TSTP Solution File: LCL813_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL813_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:38 EDT 2024
% Result : Theorem 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 454
% Syntax : Number of formulae : 1328 ( 290 unt; 77 typ; 0 def)
% Number of atoms : 3279 ( 609 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 3470 (1442 ~;1446 |; 153 &)
% ( 276 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 90 ( 42 >; 48 *; 0 +; 0 <<)
% Number of predicates : 260 ( 258 usr; 252 prp; 0-3 aty)
% Number of functors : 66 ( 66 usr; 26 con; 0-5 aty)
% Number of variables : 2835 (2721 !; 86 ?;2835 :)
% ( 28 !>; 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,
fun1: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * X1 ) > fun1(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun1(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun1(X0,fun1(X1,X2)) * fun1(X0,X1) ) > fun1(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun1(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun1(dB,fun1(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: fun1(dB,fun1(nat,dB)) ).
tff(func_def_11,type,
subst: fun1(dB,fun1(dB,fun1(nat,dB))) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,fun1(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun1(X1,fun1(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_17,type,
shift:
!>[X0: $tType] : ( ( fun1(nat,X0) * nat * X0 ) > fun1(nat,X0) ) ).
tff(func_def_18,type,
fun: fun1(type,fun1(type,type)) ).
tff(func_def_19,type,
typing: fun1(nat,type) > fun1(dB,fun1(type,bool)) ).
tff(func_def_20,type,
typings: ( fun1(nat,type) * list(dB) ) > fun1(list(type),bool) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun1(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fEx:
!>[X0: $tType] : fun1(fun1(X0,bool),bool) ).
tff(func_def_23,type,
fFalse: bool ).
tff(func_def_24,type,
fTrue: bool ).
tff(func_def_25,type,
fconj: fun1(bool,fun1(bool,bool)) ).
tff(func_def_26,type,
t2: type ).
tff(func_def_27,type,
t: type ).
tff(func_def_28,type,
t_a: type ).
tff(func_def_29,type,
t1: type ).
tff(func_def_30,type,
ts: list(type) ).
tff(func_def_31,type,
a: dB ).
tff(func_def_32,type,
as: list(dB) ).
tff(func_def_33,type,
e: fun1(nat,type) ).
tff(func_def_34,type,
ea: fun1(nat,type) ).
tff(func_def_35,type,
i: nat ).
tff(func_def_36,type,
ia: nat ).
tff(func_def_37,type,
n: nat ).
tff(func_def_38,type,
rs: list(dB) ).
tff(func_def_39,type,
t3: dB ).
tff(func_def_40,type,
u: dB ).
tff(func_def_41,type,
ua: dB ).
tff(func_def_42,type,
sK3: type ).
tff(func_def_43,type,
sK4: list(type) ).
tff(func_def_44,type,
sK5: dB > dB ).
tff(func_def_45,type,
sK6: dB > list(dB) ).
tff(func_def_46,type,
sK7: dB > nat ).
tff(func_def_47,type,
sK8: dB > dB ).
tff(func_def_48,type,
sK9: dB > dB ).
tff(func_def_49,type,
sK10: dB > list(dB) ).
tff(func_def_50,type,
sK11: ( dB * dB ) > dB ).
tff(func_def_51,type,
sK12: ( dB * dB * dB ) > dB ).
tff(func_def_52,type,
sK13: ( dB * dB * dB ) > dB ).
tff(func_def_53,type,
sK14: ( dB * dB * dB ) > dB ).
tff(func_def_54,type,
sK15: ( dB * fun1(nat,type) ) > type ).
tff(func_def_55,type,
sK16: ( dB * fun1(nat,type) ) > type ).
tff(func_def_56,type,
sK17: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_57,type,
sK18: ( type * dB * fun1(nat,type) ) > type ).
tff(func_def_58,type,
sK19: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_59,type,
sK20: ( type * list(dB) * dB * fun1(nat,type) ) > list(type) ).
tff(func_def_60,type,
sK21: ( type * list(dB) * nat * fun1(nat,type) ) > list(type) ).
tff(func_def_61,type,
sK22: ( type * dB * dB * fun1(nat,type) ) > type ).
tff(func_def_62,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( fun1(X1,X0) * fun1(X1,X0) ) > X1 ) ).
tff(func_def_63,type,
sK24: ( type * type * list(dB) * fun1(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] : ( ( fun1(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: dB > $o ).
tff(pred_def_6,type,
sP1: dB > $o ).
tff(pred_def_7,type,
sP2: ( dB * dB * dB ) > $o ).
tff(f2872,plain,
$false,
inference(avatar_sat_refutation,[],[f533,f538,f543,f547,f551,f555,f560,f565,f570,f574,f578,f589,f593,f597,f601,f608,f614,f619,f623,f628,f632,f636,f640,f644,f659,f663,f667,f671,f675,f689,f696,f700,f704,f709,f714,f720,f726,f732,f737,f742,f746,f751,f756,f768,f772,f777,f782,f787,f792,f796,f800,f807,f811,f829,f833,f838,f846,f850,f854,f868,f873,f878,f885,f891,f898,f902,f906,f910,f914,f920,f924,f932,f939,f943,f949,f954,f958,f966,f971,f977,f981,f987,f991,f995,f1000,f1008,f1012,f1052,f1058,f1064,f1069,f1077,f1082,f1088,f1109,f1114,f1118,f1134,f1140,f1144,f1151,f1155,f1161,f1165,f1169,f1173,f1177,f1181,f1186,f1190,f1299,f1304,f1308,f1313,f1320,f1326,f1339,f1343,f1347,f1353,f1363,f1368,f1376,f1381,f1390,f1396,f1405,f1411,f1416,f1423,f1429,f1459,f1465,f1471,f1478,f1487,f1495,f1502,f1515,f1520,f1527,f1536,f1544,f1553,f1558,f1567,f1573,f1577,f1582,f1588,f1602,f1629,f1635,f1643,f1647,f1653,f1662,f1671,f1677,f1691,f1697,f1712,f1719,f1731,f1738,f1746,f1752,f1765,f1771,f1775,f1781,f1791,f1797,f1801,f1809,f1819,f1825,f1834,f1838,f1846,f1856,f1860,f1874,f1879,f1887,f1895,f1902,f1911,f1919,f1935,f1943,f1951,f1970,f1976,f1980,f1987,f2008,f2014,f2021,f2030,f2038,f2048,f2057,f2063,f2076,f2085,f2094,f2098,f2102,f2106,f2114,f2129,f2143,f2147,f2159,f2164,f2561,f2565,f2594,f2598,f2602,f2606,f2611,f2616,f2652,f2660,f2671,f2675,f2679,f2687,f2691,f2696,f2700,f2704,f2708,f2712,f2718,f2734,f2739,f2743,f2747,f2751,f2755,f2821,f2829,f2834,f2838,f2842,f2848,f2871]) ).
tff(f2871,plain,
( spl25_17
| ~ spl25_249 ),
inference(avatar_contradiction_clause,[],[f2858]) ).
tff(f2858,plain,
( $false
| spl25_17
| ~ spl25_249 ),
inference(resolution,[],[f2837,f613]) ).
tff(f613,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),foldr(type,type,fun,ts,t)),var(zero_zero(nat))))
| spl25_17 ),
inference(avatar_component_clause,[],[f611]) ).
tff(f611,plain,
( spl25_17
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),foldr(type,type,fun,ts,t)),var(zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_17])]) ).
tff(f2837,plain,
( ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl25_249 ),
inference(avatar_component_clause,[],[f2836]) ).
tff(f2836,plain,
( spl25_249
<=> ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_249])]) ).
tff(f2848,plain,
( spl25_251
| ~ spl25_65
| ~ spl25_87 ),
inference(avatar_split_clause,[],[f1035,f1010,f895,f2845]) ).
tff(f2845,plain,
( spl25_251
<=> ( t1 = aa(type,type,combc(type,type,type,fun,foldr(type,type,fun,ts,t)),t2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_251])]) ).
tff(f895,plain,
( spl25_65
<=> ( aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)) = t1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_65])]) ).
tff(f1010,plain,
( spl25_87
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_87])]) ).
tff(f1035,plain,
( ( t1 = aa(type,type,combc(type,type,type,fun,foldr(type,type,fun,ts,t)),t2) )
| ~ spl25_65
| ~ spl25_87 ),
inference(superposition,[],[f1011,f897]) ).
tff(f897,plain,
( ( aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)) = t1 )
| ~ spl25_65 ),
inference(avatar_component_clause,[],[f895]) ).
tff(f1011,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) )
| ~ spl25_87 ),
inference(avatar_component_clause,[],[f1010]) ).
tff(f2842,plain,
( spl25_250
| ~ spl25_18
| ~ spl25_85 ),
inference(avatar_split_clause,[],[f1002,f998,f617,f2840]) ).
tff(f2840,plain,
( spl25_250
<=> ! [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,[spl25_250])]) ).
tff(f617,plain,
( spl25_18
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_18])]) ).
tff(f998,plain,
( spl25_85
<=> ! [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,[spl25_85])]) ).
tff(f1002,plain,
( ! [X0: dB,X1: nat] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(aa(dB,dB,combc(dB,nat,dB,lift,X1),X0)) )
| ~ spl25_18
| ~ spl25_85 ),
inference(resolution,[],[f999,f618]) ).
tff(f618,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl25_18 ),
inference(avatar_component_clause,[],[f617]) ).
tff(f999,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)) )
| ~ spl25_85 ),
inference(avatar_component_clause,[],[f998]) ).
tff(f2838,plain,
( spl25_249
| ~ spl25_33
| ~ spl25_71 ),
inference(avatar_split_clause,[],[f926,f922,f702,f2836]) ).
tff(f702,plain,
( spl25_33
<=> ! [X0: $tType,X2: fun1(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_33])]) ).
tff(f922,plain,
( spl25_71
<=> ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_71])]) ).
tff(f926,plain,
( ! [X2: type,X0: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X0,X1,X2)),X2),var(X1)))
| ~ spl25_33
| ~ spl25_71 ),
inference(superposition,[],[f923,f703]) ).
tff(f703,plain,
( ! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 )
| ~ spl25_33 ),
inference(avatar_component_clause,[],[f702]) ).
tff(f923,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl25_71 ),
inference(avatar_component_clause,[],[f922]) ).
tff(f2834,plain,
( spl25_248
| ~ spl25_42
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f821,f805,f748,f2831]) ).
tff(f2831,plain,
( spl25_248
<=> pp(aa(fun1(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,n,t1),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_248])]) ).
tff(f748,plain,
( spl25_42
<=> pp(aa(list(type),bool,typings(shift(type,e,n,t1),as),ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_42])]) ).
tff(f805,plain,
( spl25_52
<=> ! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_52])]) ).
tff(f821,plain,
( pp(aa(fun1(list(type),bool),bool,fEx(list(type)),typings(shift(type,e,n,t1),as)))
| ~ spl25_42
| ~ spl25_52 ),
inference(resolution,[],[f806,f750]) ).
tff(f750,plain,
( pp(aa(list(type),bool,typings(shift(type,e,n,t1),as),ts))
| ~ spl25_42 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f806,plain,
( ! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( ~ pp(aa(X0,bool,X2,X1))
| pp(aa(fun1(X0,bool),bool,fEx(X0),X2)) )
| ~ spl25_52 ),
inference(avatar_component_clause,[],[f805]) ).
tff(f2829,plain,
( spl25_247
| ~ spl25_28
| ~ spl25_30 ),
inference(avatar_split_clause,[],[f691,f687,f669,f2827]) ).
tff(f2827,plain,
( spl25_247
<=> ! [X0: dB,X1: dB] :
( ( sK11(X0,abs(X1)) = abs(sK11(sK11(X0,abs(X1)),X1)) )
| ~ beta(abs(abs(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_247])]) ).
tff(f669,plain,
( spl25_28
<=> ! [X0: dB,X1: dB] :
( beta(X1,sK11(X0,X1))
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_28])]) ).
tff(f687,plain,
( spl25_30
<=> ! [X0: dB,X1: dB] :
( ( abs(sK11(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_30])]) ).
tff(f691,plain,
( ! [X0: dB,X1: dB] :
( ( sK11(X0,abs(X1)) = abs(sK11(sK11(X0,abs(X1)),X1)) )
| ~ beta(abs(abs(X1)),X0) )
| ~ spl25_28
| ~ spl25_30 ),
inference(resolution,[],[f688,f670]) ).
