153 ),
inference(equality_resolution,[],[f1316]) ).
tff(f1316,plain,
( ! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( ( shift(type,X3,X0,X1) != X6 )
| typing(X3,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2),X4)
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) )
| ~ spl26_153 ),
inference(avatar_component_clause,[],[f1315]) ).
tff(f2437,plain,
( spl26_268
| ~ spl26_40
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1254,f1251,f674,f2435]) ).
tff(f2435,plain,
( spl26_268
<=> ! [X4: dB,X0: fun(nat,type),X3: type,X2: dB,X1: dB] :
( ~ typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X3)
| ~ beta(X2,X4)
| typing(X0,X4,aa(type,type,combc(type,type,type,fun1,X3),sK23(X3,X1,X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_268])]) ).
tff(f674,plain,
( spl26_40
<=> ! [X0: dB,X3: fun(nat,type),X2: dB,X1: type] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_40])]) ).
tff(f1251,plain,
( spl26_142
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| typing(X3,X2,aa(type,type,combc(type,type,type,fun1,X0),sK23(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_142])]) ).
tff(f1254,plain,
( ! [X2: dB,X3: type,X0: fun(nat,type),X1: dB,X4: dB] :
( ~ typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X3)
| ~ beta(X2,X4)
| typing(X0,X4,aa(type,type,combc(type,type,type,fun1,X3),sK23(X3,X1,X2,X0))) )
| ~ spl26_40
| ~ spl26_142 ),
inference(resolution,[],[f1252,f675]) ).
tff(f675,plain,
( ! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( ~ typing(X3,X2,X1)
| ~ beta(X2,X0)
| typing(X3,X0,X1) )
| ~ spl26_40 ),
inference(avatar_component_clause,[],[f674]) ).
tff(f1252,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X2,aa(type,type,combc(type,type,type,fun1,X0),sK23(X0,X1,X2,X3)))
| ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0) )
| ~ spl26_142 ),
inference(avatar_component_clause,[],[f1251]) ).
tff(f2411,plain,
( spl26_267
| ~ spl26_34
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1665,f1641,f637,f2409]) ).
tff(f2409,plain,
( spl26_267
<=> ! [X15: dB] :
( sP1(abs(sK11(X15)))
| ~ sP0(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_267])]) ).
tff(f637,plain,
( spl26_34
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_34])]) ).
tff(f1641,plain,
( spl26_195
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_195])]) ).
tff(f1665,plain,
( ! [X15: dB] :
( sP1(abs(sK11(X15)))
| ~ sP0(X15) )
| ~ spl26_34
| ~ spl26_195 ),
inference(resolution,[],[f1642,f638]) ).
tff(f638,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) )
| ~ spl26_34 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f1642,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(X0)) )
| ~ spl26_195 ),
inference(avatar_component_clause,[],[f1641]) ).
tff(f2407,plain,
( spl26_266
| ~ spl26_82
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1128,f1104,f881,f2405]) ).
tff(f2405,plain,
( spl26_266
<=> ! [X6: fun(nat,type),X9: type,X11: list(type),X10: list(dB),X8: nat,X7: type] :
( typings(shift(type,shift(type,X6,X8,X9),zero_zero(nat),X7),map(dB,dB,combc(dB,nat,dB,lift,suc(X8)),X10),X11)
| ~ typings(shift(type,X6,zero_zero(nat),X7),X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_266])]) ).
tff(f881,plain,
( spl26_82
<=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typings(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_82])]) ).
tff(f1104,plain,
( spl26_123
<=> ! [X0: $tType,X4: fun(nat,X0),X3: nat,X2: X0,X1: X0] : ( shift(X0,shift(X0,X4,X3,X2),zero_zero(nat),X1) = shift(X0,shift(X0,X4,zero_zero(nat),X1),suc(X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_123])]) ).
tff(f1128,plain,
( ! [X10: list(dB),X11: list(type),X8: nat,X6: fun(nat,type),X9: type,X7: type] :
( typings(shift(type,shift(type,X6,X8,X9),zero_zero(nat),X7),map(dB,dB,combc(dB,nat,dB,lift,suc(X8)),X10),X11)
| ~ typings(shift(type,X6,zero_zero(nat),X7),X10,X11) )
| ~ spl26_82
| ~ spl26_123 ),
inference(superposition,[],[f882,f1105]) ).
tff(f1105,plain,
( ! [X0: $tType,X2: X0,X3: nat,X1: X0,X4: fun(nat,X0)] : ( shift(X0,shift(X0,X4,X3,X2),zero_zero(nat),X1) = shift(X0,shift(X0,X4,zero_zero(nat),X1),suc(X3),X2) )
| ~ spl26_123 ),
inference(avatar_component_clause,[],[f1104]) ).
tff(f882,plain,
( ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typings(X4,X3,X2) )
| ~ spl26_82 ),
inference(avatar_component_clause,[],[f881]) ).
tff(f2403,plain,
( spl26_265
| ~ spl26_94
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1127,f1104,f939,f2401]) ).
tff(f2401,plain,
( spl26_265
<=> ! [X3: type,X4: dB,X0: fun(nat,type),X5: type,X2: nat,X1: type] :
( typing(shift(type,shift(type,X0,X2,X3),zero_zero(nat),X1),aa(dB,dB,combc(dB,nat,dB,lift,suc(X2)),X4),X5)
| ~ typing(shift(type,X0,zero_zero(nat),X1),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_265])]) ).
tff(f939,plain,
( spl26_94
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( typing(shift(type,X4,X1,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typing(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_94])]) ).
tff(f1127,plain,
( ! [X2: nat,X3: type,X0: fun(nat,type),X1: type,X4: dB,X5: type] :
( typing(shift(type,shift(type,X0,X2,X3),zero_zero(nat),X1),aa(dB,dB,combc(dB,nat,dB,lift,suc(X2)),X4),X5)
| ~ typing(shift(type,X0,zero_zero(nat),X1),X4,X5) )
| ~ spl26_94
| ~ spl26_123 ),
inference(superposition,[],[f940,f1105]) ).
tff(f940,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( typing(shift(type,X4,X1,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typing(X4,X3,X2) )
| ~ spl26_94 ),
inference(avatar_component_clause,[],[f939]) ).
tff(f2364,plain,
( spl26_264
| ~ spl26_52
| ~ spl26_187 ),
inference(avatar_split_clause,[],[f1594,f1585,f733,f2362]) ).
tff(f2362,plain,
( spl26_264
<=> ! [X31: dB,X33: nat,X29: dB,X32: dB,X30: nat] : ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X32),X29)),X30),X31) != var(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_264])]) ).
tff(f733,plain,
( spl26_52
<=> ! [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,[spl26_52])]) ).
tff(f1585,plain,
( spl26_187
<=> ! [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,[spl26_187])]) ).
tff(f1594,plain,
( ! [X31: dB,X29: dB,X32: dB,X30: nat,X33: nat] : ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X32),X29)),X30),X31) != var(X33) )
| ~ spl26_52
| ~ spl26_187 ),
inference(superposition,[],[f734,f1586]) ).
tff(f1586,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) )
| ~ spl26_187 ),
inference(avatar_component_clause,[],[f1585]) ).
tff(f734,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl26_52 ),
inference(avatar_component_clause,[],[f733]) ).
tff(f2360,plain,
( spl26_263
| ~ spl26_53
| ~ spl26_187 ),
inference(avatar_split_clause,[],[f1593,f1585,f737,f2358]) ).
tff(f2358,plain,
( spl26_263
<=> ! [X28: dB,X24: dB,X27: dB,X25: nat,X26: dB] : ( abs(X28) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X27),X24)),X25),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_263])]) ).
tff(f737,plain,
( spl26_53
<=> ! [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,[spl26_53])]) ).
tff(f1593,plain,
( ! [X28: dB,X26: dB,X27: dB,X24: dB,X25: nat] : ( abs(X28) != aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X27),X24)),X25),X26) )
| ~ spl26_53
| ~ spl26_187 ),
inference(superposition,[],[f738,f1586]) ).
tff(f738,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) )
| ~ spl26_53 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f2356,plain,
( spl26_262
| ~ spl26_21
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1303,f1300,f571,f2354]) ).
tff(f2354,plain,
( spl26_262
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),zero_zero(nat)),sK11(X0)),sK12(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_262])]) ).
tff(f571,plain,
( spl26_21
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_21])]) ).
tff(f1303,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK10(X0)),zero_zero(nat)),sK11(X0)),sK12(X0))) )
| ~ spl26_21
| ~ spl26_150 ),
inference(resolution,[],[f1301,f572]) ).
tff(f572,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl26_21 ),
inference(avatar_component_clause,[],[f571]) ).
tff(f2351,plain,
( spl26_261
| ~ spl26_33
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1126,f1104,f633,f2349]) ).
tff(f2349,plain,
( spl26_261
<=> ! [X6: $tType,X5: nat,X7: fun(nat,X6),X9: X6,X8: X6] :
( ( shift(X6,shift(X6,X7,sK6(X5),X8),zero_zero(nat),X9) = shift(X6,shift(X6,X7,zero_zero(nat),X9),X5,X8) )
| ( zero_zero(nat) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_261])]) ).
tff(f633,plain,
( spl26_33
<=> ! [X0: nat] :
( ( suc(sK6(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_33])]) ).
tff(f1126,plain,
( ! [X6: $tType,X8: X6,X9: X6,X7: fun(nat,X6),X5: nat] :
( ( shift(X6,shift(X6,X7,sK6(X5),X8),zero_zero(nat),X9) = shift(X6,shift(X6,X7,zero_zero(nat),X9),X5,X8) )
| ( zero_zero(nat) = X5 ) )
| ~ spl26_33
| ~ spl26_123 ),
inference(superposition,[],[f1105,f634]) ).
tff(f634,plain,
( ! [X0: nat] :
( ( suc(sK6(X0)) = X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl26_33 ),
inference(avatar_component_clause,[],[f633]) ).
tff(f2347,plain,
( spl26_260
| ~ spl26_32
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1125,f1104,f629,f2345]) ).
tff(f2345,plain,
( spl26_260
<=> ! [X1: $tType,X4: X1,X0: nat,X3: X1,X2: fun(nat,X1)] :
( ( shift(X1,shift(X1,X2,sK5(X0),X3),zero_zero(nat),X4) = shift(X1,shift(X1,X2,zero_zero(nat),X4),X0,X3) )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_260])]) ).
tff(f629,plain,
( spl26_32
<=> ! [X0: nat] :
( ( suc(sK5(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_32])]) ).
tff(f1125,plain,
( ! [X1: $tType,X2: fun(nat,X1),X3: X1,X0: nat,X4: X1] :
( ( shift(X1,shift(X1,X2,sK5(X0),X3),zero_zero(nat),X4) = shift(X1,shift(X1,X2,zero_zero(nat),X4),X0,X3) )
| ( zero_zero(nat) = X0 ) )
| ~ spl26_32
| ~ spl26_123 ),
inference(superposition,[],[f1105,f630]) ).
tff(f630,plain,
( ! [X0: nat] :
( ( suc(sK5(X0)) = X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f629]) ).
tff(f2229,plain,
( spl26_259
| ~ spl26_120
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1149,f1110,f1092,f2227]) ).
tff(f2227,plain,
( spl26_259
<=> ! [X41: type,X42: fun(type,type),X44: type,X43: type] :
( ( aa(type,type,combs(type,type,type,fun1,X42),X41) != aa(type,type,aa(type,fun(type,type),fun1,X43),X44) )
| ( aa(type,type,X42,X41) = X44 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_259])]) ).
tff(f1092,plain,
( spl26_120
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_120])]) ).
tff(f1110,plain,
( spl26_124
<=> ! [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,[spl26_124])]) ).
tff(f1149,plain,
( ! [X41: type,X44: type,X42: fun(type,type),X43: type] :
( ( aa(type,type,combs(type,type,type,fun1,X42),X41) != aa(type,type,aa(type,fun(type,type),fun1,X43),X44) )
| ( aa(type,type,X42,X41) = X44 ) )
| ~ spl26_120
| ~ spl26_124 ),
inference(superposition,[],[f1093,f1111]) ).
tff(f1111,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)) )
| ~ spl26_124 ),
inference(avatar_component_clause,[],[f1110]) ).
tff(f1093,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_120 ),
inference(avatar_component_clause,[],[f1092]) ).
tff(f2225,plain,
( spl26_258
| ~ spl26_122
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1141,f1110,f1100,f2223]) ).
tff(f2223,plain,
( spl26_258
<=> ! [X10: dB,X11: fun(dB,dB),X13: dB,X12: dB] :
( ( aa(dB,dB,combs(dB,dB,dB,app,X11),X10) != aa(dB,dB,aa(dB,fun(dB,dB),app,X12),X13) )
| ( aa(dB,dB,X11,X10) = X13 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_258])]) ).
tff(f1100,plain,
( spl26_122
<=> ! [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,[spl26_122])]) ).
tff(f1141,plain,
( ! [X10: dB,X11: fun(dB,dB),X12: dB,X13: dB] :
( ( aa(dB,dB,combs(dB,dB,dB,app,X11),X10) != aa(dB,dB,aa(dB,fun(dB,dB),app,X12),X13) )
| ( aa(dB,dB,X11,X10) = X13 ) )
| ~ spl26_122
| ~ spl26_124 ),
inference(superposition,[],[f1101,f1111]) ).
tff(f1101,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: 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 ) )
| ~ spl26_122 ),
inference(avatar_component_clause,[],[f1100]) ).
tff(f2221,plain,
( spl26_257
| ~ spl26_23
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1129,f1110,f579,f2219]) ).
tff(f2219,plain,
( spl26_257
<=> ! [X1: $tType,X0: $tType,X3: fun(fun(X0,X1),X0),X2: fun(X0,X1)] : ( aa(fun(X0,X1),X1,combs(fun(X0,X1),X0,X1,combi(fun(X0,X1)),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_257])]) ).
tff(f579,plain,
( spl26_23
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_23])]) ).
tff(f1129,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(fun(X0,X1),X0)] : ( aa(fun(X0,X1),X1,combs(fun(X0,X1),X0,X1,combi(fun(X0,X1)),X3),X2) = aa(X0,X1,X2,aa(fun(X0,X1),X0,X3,X2)) )
| ~ spl26_23
| ~ spl26_124 ),
inference(superposition,[],[f1111,f580]) ).
tff(f580,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl26_23 ),
inference(avatar_component_clause,[],[f579]) ).
tff(f2214,plain,
( spl26_256
| ~ spl26_96
| ~ spl26_135 ),
inference(avatar_split_clause,[],[f1214,f1211,f948,f2212]) ).
tff(f2212,plain,
( spl26_256
<=> ! [X4: nat,X5: dB,X3: dB] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X3),X4),aa(dB,dB,combc(dB,nat,dB,lift,X4),X5)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_256])]) ).
tff(f948,plain,
( spl26_96
<=> ! [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,[spl26_96])]) ).
tff(f1211,plain,
( spl26_135
<=> ! [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,[spl26_135])]) ).
tff(f1214,plain,
( ! [X3: dB,X4: nat,X5: dB] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X3),X4),aa(dB,dB,combc(dB,nat,dB,lift,X4),X5)) = X5 )
| ~ spl26_96
| ~ spl26_135 ),
inference(superposition,[],[f1212,f949]) ).
tff(f949,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) )
| ~ spl26_96 ),
inference(avatar_component_clause,[],[f948]) ).
tff(f1212,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 )
| ~ spl26_135 ),
inference(avatar_component_clause,[],[f1211]) ).
tff(f2210,plain,
( spl26_255
| ~ spl26_22
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1648,f1641,f575,f2208]) ).
tff(f2208,plain,
( spl26_255
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_255])]) ).
tff(f575,plain,
( spl26_22
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_22])]) ).
tff(f1648,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl26_22
| ~ spl26_195 ),
inference(resolution,[],[f1642,f576]) ).
tff(f576,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl26_22 ),
inference(avatar_component_clause,[],[f575]) ).
tff(f2187,plain,
( ~ spl26_16
| spl26_254
| ~ spl26_133
| ~ spl26_180 ),
inference(avatar_split_clause,[],[f1546,f1543,f1197,f2184,f548]) ).
tff(f548,plain,
( spl26_16
<=> pp(aa(dB,bool,it,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_16])]) ).
tff(f2184,plain,
( spl26_254
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_254])]) ).
tff(f1197,plain,
( spl26_133
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_133])]) ).
tff(f1546,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as)))
| ~ pp(aa(dB,bool,it,a))
| ~ spl26_133
| ~ spl26_180 ),
inference(resolution,[],[f1544,f1199]) ).
tff(f1199,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)))
| ~ spl26_133 ),
inference(avatar_component_clause,[],[f1197]) ).
tff(f2182,plain,
( spl26_253
| ~ spl26_111
| ~ spl26_144 ),
inference(avatar_split_clause,[],[f1270,f1267,f1039,f2180]) ).
tff(f2180,plain,
( spl26_253
<=> ! [X4: type,X0: fun(nat,type),X3: type,X2: dB,X1: dB] :
( typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X3)
| ~ typing(X0,X1,X4)
| ~ typing(shift(type,X0,zero_zero(nat),X4),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_253])]) ).
tff(f1039,plain,
( spl26_111
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,combc(type,type,type,fun1,X0),X2))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_111])]) ).
tff(f1267,plain,
( spl26_144
<=> ! [X4: fun(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ typing(X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2))
| typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3),X1)
| ~ typing(X4,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_144])]) ).
tff(f1270,plain,
( ! [X2: dB,X3: type,X0: fun(nat,type),X1: dB,X4: type] :
( typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X3)
| ~ typing(X0,X1,X4)
| ~ typing(shift(type,X0,zero_zero(nat),X4),X2,X3) )
| ~ spl26_111
| ~ spl26_144 ),
inference(resolution,[],[f1268,f1040]) ).
tff(f1040,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,combc(type,type,type,fun1,X0),X2))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) )
| ~ spl26_111 ),
inference(avatar_component_clause,[],[f1039]) ).
tff(f1268,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ typing(X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2))
| typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3),X1)
| ~ typing(X4,X0,X2) )
| ~ spl26_144 ),
inference(avatar_component_clause,[],[f1267]) ).
tff(f2178,plain,
( spl26_252
| ~ spl26_65
| ~ spl26_142 ),
inference(avatar_split_clause,[],[f1257,f1251,f794,f2176]) ).
tff(f2176,plain,
( spl26_252
<=> ! [X13: fun(nat,type),X14: dB,X16: type,X15: dB] :
( ~ typing(X13,aa(dB,dB,combc(dB,dB,dB,app,X14),abs(X15)),X16)
| typing(shift(type,X13,zero_zero(nat),sK16(X15,X13)),X15,sK17(X15,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_252])]) ).
tff(f794,plain,
( spl26_65
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( typing(shift(type,X2,zero_zero(nat),sK16(X1,X2)),X1,sK17(X1,X2))
| ~ typing(X2,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_65])]) ).
tff(f1257,plain,
( ! [X16: type,X14: dB,X15: dB,X13: fun(nat,type)] :
( ~ typing(X13,aa(dB,dB,combc(dB,dB,dB,app,X14),abs(X15)),X16)
| typing(shift(type,X13,zero_zero(nat),sK16(X15,X13)),X15,sK17(X15,X13)) )
| ~ spl26_65
| ~ spl26_142 ),
inference(resolution,[],[f1252,f795]) ).