tff(f670,plain,
( ! [X0: dB,X1: dB] :
( beta(X1,sK11(X0,X1))
| ~ beta(abs(X1),X0) )
| ~ spl25_28 ),
inference(avatar_component_clause,[],[f669]) ).
tff(f688,plain,
( ! [X0: dB,X1: dB] :
( ~ beta(abs(X1),X0)
| ( abs(sK11(X0,X1)) = X0 ) )
| ~ spl25_30 ),
inference(avatar_component_clause,[],[f687]) ).
tff(f2821,plain,
( spl25_246
| ~ spl25_65
| ~ spl25_104 ),
inference(avatar_split_clause,[],[f1191,f1163,f895,f2819]) ).
tff(f2819,plain,
( spl25_246
<=> ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X0),X1) )
| ( t2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_246])]) ).
tff(f1163,plain,
( spl25_104
<=> ! [X0: type,X3: type,X2: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_104])]) ).
tff(f1191,plain,
( ! [X0: type,X1: type] :
( ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X0),X1) )
| ( t2 = X0 ) )
| ~ spl25_65
| ~ spl25_104 ),
inference(superposition,[],[f1164,f897]) ).
tff(f1164,plain,
( ! [X2: type,X3: type,X0: type,X1: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X1 = X3 ) )
| ~ spl25_104 ),
inference(avatar_component_clause,[],[f1163]) ).
tff(f2755,plain,
( spl25_245
| ~ spl25_39
| ~ spl25_116 ),
inference(avatar_split_clause,[],[f1332,f1324,f734,f2753]) ).
tff(f2753,plain,
( spl25_245
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| ~ beta(u,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_245])]) ).
tff(f734,plain,
( spl25_39
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_39])]) ).
tff(f1324,plain,
( spl25_116
<=> ! [X0: dB,X3: fun1(nat,type),X2: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_116])]) ).
tff(f1332,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),X0))
| ~ beta(u,X0) )
| ~ spl25_39
| ~ spl25_116 ),
inference(resolution,[],[f1325,f736]) ).
tff(f736,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ~ spl25_39 ),
inference(avatar_component_clause,[],[f734]) ).
tff(f1325,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) )
| ~ spl25_116 ),
inference(avatar_component_clause,[],[f1324]) ).
tff(f2751,plain,
( spl25_244
| ~ spl25_36
| ~ spl25_116 ),
inference(avatar_split_clause,[],[f1331,f1324,f717,f2749]) ).
tff(f2749,plain,
( spl25_244
<=> ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0))
| ~ beta(ua,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_244])]) ).
tff(f717,plain,
( spl25_36
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_36])]) ).
tff(f1331,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),X0))
| ~ beta(ua,X0) )
| ~ spl25_36
| ~ spl25_116 ),
inference(resolution,[],[f1325,f719]) ).
tff(f719,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua))
| ~ spl25_36 ),
inference(avatar_component_clause,[],[f717]) ).
tff(f2747,plain,
( spl25_243
| ~ spl25_15
| ~ spl25_86 ),
inference(avatar_split_clause,[],[f1027,f1006,f599,f2745]) ).
tff(f2745,plain,
( spl25_243
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun1(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_243])]) ).
tff(f599,plain,
( spl25_15
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_15])]) ).
tff(f1006,plain,
( spl25_86
<=> ! [X1: $tType,X0: $tType,X4: fun1(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_86])]) ).
tff(f1027,plain,
( ! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) )
| ~ spl25_15
| ~ spl25_86 ),
inference(superposition,[],[f600,f1007]) ).
tff(f1007,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) )
| ~ spl25_86 ),
inference(avatar_component_clause,[],[f1006]) ).
tff(f600,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 )
| ~ spl25_15 ),
inference(avatar_component_clause,[],[f599]) ).
tff(f2743,plain,
( spl25_242
| ~ spl25_33
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f824,f805,f702,f2741]) ).
tff(f2741,plain,
( spl25_242
<=> ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun1(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_242])]) ).
tff(f824,plain,
( ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ~ pp(X2)
| pp(aa(fun1(nat,bool),bool,fEx(nat),shift(bool,X0,X1,X2))) )
| ~ spl25_33
| ~ spl25_52 ),
inference(superposition,[],[f806,f703]) ).
tff(f2739,plain,
( spl25_241
| ~ spl25_39
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f820,f805,f734,f2736]) ).
tff(f2736,plain,
( spl25_241
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_241])]) ).
tff(f820,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(e),t1)))
| ~ spl25_39
| ~ spl25_52 ),
inference(resolution,[],[f806,f736]) ).
tff(f2734,plain,
( spl25_240
| ~ spl25_36
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f819,f805,f717,f2731]) ).
tff(f2731,plain,
( spl25_240
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_240])]) ).
tff(f819,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),combc(dB,type,bool,typing(ea),t1)))
| ~ spl25_36
| ~ spl25_52 ),
inference(resolution,[],[f806,f719]) ).
tff(f2718,plain,
( spl25_239
| ~ spl25_11
| ~ spl25_33 ),
inference(avatar_split_clause,[],[f705,f702,f576,f2716]) ).
tff(f2716,plain,
( spl25_239
<=> ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_239])]) ).
tff(f576,plain,
( spl25_11
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_11])]) ).
tff(f705,plain,
( ! [X2: bool,X0: fun1(nat,bool),X1: nat] :
( ( fFalse = X2 )
| ( fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1) ) )
| ~ spl25_11
| ~ spl25_33 ),
inference(superposition,[],[f703,f577]) ).
tff(f577,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl25_11 ),
inference(avatar_component_clause,[],[f576]) ).
tff(f2712,plain,
( spl25_238
| ~ spl25_49
| ~ spl25_110 ),
inference(avatar_split_clause,[],[f1282,f1188,f790,f2710]) ).
tff(f2710,plain,
( spl25_238
<=> ! [X2: dB,X0: dB,X1: fun1(dB,dB)] : ( abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_238])]) ).
tff(f790,plain,
( spl25_49
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_49])]) ).
tff(f1188,plain,
( spl25_110
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun1(X2,fun1(X1,X0)),X4: fun1(X2,X1),X3: X2] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_110])]) ).
tff(f1282,plain,
( ! [X2: dB,X0: dB,X1: fun1(dB,dB)] : ( abs(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0) )
| ~ spl25_49
| ~ spl25_110 ),
inference(superposition,[],[f791,f1189]) ).
tff(f1189,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) )
| ~ spl25_110 ),
inference(avatar_component_clause,[],[f1188]) ).
tff(f791,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) )
| ~ spl25_49 ),
inference(avatar_component_clause,[],[f790]) ).
tff(f2708,plain,
( spl25_237
| ~ spl25_50
| ~ spl25_110 ),
inference(avatar_split_clause,[],[f1281,f1188,f794,f2706]) ).
tff(f2706,plain,
( spl25_237
<=> ! [X2: nat,X0: dB,X1: fun1(dB,dB)] : ( var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_237])]) ).
tff(f794,plain,
( spl25_50
<=> ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_50])]) ).
tff(f1281,plain,
( ! [X2: nat,X0: dB,X1: fun1(dB,dB)] : ( var(X2) != aa(dB,dB,combs(dB,dB,dB,app,X1),X0) )
| ~ spl25_50
| ~ spl25_110 ),
inference(superposition,[],[f795,f1189]) ).
tff(f795,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) )
| ~ spl25_50 ),
inference(avatar_component_clause,[],[f794]) ).
tff(f2704,plain,
( spl25_236
| ~ spl25_49
| ~ spl25_87 ),
inference(avatar_split_clause,[],[f1042,f1010,f790,f2702]) ).
tff(f2702,plain,
( spl25_236
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_236])]) ).
tff(f1042,plain,
( ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl25_49
| ~ spl25_87 ),
inference(superposition,[],[f791,f1011]) ).
tff(f2700,plain,
( spl25_235
| ~ spl25_50
| ~ spl25_87 ),
inference(avatar_split_clause,[],[f1041,f1010,f794,f2698]) ).
tff(f2698,plain,
( spl25_235
<=> ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_235])]) ).
tff(f1041,plain,
( ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) )
| ~ spl25_50
| ~ spl25_87 ),
inference(superposition,[],[f795,f1011]) ).
tff(f2696,plain,
( spl25_234
| ~ spl25_8
| ~ spl25_218 ),
inference(avatar_split_clause,[],[f2579,f2559,f562,f2693]) ).
tff(f2693,plain,
( spl25_234
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_234])]) ).
tff(f562,plain,
( spl25_8
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_8])]) ).
tff(f2559,plain,
( spl25_218
<=> ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_218])]) ).
tff(f2579,plain,
( sP1(abs(abs(ua)))
| ~ spl25_8
| ~ spl25_218 ),
inference(resolution,[],[f2560,f564]) ).
tff(f564,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f2560,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl25_218 ),
inference(avatar_component_clause,[],[f2559]) ).
tff(f2691,plain,
( spl25_233
| ~ spl25_29
| ~ spl25_57 ),
inference(avatar_split_clause,[],[f859,f844,f673,f2689]) ).
tff(f2689,plain,
( spl25_233
<=> ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_233])]) ).
tff(f673,plain,
( spl25_29
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_29])]) ).
tff(f844,plain,
( spl25_57
<=> ! [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,[spl25_57])]) ).
tff(f859,plain,
( ! [X0: list(dB),X1: nat] :
( ~ listsp(dB,it,X0)
| sP1(abs(foldl(dB,dB,app,var(X1),X0))) )
| ~ spl25_29
| ~ spl25_57 ),
inference(resolution,[],[f845,f674]) ).
tff(f674,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl25_29 ),
inference(avatar_component_clause,[],[f673]) ).
tff(f845,plain,
( ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) )
| ~ spl25_57 ),
inference(avatar_component_clause,[],[f844]) ).
tff(f2687,plain,
( spl25_232
| ~ spl25_29
| ~ spl25_54 ),
inference(avatar_split_clause,[],[f855,f827,f673,f2685]) ).
tff(f2685,plain,
( spl25_232
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(abs(sK5(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_232])]) ).
tff(f827,plain,
( spl25_54
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_54])]) ).
tff(f855,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(abs(sK5(X0))) )
| ~ spl25_29
| ~ spl25_54 ),
inference(resolution,[],[f828,f674]) ).
tff(f828,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK5(X0)))
| sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) )
| ~ spl25_54 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f2679,plain,
( spl25_231
| ~ spl25_49
| ~ spl25_108 ),
inference(avatar_split_clause,[],[f1227,f1179,f790,f2677]) ).
tff(f2677,plain,
( spl25_231
<=> ! [X2: dB,X0: dB,X1: list(dB),X3: dB] : ( abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_231])]) ).
tff(f1179,plain,
( spl25_108
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1)),X2: X1] : ( foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_108])]) ).
tff(f1227,plain,
( ! [X2: dB,X3: dB,X0: dB,X1: list(dB)] : ( abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2) )
| ~ spl25_49
| ~ spl25_108 ),
inference(superposition,[],[f791,f1180]) ).
tff(f1180,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) )
| ~ spl25_108 ),
inference(avatar_component_clause,[],[f1179]) ).
tff(f2675,plain,
( spl25_230
| ~ spl25_50
| ~ spl25_108 ),
inference(avatar_split_clause,[],[f1226,f1179,f794,f2673]) ).
tff(f2673,plain,
( spl25_230
<=> ! [X2: dB,X0: dB,X1: list(dB),X3: nat] : ( var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_230])]) ).
tff(f1226,plain,
( ! [X2: dB,X3: nat,X0: dB,X1: list(dB)] : ( var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2) )
| ~ spl25_50
| ~ spl25_108 ),
inference(superposition,[],[f795,f1180]) ).
tff(f2671,plain,
( spl25_229
| ~ spl25_18
| ~ spl25_54 ),
inference(avatar_split_clause,[],[f856,f827,f617,f2669]) ).
tff(f2669,plain,
( spl25_229
<=> ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_229])]) ).
tff(f856,plain,
( ! [X0: dB] :
( sP0(X0)
| listsp(dB,it,sK6(X0))
| ~ sP1(X0)
| sP1(sK5(X0)) )
| ~ spl25_18
| ~ spl25_54 ),
inference(resolution,[],[f828,f618]) ).
tff(f2660,plain,
( spl25_227
| spl25_228
| ~ spl25_21
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f823,f805,f630,f2658,f2654]) ).
tff(f2654,plain,
( spl25_227
<=> pp(aa(fun1(bool,bool),bool,fEx(bool),combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_227])]) ).
tff(f2658,plain,
( spl25_228
<=> ! [X0: bool] : ~ pp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_228])]) ).
tff(f630,plain,
( spl25_21
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_21])]) ).
tff(f823,plain,
( ! [X0: bool] :
( ~ pp(X0)
| pp(aa(fun1(bool,bool),bool,fEx(bool),combi(bool))) )
| ~ spl25_21
| ~ spl25_52 ),
inference(superposition,[],[f806,f631]) ).
tff(f631,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl25_21 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f2652,plain,
( spl25_226
| ~ spl25_9
| ~ spl25_218 ),
inference(avatar_split_clause,[],[f2578,f2559,f567,f2649]) ).
tff(f2649,plain,
( spl25_226
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_226])]) ).
tff(f567,plain,
( spl25_9
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_9])]) ).
tff(f2578,plain,
( sP1(abs(abs(u)))
| ~ spl25_9
| ~ spl25_218 ),
inference(resolution,[],[f2560,f569]) ).
tff(f569,plain,
( pp(aa(dB,bool,it,u))
| ~ spl25_9 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f2616,plain,
( spl25_225
| ~ spl25_33
| ~ spl25_79
| ~ spl25_138 ),
inference(avatar_split_clause,[],[f1508,f1499,f969,f702,f2613]) ).
tff(f2613,plain,
( spl25_225
<=> ( t1 = foldr(type,type,fun,cons(type,sK3,ts),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_225])]) ).
tff(f969,plain,
( spl25_79
<=> ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_79])]) ).
tff(f1499,plain,
( spl25_138
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,cons(type,sK3,ts),t)),var(n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_138])]) ).
tff(f1508,plain,
( ( t1 = foldr(type,type,fun,cons(type,sK3,ts),t) )
| ~ spl25_33
| ~ spl25_79
| ~ spl25_138 ),
inference(forward_demodulation,[],[f1503,f703]) ).
tff(f1503,plain,
( ( foldr(type,type,fun,cons(type,sK3,ts),t) = aa(nat,type,shift(type,e,n,t1),n) )
| ~ spl25_79
| ~ spl25_138 ),
inference(resolution,[],[f1501,f970]) ).
tff(f970,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl25_79 ),
inference(avatar_component_clause,[],[f969]) ).
tff(f1501,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,cons(type,sK3,ts),t)),var(n)))
| ~ spl25_138 ),
inference(avatar_component_clause,[],[f1499]) ).
tff(f2611,plain,
( spl25_224
| ~ spl25_65
| ~ spl25_108 ),
inference(avatar_split_clause,[],[f1216,f1179,f895,f2608]) ).
tff(f2608,plain,
( spl25_224
<=> ( t1 = foldr(type,type,fun,cons(type,t2,ts),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_224])]) ).
tff(f1216,plain,
( ( t1 = foldr(type,type,fun,cons(type,t2,ts),t) )
| ~ spl25_65
| ~ spl25_108 ),
inference(superposition,[],[f1180,f897]) ).
tff(f2606,plain,
( spl25_223
| ~ spl25_12
| ~ spl25_51 ),
inference(avatar_split_clause,[],[f801,f798,f586,f2604]) ).
tff(f2604,plain,
( spl25_223
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != cons(dB,X0,X1) )
| ( as = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_223])]) ).
tff(f586,plain,
( spl25_12
<=> ( rs = cons(dB,a,as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_12])]) ).
tff(f798,plain,
( spl25_51
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_51])]) ).
tff(f801,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != cons(dB,X0,X1) )
| ( as = X1 ) )
| ~ spl25_12
| ~ spl25_51 ),
inference(superposition,[],[f799,f588]) ).
tff(f588,plain,
( ( rs = cons(dB,a,as) )
| ~ spl25_12 ),
inference(avatar_component_clause,[],[f586]) ).
tff(f799,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X2,X1) != cons(X0,X4,X3) )
| ( X1 = X3 ) )
| ~ spl25_51 ),
inference(avatar_component_clause,[],[f798]) ).
tff(f2602,plain,
( spl25_222
| ~ spl25_22
| ~ spl25_30 ),
inference(avatar_split_clause,[],[f690,f687,f634,f2600]) ).
tff(f2600,plain,
( spl25_222
<=> ! [X0: dB,X1: dB] :
( ( abs(X0) = abs(sK11(abs(X0),X1)) )
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_222])]) ).
tff(f634,plain,
( spl25_22
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_22])]) ).
tff(f690,plain,
( ! [X0: dB,X1: dB] :
( ( abs(X0) = abs(sK11(abs(X0),X1)) )
| ~ beta(X1,X0) )
| ~ spl25_22
| ~ spl25_30 ),
inference(resolution,[],[f688,f635]) ).
tff(f635,plain,
( ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) )
| ~ spl25_22 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f2598,plain,
( spl25_221
| ~ spl25_11
| ~ spl25_21 ),
inference(avatar_split_clause,[],[f652,f630,f576,f2596]) ).
tff(f2596,plain,
( spl25_221
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_221])]) ).
tff(f652,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = aa(bool,bool,combi(bool),X0) ) )
| ~ spl25_11
| ~ spl25_21 ),
inference(superposition,[],[f631,f577]) ).
tff(f2594,plain,
( spl25_220
| ~ spl25_7
| ~ spl25_218 ),
inference(avatar_split_clause,[],[f2577,f2559,f557,f2591]) ).
tff(f2591,plain,
( spl25_220
<=> sP1(abs(abs(t3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_220])]) ).
tff(f557,plain,
( spl25_7
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).
tff(f2577,plain,
( sP1(abs(abs(t3)))
| ~ spl25_7
| ~ spl25_218 ),
inference(resolution,[],[f2560,f559]) ).
tff(f559,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f557]) ).
tff(f2565,plain,
( spl25_219
| ~ spl25_12
| ~ spl25_41 ),
inference(avatar_split_clause,[],[f760,f744,f586,f2563]) ).
tff(f2563,plain,
( spl25_219
<=> ! [X0: dB,X1: list(dB)] :
( ( rs != cons(dB,X0,X1) )
| ( a = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_219])]) ).
tff(f744,plain,
( spl25_41
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_41])]) ).
tff(f760,plain,
( ! [X0: dB,X1: list(dB)] :
( ( rs != cons(dB,X0,X1) )
| ( a = X0 ) )
| ~ spl25_12
| ~ spl25_41 ),
inference(superposition,[],[f745,f588]) ).
tff(f745,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X2,X1) != cons(X0,X4,X3) )
| ( X2 = X4 ) )
| ~ spl25_41 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f2561,plain,
( spl25_218
| ~ spl25_29
| ~ spl25_40 ),
inference(avatar_split_clause,[],[f757,f740,f673,f2559]) ).
tff(f740,plain,
( spl25_40
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_40])]) ).
tff(f757,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) )
| ~ spl25_29
| ~ spl25_40 ),
inference(resolution,[],[f741,f674]) ).
tff(f741,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) )
| ~ spl25_40 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f2164,plain,
( spl25_217
| ~ spl25_14
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f814,f805,f595,f2161]) ).
tff(f2161,plain,
( spl25_217
<=> pp(aa(fun1(dB,bool),bool,fEx(dB),it)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_217])]) ).
tff(f595,plain,
( spl25_14
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_14])]) ).
tff(f814,plain,
( pp(aa(fun1(dB,bool),bool,fEx(dB),it))
| ~ spl25_14
| ~ spl25_52 ),
inference(resolution,[],[f806,f596]) ).
tff(f596,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl25_14 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f2159,plain,
( spl25_216
| ~ spl25_11 ),
inference(avatar_split_clause,[],[f579,f576,f2157]) ).
tff(f2157,plain,
( spl25_216
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_216])]) ).
tff(f579,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fTrue = X1 )
| ( fTrue = X0 ) )
| ~ spl25_11 ),
inference(superposition,[],[f577,f577]) ).
tff(f2147,plain,
spl25_215,
inference(avatar_split_clause,[],[f435,f2145]) ).
tff(f2145,plain,
( spl25_215
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_215])]) ).
tff(f435,plain,
! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))
| ~ pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) )
& ( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: list(type),X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0))
<=> pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0)) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X44: list(type),X43: list(dB),X17: dB,X8: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X8,cons(dB,X17,X43)),X44))
<=> pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X8),X17))),typings(X8,X43)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_typings_Osimps_I2_J) ).
tff(f2143,plain,
spl25_214,
inference(avatar_split_clause,[],[f434,f2141]) ).
tff(f2141,plain,
( spl25_214
<=> ! [X0: list(type),X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_214])]) ).
tff(f434,plain,
! [X2: dB,X3: fun1(nat,type),X0: list(type),X1: list(dB)] :
( pp(list_case(bool,type,fFalse,combc(type,fun1(list(type),bool),fun1(list(type),bool),aa(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool))),aa(fun1(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool))),fun1(fun1(type,fun1(bool,bool)),fun1(type,fun1(fun1(list(type),bool),fun1(list(type),bool)))),combb(fun1(bool,bool),fun1(fun1(list(type),bool),fun1(list(type),bool)),type),combb(bool,bool,list(type))),aa(fun1(type,bool),fun1(type,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(type,bool),fun1(type,fun1(bool,bool))),combb(bool,fun1(bool,bool),type),fconj),aa(dB,fun1(type,bool),typing(X3),X2))),typings(X3,X1)),X0))
| ~ pp(aa(list(type),bool,typings(X3,cons(dB,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f2129,plain,
spl25_213,
inference(avatar_split_clause,[],[f468,f2127]) ).
tff(f2127,plain,
( spl25_213
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun1(X2,X1),X6: fun1(X0,fun1(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_213])]) ).
tff(f468,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun1(X0,fun1(X1,X0)),X4: fun1(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun1(X2,X1),X5: X0,X6: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X6),X4),X5,X3) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X63: list(X2),X64: fun1(X2,X1),X60: X0,X68: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X68,X60,map(X2,X1,X64,X63)) = foldl(X0,X2,combc(X0,fun1(X2,X1),fun1(X2,X0),aa(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0))),aa(fun1(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0))),fun1(fun1(X0,fun1(X1,X0)),fun1(X0,fun1(fun1(X2,X1),fun1(X2,X0)))),combb(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),X0),combb(X1,X0,X2)),X68),X64),X60,X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_foldl__map) ).
tff(f2114,plain,
( spl25_212
| ~ spl25_87
| ~ spl25_211 ),
inference(avatar_split_clause,[],[f2110,f2104,f1010,f2112]) ).
tff(f2112,plain,
( spl25_212
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_212])]) ).
tff(f2104,plain,
( spl25_211
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_211])]) ).
tff(f2110,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,X2),X3)),X0),X1) )
| ~ spl25_87
| ~ spl25_211 ),
inference(forward_demodulation,[],[f2109,f1011]) ).
tff(f2109,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X0),X1) )
| ~ spl25_87
| ~ spl25_211 ),
inference(forward_demodulation,[],[f2108,f1011]) ).
tff(f2108,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) )
| ~ spl25_87
| ~ spl25_211 ),
inference(forward_demodulation,[],[f2107,f1011]) ).
tff(f2107,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1)) )
| ~ spl25_87
| ~ spl25_211 ),
inference(forward_demodulation,[],[f2105,f1011]) ).
tff(f2105,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) )
| ~ spl25_211 ),
inference(avatar_component_clause,[],[f2104]) ).
tff(f2106,plain,
spl25_211,
inference(avatar_split_clause,[],[f421,f2104]) ).
tff(f421,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2)),X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X35: nat,X36: dB,X37: dB,X38: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,X38),X37)),X36),X35) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X38),X36),X35)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X37),X36),X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_subst__App) ).
tff(f2102,plain,
spl25_210,
inference(avatar_split_clause,[],[f520,f2100]) ).
tff(f2100,plain,
( spl25_210
<=> ! [X5: type,X3: fun1(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_210])]) ).
tff(f520,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f519,f461]) ).