tff(f795,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X2,abs(X1),X0)
| typing(shift(type,X2,zero_zero(nat),sK16(X1,X2)),X1,sK17(X1,X2)) )
| ~ spl26_65 ),
inference(avatar_component_clause,[],[f794]) ).
tff(f2174,plain,
( spl26_251
| ~ spl26_44
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1148,f1110,f695,f2172]) ).
tff(f2172,plain,
( spl26_251
<=> ! [X36: $tType,X38: X36,X40: type,X39: fun(X36,nat),X37: fun(X36,fun(nat,type))] :
( ( aa(X36,type,combs(X36,nat,type,X37,X39),X38) != X40 )
| typing(aa(X36,fun(nat,type),X37,X38),var(aa(X36,nat,X39,X38)),X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_251])]) ).
tff(f695,plain,
( spl26_44
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( typing(X2,var(X1),X0)
| ( aa(nat,type,X2,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_44])]) ).
tff(f1148,plain,
( ! [X36: $tType,X40: type,X38: X36,X39: fun(X36,nat),X37: fun(X36,fun(nat,type))] :
( ( aa(X36,type,combs(X36,nat,type,X37,X39),X38) != X40 )
| typing(aa(X36,fun(nat,type),X37,X38),var(aa(X36,nat,X39,X38)),X40) )
| ~ spl26_44
| ~ spl26_124 ),
inference(superposition,[],[f696,f1111]) ).
tff(f696,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) != X0 )
| typing(X2,var(X1),X0) )
| ~ spl26_44 ),
inference(avatar_component_clause,[],[f695]) ).
tff(f2145,plain,
( spl26_250
| ~ spl26_21
| ~ spl26_137 ),
inference(avatar_split_clause,[],[f1227,f1224,f571,f2143]) ).
tff(f2143,plain,
( spl26_250
<=> ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_250])]) ).
tff(f1224,plain,
( spl26_137
<=> ! [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,[spl26_137])]) ).
tff(f1227,plain,
( ! [X2: nat,X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X0),X1),var(X2))) )
| ~ spl26_21
| ~ spl26_137 ),
inference(resolution,[],[f1225,f572]) ).
tff(f1225,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)) )
| ~ spl26_137 ),
inference(avatar_component_clause,[],[f1224]) ).
tff(f2141,plain,
( spl26_249
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1189,f1185,f2139]) ).
tff(f2139,plain,
( spl26_249
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( X0 != X1 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) = aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_249])]) ).
tff(f1185,plain,
( spl26_131
<=> ! [X0: dB,X3: dB,X2: dB,X1: 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 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_131])]) ).
tff(f1189,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( X0 != X1 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) = aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0) ) )
| ~ spl26_131 ),
inference(equality_resolution,[],[f1186]) ).
tff(f1186,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 != X3 )
| ( X0 != X2 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) )
| ~ spl26_131 ),
inference(avatar_component_clause,[],[f1185]) ).
tff(f2137,plain,
( spl26_248
| ~ spl26_130 ),
inference(avatar_split_clause,[],[f1188,f1181,f2135]) ).
tff(f2135,plain,
( spl26_248
<=> ! [X2: type,X0: type,X1: type] :
( ( X0 != X1 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X2),X0) = aa(type,type,aa(type,fun(type,type),fun1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_248])]) ).
tff(f1181,plain,
( spl26_130
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_130])]) ).
tff(f1188,plain,
( ! [X2: type,X0: type,X1: type] :
( ( X0 != X1 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X2),X0) = aa(type,type,aa(type,fun(type,type),fun1,X2),X1) ) )
| ~ spl26_130 ),
inference(equality_resolution,[],[f1182]) ).
tff(f1182,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 != X3 )
| ( X0 != X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) )
| ~ spl26_130 ),
inference(avatar_component_clause,[],[f1181]) ).
tff(f2133,plain,
( spl26_247
| ~ spl26_40
| ~ spl26_111 ),
inference(avatar_split_clause,[],[f1044,f1039,f674,f2131]) ).
tff(f2131,plain,
( spl26_247
<=> ! [X10: dB,X11: type,X12: dB,X9: type,X8: fun(nat,type)] :
( ~ typing(shift(type,X8,zero_zero(nat),X9),X10,X11)
| ~ beta(abs(X10),X12)
| typing(X8,X12,aa(type,type,combc(type,type,type,fun1,X11),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_247])]) ).
tff(f1044,plain,
( ! [X10: dB,X11: type,X8: fun(nat,type),X9: type,X12: dB] :
( ~ typing(shift(type,X8,zero_zero(nat),X9),X10,X11)
| ~ beta(abs(X10),X12)
| typing(X8,X12,aa(type,type,combc(type,type,type,fun1,X11),X9)) )
| ~ spl26_40
| ~ spl26_111 ),
inference(resolution,[],[f1040,f675]) ).
tff(f2129,plain,
( spl26_246
| ~ spl26_40
| ~ spl26_104 ),
inference(avatar_split_clause,[],[f1009,f1005,f674,f2127]) ).
tff(f2127,plain,
( spl26_246
<=> ! [X0: dB] :
( ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),X0)
| typing(shift(type,e,i,t1),X0,t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_246])]) ).
tff(f1005,plain,
( spl26_104
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_104])]) ).
tff(f1009,plain,
( ! [X0: dB] :
( ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),X0)
| typing(shift(type,e,i,t1),X0,t) )
| ~ spl26_40
| ~ spl26_104 ),
inference(resolution,[],[f1007,f675]) ).
tff(f1007,plain,
( typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t)
| ~ spl26_104 ),
inference(avatar_component_clause,[],[f1005]) ).
tff(f2125,plain,
( spl26_245
| ~ spl26_18
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1650,f1641,f557,f2123]) ).
tff(f2123,plain,
( spl26_245
<=> ! [X2: nat] : sP1(abs(var(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_245])]) ).
tff(f557,plain,
( spl26_18
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_18])]) ).
tff(f1650,plain,
( ! [X2: nat] : sP1(abs(var(X2)))
| ~ spl26_18
| ~ spl26_195 ),
inference(resolution,[],[f1642,f558]) ).
tff(f558,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f557]) ).
tff(f2121,plain,
( spl26_244
| ~ spl26_40
| ~ spl26_102 ),
inference(avatar_split_clause,[],[f997,f993,f674,f2119]) ).
tff(f2119,plain,
( spl26_244
<=> ! [X0: dB] :
( ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),X0)
| typing(shift(type,ea,ia,t1),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_244])]) ).
tff(f993,plain,
( spl26_102
<=> typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_102])]) ).
tff(f997,plain,
( ! [X0: dB] :
( ~ beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),X0)
| typing(shift(type,ea,ia,t1),X0,t_a) )
| ~ spl26_40
| ~ spl26_102 ),
inference(resolution,[],[f995,f675]) ).
tff(f995,plain,
( typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t_a)
| ~ spl26_102 ),
inference(avatar_component_clause,[],[f993]) ).
tff(f2117,plain,
( spl26_243
| ~ spl26_43
| ~ spl26_77 ),
inference(avatar_split_clause,[],[f870,f854,f691,f2115]) ).
tff(f2115,plain,
( spl26_243
<=> ! [X6: type,X4: fun(nat,type),X5: nat] :
( ~ typing(X4,abs(var(X5)),X6)
| ( aa(nat,type,shift(type,X4,zero_zero(nat),sK18(X6,var(X5),X4)),X5) = sK19(X6,var(X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_243])]) ).
tff(f691,plain,
( spl26_43
<=> ! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ typing(X2,var(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_43])]) ).
tff(f854,plain,
( spl26_77
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( typing(shift(type,X2,zero_zero(nat),sK18(X0,X1,X2)),X1,sK19(X0,X1,X2))
| ~ typing(X2,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_77])]) ).
tff(f870,plain,
( ! [X6: type,X4: fun(nat,type),X5: nat] :
( ~ typing(X4,abs(var(X5)),X6)
| ( aa(nat,type,shift(type,X4,zero_zero(nat),sK18(X6,var(X5),X4)),X5) = sK19(X6,var(X5),X4) ) )
| ~ spl26_43
| ~ spl26_77 ),
inference(resolution,[],[f855,f692]) ).
tff(f692,plain,
( ! [X2: fun(nat,type),X0: type,X1: nat] :
( ~ typing(X2,var(X1),X0)
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl26_43 ),
inference(avatar_component_clause,[],[f691]) ).
tff(f855,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( typing(shift(type,X2,zero_zero(nat),sK18(X0,X1,X2)),X1,sK19(X0,X1,X2))
| ~ typing(X2,abs(X1),X0) )
| ~ spl26_77 ),
inference(avatar_component_clause,[],[f854]) ).
tff(f2003,plain,
( spl26_242
| ~ spl26_21
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1201,f1197,f571,f2000]) ).
tff(f2000,plain,
( spl26_242
<=> sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_242])]) ).
tff(f1201,plain,
( sP1(foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as))
| ~ spl26_21
| ~ spl26_133 ),
inference(resolution,[],[f1199,f572]) ).
tff(f1998,plain,
( spl26_241
| ~ spl26_119
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1151,f1110,f1088,f1996]) ).
tff(f1996,plain,
( spl26_241
<=> ! [X51: type,X50: fun(type,type),X49: type,X52: type] :
( ( aa(type,type,combs(type,type,type,fun1,X50),X49) != aa(type,type,aa(type,fun(type,type),fun1,X51),X52) )
| ( X49 = X51 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_241])]) ).
tff(f1088,plain,
( spl26_119
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_119])]) ).
tff(f1151,plain,
( ! [X50: fun(type,type),X51: type,X49: type,X52: type] :
( ( aa(type,type,combs(type,type,type,fun1,X50),X49) != aa(type,type,aa(type,fun(type,type),fun1,X51),X52) )
| ( X49 = X51 ) )
| ~ spl26_119
| ~ spl26_124 ),
inference(superposition,[],[f1089,f1111]) ).
tff(f1089,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl26_119 ),
inference(avatar_component_clause,[],[f1088]) ).
tff(f1994,plain,
( spl26_240
| ~ spl26_121
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1143,f1110,f1096,f1992]) ).
tff(f1992,plain,
( spl26_240
<=> ! [X18: dB,X19: fun(dB,dB),X20: dB,X21: dB] :
( ( aa(dB,dB,combs(dB,dB,dB,app,X19),X18) != aa(dB,dB,aa(dB,fun(dB,dB),app,X20),X21) )
| ( X18 = X20 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_240])]) ).
tff(f1096,plain,
( spl26_121
<=> ! [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,[spl26_121])]) ).
tff(f1143,plain,
( ! [X21: dB,X18: dB,X19: fun(dB,dB),X20: dB] :
( ( aa(dB,dB,combs(dB,dB,dB,app,X19),X18) != aa(dB,dB,aa(dB,fun(dB,dB),app,X20),X21) )
| ( X18 = X20 ) )
| ~ spl26_121
| ~ spl26_124 ),
inference(superposition,[],[f1097,f1111]) ).
tff(f1097,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
| ( X1 = X3 ) )
| ~ spl26_121 ),
inference(avatar_component_clause,[],[f1096]) ).
tff(f1990,plain,
( spl26_239
| ~ spl26_96
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1138,f1110,f948,f1988]) ).
tff(f1988,plain,
( spl26_239
<=> ! [X7: $tType,X8: $tType,X6: $tType,X10: X8,X11: fun(X8,X6),X9: fun(X8,fun(X6,X7))] : ( aa(X8,X7,combc(X8,X6,X7,X9,aa(X8,X6,X11,X10)),X10) = aa(X8,X7,combs(X8,X6,X7,X9,X11),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_239])]) ).
tff(f1138,plain,
( ! [X7: $tType,X6: $tType,X8: $tType,X10: X8,X11: fun(X8,X6),X9: fun(X8,fun(X6,X7))] : ( aa(X8,X7,combc(X8,X6,X7,X9,aa(X8,X6,X11,X10)),X10) = aa(X8,X7,combs(X8,X6,X7,X9,X11),X10) )
| ~ spl26_96
| ~ spl26_124 ),
inference(superposition,[],[f1111,f949]) ).
tff(f1986,plain,
( spl26_238
| ~ spl26_96
| ~ spl26_122 ),
inference(avatar_split_clause,[],[f1122,f1100,f948,f1984]) ).
tff(f1984,plain,
( spl26_238
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_238])]) ).
tff(f1122,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X1 = X3 ) )
| ~ spl26_96
| ~ spl26_122 ),
inference(superposition,[],[f1101,f949]) ).
tff(f1982,plain,
( spl26_237
| ~ spl26_96
| ~ spl26_121 ),
inference(avatar_split_clause,[],[f1119,f1096,f948,f1980]) ).
tff(f1980,plain,
( spl26_237
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_237])]) ).
tff(f1119,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_96
| ~ spl26_121 ),
inference(superposition,[],[f1097,f949]) ).
tff(f1978,plain,
( spl26_236
| ~ spl26_96
| ~ spl26_120 ),
inference(avatar_split_clause,[],[f1116,f1092,f948,f1976]) ).
tff(f1976,plain,
( spl26_236
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_236])]) ).
tff(f1116,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X1 = X3 ) )
| ~ spl26_96
| ~ spl26_120 ),
inference(superposition,[],[f1093,f949]) ).
tff(f1974,plain,
( spl26_235
| ~ spl26_96
| ~ spl26_119 ),
inference(avatar_split_clause,[],[f1113,f1088,f948,f1972]) ).
tff(f1972,plain,
( spl26_235
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_235])]) ).
tff(f1113,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) )
| ( X0 = X2 ) )
| ~ spl26_96
| ~ spl26_119 ),
inference(superposition,[],[f1089,f949]) ).
tff(f1968,plain,
( spl26_234
| ~ spl26_40
| ~ spl26_94 ),
inference(avatar_split_clause,[],[f942,f939,f674,f1966]) ).
tff(f1966,plain,
( spl26_234
<=> ! [X5: type,X4: dB,X0: fun(nat,type),X3: nat,X2: type,X1: dB] :
( ~ typing(X0,X1,X2)
| ~ beta(aa(dB,dB,combc(dB,nat,dB,lift,X3),X1),X4)
| typing(shift(type,X0,X3,X5),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_234])]) ).
tff(f942,plain,
( ! [X2: type,X3: nat,X0: fun(nat,type),X1: dB,X4: dB,X5: type] :
( ~ typing(X0,X1,X2)
| ~ beta(aa(dB,dB,combc(dB,nat,dB,lift,X3),X1),X4)
| typing(shift(type,X0,X3,X5),X4,X2) )
| ~ spl26_40
| ~ spl26_94 ),
inference(resolution,[],[f940,f675]) ).
tff(f1898,plain,
( spl26_233
| ~ spl26_23
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1133,f1110,f579,f1896]) ).
tff(f1896,plain,
( spl26_233
<=> ! [X2: $tType,X0: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,combs(X0,X0,X2,X3,combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_233])]) ).
tff(f1133,plain,
( ! [X0: $tType,X2: $tType,X3: fun(X0,fun(X0,X2)),X1: X0] : ( aa(X0,X2,combs(X0,X0,X2,X3,combi(X0)),X1) = aa(X0,X2,aa(X0,fun(X0,X2),X3,X1),X1) )
| ~ spl26_23
| ~ spl26_124 ),
inference(superposition,[],[f1111,f580]) ).
tff(f1894,plain,
( spl26_232
| ~ spl26_23
| ~ spl26_112 ),
inference(avatar_split_clause,[],[f1052,f1046,f579,f1892]) ).
tff(f1892,plain,
( spl26_232
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK24(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK24(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_232])]) ).
tff(f1046,plain,
( spl26_112
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK24(X0,X1,X2,X3)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_112])]) ).
tff(f1052,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK24(X0,X0,combi(X0),X1) != aa(X0,X0,X1,sK24(X0,X0,combi(X0),X1)) )
| ( combi(X0) = X1 ) )
| ~ spl26_23
| ~ spl26_112 ),
inference(superposition,[],[f1047,f580]) ).
tff(f1047,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK24(X0,X1,X2,X3)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl26_112 ),
inference(avatar_component_clause,[],[f1046]) ).
tff(f1890,plain,
( spl26_231
| ~ spl26_23
| ~ spl26_112 ),
inference(avatar_split_clause,[],[f1049,f1046,f579,f1888]) ).
tff(f1888,plain,
( spl26_231
<=> ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK24(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK24(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_231])]) ).
tff(f1049,plain,
( ! [X0: $tType,X1: fun(X0,X0)] :
( ( sK24(X0,X0,X1,combi(X0)) != aa(X0,X0,X1,sK24(X0,X0,X1,combi(X0))) )
| ( combi(X0) = X1 ) )
| ~ spl26_23
| ~ spl26_112 ),
inference(superposition,[],[f1047,f580]) ).
tff(f1886,plain,
( spl26_230
| ~ spl26_44
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f966,f948,f695,f1884]) ).
tff(f1884,plain,
( spl26_230
<=> ! [X28: $tType,X31: nat,X29: fun(X28,fun(nat,type)),X32: type,X30: X28] :
( ( aa(X28,type,combc(X28,nat,type,X29,X31),X30) != X32 )
| typing(aa(X28,fun(nat,type),X29,X30),var(X31),X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_230])]) ).
tff(f966,plain,
( ! [X28: $tType,X31: nat,X29: fun(X28,fun(nat,type)),X32: type,X30: X28] :
( ( aa(X28,type,combc(X28,nat,type,X29,X31),X30) != X32 )
| typing(aa(X28,fun(nat,type),X29,X30),var(X31),X32) )
| ~ spl26_44
| ~ spl26_96 ),
inference(superposition,[],[f696,f949]) ).
tff(f1882,plain,
( spl26_229
| ~ spl26_40
| ~ spl26_77 ),
inference(avatar_split_clause,[],[f869,f854,f674,f1880]) ).
tff(f1880,plain,
( spl26_229
<=> ! [X0: fun(nat,type),X3: dB,X2: type,X1: dB] :
( ~ typing(X0,abs(X1),X2)
| ~ beta(X1,X3)
| typing(shift(type,X0,zero_zero(nat),sK18(X2,X1,X0)),X3,sK19(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_229])]) ).
tff(f869,plain,
( ! [X2: type,X3: dB,X0: fun(nat,type),X1: dB] :
( ~ typing(X0,abs(X1),X2)
| ~ beta(X1,X3)
| typing(shift(type,X0,zero_zero(nat),sK18(X2,X1,X0)),X3,sK19(X2,X1,X0)) )
| ~ spl26_40
| ~ spl26_77 ),
inference(resolution,[],[f855,f675]) ).
tff(f1872,plain,
( spl26_228
| ~ spl26_52
| ~ spl26_176 ),
inference(avatar_split_clause,[],[f1519,f1509,f733,f1870]) ).
tff(f1870,plain,
( spl26_228
<=> ! [X25: dB,X27: nat,X24: nat,X26: dB] : ( var(X27) != aa(dB,dB,combc(dB,nat,dB,lift,X24),aa(dB,dB,combc(dB,dB,dB,app,X26),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_228])]) ).
tff(f1509,plain,
( spl26_176
<=> ! [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,[spl26_176])]) ).
tff(f1519,plain,
( ! [X26: dB,X27: nat,X24: nat,X25: dB] : ( var(X27) != aa(dB,dB,combc(dB,nat,dB,lift,X24),aa(dB,dB,combc(dB,dB,dB,app,X26),X25)) )
| ~ spl26_52
| ~ spl26_176 ),
inference(superposition,[],[f734,f1510]) ).