tff(f461,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun1(X0,fun1(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X81: X0,X82: X1,X80: fun1(X0,fun1(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X80,X82),X81) = aa(X1,X2,aa(X0,fun1(X1,X2),X80,X81),X82) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f519,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X6)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f518,f461]) ).
tff(f518,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X6),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f517,f461]) ).
tff(f517,plain,
! [X2: nat,X3: fun1(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,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f470,f461]) ).
tff(f470,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun1(type,type),fun,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X6)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X6))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X27: dB,X4: type,X7: nat,X8: fun1(nat,type),X17: dB,X28: type,X29: type] :
( ( t1 = aa(type,type,aa(type,fun1(type,type),fun,X29),X28) )
=> ( pp(aa(dB,bool,it,X17))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,X7,X29)),X17),X4))
=> ( pp(aa(dB,bool,it,X27))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X27),X29))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X17),X27),X7))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_MI1) ).
tff(f2098,plain,
( spl25_209
| ~ spl25_28
| ~ spl25_147 ),
inference(avatar_split_clause,[],[f1760,f1571,f669,f2096]) ).
tff(f2096,plain,
( spl25_209
<=> ! [X0: nat,X1: dB] : ~ beta(abs(abs(var(X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_209])]) ).
tff(f1571,plain,
( spl25_147
<=> ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_147])]) ).
tff(f1760,plain,
( ! [X0: nat,X1: dB] : ~ beta(abs(abs(var(X0))),X1)
| ~ spl25_28
| ~ spl25_147 ),
inference(resolution,[],[f1572,f670]) ).
tff(f1572,plain,
( ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1)
| ~ spl25_147 ),
inference(avatar_component_clause,[],[f1571]) ).
tff(f2094,plain,
spl25_208,
inference(avatar_split_clause,[],[f516,f2092]) ).
tff(f2092,plain,
( spl25_208
<=> ! [X5: type,X3: fun1(nat,type),X4: dB,X2: nat,X0: dB,X6: type,X1: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_208])]) ).
tff(f516,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ( t1 != aa(type,type,combc(type,type,type,fun,X5),X6) )
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4)) ),
inference(forward_demodulation,[],[f515,f461]) ).
tff(f515,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X2,X5)),X1),X4))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f514,f461]) ).
tff(f514,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X5),X0))
| pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f513,f461]) ).
tff(f513,plain,
! [X2: nat,X3: fun1(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,fun1(dB,fun1(nat,dB)),subst,X4),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(forward_demodulation,[],[f469,f461]) ).
tff(f469,plain,
! [X2: nat,X3: fun1(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
| ~ pp(aa(dB,bool,it,X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
| ~ pp(aa(dB,bool,it,X4))
| ( t1 != aa(type,type,aa(type,fun1(type,type),fun,X6),X5) ) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: dB,X1: type,X2: nat,X3: fun1(nat,type),X4: dB,X5: type,X6: type] :
( ( t1 = aa(type,type,aa(type,fun1(type,type),fun,X6),X5) )
=> ( pp(aa(dB,bool,it,X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X2,X5)),X4),X1))
=> ( pp(aa(dB,bool,it,X0))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X5))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X27: dB,X4: type,X7: nat,X8: fun1(nat,type),X17: dB,X28: type,X29: type] :
( ( t1 = aa(type,type,aa(type,fun1(type,type),fun,X29),X28) )
=> ( pp(aa(dB,bool,it,X17))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,X7,X28)),X17),X4))
=> ( pp(aa(dB,bool,it,X27))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X27),X28))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X17),X27),X7))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_MI2) ).
tff(f2085,plain,
( spl25_207
| ~ spl25_87
| ~ spl25_206 ),
inference(avatar_split_clause,[],[f2080,f2073,f1010,f2082]) ).
tff(f2082,plain,
( spl25_207
<=> pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_207])]) ).
tff(f2073,plain,
( spl25_206
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_206])]) ).
tff(f2080,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),u))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n),u))))
| ~ spl25_87
| ~ spl25_206 ),
inference(forward_demodulation,[],[f2079,f1011]) ).
tff(f2079,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,combc(dB,dB,dB,app,var(zero_zero(nat))),aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n),u))))
| ~ spl25_87
| ~ spl25_206 ),
inference(forward_demodulation,[],[f2078,f1011]) ).
tff(f2078,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n),u))))
| ~ spl25_87
| ~ spl25_206 ),
inference(forward_demodulation,[],[f2077,f1011]) ).
tff(f2077,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),zero_zero(nat)),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n))))
| ~ spl25_87
| ~ spl25_206 ),
inference(forward_demodulation,[],[f2075,f1011]) ).
tff(f2075,plain,
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)),zero_zero(nat))))
| ~ spl25_206 ),
inference(avatar_component_clause,[],[f2073]) ).
tff(f2076,plain,
spl25_206,
inference(avatar_split_clause,[],[f484,f2073]) ).
tff(f484,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)),zero_zero(nat)))),
inference(definition_unfolding,[],[f343,f323]) ).
tff(f323,plain,
i = n,
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
i = n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_True) ).
tff(f343,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,u),zero_zero(nat))),var(zero_zero(nat)))),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)),zero_zero(nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f2063,plain,
( spl25_205
| ~ spl25_87
| ~ spl25_204 ),
inference(avatar_split_clause,[],[f2059,f2055,f1010,f2061]) ).
tff(f2061,plain,
( spl25_205
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_205])]) ).
tff(f2055,plain,
( spl25_204
<=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_204])]) ).
tff(f2059,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) = aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X0),X1) )
| ~ spl25_87
| ~ spl25_204 ),
inference(forward_demodulation,[],[f2058,f1011]) ).
tff(f2058,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) )
| ~ spl25_87
| ~ spl25_204 ),
inference(forward_demodulation,[],[f2056,f1011]) ).
tff(f2056,plain,
( ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) )
| ~ spl25_204 ),
inference(avatar_component_clause,[],[f2055]) ).
tff(f2057,plain,
spl25_204,
inference(avatar_split_clause,[],[f420,f2055]) ).
tff(f420,plain,
! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X1),X0),X2)) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X7: nat,X27: dB,X43: list(dB),X17: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,foldl(dB,dB,app,X17,X43)),X27),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X17),X27),X7),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X27),X7),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subst__map) ).
tff(f2048,plain,
spl25_203,
inference(avatar_split_clause,[],[f526,f2046]) ).
tff(f2046,plain,
( spl25_203
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun1(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_203])]) ).
tff(f526,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f525,f461]) ).
tff(f525,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f473,f461]) ).
tff(f473,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
& ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f254,f316]) ).
tff(f316,plain,
! [X0: type,X2: type,X3: list(dB),X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
=> ( pp(aa(list(type),bool,typings(X6,X3),sK24(X0,X2,X3,X6)))
& ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f254,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
=> ( pp(aa(list(type),bool,typings(X6,X4),X1))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
=> ? [X7: list(type)] :
( pp(aa(list(type),bool,typings(X6,X3),X7))
& ( foldr(type,type,fun,X7,X2) = X0 ) ) ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X16: type,X44: list(type),X4: type,X52: list(dB),X43: list(dB),X7: nat,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,foldl(dB,dB,app,var(X7),X43),X52)),X4))
=> ( pp(aa(list(type),bool,typings(X8,X43),X44))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X43)),X16))
=> ? [X53: list(type)] :
( pp(aa(list(type),bool,typings(X8,X52),X53))
& ( foldr(type,type,fun,X53,X4) = X16 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_var__app__types) ).
tff(f2038,plain,
spl25_202,
inference(avatar_split_clause,[],[f528,f2036]) ).
tff(f2036,plain,
( spl25_202
<=> ! [X3: list(dB),X4: list(dB),X0: type,X6: fun1(nat,type),X5: nat,X2: type,X1: list(type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_202])]) ).
tff(f528,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X2),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1)) ),
inference(forward_demodulation,[],[f527,f461]) ).
tff(f527,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X6),X0),foldl(dB,dB,app,var(X5),X4)))
| ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(forward_demodulation,[],[f472,f461]) ).
tff(f472,plain,
! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun1(nat,type),X4: list(dB),X5: nat] :
( ( foldr(type,type,fun,sK24(X0,X2,X3,X6),X2) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,var(X5),X4)),X0))
| ~ pp(aa(list(type),bool,typings(X6,X4),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
inference(cnf_transformation,[],[f317]) ).
tff(f2030,plain,
( spl25_201
| ~ spl25_87
| ~ spl25_200 ),
inference(avatar_split_clause,[],[f2026,f2019,f1010,f2028]) ).
tff(f2028,plain,
( spl25_201
<=> ! [X4: fun1(nat,type),X0: dB,X3: dB,X2: type,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_201])]) ).
tff(f2019,plain,
( spl25_200
<=> ! [X2: type,X4: fun1(nat,type),X0: dB,X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_200])]) ).
tff(f2026,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,combc(type,type,type,fun,X1),X2)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl25_87
| ~ spl25_200 ),
inference(forward_demodulation,[],[f2025,f1011]) ).
tff(f2025,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)),X3))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) )
| ~ spl25_87
| ~ spl25_200 ),
inference(forward_demodulation,[],[f2024,f1011]) ).
tff(f2024,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X0))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl25_87
| ~ spl25_200 ),
inference(forward_demodulation,[],[f2023,f1011]) ).
tff(f2023,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl25_87
| ~ spl25_200 ),
inference(forward_demodulation,[],[f2022,f1011]) ).
tff(f2022,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl25_87
| ~ spl25_200 ),
inference(forward_demodulation,[],[f2020,f1011]) ).
tff(f2020,plain,
( ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) )
| ~ spl25_200 ),
inference(avatar_component_clause,[],[f2019]) ).
tff(f2021,plain,
spl25_200,
inference(avatar_split_clause,[],[f457,f2019]) ).
tff(f457,plain,
! [X2: type,X3: dB,X0: dB,X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1))) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: dB,X1: type,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X1)))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X0),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X0)),X1)) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X17: dB,X16: type,X4: type,X39: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X39),aa(type,type,aa(type,fun1(type,type),fun,X4),X16)))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X17),X4))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),aa(dB,dB,aa(dB,fun1(dB,dB),app,X39),X17)),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_App) ).
tff(f2014,plain,
( spl25_199
| ~ spl25_87
| ~ spl25_109
| ~ spl25_198 ),
inference(avatar_split_clause,[],[f2010,f2006,f1184,f1010,f2012]) ).
tff(f2012,plain,
( spl25_199
<=> ! [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,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,abs(X2),cons(dB,X1,X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_199])]) ).
tff(f1184,plain,
( spl25_109
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0)),X2: list(X1)] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_109])]) ).
tff(f2006,plain,
( spl25_198
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_198])]) ).
tff(f2010,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,fun1(dB,fun1(nat,dB)),subst,X2),zero_zero(nat)),X1),X0)))
| pp(aa(dB,bool,it,foldl(dB,dB,app,abs(X2),cons(dB,X1,X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl25_87
| ~ spl25_109
| ~ spl25_198 ),
inference(forward_demodulation,[],[f2009,f1011]) ).
tff(f2009,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,abs(X2),cons(dB,X1,X0))))
| ~ pp(aa(dB,bool,it,X1))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl25_109
| ~ spl25_198 ),
inference(forward_demodulation,[],[f2007,f1185]) ).
tff(f1185,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) )
| ~ spl25_109 ),
inference(avatar_component_clause,[],[f1184]) ).
tff(f2007,plain,
( ! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) )
| ~ spl25_198 ),
inference(avatar_component_clause,[],[f2006]) ).
tff(f2008,plain,
spl25_198,
inference(avatar_split_clause,[],[f415,f2006]) ).
tff(f415,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(flattening,[],[f225]) ).
tff(f225,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),zero_zero(nat)),X0))) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(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,fun1(dB,dB),app,abs(X2)),X1),X0))) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X40: list(dB),X39: dB,X41: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X41),X39),zero_zero(nat)),X40)))
=> ( pp(aa(dB,bool,it,X39))
=> pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X41)),X39),X40))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Beta) ).
tff(f1987,plain,
spl25_197,
inference(avatar_split_clause,[],[f524,f1985]) ).
tff(f1985,plain,
( spl25_197
<=> ! [X2: dB,X3: fun1(nat,type),X4: type,X0: nat,X5: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_197])]) ).