tff(f1510,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)) )
| ~ spl26_176 ),
inference(avatar_component_clause,[],[f1509]) ).
tff(f1868,plain,
( spl26_227
| ~ spl26_53
| ~ spl26_176 ),
inference(avatar_split_clause,[],[f1518,f1509,f737,f1866]) ).
tff(f1866,plain,
( spl26_227
<=> ! [X22: dB,X20: nat,X21: dB,X23: dB] : ( aa(dB,dB,combc(dB,nat,dB,lift,X20),aa(dB,dB,combc(dB,dB,dB,app,X22),X21)) != abs(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_227])]) ).
tff(f1518,plain,
( ! [X21: dB,X22: dB,X23: dB,X20: nat] : ( aa(dB,dB,combc(dB,nat,dB,lift,X20),aa(dB,dB,combc(dB,dB,dB,app,X22),X21)) != abs(X23) )
| ~ spl26_53
| ~ spl26_176 ),
inference(superposition,[],[f738,f1510]) ).
tff(f1864,plain,
( spl26_226
| ~ spl26_65
| ~ spl26_111 ),
inference(avatar_split_clause,[],[f1043,f1039,f794,f1862]) ).
tff(f1862,plain,
( spl26_226
<=> ! [X5: type,X4: fun(nat,type),X7: type,X6: dB] :
( ~ typing(shift(type,X4,zero_zero(nat),X5),X6,X7)
| typing(shift(type,X4,zero_zero(nat),sK16(X6,X4)),X6,sK17(X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_226])]) ).
tff(f1043,plain,
( ! [X6: dB,X7: type,X4: fun(nat,type),X5: type] :
( ~ typing(shift(type,X4,zero_zero(nat),X5),X6,X7)
| typing(shift(type,X4,zero_zero(nat),sK16(X6,X4)),X6,sK17(X6,X4)) )
| ~ spl26_65
| ~ spl26_111 ),
inference(resolution,[],[f1040,f795]) ).
tff(f1852,plain,
( spl26_225
| ~ spl26_40
| ~ spl26_71 ),
inference(avatar_split_clause,[],[f830,f826,f674,f1850]) ).
tff(f1850,plain,
( spl26_225
<=> ! [X0: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0)
| typing(shift(type,e,i,t1),X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_225])]) ).
tff(f826,plain,
( spl26_71
<=> typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_71])]) ).
tff(f830,plain,
( ! [X0: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0)
| typing(shift(type,e,i,t1),X0,sK4) )
| ~ spl26_40
| ~ spl26_71 ),
inference(resolution,[],[f828,f675]) ).
tff(f828,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),sK4)
| ~ spl26_71 ),
inference(avatar_component_clause,[],[f826]) ).
tff(f1848,plain,
( spl26_224
| ~ spl26_40
| ~ spl26_69 ),
inference(avatar_split_clause,[],[f818,f814,f674,f1846]) ).
tff(f1846,plain,
( spl26_224
<=> ! [X0: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0)
| typing(shift(type,e,i,t1),X0,ua1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_224])]) ).
tff(f814,plain,
( spl26_69
<=> typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),ua1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_69])]) ).
tff(f818,plain,
( ! [X0: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),X0)
| typing(shift(type,e,i,t1),X0,ua1) )
| ~ spl26_40
| ~ spl26_69 ),
inference(resolution,[],[f816,f675]) ).
tff(f816,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),ua1)
| ~ spl26_69 ),
inference(avatar_component_clause,[],[f814]) ).
tff(f1841,plain,
( spl26_223
| ~ spl26_85
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f957,f948,f895,f1839]) ).
tff(f1839,plain,
( spl26_223
<=> ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_223])]) ).
tff(f895,plain,
( spl26_85
<=> ! [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,[spl26_85])]) ).
tff(f957,plain,
( ! [X0: dB,X1: nat] : ( aa(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X0),X1),var(X1)) = X0 )
| ~ spl26_85
| ~ spl26_96 ),
inference(superposition,[],[f949,f896]) ).
tff(f896,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 )
| ~ spl26_85 ),
inference(avatar_component_clause,[],[f895]) ).
tff(f1837,plain,
( spl26_222
| ~ spl26_79
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1147,f1110,f862,f1835]) ).
tff(f1835,plain,
( spl26_222
<=> ! [X34: nat,X32: dB,X35: list(dB),X33: fun(dB,dB)] : ( aa(dB,dB,combs(dB,dB,dB,app,X33),abs(X32)) != foldl(dB,dB,app,var(X34),X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_222])]) ).
tff(f862,plain,
( spl26_79
<=> ! [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,[spl26_79])]) ).
tff(f1147,plain,
( ! [X34: nat,X35: list(dB),X32: dB,X33: fun(dB,dB)] : ( aa(dB,dB,combs(dB,dB,dB,app,X33),abs(X32)) != foldl(dB,dB,app,var(X34),X35) )
| ~ spl26_79
| ~ spl26_124 ),
inference(superposition,[],[f863,f1111]) ).
tff(f863,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) )
| ~ spl26_79 ),
inference(avatar_component_clause,[],[f862]) ).
tff(f1833,plain,
( spl26_221
| ~ spl26_79
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f964,f948,f862,f1831]) ).
tff(f1831,plain,
( spl26_221
<=> ! [X22: dB,X25: list(dB),X24: nat,X23: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X23),abs(X22)) != foldl(dB,dB,app,var(X24),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_221])]) ).
tff(f964,plain,
( ! [X24: nat,X22: dB,X25: list(dB),X23: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X23),abs(X22)) != foldl(dB,dB,app,var(X24),X25) )
| ~ spl26_79
| ~ spl26_96 ),
inference(superposition,[],[f863,f949]) ).
tff(f1825,plain,
( spl26_220
| ~ spl26_14
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1662,f1641,f538,f1822]) ).
tff(f1822,plain,
( spl26_220
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_220])]) ).
tff(f538,plain,
( spl26_14
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_14])]) ).
tff(f1662,plain,
( sP1(abs(ua))
| ~ spl26_14
| ~ spl26_195 ),
inference(resolution,[],[f1642,f540]) ).
tff(f540,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl26_14 ),
inference(avatar_component_clause,[],[f538]) ).
tff(f1820,plain,
( spl26_219
| ~ spl26_21
| ~ spl26_98 ),
inference(avatar_split_clause,[],[f976,f973,f571,f1818]) ).
tff(f1818,plain,
( spl26_219
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_219])]) ).
tff(f973,plain,
( spl26_98
<=> ! [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,[spl26_98])]) ).
tff(f976,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,dB,dB,app,var(X1)),X0)) )
| ~ spl26_21
| ~ spl26_98 ),
inference(resolution,[],[f974,f572]) ).
tff(f974,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)) )
| ~ spl26_98 ),
inference(avatar_component_clause,[],[f973]) ).
tff(f1816,plain,
( spl26_218
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f953,f930,f1814]) ).
tff(f1814,plain,
( spl26_218
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X0),X1) = foldl(dB,dB,app,abs(X2),X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_218])]) ).
tff(f930,plain,
( spl26_92
<=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_92])]) ).
tff(f953,plain,
( ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,abs(X0),X1) = foldl(dB,dB,app,abs(X2),X1) )
| ( X0 != X2 ) )
| ~ spl26_92 ),
inference(equality_resolution,[],[f931]) ).
tff(f931,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) )
| ( X1 != X3 ) )
| ~ spl26_92 ),
inference(avatar_component_clause,[],[f930]) ).
tff(f1812,plain,
( spl26_217
| ~ spl26_91 ),
inference(avatar_split_clause,[],[f952,f926,f1810]) ).
tff(f1810,plain,
( spl26_217
<=> ! [X2: nat,X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X2),X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_217])]) ).
tff(f926,plain,
( spl26_91
<=> ! [X0: list(dB),X3: nat,X2: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_91])]) ).
tff(f952,plain,
( ! [X2: nat,X0: nat,X1: list(dB)] :
( ( foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X2),X1) )
| ( X0 != X2 ) )
| ~ spl26_91 ),
inference(equality_resolution,[],[f927]) ).
tff(f927,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) )
| ( X1 != X3 ) )
| ~ spl26_91 ),
inference(avatar_component_clause,[],[f926]) ).
tff(f1808,plain,
( spl26_216
| ~ spl26_21
| ~ spl26_83 ),
inference(avatar_split_clause,[],[f951,f886,f571,f1806]) ).
tff(f1806,plain,
( spl26_216
<=> ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_216])]) ).
tff(f886,plain,
( spl26_83
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_83])]) ).
tff(f951,plain,
( ! [X0: dB] :
( sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0)
| sP1(sK7(X0)) )
| ~ spl26_21
| ~ spl26_83 ),
inference(resolution,[],[f887,f572]) ).
tff(f887,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| sP0(X0)
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) )
| ~ spl26_83 ),
inference(avatar_component_clause,[],[f886]) ).
tff(f1797,plain,
( spl26_215
| ~ spl26_71
| ~ spl26_90 ),
inference(avatar_split_clause,[],[f923,f919,f826,f1794]) ).
tff(f1794,plain,
( spl26_215
<=> typing(shift(type,e,i,t1),a,sK23(sK4,a,abs(r),shift(type,e,i,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_215])]) ).
tff(f919,plain,
( spl26_90
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| typing(X3,X1,sK23(X0,X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_90])]) ).
tff(f923,plain,
( typing(shift(type,e,i,t1),a,sK23(sK4,a,abs(r),shift(type,e,i,t1)))
| ~ spl26_71
| ~ spl26_90 ),
inference(resolution,[],[f920,f828]) ).
tff(f920,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| typing(X3,X1,sK23(X0,X1,X2,X3)) )
| ~ spl26_90 ),
inference(avatar_component_clause,[],[f919]) ).
tff(f1792,plain,
( spl26_214
| ~ spl26_69
| ~ spl26_90 ),
inference(avatar_split_clause,[],[f922,f919,f814,f1789]) ).
tff(f1789,plain,
( spl26_214
<=> typing(shift(type,e,i,t1),a,sK23(ua1,a,abs(r),shift(type,e,i,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_214])]) ).
tff(f922,plain,
( typing(shift(type,e,i,t1),a,sK23(ua1,a,abs(r),shift(type,e,i,t1)))
| ~ spl26_69
| ~ spl26_90 ),
inference(resolution,[],[f920,f816]) ).
tff(f1787,plain,
( spl26_213
| ~ spl26_15
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1661,f1641,f543,f1784]) ).
tff(f1784,plain,
( spl26_213
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_213])]) ).
tff(f1661,plain,
( sP1(abs(u))
| ~ spl26_15
| ~ spl26_195 ),
inference(resolution,[],[f1642,f545]) ).
tff(f545,plain,
( pp(aa(dB,bool,it,u))
| ~ spl26_15 ),
inference(avatar_component_clause,[],[f543]) ).
tff(f1782,plain,
( spl26_212
| ~ spl26_21
| ~ spl26_87 ),
inference(avatar_split_clause,[],[f907,f904,f571,f1780]) ).
tff(f1780,plain,
( spl26_212
<=> ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_212])]) ).
tff(f904,plain,
( spl26_87
<=> ! [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,[spl26_87])]) ).
tff(f907,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl26_21
| ~ spl26_87 ),
inference(resolution,[],[f905,f572]) ).
tff(f905,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)) )
| ~ spl26_87 ),
inference(avatar_component_clause,[],[f904]) ).
tff(f1778,plain,
( spl26_211
| ~ spl26_36
| ~ spl26_38 ),
inference(avatar_split_clause,[],[f668,f664,f645,f1776]) ).
tff(f1776,plain,
( spl26_211
<=> ! [X2: dB,X3: dB] :
( ( sK13(X2,abs(X3)) = abs(sK13(sK13(X2,abs(X3)),X3)) )
| ~ beta(abs(abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_211])]) ).
tff(f645,plain,
( spl26_36
<=> ! [X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1))
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_36])]) ).
tff(f664,plain,
( spl26_38
<=> ! [X0: dB,X1: dB] :
( ( abs(sK13(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_38])]) ).
tff(f668,plain,
( ! [X2: dB,X3: dB] :
( ( sK13(X2,abs(X3)) = abs(sK13(sK13(X2,abs(X3)),X3)) )
| ~ beta(abs(abs(X3)),X2) )
| ~ spl26_36
| ~ spl26_38 ),
inference(resolution,[],[f665,f646]) ).
tff(f646,plain,
( ! [X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1))
| ~ beta(abs(X1),X0) )
| ~ spl26_36 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f665,plain,
( ! [X0: dB,X1: dB] :
( ~ beta(abs(X1),X0)
| ( abs(sK13(X0,X1)) = X0 ) )
| ~ spl26_38 ),
inference(avatar_component_clause,[],[f664]) ).
tff(f1774,plain,
( spl26_210
| ~ spl26_52
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1146,f1110,f733,f1772]) ).
tff(f1772,plain,
( spl26_210
<=> ! [X29: dB,X30: fun(dB,dB),X31: nat] : ( var(X31) != aa(dB,dB,combs(dB,dB,dB,app,X30),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_210])]) ).
tff(f1146,plain,
( ! [X31: nat,X29: dB,X30: fun(dB,dB)] : ( var(X31) != aa(dB,dB,combs(dB,dB,dB,app,X30),X29) )
| ~ spl26_52
| ~ spl26_124 ),
inference(superposition,[],[f734,f1111]) ).
tff(f1770,plain,
( spl26_209
| ~ spl26_53
| ~ spl26_124 ),
inference(avatar_split_clause,[],[f1145,f1110,f737,f1768]) ).
tff(f1768,plain,
( spl26_209
<=> ! [X27: fun(dB,dB),X28: dB,X26: dB] : ( aa(dB,dB,combs(dB,dB,dB,app,X27),X26) != abs(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_209])]) ).
tff(f1145,plain,
( ! [X28: dB,X26: dB,X27: fun(dB,dB)] : ( aa(dB,dB,combs(dB,dB,dB,app,X27),X26) != abs(X28) )
| ~ spl26_53
| ~ spl26_124 ),
inference(superposition,[],[f738,f1111]) ).
tff(f1766,plain,
( spl26_208
| ~ spl26_52
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f963,f948,f733,f1764]) ).
tff(f1764,plain,
( spl26_208
<=> ! [X20: dB,X21: nat,X19: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X20),X19) != var(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_208])]) ).
tff(f963,plain,
( ! [X21: nat,X19: dB,X20: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X20),X19) != var(X21) )
| ~ spl26_52
| ~ spl26_96 ),
inference(superposition,[],[f734,f949]) ).
tff(f1762,plain,
( spl26_207
| ~ spl26_53
| ~ spl26_96 ),
inference(avatar_split_clause,[],[f962,f948,f737,f1760]) ).
tff(f1760,plain,
( spl26_207
<=> ! [X18: dB,X16: dB,X17: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X17),X16) != abs(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_207])]) ).
tff(f962,plain,
( ! [X18: dB,X16: dB,X17: dB] : ( aa(dB,dB,combc(dB,dB,dB,app,X17),X16) != abs(X18) )
| ~ spl26_53
| ~ spl26_96 ),
inference(superposition,[],[f738,f949]) ).
tff(f1758,plain,
( spl26_206
| ~ spl26_13
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1660,f1641,f533,f1755]) ).
tff(f1755,plain,
( spl26_206
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_206])]) ).
tff(f533,plain,
( spl26_13
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_13])]) ).
tff(f1660,plain,
( sP1(abs(t3))
| ~ spl26_13
| ~ spl26_195 ),
inference(resolution,[],[f1642,f535]) ).
tff(f535,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl26_13 ),
inference(avatar_component_clause,[],[f533]) ).
tff(f1746,plain,
( spl26_205
| ~ spl26_21
| ~ spl26_57 ),
inference(avatar_split_clause,[],[f785,f755,f571,f1744]) ).
tff(f1744,plain,
( spl26_205
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_205])]) ).
tff(f755,plain,
( spl26_57
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_57])]) ).
tff(f785,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0)
| sP1(sK7(X0)) )
| ~ spl26_21
| ~ spl26_57 ),
inference(resolution,[],[f756,f572]) ).
tff(f756,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK7(X0)))
| sP0(X0)
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) )
| ~ spl26_57 ),
inference(avatar_component_clause,[],[f755]) ).
tff(f1742,plain,
( spl26_204
| ~ spl26_55 ),
inference(avatar_split_clause,[],[f753,f746,f1740]) ).
tff(f1740,plain,
( spl26_204
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(foldl(dB,dB,app,var(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_204])]) ).
tff(f746,plain,
( spl26_55
<=> ! [X2: list(dB),X0: dB,X3: nat] :
( sP1(X0)
| ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_55])]) ).
tff(f753,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(foldl(dB,dB,app,var(X1),X0)) )
| ~ spl26_55 ),
inference(equality_resolution,[],[f747]) ).
tff(f747,plain,
( ! [X2: list(dB),X3: nat,X0: dB] :
( ( foldl(dB,dB,app,var(X3),X2) != X0 )
| ~ listsp(dB,it,X2)
| sP1(X0) )
| ~ spl26_55 ),
inference(avatar_component_clause,[],[f746]) ).
tff(f1738,plain,
( spl26_203
| ~ spl26_25
| ~ spl26_33 ),
inference(avatar_split_clause,[],[f652,f633,f587,f1736]) ).
tff(f1736,plain,
( spl26_203
<=> ! [X0: nat,X1: nat] :
( ( suc(X1) != X0 )
| ( sK6(X0) = X1 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_203])]) ).
tff(f587,plain,
( spl26_25
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_25])]) ).
tff(f652,plain,
( ! [X0: nat,X1: nat] :
( ( suc(X1) != X0 )
| ( sK6(X0) = X1 )
| ( zero_zero(nat) = X0 ) )
| ~ spl26_25
| ~ spl26_33 ),
inference(superposition,[],[f588,f634]) ).
tff(f588,plain,
( ! [X0: nat,X1: nat] :
( ( suc(X0) != suc(X1) )
| ( X0 = X1 ) )
| ~ spl26_25 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f1734,plain,
( spl26_202
| ~ spl26_25
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f648,f629,f587,f1732]) ).
tff(f1732,plain,
( spl26_202
<=> ! [X0: nat,X1: nat] :
( ( suc(X1) != X0 )
| ( sK5(X0) = X1 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_202])]) ).
tff(f648,plain,
( ! [X0: nat,X1: nat] :
( ( suc(X1) != X0 )
| ( sK5(X0) = X1 )
| ( zero_zero(nat) = X0 ) )
| ~ spl26_25
| ~ spl26_32 ),
inference(superposition,[],[f588,f630]) ).
tff(f1711,plain,
( spl26_201
| ~ spl26_16
| ~ spl26_195 ),
inference(avatar_split_clause,[],[f1659,f1641,f548,f1708]) ).
tff(f1708,plain,
( spl26_201
<=> sP1(abs(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_201])]) ).
tff(f1659,plain,
( sP1(abs(a))
| ~ spl26_16
| ~ spl26_195 ),
inference(resolution,[],[f1642,f550]) ).
tff(f550,plain,
( pp(aa(dB,bool,it,a))
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f548]) ).
tff(f1687,plain,
( spl26_200
| ~ spl26_54 ),
inference(avatar_split_clause,[],[f744,f741,f1685]) ).
tff(f1685,plain,
( spl26_200
<=> ! [X0: $tType,X3: X0,X2: nat,X1: fun(nat,X0)] : ( aa(nat,X0,shift(X0,X1,X2,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_200])]) ).
tff(f741,plain,
( spl26_54
<=> ! [X0: $tType,X4: nat,X3: nat,X2: fun(nat,X0),X1: X0] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_54])]) ).
tff(f744,plain,
( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,X0)] : ( aa(nat,X0,shift(X0,X1,X2,X3),X2) = X3 )
| ~ spl26_54 ),
inference(equality_resolution,[],[f742]) ).
tff(f742,plain,
( ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( X3 != X4 )
| ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) )
| ~ spl26_54 ),
inference(avatar_component_clause,[],[f741]) ).
tff(f1683,plain,
( spl26_199
| ~ spl26_20
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f680,f674,f566,f1681]) ).
tff(f1681,plain,
( spl26_199
<=> ! [X3: dB] :
( ~ beta(a,X3)
| typing(shift(type,e,i,t1),X3,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_199])]) ).
tff(f566,plain,
( spl26_20
<=> typing(shift(type,e,i,t1),a,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_20])]) ).
tff(f680,plain,
( ! [X3: dB] :
( ~ beta(a,X3)
| typing(shift(type,e,i,t1),X3,sK3) )
| ~ spl26_20
| ~ spl26_40 ),
inference(resolution,[],[f675,f568]) ).
tff(f568,plain,
( typing(shift(type,e,i,t1),a,sK3)
| ~ spl26_20 ),
inference(avatar_component_clause,[],[f566]) ).
tff(f1679,plain,
( spl26_198
| ~ spl26_19
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f679,f674,f561,f1677]) ).
tff(f1677,plain,
( spl26_198
<=> ! [X2: dB] :
( ~ beta(a,X2)
| typing(shift(type,e,i,t1),X2,t2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_198])]) ).
tff(f679,plain,
( ! [X2: dB] :
( ~ beta(a,X2)
| typing(shift(type,e,i,t1),X2,t2) )
| ~ spl26_19
| ~ spl26_40 ),
inference(resolution,[],[f675,f563]) ).
tff(f1675,plain,
( spl26_197
| ~ spl26_24
| ~ spl26_38 ),
inference(avatar_split_clause,[],[f667,f664,f583,f1673]) ).
tff(f1673,plain,
( spl26_197
<=> ! [X0: dB,X1: dB] :
( ( abs(X0) = abs(sK13(abs(X0),X1)) )
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_197])]) ).
tff(f583,plain,
( spl26_24
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_24])]) ).
tff(f667,plain,
( ! [X0: dB,X1: dB] :
( ( abs(X0) = abs(sK13(abs(X0),X1)) )
| ~ beta(X1,X0) )
| ~ spl26_24
| ~ spl26_38 ),
inference(resolution,[],[f665,f584]) ).
tff(f584,plain,
( ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) )
| ~ spl26_24 ),
inference(avatar_component_clause,[],[f583]) ).
tff(f1647,plain,
( spl26_196
| ~ spl26_44 ),
inference(avatar_split_clause,[],[f699,f695,f1645]) ).
tff(f1645,plain,
( spl26_196
<=> ! [X0: fun(nat,type),X1: nat] : typing(X0,var(X1),aa(nat,type,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_196])]) ).
tff(f699,plain,
( ! [X0: fun(nat,type),X1: nat] : typing(X0,var(X1),aa(nat,type,X0,X1))
| ~ spl26_44 ),
inference(equality_resolution,[],[f696]) ).
tff(f1643,plain,
( spl26_195
| ~ spl26_41 ),
inference(avatar_split_clause,[],[f698,f682,f1641]) ).
tff(f682,plain,
( spl26_41
<=> ! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_41])]) ).
tff(f698,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(X0)) )
| ~ spl26_41 ),
inference(equality_resolution,[],[f683]) ).
tff(f683,plain,
( ! [X0: dB,X1: dB] :
( ( abs(X1) != X0 )
| ~ pp(aa(dB,bool,it,X1))
| sP1(X0) )
| ~ spl26_41 ),
inference(avatar_component_clause,[],[f682]) ).
tff(f1639,plain,
( spl26_194
| ~ spl26_36
| ~ spl26_168 ),
inference(avatar_split_clause,[],[f1495,f1451,f645,f1637]) ).
tff(f1637,plain,
( spl26_194
<=> ! [X2: nat,X3: dB] : ~ beta(abs(abs(abs(abs(var(X2))))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_194])]) ).
tff(f1451,plain,
( spl26_168
<=> ! [X2: nat,X3: dB] : ~ beta(abs(abs(abs(var(X2)))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_168])]) ).
tff(f1495,plain,
( ! [X2: nat,X3: dB] : ~ beta(abs(abs(abs(abs(var(X2))))),X3)
| ~ spl26_36
| ~ spl26_168 ),
inference(resolution,[],[f1452,f646]) ).
tff(f1452,plain,
( ! [X2: nat,X3: dB] : ~ beta(abs(abs(abs(var(X2)))),X3)
| ~ spl26_168 ),
inference(avatar_component_clause,[],[f1451]) ).
tff(f1633,plain,
( spl26_193
| ~ spl26_96
| ~ spl26_192 ),
inference(avatar_split_clause,[],[f1628,f1621,f948,f1630]) ).
tff(f1630,plain,
( spl26_193
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),suc(i)),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_193])]) ).
tff(f1621,plain,
( spl26_192
<=> 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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_192])]) ).
tff(f1628,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),suc(i)),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl26_96
| ~ spl26_192 ),
inference(forward_demodulation,[],[f1627,f949]) ).
tff(f1627,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),suc(i)),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl26_96
| ~ spl26_192 ),
inference(forward_demodulation,[],[f1626,f949]) ).
tff(f1626,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl26_96
| ~ spl26_192 ),
inference(forward_demodulation,[],[f1625,f949]) ).
tff(f1625,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),zero_zero(nat)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl26_96
| ~ spl26_192 ),
inference(forward_demodulation,[],[f1623,f949]) ).
tff(f1623,plain,
( 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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as))))
| ~ spl26_192 ),
inference(avatar_component_clause,[],[f1621]) ).
tff(f1624,plain,
spl26_192,
inference(avatar_split_clause,[],[f342,f1621]) ).
tff(f342,plain,
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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),
inference(cnf_transformation,[],[f67]) ).
tff(f67,axiom,
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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096) ).
tff(f1616,plain,
( spl26_191
| ~ spl26_96
| ~ spl26_190 ),
inference(avatar_split_clause,[],[f1612,f1607,f948,f1614]) ).
tff(f1614,plain,
( spl26_191
<=> ! [X0: dB,X3: fun(nat,type),X2: nat,X1: type] :
( ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as),X1)
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_191])]) ).
tff(f1607,plain,
( spl26_190
<=> ! [X0: dB,X3: fun(nat,type),X2: nat,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_190])]) ).
tff(f1612,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as),X1)
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl26_96
| ~ spl26_190 ),
inference(forward_demodulation,[],[f1611,f949]) ).
tff(f1611,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) )
| ~ spl26_96
| ~ spl26_190 ),
inference(forward_demodulation,[],[f1610,f949]) ).
tff(f1610,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) )
| ~ spl26_96
| ~ spl26_190 ),
inference(forward_demodulation,[],[f1608,f949]) ).
tff(f1608,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) )
| ~ spl26_190 ),
inference(avatar_component_clause,[],[f1607]) ).
tff(f1609,plain,
spl26_190,
inference(avatar_split_clause,[],[f437,f1607]) ).
tff(f437,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( typing(shift(type,X3,X2,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X1)
=> ( pp(aa(dB,bool,it,X0))
=> ( typing(X3,X0,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X0),X2))) ) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X4: dB,X15: type,X6: nat,X7: fun(nat,type)] :
( typing(shift(type,X7,X6,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),X15)
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(X7,X4,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),X4),X6))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_25_SI1) ).
tff(f1604,plain,
spl26_189,
inference(avatar_split_clause,[],[f465,f1602]) ).
tff(f1602,plain,
( spl26_189
<=> ! [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,[spl26_189])]) ).
tff(f465,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,[],[f197]) ).
tff(f197,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,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X65: list(X2),X60: fun(X2,X1),X66: X0,X59: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X59,X66,map(X2,X1,X60,X65)) = 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)),X59),X60),X66,X65) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_83_foldl__map) ).
tff(f1600,plain,
( spl26_188
| ~ spl26_6
| ~ spl26_33 ),
inference(avatar_split_clause,[],[f655,f633,f502,f1598]) ).
tff(f1598,plain,
( spl26_188
<=> ! [X5: nat] :
( ( sK6(X5) != X5 )
| ( zero_zero(nat) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_188])]) ).
tff(f502,plain,
( spl26_6
<=> ! [X0: nat] : ( suc(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
tff(f655,plain,
( ! [X5: nat] :
( ( sK6(X5) != X5 )
| ( zero_zero(nat) = X5 ) )
| ~ spl26_6
| ~ spl26_33 ),
inference(superposition,[],[f503,f634]) ).
tff(f503,plain,
( ! [X0: nat] : ( suc(X0) != X0 )
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f502]) ).
tff(f1587,plain,
( spl26_187
| ~ spl26_96
| ~ spl26_186 ),
inference(avatar_split_clause,[],[f1583,f1577,f948,f1585]) ).
tff(f1577,plain,
( spl26_186
<=> ! [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,[spl26_186])]) ).
tff(f1583,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) )
| ~ spl26_96
| ~ spl26_186 ),
inference(forward_demodulation,[],[f1582,f949]) ).
tff(f1582,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) )
| ~ spl26_96
| ~ spl26_186 ),
inference(forward_demodulation,[],[f1581,f949]) ).
tff(f1581,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)) )
| ~ spl26_96
| ~ spl26_186 ),
inference(forward_demodulation,[],[f1580,f949]) ).
tff(f1580,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)) )
| ~ spl26_96
| ~ spl26_186 ),
inference(forward_demodulation,[],[f1578,f949]) ).
tff(f1578,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)) )
| ~ spl26_186 ),
inference(avatar_component_clause,[],[f1577]) ).
tff(f1579,plain,
spl26_186,
inference(avatar_split_clause,[],[f430,f1577]) ).
tff(f430,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,[],[f173]) ).
tff(f173,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,[],[f47]) ).
tff(f47,axiom,
! [X35: nat,X36: dB,X45: dB,X14: 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,X14),X45)),X36),X35) = 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,X14),X36),X35)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X45),X36),X35)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_46_subst__App) ).
tff(f1570,plain,
( spl26_185
| ~ spl26_96
| ~ spl26_184 ),
inference(avatar_split_clause,[],[f1566,f1562,f948,f1568]) ).
tff(f1568,plain,
( spl26_185
<=> ! [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,[spl26_185])]) ).
tff(f1562,plain,
( spl26_184
<=> ! [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,[spl26_184])]) ).
tff(f1566,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) )
| ~ spl26_96
| ~ spl26_184 ),
inference(forward_demodulation,[],[f1565,f949]) ).
tff(f1565,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)) )
| ~ spl26_96
| ~ spl26_184 ),
inference(forward_demodulation,[],[f1563,f949]) ).
tff(f1563,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)) )
| ~ spl26_184 ),
inference(avatar_component_clause,[],[f1562]) ).
tff(f1564,plain,
spl26_184,
inference(avatar_split_clause,[],[f429,f1562]) ).
tff(f429,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,[],[f172]) ).
tff(f172,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,[],[f70]) ).
tff(f70,axiom,
! [X6: nat,X4: dB,X28: list(dB),X8: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X8,X28)),X4),X6) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X8),X4),X6),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X6),X28)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_69_subst__map) ).
tff(f1560,plain,
spl26_183,
inference(avatar_split_clause,[],[f475,f1558]) ).
tff(f1558,plain,
( spl26_183
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X0: dB,X6: type,X2: nat,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_183])]) ).
tff(f475,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f474,f461]) ).
tff(f461,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,[],[f193]) ).
tff(f193,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,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X82: X0,X83: X1,X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X84,X83),X82) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X82),X83) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_COMBC_1_1_U) ).
tff(f474,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f468,f461]) ).
tff(f468,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X6)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X6),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(shift(type,X3,X2,X6),X4,X1)
=> ( pp(aa(dB,bool,it,X0))
=> ( typing(X3,X0,X6)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X4: dB,X5: type,X6: nat,X7: fun(nat,type),X8: dB,X9: type,X10: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X10),X9) )
=> ( pp(aa(dB,bool,it,X8))
=> ( typing(shift(type,X7,X6,X10),X8,X5)
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(X7,X4,X10)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X8),X4),X6))) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_7_MI1) ).
tff(f1556,plain,
spl26_182,
inference(avatar_split_clause,[],[f473,f1554]) ).
tff(f1554,plain,
( spl26_182
<=> ! [X5: type,X3: fun(nat,type),X4: dB,X0: dB,X6: type,X2: nat,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_182])]) ).
tff(f473,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun1,X5),X6) )
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f472,f461]) ).
tff(f472,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X4),X2),X0)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(forward_demodulation,[],[f467,f461]) ).
tff(f467,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(flattening,[],[f255]) ).
tff(f255,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
| ~ typing(X3,X0,X5)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,X5),X4,X1)
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(shift(type,X3,X2,X5),X4,X1)
=> ( pp(aa(dB,bool,it,X0))
=> ( typing(X3,X0,X5)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X4: dB,X5: type,X6: nat,X7: fun(nat,type),X8: dB,X9: type,X10: type] :
( ( t1 = aa(type,type,aa(type,fun(type,type),fun1,X10),X9) )
=> ( pp(aa(dB,bool,it,X8))
=> ( typing(shift(type,X7,X6,X9),X8,X5)
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(X7,X4,X9)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X8),X4),X6))) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_8_MI2) ).
tff(f1552,plain,
( spl26_181
| ~ spl26_6
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f651,f629,f502,f1550]) ).
tff(f1550,plain,
( spl26_181
<=> ! [X5: nat] :
( ( sK5(X5) != X5 )
| ( zero_zero(nat) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_181])]) ).
tff(f651,plain,
( ! [X5: nat] :
( ( sK5(X5) != X5 )
| ( zero_zero(nat) = X5 ) )
| ~ spl26_6
| ~ spl26_32 ),
inference(superposition,[],[f503,f630]) ).
tff(f1545,plain,
( spl26_180
| ~ spl26_96
| ~ spl26_179 ),
inference(avatar_split_clause,[],[f1541,f1537,f948,f1543]) ).
tff(f1537,plain,
( spl26_179
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_179])]) ).
tff(f1541,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl26_96
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1540,f949]) ).
tff(f1540,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl26_96
| ~ spl26_179 ),
inference(forward_demodulation,[],[f1538,f949]) ).
tff(f1538,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))) )
| ~ spl26_179 ),
inference(avatar_component_clause,[],[f1537]) ).
tff(f1539,plain,
spl26_179,
inference(avatar_split_clause,[],[f424,f1537]) ).
tff(f424,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f230]) ).
tff(f230,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,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,[],[f33]) ).
tff(f33,axiom,
! [X29: list(dB),X26: dB,X30: 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,X30),X26),zero_zero(nat)),X29)))
=> ( pp(aa(dB,bool,it,X26))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X30)),X26),X29))) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_32_IT_OBeta) ).
tff(f1534,plain,
( spl26_178
| ~ spl26_96
| ~ spl26_177 ),
inference(avatar_split_clause,[],[f1530,f1526,f948,f1532]) ).
tff(f1532,plain,
( spl26_178
<=> ! [X0: dB,X3: list(dB),X2: dB,X1: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3) != 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,X1),zero_zero(nat)),X2),X3)))
| sP0(X0)
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_178])]) ).
tff(f1526,plain,
( spl26_177
<=> ! [X0: dB,X3: list(dB),X2: 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 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_177])]) ).
tff(f1530,plain,
( ! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1)),X3) != 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,X1),zero_zero(nat)),X2),X3)))
| sP0(X0)
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl26_96
| ~ spl26_177 ),
inference(forward_demodulation,[],[f1529,f949]) ).
tff(f1529,plain,
( ! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(X0)
| ~ pp(aa(dB,bool,it,X2))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) )
| ~ spl26_96
| ~ spl26_177 ),
inference(forward_demodulation,[],[f1527,f949]) ).
tff(f1527,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 ) )
| ~ spl26_177 ),
inference(avatar_component_clause,[],[f1526]) ).
tff(f1528,plain,
spl26_177,
inference(avatar_split_clause,[],[f371,f1526]) ).
tff(f371,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,[],[f284]) ).
tff(f284,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,sK11(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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f282,f283]) ).
tff(f283,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,sK11(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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f282,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,[],[f281]) ).
tff(f281,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,[],[f261]) ).
tff(f261,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(f1511,plain,
( spl26_176
| ~ spl26_96
| ~ spl26_175 ),
inference(avatar_split_clause,[],[f1507,f1501,f948,f1509]) ).
tff(f1501,plain,
( spl26_175
<=> ! [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,[spl26_175])]) ).
tff(f1507,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)) )
| ~ spl26_96
| ~ spl26_175 ),
inference(forward_demodulation,[],[f1506,f949]) ).
tff(f1506,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)) )
| ~ spl26_96
| ~ spl26_175 ),
inference(forward_demodulation,[],[f1505,f949]) ).
tff(f1505,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)) )
| ~ spl26_96
| ~ spl26_175 ),
inference(forward_demodulation,[],[f1504,f949]) ).
tff(f1504,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)) )
| ~ spl26_96
| ~ spl26_175 ),
inference(forward_demodulation,[],[f1502,f949]) ).
tff(f1502,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)) )
| ~ spl26_175 ),
inference(avatar_component_clause,[],[f1501]) ).
tff(f1503,plain,
spl26_175,
inference(avatar_split_clause,[],[f407,f1501]) ).
tff(f407,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,[],[f157]) ).
tff(f157,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,[],[f40]) ).
tff(f40,axiom,
! [X35: nat,X14: dB,X36: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X14)),X35) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X36),X35)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X14),X35)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_39_lift_Osimps_I2_J) ).
tff(f1493,plain,
( spl26_174
| ~ spl26_96
| ~ spl26_173 ),
inference(avatar_split_clause,[],[f1489,f1484,f948,f1491]) ).
tff(f1491,plain,
( spl26_174
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_174])]) ).
tff(f1484,plain,
( spl26_173
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_173])]) ).
tff(f1489,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1) )
| ~ spl26_96
| ~ spl26_173 ),
inference(forward_demodulation,[],[f1488,f949]) ).
tff(f1488,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_96
| ~ spl26_173 ),
inference(forward_demodulation,[],[f1487,f949]) ).
tff(f1487,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_96
| ~ spl26_173 ),
inference(forward_demodulation,[],[f1485,f949]) ).
tff(f1485,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_173 ),
inference(avatar_component_clause,[],[f1484]) ).
tff(f1486,plain,
spl26_173,
inference(avatar_split_clause,[],[f420,f1484]) ).
tff(f420,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( beta(X1,sK21(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 ) )
| ( beta(X2,sK22(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f303,f305,f304]) ).
tff(f304,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( beta(X1,X3)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0 ) )
=> ( beta(X1,sK21(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f305,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
=> ( beta(X2,sK22(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f303,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( beta(X1,X3)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(rectify,[],[f265]) ).
tff(f265,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(definition_folding,[],[f229,f264]) ).
tff(f264,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f229,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(flattening,[],[f228]) ).