tff(f524,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,X0,X1)),X4),X5))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2))) ),
inference(forward_demodulation,[],[f523,f461]) ).
tff(f523,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f522,f461]) ).
tff(f522,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X0),X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f521,f461]) ).
tff(f521,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X4),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(forward_demodulation,[],[f509,f461]) ).
tff(f509,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,X0,X1)),X5),X4)) ),
inference(equality_resolution,[],[f471]) ).
tff(f471,plain,
! [X2: dB,X3: fun1(nat,type),X0: nat,X1: type,X6: fun1(nat,type),X4: type,X5: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4))
| ( shift(type,X3,X0,X1) != X6 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4)) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: nat,X1: type,X2: dB,X3: fun1(nat,type),X4: type,X5: dB,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),X5),X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
=> ( ( shift(type,X3,X0,X1) = X6 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X7: nat,X16: type,X27: dB,X51: fun1(nat,type),X4: type,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X51),X27),X16))
=> ( ( shift(type,X51,X7,X16) = X8 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X51),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X17),X27),X7)),X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_subst__lemma) ).
tff(f1980,plain,
( spl25_196
| ~ spl25_26
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f684,f673,f661,f1978]) ).
tff(f1978,plain,
( spl25_196
<=> ! [X0: dB] :
( sP1(abs(sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_196])]) ).
tff(f661,plain,
( spl25_26
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_26])]) ).
tff(f684,plain,
( ! [X0: dB] :
( sP1(abs(sK9(X0)))
| ~ sP0(X0) )
| ~ spl25_26
| ~ spl25_29 ),
inference(resolution,[],[f674,f662]) ).
tff(f662,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) )
| ~ spl25_26 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f1976,plain,
( spl25_195
| ~ spl25_87
| ~ spl25_109
| ~ spl25_194 ),
inference(avatar_split_clause,[],[f1972,f1968,f1184,f1010,f1974]) ).
tff(f1974,plain,
( spl25_195
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_195])]) ).
tff(f1968,plain,
( spl25_194
<=> ! [X2: dB,X1: dB,X3: list(dB)] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_194])]) ).
tff(f1972,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X2),X3)))
| sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl25_87
| ~ spl25_109
| ~ spl25_194 ),
inference(forward_demodulation,[],[f1971,f1011]) ).
tff(f1971,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,abs(X1),cons(dB,X2,X3)))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl25_109
| ~ spl25_194 ),
inference(forward_demodulation,[],[f1969,f1185]) ).
tff(f1969,plain,
( ! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) )
| ~ spl25_194 ),
inference(avatar_component_clause,[],[f1968]) ).
tff(f1970,plain,
spl25_194,
inference(avatar_split_clause,[],[f493,f1968]) ).
tff(f493,plain,
! [X2: dB,X3: list(dB),X1: dB] :
( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3))
| ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3))) ),
inference(equality_resolution,[],[f365]) ).
tff(f365,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f272,f273]) ).
tff(f273,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f272,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X4),X5),zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f271]) ).
tff(f271,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f255]) ).
tff(f255,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1951,plain,
( spl25_193
| ~ spl25_87
| ~ spl25_192 ),
inference(avatar_split_clause,[],[f1947,f1941,f1010,f1949]) ).
tff(f1949,plain,
( spl25_193
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(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,[spl25_193])]) ).
tff(f1941,plain,
( spl25_192
<=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_192])]) ).
tff(f1947,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(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)) )
| ~ spl25_87
| ~ spl25_192 ),
inference(forward_demodulation,[],[f1946,f1011]) ).
tff(f1946,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(dB,dB,aa(dB,fun1(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,fun1(dB,dB),app,X2),X1)) )
| ~ spl25_87
| ~ spl25_192 ),
inference(forward_demodulation,[],[f1945,f1011]) ).
tff(f1945,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(dB,dB,combc(dB,nat,dB,lift,X0),X2)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl25_87
| ~ spl25_192 ),
inference(forward_demodulation,[],[f1944,f1011]) ).
tff(f1944,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl25_87
| ~ spl25_192 ),
inference(forward_demodulation,[],[f1942,f1011]) ).
tff(f1942,plain,
( ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) )
| ~ spl25_192 ),
inference(avatar_component_clause,[],[f1941]) ).
tff(f1943,plain,
spl25_192,
inference(avatar_split_clause,[],[f396,f1941]) ).
tff(f396,plain,
! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X35: nat,X38: dB,X36: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,aa(dB,dB,aa(dB,fun1(dB,dB),app,X36),X38)),X35) = aa(dB,dB,aa(dB,fun1(dB,dB),app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X36),X35)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X38),X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_lift_Osimps_I2_J) ).
tff(f1935,plain,
spl25_191,
inference(avatar_split_clause,[],[f512,f1933]) ).
tff(f1933,plain,
( spl25_191
<=> ! [X2: nat,X4: dB,X0: list(type),X5: fun1(nat,type),X3: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_191])]) ).
tff(f512,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X5),X3),X4))
| pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0)) ),
inference(forward_demodulation,[],[f467,f461]) ).
tff(f467,plain,
! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0))
| ~ pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3)) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X5),X4),X3))
=> ( pp(aa(list(type),bool,typings(shift(type,X5,X2,X3),X1),X0))
=> pp(aa(list(type),bool,typings(X5,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X4),X2),X1)),X0)) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X44: list(type),X43: list(dB),X7: nat,X4: type,X27: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X27),X4))
=> ( pp(aa(list(type),bool,typings(shift(type,X8,X7,X4),X43),X44))
=> pp(aa(list(type),bool,typings(X8,map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,X27),X7),X43)),X44)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_substs__lemma) ).
tff(f1919,plain,
( spl25_190
| ~ spl25_87
| ~ spl25_189 ),
inference(avatar_split_clause,[],[f1915,f1909,f1010,f1917]) ).
tff(f1917,plain,
( spl25_190
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK22(X0,X1,X2,X3))),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_190])]) ).
tff(f1909,plain,
( spl25_189
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_189])]) ).
tff(f1915,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK22(X0,X1,X2,X3))),X2)) )
| ~ spl25_87
| ~ spl25_189 ),
inference(forward_demodulation,[],[f1914,f1011]) ).
tff(f1914,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK22(X0,X1,X2,X3))),X2)) )
| ~ spl25_87
| ~ spl25_189 ),
inference(forward_demodulation,[],[f1913,f1011]) ).
tff(f1913,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),sK22(X0,X1,X2,X3))),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl25_87
| ~ spl25_189 ),
inference(forward_demodulation,[],[f1912,f1011]) ).
tff(f1912,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl25_87
| ~ spl25_189 ),
inference(forward_demodulation,[],[f1910,f1011]) ).
tff(f1910,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl25_189 ),
inference(avatar_component_clause,[],[f1909]) ).
tff(f1911,plain,
spl25_189,
inference(avatar_split_clause,[],[f431,f1909]) ).
tff(f431,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK22(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f234,f299]) ).
tff(f299,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0))) )
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK22(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,sK22(X0,X1,X2,X3)),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f234,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( ? [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: type,X1: dB,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0))
=> ~ ! [X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),aa(type,type,aa(type,fun1(type,type),fun,X4),X0)))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),X4)) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X4: type,X27: dB,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),aa(dB,dB,aa(dB,fun1(dB,dB),app,X17),X27)),X4))
=> ~ ! [X23: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),aa(type,type,aa(type,fun1(type,type),fun,X23),X4)))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X27),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_typing__elims_I2_J) ).
tff(f1902,plain,
( spl25_188
| ~ spl25_87
| ~ spl25_187 ),
inference(avatar_split_clause,[],[f1898,f1893,f1010,f1900]) ).
tff(f1900,plain,
( spl25_188
<=> ! [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),sK14(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK13(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_188])]) ).
tff(f1893,plain,
( spl25_187
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_187])]) ).
tff(f1898,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),sK14(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK13(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1) )
| ~ spl25_87
| ~ spl25_187 ),
inference(forward_demodulation,[],[f1897,f1011]) ).
tff(f1897,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK14(X0,X1,X2)) = X0 )
| ( aa(dB,dB,combc(dB,dB,dB,app,sK13(X0,X1,X2)),X2) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_87
| ~ spl25_187 ),
inference(forward_demodulation,[],[f1896,f1011]) ).
tff(f1896,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,sK13(X0,X1,X2)),X2) = X0 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_87
| ~ spl25_187 ),
inference(forward_demodulation,[],[f1894,f1011]) ).
tff(f1894,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_187 ),
inference(avatar_component_clause,[],[f1893]) ).
tff(f1895,plain,
spl25_187,
inference(avatar_split_clause,[],[f407,f1893]) ).
tff(f407,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( beta(X1,sK13(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 ) )
| ( beta(X2,sK14(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f284,f286,f285]) ).
tff(f285,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( beta(X1,X3)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) = X0 ) )
=> ( beta(X1,sK13(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f286,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 ) )
=> ( beta(X2,sK14(X0,X1,X2))
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f284,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( beta(X1,X3)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X3) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(rectify,[],[f259]) ).
tff(f259,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 ) )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(definition_folding,[],[f221,f258]) ).
tff(f258,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f221,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(flattening,[],[f220]) ).
tff(f220,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X5: dB] :
( beta(X1,X5)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X5) = X0 ) )
| ? [X4: dB] :
( beta(X2,X4)
& ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 ) )
| ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0)
=> ( ! [X3: dB] :
( ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 )
=> ( abs(X3) != X2 ) )
=> ( ! [X4: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X4),X1) = X0 )
=> ~ beta(X2,X4) )
=> ~ ! [X5: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X5) = X0 )
=> ~ beta(X1,X5) ) ) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X37: dB,X38: dB,X36: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X36),X38),X37)
=> ( ! [X79: dB] :
( ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X79),X38),zero_zero(nat)) = X37 )
=> ( abs(X79) != X36 ) )
=> ( ! [X71: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X71),X38) = X37 )
=> ~ beta(X36,X71) )
=> ~ ! [X71: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X36),X71) = X37 )
=> ~ beta(X38,X71) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_beta__cases_I3_J) ).
tff(f1887,plain,
spl25_186,
inference(avatar_split_clause,[],[f450,f1885]) ).
tff(f1885,plain,
( spl25_186
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_186])]) ).
tff(f450,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3)
| ~ listsp(X0,X1,X3)
| ~ listsp(X0,X2,X3) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(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(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( ( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(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(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: fun1(X0,bool),X2: fun1(X0,bool),X3: list(X0)] :
( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3)
<=> ( listsp(X0,X1,X3)
& listsp(X0,X2,X3) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X65: fun1(X0,bool),X66: fun1(X0,bool),X67: list(X0)] :
( listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X66),X65),X67)
<=> ( listsp(X0,X65,X67)
& listsp(X0,X66,X67) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_listsp__conj__eq) ).
tff(f1879,plain,
( spl25_185
| ~ spl25_87
| ~ spl25_184 ),
inference(avatar_split_clause,[],[f1875,f1872,f1010,f1877]) ).
tff(f1877,plain,
( spl25_185
<=> ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_185])]) ).
tff(f1872,plain,
( spl25_184
<=> ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_184])]) ).
tff(f1875,plain,
( ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(X2)),fEx(type)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl25_87
| ~ spl25_184 ),
inference(forward_demodulation,[],[f1873,f1011]) ).
tff(f1873,plain,
( ! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) )
| ~ spl25_184 ),
inference(avatar_component_clause,[],[f1872]) ).
tff(f1874,plain,
spl25_184,
inference(avatar_split_clause,[],[f404,f1872]) ).
tff(f404,plain,
! [X2: fun1(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(type),X1: list(dB),X2: fun1(nat,type)] :
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1)
| ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: list(type),X1: list(dB),X2: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X2,X1),X0))
=> listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X2)),X1) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X44: list(type),X43: list(dB),X8: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X43),X44))
=> listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(X8)),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_lists__typings) ).
tff(f1860,plain,
( spl25_183
| ~ spl25_87
| ~ spl25_180 ),
inference(avatar_split_clause,[],[f1848,f1844,f1010,f1858]) ).
tff(f1858,plain,
( spl25_183
<=> ! [X4: fun1(nat,type),X0: list(dB),X3: dB,X2: list(type),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_183])]) ).
tff(f1844,plain,
( spl25_180
<=> ! [X2: list(type),X4: fun1(nat,type),X0: list(dB),X3: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_180])]) ).