tff(f228,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
=> ( ! [X3: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 )
=> ( abs(X3) != X2 ) )
=> ( ! [X4: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X1) = X0 )
=> ~ beta(X2,X4) )
=> ~ ! [X5: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X5) = X0 )
=> ~ beta(X1,X5) ) ) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X45: dB,X14: dB,X36: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X14),X45)
=> ( ! [X55: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X55),X14),zero_zero(nat)) = X45 )
=> ( abs(X55) != X36 ) )
=> ( ! [X53: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X53),X14) = X45 )
=> ~ beta(X36,X53) )
=> ~ ! [X53: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X53) = X45 )
=> ~ beta(X14,X53) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_67_beta__cases_I3_J) ).
tff(f1478,plain,
spl26_172,
inference(avatar_split_clause,[],[f453,f1476]) ).
tff(f1476,plain,
( spl26_172
<=> ! [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,[spl26_172])]) ).
tff(f453,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,[],[f321]) ).
tff(f321,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,[],[f320]) ).
tff(f320,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,[],[f185]) ).
tff(f185,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,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType,X73: fun(X0,bool),X74: fun(X0,bool),X56: 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),X74),X73),X56)
<=> ( listsp(X0,X73,X56)
& listsp(X0,X74,X56) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_92_listsp__conj__eq) ).
tff(f1473,plain,
( spl26_171
| ~ spl26_96
| ~ spl26_170 ),
inference(avatar_split_clause,[],[f1468,f1463,f948,f1470]) ).
tff(f1470,plain,
( spl26_171
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)),i),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_171])]) ).
tff(f1463,plain,
( spl26_170
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_170])]) ).
tff(f1468,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)),i),u)))
| ~ spl26_96
| ~ spl26_170 ),
inference(forward_demodulation,[],[f1467,f949]) ).
tff(f1467,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),i),u)))
| ~ spl26_96
| ~ spl26_170 ),
inference(forward_demodulation,[],[f1465,f949]) ).
tff(f1465,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i)))
| ~ spl26_170 ),
inference(avatar_component_clause,[],[f1463]) ).
tff(f1466,plain,
spl26_170,
inference(avatar_split_clause,[],[f341,f1463]) ).
tff(f341,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096) ).
tff(f1457,plain,
spl26_169,
inference(avatar_split_clause,[],[f452,f1455]) ).
tff(f1455,plain,
( spl26_169
<=> ! [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,[spl26_169])]) ).
tff(f452,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,[],[f321]) ).
tff(f1453,plain,
( spl26_168
| ~ spl26_36
| ~ spl26_127 ),
inference(avatar_split_clause,[],[f1203,f1165,f645,f1451]) ).
tff(f1165,plain,
( spl26_127
<=> ! [X2: nat,X3: dB] : ~ beta(abs(abs(var(X2))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_127])]) ).
tff(f1203,plain,
( ! [X2: nat,X3: dB] : ~ beta(abs(abs(abs(var(X2)))),X3)
| ~ spl26_36
| ~ spl26_127 ),
inference(resolution,[],[f1166,f646]) ).
tff(f1166,plain,
( ! [X2: nat,X3: dB] : ~ beta(abs(abs(var(X2))),X3)
| ~ spl26_127 ),
inference(avatar_component_clause,[],[f1165]) ).
tff(f1449,plain,
spl26_167,
inference(avatar_split_clause,[],[f451,f1447]) ).
tff(f1447,plain,
( spl26_167
<=> ! [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,[spl26_167])]) ).
tff(f451,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,[],[f321]) ).
tff(f1445,plain,
( spl26_166
| ~ spl26_96
| ~ spl26_165 ),
inference(avatar_split_clause,[],[f1440,f1435,f948,f1442]) ).
tff(f1442,plain,
( spl26_166
<=> beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_166])]) ).
tff(f1435,plain,
( spl26_165
<=> beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_165])]) ).
tff(f1440,plain,
( beta(foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as))
| ~ spl26_96
| ~ spl26_165 ),
inference(forward_demodulation,[],[f1439,f949]) ).
tff(f1439,plain,
( beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as))
| ~ spl26_96
| ~ spl26_165 ),
inference(forward_demodulation,[],[f1437,f949]) ).
tff(f1437,plain,
( beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))
| ~ spl26_165 ),
inference(avatar_component_clause,[],[f1435]) ).
tff(f1438,plain,
spl26_165,
inference(avatar_split_clause,[],[f340,f1435]) ).
tff(f340,plain,
beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096) ).
tff(f1429,plain,
( spl26_164
| ~ spl26_96
| ~ spl26_163 ),
inference(avatar_split_clause,[],[f1425,f1422,f948,f1427]) ).
tff(f1422,plain,
( spl26_163
<=> ! [X0: dB,X3: fun(nat,type),X2: nat,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_163])]) ).
tff(f1425,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X0)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) )
| ~ spl26_96
| ~ spl26_163 ),
inference(forward_demodulation,[],[f1423,f949]) ).
tff(f1423,plain,
( ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) )
| ~ spl26_163 ),
inference(avatar_component_clause,[],[f1422]) ).
tff(f1424,plain,
spl26_163,
inference(avatar_split_clause,[],[f433,f1422]) ).
tff(f433,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(flattening,[],[f235]) ).
tff(f235,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( typing(shift(type,X3,X2,t1),a,X1)
=> ( pp(aa(dB,bool,it,X0))
=> ( typing(X3,X0,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2))) ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X4: dB,X15: type,X6: nat,X7: fun(nat,type)] :
( typing(shift(type,X7,X6,t1),a,X15)
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(X7,X4,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X4),X6))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_12_SI2) ).
tff(f1420,plain,
( spl26_162
| ~ spl26_96
| ~ spl26_161 ),
inference(avatar_split_clause,[],[f1416,f1412,f948,f1418]) ).
tff(f1418,plain,
( spl26_162
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(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))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_162])]) ).
tff(f1412,plain,
( spl26_161
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(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))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_161])]) ).
tff(f1416,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(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))
| ~ beta(X3,X2) )
| ~ spl26_96
| ~ spl26_161 ),
inference(forward_demodulation,[],[f1415,f949]) ).
tff(f1415,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(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))
| ~ beta(X3,X2) )
| ~ spl26_96
| ~ spl26_161 ),
inference(forward_demodulation,[],[f1413,f949]) ).
tff(f1413,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(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))
| ~ beta(X3,X2) )
| ~ spl26_161 ),
inference(avatar_component_clause,[],[f1412]) ).
tff(f1414,plain,
spl26_161,
inference(avatar_split_clause,[],[f431,f1412]) ).
tff(f431,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(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))
| ~ beta(X3,X2) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(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))
| ~ beta(X3,X2) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(X3,X2)
=> beta(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,[],[f51]) ).
tff(f51,axiom,
! [X12: nat,X14: dB,X36: dB,X13: dB] :
( beta(X13,X36)
=> beta(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X13),X14),X12),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X36),X14),X12)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_50_subst__preserves__beta) ).
tff(f1398,plain,
( spl26_160
| ~ spl26_96
| ~ spl26_159 ),
inference(avatar_split_clause,[],[f1394,f1390,f948,f1396]) ).
tff(f1396,plain,
( spl26_160
<=> ! [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,[spl26_160])]) ).
tff(f1390,plain,
( spl26_159
<=> ! [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,[spl26_159])]) ).
tff(f1394,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)) )
| ~ spl26_96
| ~ spl26_159 ),
inference(forward_demodulation,[],[f1393,f949]) ).
tff(f1393,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)) )
| ~ spl26_96
| ~ spl26_159 ),
inference(forward_demodulation,[],[f1391,f949]) ).
tff(f1391,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)) )
| ~ spl26_159 ),
inference(avatar_component_clause,[],[f1390]) ).
tff(f1392,plain,
spl26_159,
inference(avatar_split_clause,[],[f406,f1390]) ).
tff(f406,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,[],[f156]) ).
tff(f156,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,[],[f71]) ).
tff(f71,axiom,
! [X6: nat,X28: list(dB),X8: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X8,X28)),X6) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X8),X6),map(dB,dB,combc(dB,nat,dB,lift,X6),X28)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_70_lift__map) ).
tff(f1385,plain,
spl26_158,
inference(avatar_split_clause,[],[f469,f1383]) ).
tff(f1383,plain,
( spl26_158
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_158])]) ).
tff(f469,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 )
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ( typings(X6,X3,sK25(X0,X2,X3,X6))
& ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 ) )
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f260,f322]) ).
tff(f322,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
=> ( typings(X6,X3,sK25(X0,X2,X3,X6))
& ( foldr(type,type,fun1,sK25(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f260,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) )
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
( typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2)
=> ( typings(X6,X4,X1)
=> ( typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
=> ? [X7: list(type)] :
( typings(X6,X3,X7)
& ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X17: type,X72: list(type),X5: type,X80: list(dB),X28: list(dB),X6: nat,X7: fun(nat,type)] :
( typing(X7,foldl(dB,dB,app,foldl(dB,dB,app,var(X6),X28),X80),X5)
=> ( typings(X7,X28,X72)
=> ( typing(X7,foldl(dB,dB,app,var(X6),X28),X17)
=> ? [X81: list(type)] :
( typings(X7,X80,X81)
& ( foldr(type,type,fun1,X81,X5) = X17 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_97_var__app__types) ).
tff(f1377,plain,
( spl26_157
| ~ spl26_96
| ~ spl26_156 ),
inference(avatar_split_clause,[],[f1373,f1369,f948,f1375]) ).
tff(f1375,plain,
( spl26_157
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| beta(X1,sK21(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_157])]) ).
tff(f1369,plain,
( spl26_156
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_156])]) ).
tff(f1373,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| beta(X1,sK21(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl26_96
| ~ spl26_156 ),
inference(forward_demodulation,[],[f1372,f949]) ).
tff(f1372,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK22(X0,X1,X2)) = X0 )
| beta(X1,sK21(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_96
| ~ spl26_156 ),
inference(forward_demodulation,[],[f1370,f949]) ).
tff(f1370,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_156 ),
inference(avatar_component_clause,[],[f1369]) ).
tff(f1371,plain,
spl26_156,
inference(avatar_split_clause,[],[f422,f1369]) ).
tff(f422,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun(dB,dB),app,sK22(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1363,plain,
( spl26_155
| ~ spl26_96
| ~ spl26_154 ),
inference(avatar_split_clause,[],[f1352,f1348,f948,f1361]) ).
tff(f1361,plain,
( spl26_155
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_155])]) ).
tff(f1348,plain,
( spl26_154
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_154])]) ).
tff(f1352,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl26_96
| ~ spl26_154 ),
inference(forward_demodulation,[],[f1351,f949]) ).
tff(f1351,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,sK21(X0,X1,X2)),X2) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_96
| ~ spl26_154 ),
inference(forward_demodulation,[],[f1349,f949]) ).
tff(f1349,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_154 ),
inference(avatar_component_clause,[],[f1348]) ).
tff(f1350,plain,
spl26_154,
inference(avatar_split_clause,[],[f421,f1348]) ).
tff(f421,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK21(X0,X1,X2)) = X0 )
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1317,plain,
spl26_153,
inference(avatar_split_clause,[],[f471,f1315]) ).
tff(f471,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( typing(X3,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X5),X0),X2),X4)
| ( shift(type,X3,X0,X1) != X6 )
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) ),
inference(forward_demodulation,[],[f466,f461]) ).
tff(f466,plain,
! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
( typing(X3,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0),X4)
| ( shift(type,X3,X0,X1) != X6 )
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( typing(X3,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0),X4)
| ( shift(type,X3,X0,X1) != X6 )
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( typing(X3,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0),X4)
| ( shift(type,X3,X0,X1) != X6 )
| ~ typing(X3,X2,X1)
| ~ typing(X6,X5,X4) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
( typing(X6,X5,X4)
=> ( typing(X3,X2,X1)
=> ( ( shift(type,X3,X0,X1) = X6 )
=> typing(X3,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0),X4) ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X6: nat,X17: type,X4: dB,X18: fun(nat,type),X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,X8,X5)
=> ( typing(X18,X4,X17)
=> ( ( shift(type,X18,X6,X17) = X7 )
=> typing(X18,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X8),X4),X6),X5) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_14_subst__lemma) ).
tff(f1313,plain,
spl26_152,
inference(avatar_split_clause,[],[f463,f1311]) ).
tff(f1311,plain,
( spl26_152
<=> ! [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,[spl26_152])]) ).
tff(f463,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X82: X0,X83: fun(X0,X1),X84: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X84),X83),X82) = aa(X1,X2,X84,aa(X0,X1,X83,X82)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_COMBB_1_1_U) ).
tff(f1307,plain,
spl26_151,
inference(avatar_split_clause,[],[f470,f1305]) ).
tff(f1305,plain,
( spl26_151
<=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
( typings(X6,X3,sK25(X0,X2,X3,X6))
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_151])]) ).
tff(f470,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
( typings(X6,X3,sK25(X0,X2,X3,X6))
| ~ typing(X6,foldl(dB,dB,app,var(X5),X4),X0)
| ~ typings(X6,X4,X1)
| ~ typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3),X2) ),
inference(cnf_transformation,[],[f323]) ).
tff(f1302,plain,
( spl26_150
| ~ spl26_96
| ~ spl26_149 ),
inference(avatar_split_clause,[],[f1298,f1295,f948,f1300]) ).
tff(f1295,plain,
( spl26_149
<=> ! [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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_149])]) ).
tff(f1298,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,sK10(X0)),zero_zero(nat)),sK11(X0)),sK12(X0))))
| ~ sP0(X0) )
| ~ spl26_96
| ~ spl26_149 ),
inference(forward_demodulation,[],[f1296,f949]) ).
tff(f1296,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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) )
| ~ spl26_149 ),
inference(avatar_component_clause,[],[f1295]) ).
tff(f1297,plain,
spl26_149,
inference(avatar_split_clause,[],[f369,f1295]) ).
tff(f369,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,sK10(X0)),sK11(X0)),zero_zero(nat)),sK12(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f1293,plain,
( spl26_148
| ~ spl26_5
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f678,f674,f497,f1291]) ).
tff(f1291,plain,
( spl26_148
<=> ! [X1: dB] :
( ~ beta(u,X1)
| typing(e,X1,t1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_148])]) ).
tff(f678,plain,
( ! [X1: dB] :
( ~ beta(u,X1)
| typing(e,X1,t1) )
| ~ spl26_5
| ~ spl26_40 ),
inference(resolution,[],[f675,f499]) ).
tff(f499,plain,
( typing(e,u,t1)
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f497]) ).
tff(f1288,plain,
( spl26_147
| ~ spl26_96
| ~ spl26_146 ),
inference(avatar_split_clause,[],[f1284,f1280,f948,f1286]) ).
tff(f1286,plain,
( spl26_147
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_147])]) ).
tff(f1280,plain,
( spl26_146
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_146])]) ).
tff(f1284,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl26_96
| ~ spl26_146 ),
inference(forward_demodulation,[],[f1283,f949]) ).
tff(f1283,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl26_96
| ~ spl26_146 ),
inference(forward_demodulation,[],[f1281,f949]) ).
tff(f1281,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)))
| ~ spl26_146 ),
inference(avatar_component_clause,[],[f1280]) ).
tff(f1282,plain,
spl26_146,
inference(avatar_split_clause,[],[f380,f1280]) ).
tff(f380,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X14: dB,X36: dB] : beta(aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X36)),X14),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X36),X14),zero_zero(nat))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_49_beta) ).
tff(f1276,plain,
spl26_145,
inference(avatar_split_clause,[],[f464,f1274]) ).
tff(f1274,plain,
( spl26_145
<=> ! [X3: type,X4: dB,X0: list(type),X5: fun(nat,type),X2: nat,X1: list(dB)] :
( typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1),X0)
| ~ typings(shift(type,X5,X2,X3),X1,X0)
| ~ typing(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_145])]) ).
tff(f464,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1),X0)
| ~ typings(shift(type,X5,X2,X3),X1,X0)
| ~ typing(X5,X4,X3) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1),X0)
| ~ typings(shift(type,X5,X2,X3),X1,X0)
| ~ typing(X5,X4,X3) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1),X0)
| ~ typings(shift(type,X5,X2,X3),X1,X0)
| ~ typing(X5,X4,X3) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
( typing(X5,X4,X3)
=> ( typings(shift(type,X5,X2,X3),X1,X0)
=> typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X2),X1),X0) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X72: list(type),X28: list(dB),X6: nat,X5: type,X4: dB,X7: fun(nat,type)] :
( typing(X7,X4,X5)
=> ( typings(shift(type,X7,X6,X5),X28,X72)
=> typings(X7,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,X4),X6),X28),X72) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_91_substs__lemma) ).
tff(f1269,plain,
( spl26_144
| ~ spl26_96
| ~ spl26_143 ),
inference(avatar_split_clause,[],[f1265,f1261,f948,f1267]) ).
tff(f1261,plain,
( spl26_143
<=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
( typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_143])]) ).
tff(f1265,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( ~ typing(X4,X3,aa(type,type,combc(type,type,type,fun1,X1),X2))
| typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3),X1)
| ~ typing(X4,X0,X2) )
| ~ spl26_96
| ~ spl26_143 ),
inference(forward_demodulation,[],[f1264,f949]) ).
tff(f1264,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( typing(X4,aa(dB,dB,combc(dB,dB,dB,app,X0),X3),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) )
| ~ spl26_96
| ~ spl26_143 ),
inference(forward_demodulation,[],[f1262,f949]) ).
tff(f1262,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) )
| ~ spl26_143 ),
inference(avatar_component_clause,[],[f1261]) ).
tff(f1263,plain,
spl26_143,
inference(avatar_split_clause,[],[f460,f1261]) ).
tff(f460,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
( typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1)
| ~ typing(X4,X0,X2)
| ~ typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
( typing(X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1))
=> ( typing(X4,X0,X2)
=> typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0),X1) ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X8: dB,X17: type,X5: type,X26: dB,X25: fun(nat,type)] :
( typing(X25,X26,aa(type,type,aa(type,fun(type,type),fun1,X5),X17))
=> ( typing(X25,X8,X5)
=> typing(X25,aa(dB,dB,aa(dB,fun(dB,dB),app,X26),X8),X17) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_22_App) ).
tff(f1253,plain,
( spl26_142
| ~ spl26_96
| ~ spl26_140 ),
inference(avatar_split_clause,[],[f1245,f1241,f948,f1251]) ).
tff(f1241,plain,
( spl26_140
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_140])]) ).
tff(f1245,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| typing(X3,X2,aa(type,type,combc(type,type,type,fun1,X0),sK23(X0,X1,X2,X3))) )
| ~ spl26_96
| ~ spl26_140 ),
inference(forward_demodulation,[],[f1244,f949]) ).
tff(f1244,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X2,aa(type,type,combc(type,type,type,fun1,X0),sK23(X0,X1,X2,X3)))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_96
| ~ spl26_140 ),
inference(forward_demodulation,[],[f1242,f949]) ).
tff(f1242,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_140 ),
inference(avatar_component_clause,[],[f1241]) ).
tff(f1249,plain,
( spl26_141
| ~ spl26_4
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f677,f674,f492,f1247]) ).
tff(f1247,plain,
( spl26_141
<=> ! [X0: dB] :
( ~ beta(ua,X0)
| typing(ea,X0,t1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_141])]) ).
tff(f492,plain,
( spl26_4
<=> typing(ea,ua,t1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
tff(f677,plain,
( ! [X0: dB] :
( ~ beta(ua,X0)
| typing(ea,X0,t1) )
| ~ spl26_4
| ~ spl26_40 ),
inference(resolution,[],[f675,f494]) ).