tff(f1848,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),foldr(type,type,fun,X2,X1)),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2)) )
| ~ spl25_87
| ~ spl25_180 ),
inference(forward_demodulation,[],[f1847,f1011]) ).
tff(f1847,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,X3,X0)))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) )
| ~ spl25_87
| ~ spl25_180 ),
inference(forward_demodulation,[],[f1845,f1011]) ).
tff(f1845,plain,
( ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) )
| ~ spl25_180 ),
inference(avatar_component_clause,[],[f1844]) ).
tff(f1856,plain,
( spl25_181
| ~ spl25_182
| ~ spl25_11 ),
inference(avatar_split_clause,[],[f584,f576,f1853,f1850]) ).
tff(f1850,plain,
( spl25_181
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_181])]) ).
tff(f1853,plain,
( spl25_182
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_182])]) ).
tff(f584,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl25_11 ),
inference(equality_factoring,[],[f577]) ).
tff(f1846,plain,
spl25_180,
inference(avatar_split_clause,[],[f455,f1844]) ).
tff(f455,plain,
! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1))
| ~ pp(aa(list(type),bool,typings(X4,X0),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1))) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),foldr(type,type,fun,X2,X1)))
=> ( pp(aa(list(type),bool,typings(X4,X0),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X43: list(dB),X4: type,X44: list(type),X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),foldr(type,type,fun,X44,X4)))
=> ( pp(aa(list(type),bool,typings(X8,X43),X44))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,X17,X43)),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list__app__typeI) ).
tff(f1838,plain,
spl25_179,
inference(avatar_split_clause,[],[f449,f1836]) ).
tff(f1836,plain,
( spl25_179
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_179])]) ).
tff(f449,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,X1,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1834,plain,
spl25_178,
inference(avatar_split_clause,[],[f448,f1832]) ).
tff(f1832,plain,
( spl25_178
<=> ! [X0: $tType,X3: list(X0),X2: fun1(X0,bool),X1: fun1(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_178])]) ).
tff(f448,plain,
! [X0: $tType,X2: fun1(X0,bool),X3: list(X0),X1: fun1(X0,bool)] :
( listsp(X0,X2,X3)
| ~ listsp(X0,combs(X0,bool,bool,aa(fun1(X0,bool),fun1(X0,fun1(bool,bool)),aa(fun1(bool,fun1(bool,bool)),fun1(fun1(X0,bool),fun1(X0,fun1(bool,bool))),combb(bool,fun1(bool,bool),X0),fconj),X2),X1),X3) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1825,plain,
( spl25_177
| ~ spl25_87
| ~ spl25_176 ),
inference(avatar_split_clause,[],[f1821,f1817,f1010,f1823]) ).
tff(f1823,plain,
( spl25_177
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)),var(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_177])]) ).
tff(f1817,plain,
( spl25_176
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_176])]) ).
tff(f1821,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)),var(X2))) )
| ~ spl25_87
| ~ spl25_176 ),
inference(forward_demodulation,[],[f1820,f1011]) ).
tff(f1820,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)),var(X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl25_87
| ~ spl25_176 ),
inference(forward_demodulation,[],[f1818,f1011]) ).
tff(f1818,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl25_176 ),
inference(avatar_component_clause,[],[f1817]) ).
tff(f1819,plain,
spl25_176,
inference(avatar_split_clause,[],[f429,f1817]) ).
tff(f429,plain,
! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f233,f297]) ).
tff(f297,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,sK21(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f233,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),var(X2)),foldr(type,type,fun,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X4: type,X43: list(dB),X7: nat,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X43)),X4))
=> ~ ! [X42: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),var(X7)),foldr(type,type,fun,X42,X4)))
=> ~ pp(aa(list(type),bool,typings(X8,X43),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_var__app__typesE) ).
tff(f1809,plain,
( spl25_175
| ~ spl25_87
| ~ spl25_174 ),
inference(avatar_split_clause,[],[f1804,f1799,f1010,f1807]) ).
tff(f1807,plain,
( spl25_175
<=> ! [X0: type,X3: fun1(nat,type),X2: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_175])]) ).
tff(f1799,plain,
( spl25_174
<=> ! [X0: type,X3: fun1(nat,type),X2: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_174])]) ).
tff(f1804,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X3,zero_zero(nat),X2)),X0),X1))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1))) )
| ~ spl25_87
| ~ spl25_174 ),
inference(forward_demodulation,[],[f1803,f1011]) ).
tff(f1803,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,combc(type,type,type,fun,X0),X2)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl25_87
| ~ spl25_174 ),
inference(forward_demodulation,[],[f1802,f1011]) ).
tff(f1802,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)),abs(X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl25_87
| ~ spl25_174 ),
inference(forward_demodulation,[],[f1800,f1011]) ).
tff(f1800,plain,
( ! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) )
| ~ spl25_174 ),
inference(avatar_component_clause,[],[f1799]) ).
tff(f1801,plain,
spl25_174,
inference(avatar_split_clause,[],[f428,f1799]) ).
tff(f428,plain,
! [X2: type,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: type,X1: dB,X2: type,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0)) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: type,X1: dB,X2: type,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X3,zero_zero(nat),X2)),X1),X0))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),abs(X1)),aa(type,type,aa(type,fun1(type,type),fun,X2),X0))) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X16: type,X17: dB,X4: type,X6: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X6,zero_zero(nat),X4)),X17),X16))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),abs(X17)),aa(type,type,aa(type,fun1(type,type),fun,X4),X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Abs) ).
tff(f1797,plain,
( spl25_173
| ~ spl25_87
| ~ spl25_172 ),
inference(avatar_split_clause,[],[f1793,f1789,f1010,f1795]) ).
tff(f1795,plain,
( spl25_173
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_173])]) ).
tff(f1789,plain,
( spl25_172
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_172])]) ).
tff(f1793,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X0),X1),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) )
| ~ spl25_87
| ~ spl25_172 ),
inference(forward_demodulation,[],[f1792,f1011]) ).
tff(f1792,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),X1))
| ~ beta(X3,X2) )
| ~ spl25_87
| ~ spl25_172 ),
inference(forward_demodulation,[],[f1790,f1011]) ).
tff(f1790,plain,
( ! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) )
| ~ spl25_172 ),
inference(avatar_component_clause,[],[f1789]) ).
tff(f1791,plain,
spl25_172,
inference(avatar_split_clause,[],[f422,f1789]) ).
tff(f422,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0))
| ~ beta(X3,X2) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(X3,X2)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X1),X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X49: nat,X38: dB,X36: dB,X26: dB] :
( beta(X26,X36)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X26),X38),X49),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X36),X38),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_subst__preserves__beta) ).
tff(f1781,plain,
( spl25_171
| ~ spl25_87
| ~ spl25_170 ),
inference(avatar_split_clause,[],[f1777,f1773,f1010,f1779]) ).
tff(f1779,plain,
( spl25_171
<=> ! [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,[spl25_171])]) ).
tff(f1773,plain,
( spl25_170
<=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_170])]) ).
tff(f1777,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)) )
| ~ spl25_87
| ~ spl25_170 ),
inference(forward_demodulation,[],[f1776,f1011]) ).
tff(f1776,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(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)) )
| ~ spl25_87
| ~ spl25_170 ),
inference(forward_demodulation,[],[f1774,f1011]) ).
tff(f1774,plain,
( ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) )
| ~ spl25_170 ),
inference(avatar_component_clause,[],[f1773]) ).
tff(f1775,plain,
spl25_170,
inference(avatar_split_clause,[],[f395,f1773]) ).
tff(f395,plain,
! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),map(dB,dB,combc(dB,nat,dB,lift,X0),X1)) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X7: nat,X43: list(dB),X17: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),lift,foldl(dB,dB,app,X17,X43)),X7) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X17),X7),map(dB,dB,combc(dB,nat,dB,lift,X7),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_lift__map) ).
tff(f1771,plain,
( spl25_169
| ~ spl25_87
| ~ spl25_168 ),
inference(avatar_split_clause,[],[f1766,f1762,f1010,f1768]) ).
tff(f1768,plain,
( spl25_169
<=> listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(shift(type,e,n,t1))),fEx(type)),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_169])]) ).
tff(f1762,plain,
( spl25_168
<=> listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(shift(type,e,n,t1))),as) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_168])]) ).
tff(f1766,plain,
( listsp(dB,aa(fun1(fun1(type,bool),bool),fun1(dB,bool),combc(fun1(fun1(type,bool),bool),fun1(dB,fun1(type,bool)),fun1(dB,bool),combb(fun1(type,bool),bool,dB),typing(shift(type,e,n,t1))),fEx(type)),as)
| ~ spl25_87
| ~ spl25_168 ),
inference(forward_demodulation,[],[f1764,f1011]) ).
tff(f1764,plain,
( listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(shift(type,e,n,t1))),as)
| ~ spl25_168 ),
inference(avatar_component_clause,[],[f1762]) ).
tff(f1765,plain,
spl25_168,
inference(avatar_split_clause,[],[f483,f1762]) ).
tff(f483,plain,
listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(shift(type,e,n,t1))),as),
inference(definition_unfolding,[],[f342,f323]) ).
tff(f342,plain,
listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as),
inference(cnf_transformation,[],[f82]) ).
tff(f82,axiom,
listsp(dB,aa(fun1(dB,fun1(type,bool)),fun1(dB,bool),aa(fun1(fun1(type,bool),bool),fun1(fun1(dB,fun1(type,bool)),fun1(dB,bool)),combb(fun1(type,bool),bool,dB),fEx(type)),typing(shift(type,e,i,t1))),as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096) ).
tff(f1752,plain,
( spl25_167
| ~ spl25_87
| ~ spl25_166 ),
inference(avatar_split_clause,[],[f1748,f1744,f1010,f1750]) ).
tff(f1750,plain,
( spl25_167
<=> ! [X4: fun1(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_167])]) ).
tff(f1744,plain,
( spl25_166
<=> ! [X4: fun1(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_166])]) ).
tff(f1748,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X1),foldl(dB,dB,app,var(X3),X2)))
| ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 ) )
| ~ spl25_87
| ~ spl25_166 ),
inference(forward_demodulation,[],[f1747,f1011]) ).
tff(f1747,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X0),foldl(dB,dB,app,var(X3),X2)))
| ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl25_87
| ~ spl25_166 ),
inference(forward_demodulation,[],[f1745,f1011]) ).
tff(f1745,plain,
( ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) )
| ~ spl25_166 ),
inference(avatar_component_clause,[],[f1744]) ).
tff(f1746,plain,
spl25_166,
inference(avatar_split_clause,[],[f456,f1744]) ).
tff(f456,plain,
! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( ( X0 = X1 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X1))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),foldl(dB,dB,app,var(X3),X2)),X0))
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X16: type,X4: type,X43: list(dB),X7: nat,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X43)),X4))
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,var(X7),X43)),X16))
=> ( X4 = X16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_var__app__type__eq) ).
tff(f1738,plain,
( spl25_165
| ~ spl25_87
| ~ spl25_164 ),
inference(avatar_split_clause,[],[f1734,f1729,f1010,f1736]) ).
tff(f1736,plain,
( spl25_165
<=> ! [X4: fun1(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_165])]) ).
tff(f1729,plain,
( spl25_164
<=> ! [X4: fun1(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_164])]) ).
tff(f1734,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X4),X2),X3))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3))) )
| ~ spl25_87
| ~ spl25_164 ),
inference(forward_demodulation,[],[f1733,f1011]) ).
tff(f1733,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(dB,dB,combc(dB,nat,dB,lift,X1),X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl25_87
| ~ spl25_164 ),
inference(forward_demodulation,[],[f1732,f1011]) ).
tff(f1732,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X4,X1,X0)),X2),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl25_87
| ~ spl25_164 ),
inference(forward_demodulation,[],[f1730,f1011]) ).
tff(f1730,plain,
( ! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) )
| ~ spl25_164 ),
inference(avatar_component_clause,[],[f1729]) ).
tff(f1731,plain,
spl25_164,
inference(avatar_split_clause,[],[f454,f1729]) ).
tff(f454,plain,
! [X2: type,X3: dB,X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2)) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: type,X1: nat,X2: type,X3: dB,X4: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X4),X3),X2))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X4,X1,X0)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X3),X1)),X2)) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X16: type,X7: nat,X4: type,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),X4))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,X7,X16)),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X17),X7)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_lift__type) ).