tff(f494,plain,
( typing(ea,ua,t1)
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f492]) ).
tff(f1243,plain,
spl26_140,
inference(avatar_split_clause,[],[f435,f1241]) ).
tff(f435,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( typing(X3,X1,sK23(X0,X1,X2,X3))
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f238,f308]) ).
tff(f308,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( typing(X3,X1,X4)
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
=> ( typing(X3,X1,sK23(X0,X1,X2,X3))
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f238,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( typing(X3,X1,X4)
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
=> ~ ! [X4: type] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0))
=> ~ typing(X3,X1,X4) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X5: type,X4: dB,X8: dB,X7: fun(nat,type)] :
( typing(X7,aa(dB,dB,aa(dB,fun(dB,dB),app,X8),X4),X5)
=> ~ ! [X31: type] :
( typing(X7,X8,aa(type,type,aa(type,fun(type,type),fun1,X31),X5))
=> ~ typing(X7,X4,X31) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_34_typing__elims_I2_J) ).
tff(f1238,plain,
( spl26_139
| ~ spl26_96
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1233,f1229,f948,f1235]) ).
tff(f1235,plain,
( spl26_139
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_139])]) ).
tff(f1229,plain,
( spl26_138
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_138])]) ).
tff(f1233,plain,
( typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as),t)
| ~ spl26_96
| ~ spl26_138 ),
inference(forward_demodulation,[],[f1231,f949]) ).
tff(f1231,plain,
( typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t)
| ~ spl26_138 ),
inference(avatar_component_clause,[],[f1229]) ).
tff(f1232,plain,
spl26_138,
inference(avatar_split_clause,[],[f339,f1229]) ).
tff(f339,plain,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f1226,plain,
( spl26_137
| ~ spl26_96
| ~ spl26_136 ),
inference(avatar_split_clause,[],[f1222,f1219,f948,f1224]) ).
tff(f1219,plain,
( spl26_136
<=> ! [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,[spl26_136])]) ).
tff(f1222,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)) )
| ~ spl26_96
| ~ spl26_136 ),
inference(forward_demodulation,[],[f1220,f949]) ).
tff(f1220,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)) )
| ~ spl26_136 ),
inference(avatar_component_clause,[],[f1219]) ).
tff(f1221,plain,
spl26_136,
inference(avatar_split_clause,[],[f416,f1219]) ).
tff(f416,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,[],[f226]) ).
tff(f226,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X11: nat,X12: nat,X13: dB] :
( pp(aa(dB,bool,it,X13))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X13),var(X12)),X11))) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_9_subst__Var__IT) ).
tff(f1213,plain,
( spl26_135
| ~ spl26_96
| ~ spl26_134 ),
inference(avatar_split_clause,[],[f1209,f1205,f948,f1211]) ).
tff(f1205,plain,
( spl26_134
<=> ! [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,[spl26_134])]) ).
tff(f1209,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 )
| ~ spl26_96
| ~ spl26_134 ),
inference(forward_demodulation,[],[f1208,f949]) ).
tff(f1208,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 )
| ~ spl26_96
| ~ spl26_134 ),
inference(forward_demodulation,[],[f1206,f949]) ).
tff(f1206,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 )
| ~ spl26_134 ),
inference(avatar_component_clause,[],[f1205]) ).
tff(f1207,plain,
spl26_134,
inference(avatar_split_clause,[],[f405,f1205]) ).
tff(f405,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,[],[f155]) ).
tff(f155,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,[],[f61]) ).
tff(f61,axiom,
! [X36: dB,X35: nat,X14: 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,X14),X35)),X36),X35) = X14 ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_60_subst__lift) ).
tff(f1200,plain,
( spl26_133
| ~ spl26_96
| ~ spl26_132 ),
inference(avatar_split_clause,[],[f1195,f1191,f948,f1197]) ).
tff(f1191,plain,
( spl26_132
<=> 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,r),a),zero_zero(nat)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_132])]) ).
tff(f1195,plain,
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,r),zero_zero(nat)),a),as)))
| ~ spl26_96
| ~ spl26_132 ),
inference(forward_demodulation,[],[f1193,f949]) ).
tff(f1193,plain,
( 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,r),a),zero_zero(nat)),as)))
| ~ spl26_132 ),
inference(avatar_component_clause,[],[f1191]) ).
tff(f1194,plain,
spl26_132,
inference(avatar_split_clause,[],[f338,f1191]) ).
tff(f338,plain,
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,r),a),zero_zero(nat)),as))),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
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,r),a),zero_zero(nat)),as))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_17_Beta_I1_J) ).
tff(f1187,plain,
spl26_131,
inference(avatar_split_clause,[],[f450,f1185]) ).
tff(f450,plain,
! [X2: dB,X3: dB,X0: dB,X1: 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(cnf_transformation,[],[f319]) ).
tff(f319,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,[],[f318]) ).
tff(f318,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,[],[f184]) ).
tff(f184,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,[],[f41]) ).
tff(f41,axiom,
! [X37: dB,X38: dB,X39: dB,X40: dB] :
( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X40),X39) = aa(dB,dB,aa(dB,fun(dB,dB),app,X38),X37) )
<=> ( ( X37 = X39 )
& ( X38 = X40 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_40_dB_Osimps_I2_J) ).
tff(f1183,plain,
spl26_130,
inference(avatar_split_clause,[],[f447,f1181]) ).
tff(f447,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(flattening,[],[f316]) ).
tff(f316,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X20: type,X21: type,X22: type,X23: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X23),X22) = aa(type,type,aa(type,fun(type,type),fun1,X21),X20) )
<=> ( ( X20 = X22 )
& ( X21 = X23 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_19_type_Osimps_I2_J) ).
tff(f1176,plain,
( spl26_129
| ~ spl26_96
| ~ spl26_128 ),
inference(avatar_split_clause,[],[f1172,f1169,f948,f1174]) ).
tff(f1174,plain,
( spl26_129
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| beta(X1,sK21(X0,X1,X2))
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_129])]) ).
tff(f1169,plain,
( spl26_128
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_128])]) ).
tff(f1172,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| beta(X1,sK21(X0,X1,X2))
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl26_96
| ~ spl26_128 ),
inference(forward_demodulation,[],[f1170,f949]) ).
tff(f1170,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_128 ),
inference(avatar_component_clause,[],[f1169]) ).
tff(f1171,plain,
spl26_128,
inference(avatar_split_clause,[],[f423,f1169]) ).
tff(f423,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK21(X0,X1,X2))
| beta(X2,sK22(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1167,plain,
( spl26_127
| ~ spl26_36
| ~ spl26_109 ),
inference(avatar_split_clause,[],[f1108,f1029,f645,f1165]) ).
tff(f1029,plain,
( spl26_109
<=> ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_109])]) ).
tff(f1108,plain,
( ! [X2: nat,X3: dB] : ~ beta(abs(abs(var(X2))),X3)
| ~ spl26_36
| ~ spl26_109 ),
inference(resolution,[],[f1030,f646]) ).
tff(f1030,plain,
( ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1)
| ~ spl26_109 ),
inference(avatar_component_clause,[],[f1029]) ).
tff(f1163,plain,
( spl26_126
| ~ spl26_96
| ~ spl26_125 ),
inference(avatar_split_clause,[],[f1159,f1156,f948,f1161]) ).
tff(f1161,plain,
( spl26_126
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),zero_zero(nat)),X2) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_126])]) ).
tff(f1156,plain,
( spl26_125
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_125])]) ).
tff(f1159,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),zero_zero(nat)),X2) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl26_96
| ~ spl26_125 ),
inference(forward_demodulation,[],[f1157,f949]) ).
tff(f1157,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl26_125 ),
inference(avatar_component_clause,[],[f1156]) ).
tff(f1158,plain,
spl26_125,
inference(avatar_split_clause,[],[f418,f1156]) ).
tff(f418,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( ( abs(sK20(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f300,f301]) ).
tff(f301,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
=> ( ( abs(sK20(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK20(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f300,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f299]) ).
tff(f299,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
inference(nnf_transformation,[],[f264]) ).
tff(f1112,plain,
spl26_124,
inference(avatar_split_clause,[],[f462,f1110]) ).
tff(f462,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,[],[f194]) ).
tff(f194,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,[],[f105]) ).
tff(f105,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X82: X0,X83: fun(X0,X1),X84: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X84,X83),X82) = aa(X1,X2,aa(X0,fun(X1,X2),X84,X82),aa(X0,X1,X83,X82)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_COMBS_1_1_U) ).
tff(f1106,plain,
spl26_123,
inference(avatar_split_clause,[],[f454,f1104]) ).
tff(f454,plain,
! [X0: $tType,X2: X0,X3: nat,X1: X0,X4: fun(nat,X0)] : ( shift(X0,shift(X0,X4,X3,X2),zero_zero(nat),X1) = shift(X0,shift(X0,X4,zero_zero(nat),X1),suc(X3),X2) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: X0,X2: X0,X3: nat,X4: fun(nat,X0)] : ( shift(X0,shift(X0,X4,X3,X2),zero_zero(nat),X1) = shift(X0,shift(X0,X4,zero_zero(nat),X1),suc(X3),X2) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X5: X0,X17: X0,X6: nat,X7: fun(nat,X0)] : ( shift(X0,shift(X0,X7,X6,X17),zero_zero(nat),X5) = shift(X0,shift(X0,X7,zero_zero(nat),X5),suc(X6),X17) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_68_shift__commute) ).
tff(f1102,plain,
spl26_122,
inference(avatar_split_clause,[],[f449,f1100]) ).
tff(f449,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,[],[f319]) ).
tff(f1098,plain,
spl26_121,
inference(avatar_split_clause,[],[f448,f1096]) ).
tff(f448,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,[],[f319]) ).
tff(f1094,plain,
spl26_120,
inference(avatar_split_clause,[],[f446,f1092]) ).
tff(f446,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1090,plain,
spl26_119,
inference(avatar_split_clause,[],[f445,f1088]) ).
tff(f445,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1086,plain,
( spl26_118
| ~ spl26_96
| ~ spl26_117 ),
inference(avatar_split_clause,[],[f1082,f1078,f948,f1084]) ).
tff(f1084,plain,
( spl26_118
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_118])]) ).
tff(f1078,plain,
( spl26_117
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_117])]) ).
tff(f1082,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_117 ),
inference(forward_demodulation,[],[f1081,f949]) ).
tff(f1081,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_117 ),
inference(forward_demodulation,[],[f1079,f949]) ).
tff(f1079,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_117 ),
inference(avatar_component_clause,[],[f1078]) ).
tff(f1080,plain,
spl26_117,
inference(avatar_split_clause,[],[f411,f1078]) ).
tff(f411,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X45: dB,X14: dB,X36: dB] :
( beta(X36,X14)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X36),X45),aa(dB,dB,aa(dB,fun(dB,dB),app,X14),X45)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_45_appL) ).
tff(f1076,plain,
( spl26_116
| ~ spl26_96
| ~ spl26_115 ),
inference(avatar_split_clause,[],[f1071,f1067,f948,f1074]) ).
tff(f1074,plain,
( spl26_116
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_116])]) ).
tff(f1067,plain,
( spl26_115
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_115])]) ).
tff(f1071,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,dB,dB,app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_115 ),
inference(forward_demodulation,[],[f1070,f949]) ).
tff(f1070,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_115 ),
inference(forward_demodulation,[],[f1068,f949]) ).
tff(f1068,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_115 ),
inference(avatar_component_clause,[],[f1067]) ).
tff(f1069,plain,
spl26_115,
inference(avatar_split_clause,[],[f410,f1067]) ).
tff(f410,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X45: dB,X14: dB,X36: dB] :
( beta(X36,X14)
=> beta(aa(dB,dB,aa(dB,fun(dB,dB),app,X45),X36),aa(dB,dB,aa(dB,fun(dB,dB),app,X45),X14)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_44_appR) ).
tff(f1065,plain,
( spl26_114
| ~ spl26_96
| ~ spl26_113 ),
inference(avatar_split_clause,[],[f1061,f1057,f948,f1063]) ).
tff(f1063,plain,
( spl26_114
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_114])]) ).
tff(f1057,plain,
( spl26_113
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_113])]) ).
tff(f1061,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,lift,X0),X2),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_113 ),
inference(forward_demodulation,[],[f1060,f949]) ).
tff(f1060,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) )
| ~ spl26_96
| ~ spl26_113 ),
inference(forward_demodulation,[],[f1058,f949]) ).
tff(f1058,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) )
| ~ spl26_113 ),
inference(avatar_component_clause,[],[f1057]) ).
tff(f1059,plain,
spl26_113,
inference(avatar_split_clause,[],[f409,f1057]) ).
tff(f409,plain,
! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X12: nat,X36: dB,X13: dB] :
( beta(X13,X36)
=> beta(aa(nat,dB,aa(dB,fun(nat,dB),lift,X13),X12),aa(nat,dB,aa(dB,fun(nat,dB),lift,X36),X12)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_51_lift__preserves__beta) ).
tff(f1048,plain,
spl26_112,
inference(avatar_split_clause,[],[f438,f1046]) ).
tff(f438,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK24(X0,X1,X2,X3)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK24(X0,X1,X2,X3)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f241,f310]) ).
tff(f310,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,sK24(X0,X1,X2,X3)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f241,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,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X59: fun(X0,X1),X60: fun(X0,X1)] :
( ! [X61: X0] : ( aa(X0,X1,X60,X61) = aa(X0,X1,X59,X61) )
=> ( X59 = X60 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_74_ext) ).
tff(f1041,plain,
( spl26_111
| ~ spl26_96
| ~ spl26_110 ),
inference(avatar_split_clause,[],[f1037,f1034,f948,f1039]) ).
tff(f1034,plain,
( spl26_110
<=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_110])]) ).
tff(f1037,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,combc(type,type,type,fun1,X0),X2))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) )
| ~ spl26_96
| ~ spl26_110 ),
inference(forward_demodulation,[],[f1035,f949]) ).
tff(f1035,plain,
( ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) )
| ~ spl26_110 ),
inference(avatar_component_clause,[],[f1034]) ).
tff(f1036,plain,
spl26_110,
inference(avatar_split_clause,[],[f434,f1034]) ).
tff(f434,plain,
! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,abs(X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( typing(X3,abs(X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))
| ~ typing(shift(type,X3,zero_zero(nat),X2),X1,X0) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
( typing(shift(type,X3,zero_zero(nat),X2),X1,X0)
=> typing(X3,abs(X1),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X17: type,X8: dB,X5: type,X25: fun(nat,type)] :
( typing(shift(type,X25,zero_zero(nat),X5),X8,X17)
=> typing(X25,abs(X8),aa(type,type,aa(type,fun(type,type),fun1,X5),X17)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_26_Abs) ).
tff(f1031,plain,
( spl26_109
| ~ spl26_8
| ~ spl26_36 ),
inference(avatar_split_clause,[],[f662,f645,f510,f1029]) ).
tff(f510,plain,
( spl26_8
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
tff(f662,plain,
( ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1)
| ~ spl26_8
| ~ spl26_36 ),
inference(resolution,[],[f646,f511]) ).
tff(f511,plain,
( ! [X0: dB,X1: nat] : ~ beta(var(X1),X0)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f510]) ).
tff(f1027,plain,
( spl26_108
| ~ spl26_96
| ~ spl26_107 ),
inference(avatar_split_clause,[],[f1023,f1020,f948,f1025]) ).
tff(f1025,plain,
( spl26_108
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun1,sK19(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ typing(X2,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_108])]) ).
tff(f1020,plain,
( spl26_107
<=> ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X0 )
| ~ typing(X2,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_107])]) ).
tff(f1023,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun1,sK19(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ typing(X2,abs(X1),X0) )
| ~ spl26_96
| ~ spl26_107 ),
inference(forward_demodulation,[],[f1021,f949]) ).
tff(f1021,plain,
( ! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X0 )
| ~ typing(X2,abs(X1),X0) )
| ~ spl26_107 ),
inference(avatar_component_clause,[],[f1020]) ).
tff(f1022,plain,
spl26_107,
inference(avatar_split_clause,[],[f414,f1020]) ).
tff(f414,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun(type,type),fun1,sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X0 )
| ~ typing(X2,abs(X1),X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ( typing(shift(type,X2,zero_zero(nat),sK18(X0,X1,X2)),X1,sK19(X0,X1,X2))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X0 ) )
| ~ typing(X2,abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f225,f297]) ).
tff(f297,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( typing(shift(type,X2,zero_zero(nat),X3),X1,X4)
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
=> ( typing(shift(type,X2,zero_zero(nat),sK18(X0,X1,X2)),X1,sK19(X0,X1,X2))
& ( aa(type,type,aa(type,fun(type,type),fun1,sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f225,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] :
( typing(shift(type,X2,zero_zero(nat),X3),X1,X4)
& ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
| ~ typing(X2,abs(X1),X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( typing(X2,abs(X1),X0)
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 )
=> ~ typing(shift(type,X2,zero_zero(nat),X3),X1,X4) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,abs(X8),X5)
=> ~ ! [X31: type,X19: type] :
( ( aa(type,type,aa(type,fun(type,type),fun1,X31),X19) = X5 )
=> ~ typing(shift(type,X7,zero_zero(nat),X31),X8,X19) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_33_typing__elims_I3_J) ).
tff(f1018,plain,
( spl26_106
| ~ spl26_96
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f1014,f1011,f948,f1016]) ).
tff(f1016,plain,
( spl26_106
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK11(X0)),abs(sK10(X0))),sK12(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_106])]) ).
tff(f1011,plain,
( spl26_105
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_105])]) ).
tff(f1014,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,sK11(X0)),abs(sK10(X0))),sK12(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl26_96
| ~ spl26_105 ),
inference(forward_demodulation,[],[f1012,f949]) ).
tff(f1012,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl26_105 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f1013,plain,
spl26_105,
inference(avatar_split_clause,[],[f368,f1011]) ).
tff(f368,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK10(X0))),sK11(X0)),sK12(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f1008,plain,
( spl26_104
| ~ spl26_96
| ~ spl26_103 ),
inference(avatar_split_clause,[],[f1003,f999,f948,f1005]) ).
tff(f999,plain,
( spl26_103
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_103])]) ).
tff(f1003,plain,
( typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t)
| ~ spl26_96
| ~ spl26_103 ),
inference(forward_demodulation,[],[f1001,f949]) ).
tff(f1001,plain,
( typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t)
| ~ spl26_103 ),
inference(avatar_component_clause,[],[f999]) ).
tff(f1002,plain,
spl26_103,
inference(avatar_split_clause,[],[f337,f999]) ).
tff(f337,plain,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_23_T) ).
tff(f996,plain,
( spl26_102
| ~ spl26_96
| ~ spl26_100 ),
inference(avatar_split_clause,[],[f987,f983,f948,f993]) ).
tff(f983,plain,
( spl26_100
<=> typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_100])]) ).
tff(f987,plain,
( typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),as),t_a)
| ~ spl26_96
| ~ spl26_100 ),
inference(forward_demodulation,[],[f985,f949]) ).
tff(f985,plain,
( typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a)
| ~ spl26_100 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f991,plain,
( spl26_101
| ~ spl26_21
| ~ spl26_34 ),
inference(avatar_split_clause,[],[f661,f637,f571,f989]) ).
tff(f989,plain,
( spl26_101
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_101])]) ).
tff(f661,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK11(X0)) )
| ~ spl26_21
| ~ spl26_34 ),
inference(resolution,[],[f638,f572]) ).
tff(f986,plain,
spl26_100,
inference(avatar_split_clause,[],[f336,f983]) ).
tff(f336,plain,
typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_27_Beta_I5_J) ).
tff(f980,plain,
spl26_99,
inference(avatar_split_clause,[],[f459,f978]) ).
tff(f978,plain,
( spl26_99
<=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X0)
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_99])]) ).
tff(f459,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X0)
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X1) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X0)
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X1) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( ( X0 = X1 )
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X0)
| ~ typing(X4,foldl(dB,dB,app,var(X3),X2),X1) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
( typing(X4,foldl(dB,dB,app,var(X3),X2),X1)
=> ( typing(X4,foldl(dB,dB,app,var(X3),X2),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X17: type,X5: type,X28: list(dB),X6: nat,X7: fun(nat,type)] :
( typing(X7,foldl(dB,dB,app,var(X6),X28),X5)
=> ( typing(X7,foldl(dB,dB,app,var(X6),X28),X17)
=> ( X5 = X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_30_var__app__type__eq) ).
tff(f975,plain,
( spl26_98
| ~ spl26_96
| ~ spl26_97 ),
inference(avatar_split_clause,[],[f971,f968,f948,f973]) ).
tff(f968,plain,
( spl26_97
<=> ! [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,[spl26_97])]) ).
tff(f971,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)) )
| ~ spl26_96
| ~ spl26_97 ),
inference(forward_demodulation,[],[f969,f949]) ).
tff(f969,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)) )
| ~ spl26_97 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f970,plain,
spl26_97,
inference(avatar_split_clause,[],[f390,f968]) ).
tff(f390,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,[],[f214]) ).
tff(f214,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,[],[f145]) ).
tff(f145,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,[],[f32]) ).
tff(f32,axiom,
! [X12: nat,X14: dB] :
( pp(aa(dB,bool,it,X14))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X14),var(X12)))) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_31_app__Var__IT) ).
tff(f950,plain,
spl26_96,
inference(avatar_split_clause,[],[f461,f948]) ).
tff(f946,plain,
spl26_95,
inference(avatar_split_clause,[],[f458,f944]) ).
tff(f944,plain,
( spl26_95
<=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
( typing(X4,foldl(dB,dB,app,X3,X0),X1)
| ~ typings(X4,X0,X2)
| ~ typing(X4,X3,foldr(type,type,fun1,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_95])]) ).
tff(f458,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
( typing(X4,foldl(dB,dB,app,X3,X0),X1)
| ~ typings(X4,X0,X2)
| ~ typing(X4,X3,foldr(type,type,fun1,X2,X1)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( typing(X4,foldl(dB,dB,app,X3,X0),X1)
| ~ typings(X4,X0,X2)
| ~ typing(X4,X3,foldr(type,type,fun1,X2,X1)) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( typing(X4,foldl(dB,dB,app,X3,X0),X1)
| ~ typings(X4,X0,X2)
| ~ typing(X4,X3,foldr(type,type,fun1,X2,X1)) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
( typing(X4,X3,foldr(type,type,fun1,X2,X1))
=> ( typings(X4,X0,X2)
=> typing(X4,foldl(dB,dB,app,X3,X0),X1) ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X28: list(dB),X5: type,X72: list(type),X8: dB,X7: fun(nat,type)] :
( typing(X7,X8,foldr(type,type,fun1,X72,X5))
=> ( typings(X7,X28,X72)
=> typing(X7,foldl(dB,dB,app,X8,X28),X5) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_96_list__app__typeI) ).
tff(f941,plain,
( spl26_94
| ~ spl26_93 ),
inference(avatar_split_clause,[],[f937,f934,f939]) ).
tff(f934,plain,
( spl26_93
<=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1),X2)
| ~ typing(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_93])]) ).
tff(f937,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( typing(shift(type,X4,X1,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typing(X4,X3,X2) )
| ~ spl26_93 ),
inference(forward_demodulation,[],[f935,f461]) ).
tff(f935,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1),X2)
| ~ typing(X4,X3,X2) )
| ~ spl26_93 ),
inference(avatar_component_clause,[],[f934]) ).
tff(f936,plain,
spl26_93,
inference(avatar_split_clause,[],[f457,f934]) ).
tff(f457,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun(nat,type)] :
( typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1),X2)
| ~ typing(X4,X3,X2) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1),X2)
| ~ typing(X4,X3,X2) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
( typing(X4,X3,X2)
=> typing(shift(type,X4,X1,X0),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1),X2) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X17: type,X6: nat,X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,X8,X5)
=> typing(shift(type,X7,X6,X17),aa(nat,dB,aa(dB,fun(nat,dB),lift,X8),X6),X5) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_24_lift__type) ).
tff(f932,plain,
spl26_92,
inference(avatar_split_clause,[],[f444,f930]) ).
tff(f444,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,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,[],[f314]) ).
tff(f314,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,[],[f182]) ).
tff(f182,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,[],[f38]) ).
tff(f38,axiom,
! [X29: list(dB),X26: dB,X33: list(dB),X30: dB] :
( ( foldl(dB,dB,app,abs(X30),X33) = foldl(dB,dB,app,abs(X26),X29) )
<=> ( ( X29 = X33 )
& ( X26 = X30 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_37_Abs__apps__eq__Abs__apps__conv) ).
tff(f928,plain,
spl26_91,
inference(avatar_split_clause,[],[f441,f926]) ).
tff(f441,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,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,[],[f312]) ).
tff(f312,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,[],[f181]) ).
tff(f181,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,[],[f37]) ).
tff(f37,axiom,
! [X29: list(dB),X32: nat,X33: list(dB),X34: nat] :
( ( foldl(dB,dB,app,var(X34),X33) = foldl(dB,dB,app,var(X32),X29) )
<=> ( ( X29 = X33 )
& ( X32 = X34 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_36_Var__apps__eq__Var__apps__conv) ).
tff(f921,plain,
( spl26_90
| ~ spl26_88 ),
inference(avatar_split_clause,[],[f912,f909,f919]) ).
tff(f909,plain,
( spl26_88
<=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
( typing(X3,X1,sK23(X0,X1,X2,X3))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_88])]) ).
tff(f912,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| typing(X3,X1,sK23(X0,X1,X2,X3)) )
| ~ spl26_88 ),
inference(forward_demodulation,[],[f910,f461]) ).
tff(f910,plain,
( ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X1,sK23(X0,X1,X2,X3))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) )
| ~ spl26_88 ),
inference(avatar_component_clause,[],[f909]) ).
tff(f917,plain,
( ~ spl26_89
| spl26_12
| ~ spl26_22 ),
inference(avatar_split_clause,[],[f615,f575,f528,f914]) ).
tff(f914,plain,
( spl26_89
<=> sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_89])]) ).
tff(f615,plain,
( ~ sP1(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u))
| spl26_12
| ~ spl26_22 ),
inference(resolution,[],[f576,f530]) ).
tff(f911,plain,
spl26_88,
inference(avatar_split_clause,[],[f436,f909]) ).
tff(f436,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( typing(X3,X1,sK23(X0,X1,X2,X3))
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f309]) ).
tff(f906,plain,
( spl26_87
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f902,f899,f904]) ).
tff(f899,plain,
( spl26_86
<=> ! [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,[spl26_86])]) ).
tff(f902,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)) )
| ~ spl26_86 ),
inference(forward_demodulation,[],[f900,f461]) ).
tff(f900,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)) )
| ~ spl26_86 ),
inference(avatar_component_clause,[],[f899]) ).
tff(f901,plain,
spl26_86,
inference(avatar_split_clause,[],[f389,f899]) ).
tff(f389,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,[],[f213]) ).
tff(f213,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,[],[f144]) ).
tff(f144,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,[],[f11]) ).
tff(f11,axiom,
! [X12: nat,X14: dB] :
( pp(aa(dB,bool,it,X14))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X14),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_10_lift__IT) ).
tff(f897,plain,
( spl26_85
| ~ spl26_84 ),
inference(avatar_split_clause,[],[f893,f890,f895]) ).
tff(f890,plain,
( spl26_84
<=> ! [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,[spl26_84])]) ).
tff(f893,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 )
| ~ spl26_84 ),
inference(forward_demodulation,[],[f891,f461]) ).
tff(f891,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 )
| ~ spl26_84 ),
inference(avatar_component_clause,[],[f890]) ).
tff(f892,plain,
spl26_84,
inference(avatar_split_clause,[],[f379,f890]) ).
tff(f379,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,[],[f135]) ).
tff(f135,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,[],[f58]) ).
tff(f58,axiom,
! [X45: dB,X35: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X35)),X45),X35) = X45 ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_57_subst__eq) ).
tff(f888,plain,
spl26_83,
inference(avatar_split_clause,[],[f363,f886]) ).
tff(f363,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,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,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) )
| ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f277,f279,f278]) ).
tff(f278,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f279,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f277,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,[],[f276]) ).
tff(f276,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,[],[f275]) ).
tff(f275,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,[],[f262]) ).
tff(f262,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(f883,plain,
spl26_82,
inference(avatar_split_clause,[],[f456,f881]) ).
tff(f456,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
( typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typings(X4,X3,X2) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2)
| ~ typings(X4,X3,X2) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
( typings(X4,X3,X2)
=> typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3),X2) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X17: type,X6: nat,X72: list(type),X28: list(dB),X7: fun(nat,type)] :
( typings(X7,X28,X72)
=> typings(shift(type,X7,X6,X17),map(dB,dB,combc(dB,nat,dB,lift,X6),X28),X72) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_93_lift__types) ).
tff(f879,plain,
spl26_81,
inference(avatar_split_clause,[],[f394,f877]) ).
tff(f877,plain,
( spl26_81
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK15(X1))))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_81])]) ).
tff(f394,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ~ pp(aa(nat,bool,X1,suc(sK15(X1))))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| ( ~ pp(aa(nat,bool,X1,suc(sK15(X1))))
& pp(aa(nat,bool,X1,sK15(X1))) )
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f218,f290]) ).
tff(f290,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(sK15(X1))))
& pp(aa(nat,bool,X1,sK15(X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f218,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,[],[f217]) ).
tff(f217,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,[],[f147]) ).
tff(f147,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,[],[f89]) ).
tff(f89,axiom,
! [X32: 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,X32)) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_88_nat__induct) ).
tff(f875,plain,
spl26_80,
inference(avatar_split_clause,[],[f391,f873]) ).
tff(f873,plain,
( spl26_80
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| pp(aa(nat,bool,X1,suc(sK14(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_80])]) ).
tff(f391,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| pp(aa(nat,bool,X1,suc(sK14(X1))))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ( ~ pp(aa(nat,bool,X1,sK14(X1)))
& pp(aa(nat,bool,X1,suc(sK14(X1)))) )
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f216,f288]) ).
tff(f288,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,sK14(X1)))
& pp(aa(nat,bool,X1,suc(sK14(X1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f216,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,[],[f215]) ).
tff(f215,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,[],[f146]) ).
tff(f146,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,[],[f88]) ).
tff(f88,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/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_87_zero__induct) ).
tff(f864,plain,
spl26_79,
inference(avatar_split_clause,[],[f428,f862]) ).
tff(f428,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,[],[f171]) ).
tff(f171,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,[],[f63]) ).
tff(f63,axiom,
! [X29: list(dB),X32: nat,X8: dB,X26: dB] : ( foldl(dB,dB,app,var(X32),X29) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X26)),X8) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_62_Abs__App__neq__Var__apps) ).
tff(f860,plain,
( spl26_78
| ~ spl26_18
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f610,f571,f557,f858]) ).
tff(f858,plain,
( spl26_78
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_78])]) ).
tff(f610,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl26_18
| ~ spl26_21 ),
inference(resolution,[],[f572,f558]) ).
tff(f856,plain,
spl26_77,
inference(avatar_split_clause,[],[f415,f854]) ).
tff(f415,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( typing(shift(type,X2,zero_zero(nat),sK18(X0,X1,X2)),X1,sK19(X0,X1,X2))
| ~ typing(X2,abs(X1),X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f852,plain,
spl26_76,
inference(avatar_split_clause,[],[f393,f850]) ).
tff(f850,plain,
( spl26_76
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK15(X1)))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_76])]) ).
tff(f393,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,X0))
| pp(aa(nat,bool,X1,sK15(X1)))
| ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
inference(cnf_transformation,[],[f291]) ).
tff(f848,plain,
spl26_75,
inference(avatar_split_clause,[],[f392,f846]) ).
tff(f846,plain,
( spl26_75
<=> ! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ~ pp(aa(nat,bool,X1,sK14(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_75])]) ).
tff(f392,plain,
! [X0: nat,X1: fun(nat,bool)] :
( pp(aa(nat,bool,X1,zero_zero(nat)))
| ~ pp(aa(nat,bool,X1,sK14(X1)))
| ~ pp(aa(nat,bool,X1,X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f844,plain,
spl26_74,
inference(avatar_split_clause,[],[f361,f842]) ).
tff(f842,plain,
( spl26_74
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_74])]) ).
tff(f361,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f838,plain,
spl26_73,
inference(avatar_split_clause,[],[f443,f836]) ).
tff(f836,plain,
( spl26_73
<=> ! [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,[spl26_73])]) ).
tff(f443,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,[],[f315]) ).
tff(f834,plain,
spl26_72,
inference(avatar_split_clause,[],[f440,f832]) ).
tff(f832,plain,
( spl26_72
<=> ! [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,[spl26_72])]) ).
tff(f440,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,[],[f313]) ).
tff(f829,plain,
( spl26_71
| ~ spl26_70 ),
inference(avatar_split_clause,[],[f824,f820,f826]) ).
tff(f820,plain,
( spl26_70
<=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_70])]) ).
tff(f824,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),sK4)
| ~ spl26_70 ),
inference(forward_demodulation,[],[f822,f461]) ).
tff(f822,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4)
| ~ spl26_70 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f823,plain,
spl26_70,
inference(avatar_split_clause,[],[f344,f820]) ).
tff(f344,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f203,f268]) ).
tff(f268,plain,
( ? [X0: type] : typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
? [X0: type] : typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
inference(ennf_transformation,[],[f113]) ).
tff(f113,plain,
~ ! [X0: type] : ~ typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
~ ! [X19: type] : ~ typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X19),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f817,plain,
( spl26_69
| ~ spl26_68 ),
inference(avatar_split_clause,[],[f812,f808,f814]) ).
tff(f808,plain,
( spl26_68
<=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_68])]) ).
tff(f812,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,combc(dB,dB,dB,app,a),abs(r)),ua1)
| ~ spl26_68 ),
inference(forward_demodulation,[],[f810,f461]) ).
tff(f810,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1)
| ~ spl26_68 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f811,plain,
spl26_68,
inference(avatar_split_clause,[],[f335,f808]) ).
tff(f335,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
tff(f804,plain,
spl26_67,
inference(avatar_split_clause,[],[f442,f802]) ).
tff(f802,plain,
( spl26_67
<=> ! [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,[spl26_67])]) ).
tff(f442,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,[],[f315]) ).
tff(f800,plain,
spl26_66,
inference(avatar_split_clause,[],[f439,f798]) ).
tff(f798,plain,
( spl26_66
<=> ! [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,[spl26_66])]) ).
tff(f439,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,[],[f313]) ).
tff(f796,plain,
spl26_65,
inference(avatar_split_clause,[],[f413,f794]) ).
tff(f413,plain,
! [X2: fun(nat,type),X0: type,X1: dB] :
( typing(shift(type,X2,zero_zero(nat),sK16(X1,X2)),X1,sK17(X1,X2))
| ~ typing(X2,abs(X1),X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( typing(shift(type,X2,zero_zero(nat),sK16(X1,X2)),X1,sK17(X1,X2))
| ~ typing(X2,abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f224,f295]) ).
tff(f295,plain,
! [X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : typing(shift(type,X2,zero_zero(nat),X3),X1,X4)
=> typing(shift(type,X2,zero_zero(nat),sK16(X1,X2)),X1,sK17(X1,X2)) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( ? [X3: type,X4: type] : typing(shift(type,X2,zero_zero(nat),X3),X1,X4)
| ~ typing(X2,abs(X1),X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: type,X1: dB,X2: fun(nat,type)] :
( typing(X2,abs(X1),X0)
=> ~ ! [X3: type,X4: type] : ~ typing(shift(type,X2,zero_zero(nat),X3),X1,X4) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,abs(X8),X5)
=> ~ ! [X19: type,X54: type] : ~ typing(shift(type,X7,zero_zero(nat),X19),X8,X54) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_64_abs__typeE) ).
tff(f792,plain,
spl26_64,
inference(avatar_split_clause,[],[f359,f790]) ).
tff(f790,plain,
( spl26_64
<=> ! [X0: list(dB)] :
( listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X0))
| ~ listsp(dB,it,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_64])]) ).
tff(f359,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,[],[f207]) ).
tff(f207,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,[],[f127]) ).
tff(f127,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,[],[f95]) ).
tff(f95,axiom,
! [X28: list(dB)] :
( listsp(dB,it,X28)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X28)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_94_lifts__IT) ).
tff(f784,plain,
spl26_63,
inference(avatar_split_clause,[],[f426,f782]) ).
tff(f782,plain,
( spl26_63
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_63])]) ).
tff(f426,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,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,[],[f169]) ).
tff(f169,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X26: dB,X28: list(dB),X30: dB] :
( ( foldl(dB,dB,app,X30,X28) = foldl(dB,dB,app,X26,X28) )
<=> ( X26 = X30 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_43_apps__eq__tail__conv) ).
tff(f780,plain,
spl26_62,
inference(avatar_split_clause,[],[f425,f778]) ).
tff(f778,plain,
( spl26_62
<=> ! [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,[spl26_62])]) ).
tff(f425,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,[],[f307]) ).
tff(f776,plain,
spl26_61,
inference(avatar_split_clause,[],[f408,f774]) ).
tff(f774,plain,
( spl26_61
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_61])]) ).
tff(f408,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0)) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X29: list(dB),X26: dB,X30: dB] :
( beta(X30,X26)
=> beta(foldl(dB,dB,app,X30,X29),foldl(dB,dB,app,X26,X29)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_65_apps__preserves__beta) ).
tff(f772,plain,
spl26_60,
inference(avatar_split_clause,[],[f387,f770]) ).
tff(f770,plain,
( spl26_60
<=> ! [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,[spl26_60])]) ).
tff(f387,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,[],[f211]) ).
tff(f211,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,[],[f142]) ).
tff(f142,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X32: nat,X33: list(dB)] :
( listsp(dB,it,X33)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X32),X33))) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_90_IT_OVar) ).
tff(f766,plain,
( spl26_59
| ~ spl26_58 ),
inference(avatar_split_clause,[],[f762,f759,f764]) ).
tff(f764,plain,
( spl26_59
<=> ! [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,[spl26_59])]) ).
tff(f759,plain,
( spl26_58
<=> ! [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,[spl26_58])]) ).
tff(f762,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl26_58 ),
inference(forward_demodulation,[],[f760,f461]) ).
tff(f760,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl26_58 ),
inference(avatar_component_clause,[],[f759]) ).
tff(f761,plain,
spl26_58,
inference(avatar_split_clause,[],[f381,f759]) ).
tff(f381,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X83: bool,X84: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X83))
| ~ pp(X83)
| ~ pp(X84) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_fconj_1_1_U) ).