tff(f1719,plain,
( spl25_163
| ~ spl25_87
| ~ spl25_162 ),
inference(avatar_split_clause,[],[f1715,f1710,f1010,f1717]) ).
tff(f1717,plain,
( spl25_163
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK22(X0,X1,X2,X3)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_163])]) ).
tff(f1710,plain,
( spl25_162
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK22(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_162])]) ).
tff(f1715,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,combc(dB,dB,dB,app,X1),X2)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK22(X0,X1,X2,X3)),X1)) )
| ~ spl25_87
| ~ spl25_162 ),
inference(forward_demodulation,[],[f1714,f1011]) ).
tff(f1714,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK22(X0,X1,X2,X3)),X1)) )
| ~ spl25_87
| ~ spl25_162 ),
inference(forward_demodulation,[],[f1713,f1011]) ).
tff(f1713,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),sK22(X0,X1,X2,X3)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl25_87
| ~ spl25_162 ),
inference(forward_demodulation,[],[f1711,f1011]) ).
tff(f1711,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK22(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) )
| ~ spl25_162 ),
inference(avatar_component_clause,[],[f1710]) ).
tff(f1712,plain,
spl25_162,
inference(avatar_split_clause,[],[f432,f1710]) ).
tff(f432,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X1),sK22(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f1697,plain,
( spl25_161
| ~ spl25_87
| ~ spl25_160 ),
inference(avatar_split_clause,[],[f1693,f1689,f1010,f1695]) ).
tff(f1695,plain,
( spl25_161
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_161])]) ).
tff(f1689,plain,
( spl25_160
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_160])]) ).
tff(f1693,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)),X2)) )
| ~ spl25_87
| ~ spl25_160 ),
inference(forward_demodulation,[],[f1692,f1011]) ).
tff(f1692,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_87
| ~ spl25_160 ),
inference(forward_demodulation,[],[f1690,f1011]) ).
tff(f1690,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_160 ),
inference(avatar_component_clause,[],[f1689]) ).
tff(f1691,plain,
spl25_160,
inference(avatar_split_clause,[],[f426,f1689]) ).
tff(f426,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f231,f295]) ).
tff(f295,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK20(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f231,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X4: type,X43: list(dB),X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,X17,X43)),X4))
=> ? [X42: list(type)] :
( pp(aa(list(type),bool,typings(X8,X43),X42))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),foldr(type,type,fun,X42,X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_list__app__typeD) ).
tff(f1677,plain,
( spl25_159
| ~ spl25_87
| ~ spl25_158 ),
inference(avatar_split_clause,[],[f1673,f1669,f1010,f1675]) ).
tff(f1675,plain,
( spl25_159
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_159])]) ).
tff(f1669,plain,
( spl25_158
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_158])]) ).
tff(f1673,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)),X2)) )
| ~ spl25_87
| ~ spl25_158 ),
inference(forward_demodulation,[],[f1672,f1011]) ).
tff(f1672,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)),X2))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_87
| ~ spl25_158 ),
inference(forward_demodulation,[],[f1670,f1011]) ).
tff(f1670,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_158 ),
inference(avatar_component_clause,[],[f1669]) ).
tff(f1671,plain,
spl25_158,
inference(avatar_split_clause,[],[f424,f1669]) ).
tff(f424,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f230,f293]) ).
tff(f293,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
=> ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,sK19(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( ? [X4: list(type)] :
( pp(aa(list(type),bool,typings(X3,X1),X4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),foldr(type,type,fun,X4,X0)))
=> ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X4: type,X43: list(dB),X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),foldl(dB,dB,app,X17,X43)),X4))
=> ~ ! [X42: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),foldr(type,type,fun,X42,X4)))
=> ~ pp(aa(list(type),bool,typings(X8,X43),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_list__app__typeE) ).
tff(f1662,plain,
spl25_157,
inference(avatar_split_clause,[],[f482,f1659]) ).
tff(f1659,plain,
( spl25_157
<=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),n),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_157])]) ).
tff(f482,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),n),as))))),
inference(definition_unfolding,[],[f341,f323]) ).
tff(f341,plain,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),i),as))))),
inference(cnf_transformation,[],[f83]) ).
tff(f83,axiom,
pp(aa(dB,bool,it,foldl(dB,dB,app,var(zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),i),as))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82__096IT_A_IVar_A0_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1653,plain,
( spl25_156
| ~ spl25_87
| ~ spl25_155 ),
inference(avatar_split_clause,[],[f1649,f1645,f1010,f1651]) ).
tff(f1651,plain,
( spl25_156
<=> ! [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),sK14(X0,X1,X2)) = X0 )
| beta(X1,sK13(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_156])]) ).
tff(f1645,plain,
( spl25_155
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_155])]) ).
tff(f1649,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),sK14(X0,X1,X2)) = X0 )
| beta(X1,sK13(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl25_87
| ~ spl25_155 ),
inference(forward_demodulation,[],[f1648,f1011]) ).
tff(f1648,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,X1),sK14(X0,X1,X2)) = X0 )
| beta(X1,sK13(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_87
| ~ spl25_155 ),
inference(forward_demodulation,[],[f1646,f1011]) ).
tff(f1646,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_155 ),
inference(avatar_component_clause,[],[f1645]) ).
tff(f1647,plain,
spl25_155,
inference(avatar_split_clause,[],[f409,f1645]) ).
tff(f409,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,sK14(X0,X1,X2)),X1) = X0 )
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1643,plain,
( spl25_154
| ~ spl25_19
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f679,f673,f621,f1641]) ).
tff(f1641,plain,
( spl25_154
<=> ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_154])]) ).
tff(f621,plain,
( spl25_19
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_19])]) ).
tff(f679,plain,
( ! [X0: dB] :
( sP1(abs(X0))
| ~ sP1(X0) )
| ~ spl25_19
| ~ spl25_29 ),
inference(resolution,[],[f674,f622]) ).
tff(f622,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl25_19 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f1635,plain,
( spl25_153
| ~ spl25_87
| ~ spl25_152 ),
inference(avatar_split_clause,[],[f1631,f1627,f1010,f1633]) ).
tff(f1633,plain,
( spl25_153
<=> ! [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,sK13(X0,X1,X2)),X2) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_153])]) ).
tff(f1627,plain,
( spl25_152
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_152])]) ).
tff(f1631,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,sK13(X0,X1,X2)),X2) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl25_87
| ~ spl25_152 ),
inference(forward_demodulation,[],[f1630,f1011]) ).
tff(f1630,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,dB,dB,app,sK13(X0,X1,X2)),X2) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_87
| ~ spl25_152 ),
inference(forward_demodulation,[],[f1628,f1011]) ).
tff(f1628,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_152 ),
inference(avatar_component_clause,[],[f1627]) ).
tff(f1629,plain,
spl25_152,
inference(avatar_split_clause,[],[f408,f1627]) ).
tff(f408,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),sK13(X0,X1,X2)) = X0 )
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1602,plain,
spl25_151,
inference(avatar_split_clause,[],[f466,f1600]) ).
tff(f1600,plain,
( spl25_151
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun1(X1,X0),X4: fun1(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_151])]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X1,X0)] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X1,X0)] : ( aa(X2,X0,aa(fun1(X2,X1),fun1(X2,X0),aa(fun1(X1,X0),fun1(fun1(X2,X1),fun1(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X81: X0,X82: fun1(X0,X1),X80: fun1(X1,X2)] : ( aa(X0,X2,aa(fun1(X0,X1),fun1(X0,X2),aa(fun1(X1,X2),fun1(fun1(X0,X1),fun1(X0,X2)),combb(X1,X2,X0),X80),X82),X81) = aa(X1,X2,X80,aa(X0,X1,X82,X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1588,plain,
( spl25_150
| ~ spl25_87
| ~ spl25_149 ),
inference(avatar_split_clause,[],[f1584,f1580,f1010,f1586]) ).
tff(f1586,plain,
( spl25_150
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),sK18(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_150])]) ).
tff(f1580,plain,
( spl25_149
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_149])]) ).
tff(f1584,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),sK18(X0,X1,X2)),X1)) )
| ~ spl25_87
| ~ spl25_149 ),
inference(forward_demodulation,[],[f1583,f1011]) ).
tff(f1583,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),sK18(X0,X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_87
| ~ spl25_149 ),
inference(forward_demodulation,[],[f1581,f1011]) ).
tff(f1581,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_149 ),
inference(avatar_component_clause,[],[f1580]) ).
tff(f1582,plain,
spl25_149,
inference(avatar_split_clause,[],[f413,f1580]) ).
tff(f413,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
& ( aa(type,type,aa(type,fun1(type,type),fun,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f223,f290]) ).
tff(f290,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 ) )
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
& ( aa(type,type,aa(type,fun1(type,type),fun,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f223,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
& ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 ) )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X4) = X0 )
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X4: type,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),abs(X17)),X4))
=> ~ ! [X23: type,X24: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X23),X24) = X4 )
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,zero_zero(nat),X23)),X17),X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_typing__elims_I3_J) ).
tff(f1577,plain,
( spl25_148
| ~ spl25_87
| ~ spl25_146 ),
inference(avatar_split_clause,[],[f1569,f1565,f1010,f1575]) ).
tff(f1575,plain,
( spl25_148
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),sK16(X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_148])]) ).
tff(f1565,plain,
( spl25_146
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_146])]) ).
tff(f1569,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),sK16(X1,X2)),X1)) )
| ~ spl25_87
| ~ spl25_146 ),
inference(forward_demodulation,[],[f1568,f1011]) ).
tff(f1568,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),sK16(X1,X2)),X1))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_87
| ~ spl25_146 ),
inference(forward_demodulation,[],[f1566,f1011]) ).
tff(f1566,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_146 ),
inference(avatar_component_clause,[],[f1565]) ).
tff(f1573,plain,
( spl25_147
| ~ spl25_5
| ~ spl25_28 ),
inference(avatar_split_clause,[],[f678,f669,f549,f1571]) ).
tff(f549,plain,
( spl25_5
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_5])]) ).
tff(f678,plain,
( ! [X0: nat,X1: dB] : ~ beta(abs(var(X0)),X1)
| ~ spl25_5
| ~ spl25_28 ),
inference(resolution,[],[f670,f550]) ).
tff(f550,plain,
( ! [X0: dB,X1: nat] : ~ beta(var(X1),X0)
| ~ spl25_5 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f1567,plain,
spl25_146,
inference(avatar_split_clause,[],[f411,f1565]) ).
tff(f411,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),X1),sK16(X1,X2)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f222,f288]) ).
tff(f288,plain,
! [X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),sK15(X1,X2))),X1),sK16(X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f222,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( ? [X3: type,X4: type] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: type,X1: dB,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0))
=> ~ ! [X3: type,X4: type] : ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X2,zero_zero(nat),X3)),X1),X4)) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X4: type,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),abs(X17)),X4))
=> ~ ! [X24: type,X30: type] : ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,X8,zero_zero(nat),X24)),X17),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_abs__typeE) ).
tff(f1558,plain,
( spl25_145
| ~ spl25_87
| ~ spl25_144 ),
inference(avatar_split_clause,[],[f1554,f1551,f1010,f1556]) ).
tff(f1556,plain,
( spl25_145
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_145])]) ).
tff(f1551,plain,
( spl25_144
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_144])]) ).
tff(f1554,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),zero_zero(nat)),sK9(X0)),sK10(X0))))
| ~ sP0(X0) )
| ~ spl25_87
| ~ spl25_144 ),
inference(forward_demodulation,[],[f1552,f1011]) ).
tff(f1552,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) )
| ~ spl25_144 ),
inference(avatar_component_clause,[],[f1551]) ).
tff(f1553,plain,
spl25_144,
inference(avatar_split_clause,[],[f363,f1551]) ).
tff(f363,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK8(X0)),sK9(X0)),zero_zero(nat)),sK10(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f1544,plain,
( spl25_143
| ~ spl25_87
| ~ spl25_110
| ~ spl25_142 ),
inference(avatar_split_clause,[],[f1539,f1533,f1188,f1010,f1541]) ).
tff(f1541,plain,
( spl25_143
<=> pp(aa(dB,bool,it,aa(dB,dB,combs(dB,dB,dB,app,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n)),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_143])]) ).