tff(f757,plain,
spl26_57,
inference(avatar_split_clause,[],[f364,f755]) ).
tff(f364,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK7(X0)))
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f752,plain,
spl26_56,
inference(avatar_split_clause,[],[f427,f750]) ).
tff(f750,plain,
( spl26_56
<=> ! [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,[spl26_56])]) ).
tff(f427,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,[],[f170]) ).
tff(f170,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,[],[f62]) ).
tff(f62,axiom,
! [X29: list(dB),X30: dB,X28: list(dB),X32: nat] : ( foldl(dB,dB,app,var(X32),X28) != foldl(dB,dB,app,abs(X30),X29) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_61_Var__apps__neq__Abs__apps) ).
tff(f748,plain,
spl26_55,
inference(avatar_split_clause,[],[f365,f746]) ).
tff(f365,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,[],[f280]) ).
tff(f743,plain,
spl26_54,
inference(avatar_split_clause,[],[f455,f741]) ).
tff(f455,plain,
! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X5: X0,X7: fun(nat,X0),X27: nat,X6: nat] :
( ( X6 = X27 )
=> ( aa(nat,X0,shift(X0,X7,X6,X5),X27) = X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_29_shift__eq) ).
tff(f739,plain,
spl26_53,
inference(avatar_split_clause,[],[f403,f737]) ).
tff(f403,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X47: dB,X48: dB,X49: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X49),X48) != abs(X47) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_53_dB_Osimps_I8_J) ).
tff(f735,plain,
spl26_52,
inference(avatar_split_clause,[],[f401,f733]) ).
tff(f401,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X50: nat,X51: dB,X52: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X52),X51) != var(X50) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_55_dB_Osimps_I5_J) ).
tff(f731,plain,
( spl26_51
| ~ spl26_50 ),
inference(avatar_split_clause,[],[f727,f724,f729]) ).
tff(f729,plain,
( spl26_51
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_51])]) ).
tff(f724,plain,
( spl26_50
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_50])]) ).
tff(f727,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl26_50 ),
inference(forward_demodulation,[],[f725,f461]) ).
tff(f725,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl26_50 ),
inference(avatar_component_clause,[],[f724]) ).
tff(f726,plain,
spl26_50,
inference(avatar_split_clause,[],[f383,f724]) ).
tff(f383,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X83: bool,X84: bool] :
( pp(X84)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X83)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_fconj_2_1_U) ).
tff(f722,plain,
( spl26_49
| ~ spl26_14
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f614,f571,f538,f719]) ).
tff(f719,plain,
( spl26_49
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_49])]) ).
tff(f614,plain,
( sP1(ua)
| ~ spl26_14
| ~ spl26_21 ),
inference(resolution,[],[f572,f540]) ).
tff(f717,plain,
( spl26_48
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f713,f710,f715]) ).
tff(f715,plain,
( spl26_48
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_48])]) ).
tff(f710,plain,
( spl26_47
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_47])]) ).
tff(f713,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl26_47 ),
inference(forward_demodulation,[],[f711,f461]) ).
tff(f711,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl26_47 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f712,plain,
spl26_47,
inference(avatar_split_clause,[],[f382,f710]) ).
tff(f382,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X83: bool,X84: bool] :
( pp(X83)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X84),X83)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_fconj_3_1_U) ).
tff(f708,plain,
spl26_46,
inference(avatar_split_clause,[],[f362,f706]) ).
tff(f706,plain,
( spl26_46
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_46])]) ).
tff(f362,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK7(X0)) = X0 )
| listsp(dB,it,sK8(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f703,plain,
spl26_45,
inference(avatar_split_clause,[],[f360,f701]) ).
tff(f701,plain,
( spl26_45
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_45])]) ).
tff(f360,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X13: dB] :
( pp(aa(dB,bool,it,X13))
=> pp(aa(dB,bool,it,abs(X13))) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_38_Lambda) ).
tff(f697,plain,
spl26_44,
inference(avatar_split_clause,[],[f417,f695]) ).
tff(f417,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( typing(X2,var(X1),X0)
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( typing(X2,var(X1),X0)
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> typing(X2,var(X1),X0) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X5: type,X24: nat,X25: fun(nat,type)] :
( ( aa(nat,type,X25,X24) = X5 )
=> typing(X25,var(X24),X5) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_20_typing_OVar) ).
tff(f693,plain,
spl26_43,
inference(avatar_split_clause,[],[f412,f691]) ).
tff(f412,plain,
! [X2: fun(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ typing(X2,var(X1),X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ typing(X2,var(X1),X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: type,X1: nat,X2: fun(nat,type)] :
( typing(X2,var(X1),X0)
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X5: type,X6: nat,X7: fun(nat,type)] :
( typing(X7,var(X6),X5)
=> ( aa(nat,type,X7,X6) = X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_21_typing__elims_I1_J) ).
tff(f689,plain,
( spl26_42
| ~ spl26_15
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f613,f571,f543,f686]) ).
tff(f686,plain,
( spl26_42
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_42])]) ).
tff(f613,plain,
( sP1(u)
| ~ spl26_15
| ~ spl26_21 ),
inference(resolution,[],[f572,f545]) ).
tff(f684,plain,
spl26_41,
inference(avatar_split_clause,[],[f366,f682]) ).
tff(f366,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f280]) ).
tff(f676,plain,
spl26_40,
inference(avatar_split_clause,[],[f432,f674]) ).
tff(f432,plain,
! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X2,X1)
=> ( beta(X2,X0)
=> typing(X3,X0,X1) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X46: dB,X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,X8,X5)
=> ( beta(X8,X46)
=> typing(X7,X46,X5) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_52_subject__reduction) ).
tff(f672,plain,
spl26_39,
inference(avatar_split_clause,[],[f419,f670]) ).
tff(f670,plain,
( spl26_39
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK20(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_39])]) ).
tff(f419,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK20(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f302]) ).
tff(f666,plain,
spl26_38,
inference(avatar_split_clause,[],[f385,f664]) ).
tff(f385,plain,
! [X0: dB,X1: dB] :
( ( abs(sK13(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: dB,X1: dB] :
( ( beta(X1,sK13(X0,X1))
& ( abs(sK13(X0,X1)) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f210,f286]) ).
tff(f286,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
=> ( beta(X1,sK13(X0,X1))
& ( abs(sK13(X0,X1)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f210,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),X0)
=> ~ ! [X2: dB] :
( ( abs(X2) = X0 )
=> ~ beta(X1,X2) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X36: dB,X13: dB] :
( beta(abs(X13),X36)
=> ~ ! [X53: dB] :
( ( abs(X53) = X36 )
=> ~ beta(X13,X53) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_63_beta__cases_I2_J) ).
tff(f660,plain,
( spl26_37
| ~ spl26_13
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f612,f571,f533,f657]) ).
tff(f657,plain,
( spl26_37
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_37])]) ).
tff(f612,plain,
( sP1(t3)
| ~ spl26_13
| ~ spl26_21 ),
inference(resolution,[],[f572,f535]) ).
tff(f647,plain,
spl26_36,
inference(avatar_split_clause,[],[f386,f645]) ).
tff(f386,plain,
! [X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1))
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f643,plain,
spl26_35,
inference(avatar_split_clause,[],[f378,f641]) ).
tff(f641,plain,
( spl26_35
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_35])]) ).
tff(f378,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X56: list(X0)] : ( map(X0,X0,combi(X0),X56) = X56 ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_71_map__ident) ).
tff(f639,plain,
spl26_34,
inference(avatar_split_clause,[],[f370,f637]) ).
tff(f370,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK11(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f635,plain,
spl26_33,
inference(avatar_split_clause,[],[f358,f633]) ).
tff(f358,plain,
! [X0: nat] :
( ( suc(sK6(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: nat] :
( ( suc(sK6(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f206,f273]) ).
tff(f273,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK6(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f206,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ? [X1: nat] : ( suc(X1) = X0 ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X16: nat] :
( ( zero_zero(nat) != X16 )
=> ? [X67: nat] : ( suc(X67) = X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_84_not0__implies__Suc) ).
tff(f631,plain,
spl26_32,
inference(avatar_split_clause,[],[f357,f629]) ).
tff(f357,plain,
! [X0: nat] :
( ( suc(sK5(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: nat] :
( ( suc(sK5(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f205,f271]) ).
tff(f271,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK5(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ~ ! [X1: nat] : ( suc(X1) != X0 ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X57: nat] :
( ( zero_zero(nat) != X57 )
=> ~ ! [X68: nat] : ( suc(X68) != X57 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_86_nat_Oexhaust) ).
tff(f624,plain,
( spl26_31
| ~ spl26_16
| ~ spl26_21 ),
inference(avatar_split_clause,[],[f611,f571,f548,f621]) ).
tff(f621,plain,
( spl26_31
<=> sP1(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_31])]) ).
tff(f611,plain,
( sP1(a)
| ~ spl26_16
| ~ spl26_21 ),
inference(resolution,[],[f572,f550]) ).
tff(f609,plain,
spl26_30,
inference(avatar_split_clause,[],[f400,f607]) ).
tff(f607,plain,
( spl26_30
<=> ! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_30])]) ).
tff(f400,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X41: dB,X42: dB] :
( ( abs(X42) = abs(X41) )
<=> ( X41 = X42 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_41_dB_Osimps_I3_J) ).
tff(f605,plain,
spl26_29,
inference(avatar_split_clause,[],[f399,f603]) ).
tff(f603,plain,
( spl26_29
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_29])]) ).
tff(f399,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f601,plain,
spl26_28,
inference(avatar_split_clause,[],[f398,f599]) ).
tff(f599,plain,
( spl26_28
<=> ! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_28])]) ).
tff(f398,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X43: nat,X44: nat] :
( ( var(X44) = var(X43) )
<=> ( X43 = X44 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_42_dB_Osimps_I1_J) ).
tff(f597,plain,
spl26_27,
inference(avatar_split_clause,[],[f397,f595]) ).
tff(f595,plain,
( spl26_27
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_27])]) ).
tff(f397,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f593,plain,
spl26_26,
inference(avatar_split_clause,[],[f396,f591]) ).
tff(f591,plain,
( spl26_26
<=> ! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_26])]) ).
tff(f396,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: nat,X1: nat] :
( ( ( suc(X0) = suc(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
inference(nnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X43: nat,X44: nat] :
( ( suc(X44) = suc(X43) )
<=> ( X43 = X44 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_72_nat_Oinject) ).
tff(f589,plain,
spl26_25,
inference(avatar_split_clause,[],[f388,f587]) ).
tff(f388,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X57: nat,X58: nat] :
( ( suc(X58) = suc(X57) )
=> ( X57 = X58 ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_73_Suc__inject) ).
tff(f585,plain,
spl26_24,
inference(avatar_split_clause,[],[f384,f583]) ).
tff(f384,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: dB,X1: dB] :
( beta(X1,X0)
=> beta(abs(X1),abs(X0)) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X14: dB,X36: dB] :
( beta(X36,X14)
=> beta(abs(X36),abs(X14)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_47_abs) ).
tff(f581,plain,
spl26_23,
inference(avatar_split_clause,[],[f377,f579]) ).
tff(f377,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X0: $tType,X84: X0] : ( aa(X0,X0,combi(X0),X84) = X84 ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_COMBI_1_1_U) ).
tff(f577,plain,
spl26_22,
inference(avatar_split_clause,[],[f373,f575]) ).
tff(f373,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f129,f262,f261]) ).
tff(f129,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X66: dB] :
( pp(aa(dB,bool,it,X66))
<=> ( ? [X77: dB,X78: dB,X79: list(dB)] :
( pp(aa(dB,bool,it,X78))
& 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,X77),X78),zero_zero(nat)),X79)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X77)),X78),X79) = X66 ) )
| ? [X77: dB] :
( pp(aa(dB,bool,it,X77))
& ( abs(X77) = X66 ) )
| ? [X75: list(dB),X76: nat] :
( listsp(dB,it,X75)
& ( foldl(dB,dB,app,var(X76),X75) = X66 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_95_IT_Osimps) ).
tff(f573,plain,
spl26_21,
inference(avatar_split_clause,[],[f372,f571]) ).
tff(f372,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f569,plain,
spl26_20,
inference(avatar_split_clause,[],[f343,f566]) ).
tff(f343,plain,
typing(shift(type,e,i,t1),a,sK3),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
typing(shift(type,e,i,t1),a,sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f202,f266]) ).
tff(f266,plain,
( ? [X0: type] : typing(shift(type,e,i,t1),a,X0)
=> typing(shift(type,e,i,t1),a,sK3) ),
introduced(choice_axiom,[]) ).
tff(f202,plain,
? [X0: type] : typing(shift(type,e,i,t1),a,X0),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
~ ! [X0: type] : ~ typing(shift(type,e,i,t1),a,X0),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
~ ! [X3: type] : ~ typing(shift(type,e,i,t1),a,X3),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f564,plain,
spl26_19,
inference(avatar_split_clause,[],[f334,f561]) ).
tff(f334,plain,
typing(shift(type,e,i,t1),a,t2),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
typing(shift(type,e,i,t1),a,t2),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096) ).
tff(f559,plain,
spl26_18,
inference(avatar_split_clause,[],[f354,f557]) ).
tff(f354,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X16: nat] : pp(aa(dB,bool,it,var(X16))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_13_Var__IT) ).
tff(f555,plain,
spl26_17,
inference(avatar_split_clause,[],[f353,f553]) ).
tff(f553,plain,
( spl26_17
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_17])]) ).
tff(f353,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X50: nat] : ( zero_zero(nat) = dB_size(var(X50)) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_89_dB_Osize_I1_J) ).
tff(f551,plain,
spl26_16,
inference(avatar_split_clause,[],[f333,f548]) ).
tff(f333,plain,
pp(aa(dB,bool,it,a)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(dB,bool,it,a)),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_4_Beta_I3_J) ).
tff(f546,plain,
spl26_15,
inference(avatar_split_clause,[],[f332,f543]) ).
tff(f332,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_2_uIT) ).
tff(f541,plain,
spl26_14,
inference(avatar_split_clause,[],[f331,f538]) ).
tff(f331,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_1_Beta_I6_J) ).
tff(f536,plain,
spl26_13,
inference(avatar_split_clause,[],[f330,f533]) ).
tff(f330,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_0__096IT_At_096) ).
tff(f531,plain,
( ~ spl26_12
| spl26_11 ),
inference(avatar_split_clause,[],[f526,f522,f528]) ).
tff(f522,plain,
( spl26_11
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
tff(f526,plain,
( ~ pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun(dB,fun(nat,dB)),subst,a),i),u)))
| spl26_11 ),
inference(forward_demodulation,[],[f524,f461]) ).
tff(f524,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))
| spl26_11 ),
inference(avatar_component_clause,[],[f522]) ).
tff(f525,plain,
~ spl26_11,
inference(avatar_split_clause,[],[f324,f522]) ).
tff(f324,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(cnf_transformation,[],[f111]) ).
tff(f111,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(flattening,[],[f110]) ).
tff(f110,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(negated_conjecture,[],[f109]) ).
tff(f109,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',conj_0) ).
tff(f520,plain,
spl26_10,
inference(avatar_split_clause,[],[f375,f518]) ).
tff(f518,plain,
( spl26_10
<=> ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
tff(f375,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X50: nat,X47: dB] : ( abs(X47) != var(X50) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_59_dB_Osimps_I7_J) ).
tff(f516,plain,
spl26_9,
inference(avatar_split_clause,[],[f347,f514]) ).
tff(f514,plain,
( spl26_9
<=> ! [X0: nat] : ( zero_zero(nat) != suc(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
tff(f347,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X62: nat] : ( zero_zero(nat) != suc(X62) ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_77_Zero__not__Suc) ).
tff(f512,plain,
spl26_8,
inference(avatar_split_clause,[],[f374,f510]) ).
tff(f374,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X14: dB,X12: nat] : ~ beta(var(X12),X14),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_48_beta__cases_I1_J) ).
tff(f508,plain,
spl26_7,
inference(avatar_split_clause,[],[f367,f506]) ).
tff(f506,plain,
( spl26_7
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
tff(f367,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f504,plain,
spl26_6,
inference(avatar_split_clause,[],[f345,f502]) ).
tff(f345,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X16: nat] : ( suc(X16) != X16 ),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_76_n__not__Suc__n) ).
tff(f500,plain,
spl26_5,
inference(avatar_split_clause,[],[f329,f497]) ).
tff(f329,plain,
typing(e,u,t1),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
typing(e,u,t1),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_3_uT) ).
tff(f495,plain,
spl26_4,
inference(avatar_split_clause,[],[f328,f492]) ).
tff(f328,plain,
typing(ea,ua,t1),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
typing(ea,ua,t1),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',fact_18_Beta_I7_J) ).
tff(f490,plain,
spl26_3,
inference(avatar_split_clause,[],[f327,f487]) ).
tff(f487,plain,
( spl26_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
tff(f327,plain,
pp(fTrue),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
pp(fTrue),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_pp_2_1_U) ).
tff(f485,plain,
spl26_2,
inference(avatar_split_clause,[],[f326,f482]) ).
tff(f482,plain,
( spl26_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
tff(f326,plain,
zero(nat),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
zero(nat),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',arity_Nat_Onat___Groups_Ozero) ).
tff(f480,plain,
~ spl26_1,
inference(avatar_split_clause,[],[f325,f477]) ).
tff(f477,plain,
( spl26_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
tff(f325,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/tmp/tmp.eUNTsGvSMF/Vampire---4.8_9890',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 30 15:02:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.19/0.42 % (10063)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43 % (10067)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.19/0.43 % (10071)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 Vampire---4 for (522ds/0Mi)
% 0.19/0.43 % (10065)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.19/0.43 % (10072)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 Vampire---4 for (497ds/0Mi)
% 0.19/0.43 % (10068)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 Vampire---4 for (531ds/0Mi)
% 0.19/0.43 % (10066)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 Vampire---4 for (569ds/0Mi)
% 0.19/0.44 % (10064)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.19/0.44 % (10072)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.44 % Exception at run slice level% Exception at run slice level
% 0.19/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.44
% 0.19/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.44 % Exception at run slice level
% 0.19/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.44 % (10073)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on Vampire---4 for (411ds/0Mi)
% 0.19/0.44 % (10074)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on Vampire---4 for (382ds/0Mi)
% 0.19/0.44 % (10075)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on Vampire---4 for (367ds/0Mi)
% 0.19/0.45 % (10073)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.45 % (10074)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.45 % Exception at run slice level
% 0.19/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.45 % (10076)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 Vampire---4 for (354ds/0Mi)
% 0.19/0.54 % (10068)First to succeed.
% 0.19/0.57 % (10075)Also succeeded, but the first one will report.
% 0.19/0.57 % (10068)Refutation found. Thanks to Tanya!
% 0.19/0.57 % SZS status Theorem for Vampire---4
% 0.19/0.57 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.58 % (10068)------------------------------
% 0.19/0.58 % (10068)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.58 % (10068)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.58 % (10068)Termination reason: Refutation
% 0.19/0.58
% 0.19/0.58 % (10068)Memory used [KB]: 8955
% 0.19/0.58 % (10068)Time elapsed: 0.133 s
% 0.19/0.58 % (10068)------------------------------
% 0.19/0.58 % (10068)------------------------------
% 0.19/0.58 % (10063)Success in time 0.214 s
% 0.19/0.58 % Vampire---4.8 exiting
%------------------------------------------------------------------------------