tff(f1533,plain,
( spl25_142
<=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_142])]) ).
tff(f1539,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combs(dB,dB,dB,app,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n)),u)))
| ~ spl25_87
| ~ spl25_110
| ~ spl25_142 ),
inference(forward_demodulation,[],[f1538,f1269]) ).
tff(f1269,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun1(X2,fun1(X0,X1)),X4: X2,X5: fun1(X2,X0)] : ( aa(X2,X1,combs(X2,X0,X1,X3,X5),X4) = aa(X2,X1,combc(X2,X0,X1,X3,aa(X2,X0,X5,X4)),X4) )
| ~ spl25_87
| ~ spl25_110 ),
inference(superposition,[],[f1189,f1011]) ).
tff(f1538,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,a),n),u)),u)))
| ~ spl25_87
| ~ spl25_142 ),
inference(forward_demodulation,[],[f1537,f1011]) ).
tff(f1537,plain,
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)),u)))
| ~ spl25_87
| ~ spl25_142 ),
inference(forward_demodulation,[],[f1535,f1011]) ).
tff(f1535,plain,
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n))))
| ~ spl25_142 ),
inference(avatar_component_clause,[],[f1533]) ).
tff(f1536,plain,
spl25_142,
inference(avatar_split_clause,[],[f481,f1533]) ).
tff(f481,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),n)))),
inference(definition_unfolding,[],[f340,f323]) ).
tff(f340,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)))),
inference(cnf_transformation,[],[f32]) ).
tff(f32,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,u),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,a),u),i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).
tff(f1527,plain,
( spl25_141
| ~ spl25_87
| ~ spl25_140 ),
inference(avatar_split_clause,[],[f1522,f1517,f1010,f1524]) ).
tff(f1524,plain,
( spl25_141
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,sK4,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_141])]) ).
tff(f1517,plain,
( spl25_140
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_140])]) ).
tff(f1522,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,sK4,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(n))))
| ~ spl25_87
| ~ spl25_140 ),
inference(forward_demodulation,[],[f1521,f1011]) ).
tff(f1521,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,sK4,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)))
| ~ spl25_87
| ~ spl25_140 ),
inference(forward_demodulation,[],[f1519,f1011]) ).
tff(f1519,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t)))
| ~ spl25_140 ),
inference(avatar_component_clause,[],[f1517]) ).
tff(f1520,plain,
spl25_140,
inference(avatar_split_clause,[],[f488,f1517]) ).
tff(f488,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t))),
inference(definition_unfolding,[],[f346,f323]) ).
tff(f346,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t))),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f204,f262]) ).
tff(f262,plain,
( ? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t))) )
=> ( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK4))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,sK4,t))) ) ),
introduced(choice_axiom,[]) ).
tff(f204,plain,
? [X0: list(type)] :
( pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t))) ),
inference(ennf_transformation,[],[f117]) ).
tff(f117,plain,
~ ! [X0: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X0,t)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X0)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
~ ! [X42: list(type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,X42,t)))
=> ~ pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1515,plain,
( spl25_139
| ~ spl25_18
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f676,f661,f617,f1513]) ).
tff(f1513,plain,
( spl25_139
<=> ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_139])]) ).
tff(f676,plain,
( ! [X0: dB] :
( ~ sP0(X0)
| sP1(sK9(X0)) )
| ~ spl25_18
| ~ spl25_26 ),
inference(resolution,[],[f662,f618]) ).
tff(f1502,plain,
( spl25_138
| ~ spl25_87
| ~ spl25_108
| ~ spl25_137 ),
inference(avatar_split_clause,[],[f1497,f1492,f1179,f1010,f1499]) ).
tff(f1492,plain,
( spl25_137
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_137])]) ).
tff(f1497,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,cons(type,sK3,ts),t)),var(n)))
| ~ spl25_87
| ~ spl25_108
| ~ spl25_137 ),
inference(forward_demodulation,[],[f1496,f1180]) ).
tff(f1496,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t))),var(n)))
| ~ spl25_87
| ~ spl25_137 ),
inference(forward_demodulation,[],[f1494,f1011]) ).
tff(f1494,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t))))
| ~ spl25_137 ),
inference(avatar_component_clause,[],[f1492]) ).
tff(f1495,plain,
spl25_137,
inference(avatar_split_clause,[],[f486,f1492]) ).
tff(f486,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t)))),
inference(definition_unfolding,[],[f344,f323]) ).
tff(f344,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t)))),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),sK3))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f203,f260]) ).
tff(f260,plain,
( ? [X0: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) )
=> ( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),sK3))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,sK3),foldr(type,type,fun,ts,t)))) ) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
? [X0: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),X0))
& pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t)))) ),
inference(ennf_transformation,[],[f116]) ).
tff(f116,plain,
~ ! [X0: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X0),foldr(type,type,fun,ts,t))))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),X0)) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
~ ! [X25: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,X25),foldr(type,type,fun,ts,t))))
=> ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1487,plain,
spl25_136,
inference(avatar_split_clause,[],[f480,f1484]) ).
tff(f1484,plain,
( spl25_136
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_136])]) ).
tff(f480,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t)),
inference(definition_unfolding,[],[f339,f323]) ).
tff(f339,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t)),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a),as)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f1478,plain,
( spl25_135
| ~ spl25_87
| ~ spl25_134 ),
inference(avatar_split_clause,[],[f1473,f1468,f1010,f1475]) ).
tff(f1475,plain,
( spl25_135
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,ts,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_135])]) ).
tff(f1468,plain,
( spl25_134
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,ts,t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_134])]) ).
tff(f1473,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,ts,t)),aa(dB,dB,combc(dB,dB,dB,app,a),var(n))))
| ~ spl25_87
| ~ spl25_134 ),
inference(forward_demodulation,[],[f1472,f1011]) ).
tff(f1472,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),foldr(type,type,fun,ts,t)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)))
| ~ spl25_87
| ~ spl25_134 ),
inference(forward_demodulation,[],[f1470,f1011]) ).
tff(f1470,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,ts,t)))
| ~ spl25_134 ),
inference(avatar_component_clause,[],[f1468]) ).
tff(f1471,plain,
spl25_134,
inference(avatar_split_clause,[],[f479,f1468]) ).
tff(f479,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,ts,t))),
inference(definition_unfolding,[],[f338,f323]) ).
tff(f338,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),aa(dB,dB,aa(dB,fun1(dB,dB),app,var(n)),a)),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_headT) ).
tff(f1465,plain,
( spl25_133
| ~ spl25_87
| ~ spl25_132 ),
inference(avatar_split_clause,[],[f1461,f1457,f1010,f1463]) ).
tff(f1463,plain,
( spl25_133
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun,sK18(X0,X1,X2)),sK17(X0,X1,X2)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_133])]) ).
tff(f1457,plain,
( spl25_132
<=> ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_132])]) ).
tff(f1461,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),abs(X1)))
| ( aa(type,type,combc(type,type,type,fun,sK18(X0,X1,X2)),sK17(X0,X1,X2)) = X0 ) )
| ~ spl25_87
| ~ spl25_132 ),
inference(forward_demodulation,[],[f1460,f1011]) ).
tff(f1460,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,combc(type,type,type,fun,sK18(X0,X1,X2)),sK17(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_87
| ~ spl25_132 ),
inference(forward_demodulation,[],[f1458,f1011]) ).
tff(f1458,plain,
( ! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) )
| ~ spl25_132 ),
inference(avatar_component_clause,[],[f1457]) ).
tff(f1459,plain,
spl25_132,
inference(avatar_split_clause,[],[f412,f1457]) ).
tff(f412,plain,
! [X2: fun1(nat,type),X0: type,X1: dB] :
( ( aa(type,type,aa(type,fun1(type,type),fun,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),abs(X1)),X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f1429,plain,
( spl25_131
| ~ spl25_87
| ~ spl25_130 ),
inference(avatar_split_clause,[],[f1425,f1421,f1010,f1427]) ).
tff(f1427,plain,
( spl25_131
<=> ! [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,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_131])]) ).
tff(f1421,plain,
( spl25_130
<=> ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_130])]) ).
tff(f1425,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,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl25_87
| ~ spl25_130 ),
inference(forward_demodulation,[],[f1424,f1011]) ).
tff(f1424,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),zero_zero(nat)),X0))
| ~ spl25_87
| ~ spl25_130 ),
inference(forward_demodulation,[],[f1422,f1011]) ).
tff(f1422,plain,
( ! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat)))
| ~ spl25_130 ),
inference(avatar_component_clause,[],[f1421]) ).
tff(f1423,plain,
spl25_130,
inference(avatar_split_clause,[],[f374,f1421]) ).
tff(f374,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: dB,X1: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X1)),X0),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X0),zero_zero(nat))),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X38: dB,X36: dB] : beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X36)),X38),aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X36),X38),zero_zero(nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_beta) ).
tff(f1416,plain,
( spl25_129
| ~ spl25_87
| ~ spl25_128 ),
inference(avatar_split_clause,[],[f1412,f1409,f1010,f1414]) ).
tff(f1414,plain,
( spl25_129
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_129])]) ).
tff(f1409,plain,
( spl25_128
<=> ! [X0: type,X3: fun1(nat,type),X2: nat,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_128])]) ).
tff(f1412,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,var(X2),X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3))) )
| ~ spl25_87
| ~ spl25_128 ),
inference(forward_demodulation,[],[f1410,f1011]) ).
tff(f1410,plain,
( ! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) )
| ~ spl25_128 ),
inference(avatar_component_clause,[],[f1409]) ).
tff(f1411,plain,
spl25_128,
inference(avatar_split_clause,[],[f430,f1409]) ).
tff(f430,plain,
! [X2: nat,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1405,plain,
spl25_127,
inference(avatar_split_clause,[],[f453,f1403]) ).
tff(f1403,plain,
( spl25_127
<=> ! [X4: fun1(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_127])]) ).
tff(f453,plain,
! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2))
| ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X4,X3),X2))
=> pp(aa(list(type),bool,typings(shift(type,X4,X1,X0),map(dB,dB,combc(dB,nat,dB,lift,X1),X3)),X2)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X16: type,X7: nat,X44: list(type),X43: list(dB),X8: fun1(nat,type)] :
( pp(aa(list(type),bool,typings(X8,X43),X44))
=> pp(aa(list(type),bool,typings(shift(type,X8,X7,X16),map(dB,dB,combc(dB,nat,dB,lift,X7),X43)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_lift__types) ).
tff(f1396,plain,
( spl25_126
| ~ spl25_87
| ~ spl25_125 ),
inference(avatar_split_clause,[],[f1391,f1388,f1010,f1394]) ).
tff(f1394,plain,
( spl25_126
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_126])]) ).
tff(f1388,plain,
( spl25_125
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_125])]) ).
tff(f1391,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3))) )
| ~ spl25_87
| ~ spl25_125 ),
inference(forward_demodulation,[],[f1389,f1011]) ).
tff(f1389,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_125 ),
inference(avatar_component_clause,[],[f1388]) ).
tff(f1390,plain,
spl25_125,
inference(avatar_split_clause,[],[f427,f1388]) ).
tff(f427,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f1381,plain,
( spl25_124
| ~ spl25_87
| ~ spl25_123 ),
inference(avatar_split_clause,[],[f1377,f1374,f1010,f1379]) ).
tff(f1379,plain,
( spl25_124
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_124])]) ).
tff(f1374,plain,
( spl25_123
<=> ! [X0: type,X3: fun1(nat,type),X2: dB,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_123])]) ).
tff(f1377,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X0),foldl(dB,dB,app,X2,X1)))
| pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) )
| ~ spl25_87
| ~ spl25_123 ),
inference(forward_demodulation,[],[f1375,f1011]) ).
tff(f1375,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) )
| ~ spl25_123 ),
inference(avatar_component_clause,[],[f1374]) ).
tff(f1376,plain,
spl25_123,
inference(avatar_split_clause,[],[f425,f1374]) ).
tff(f425,plain,
! [X2: dB,X3: fun1(nat,type),X0: type,X1: list(dB)] :
( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f294]) ).
tff(f1368,plain,
( spl25_122
| ~ spl25_87
| ~ spl25_121 ),
inference(avatar_split_clause,[],[f1364,f1361,f1010,f1366]) ).
tff(f1366,plain,
( spl25_122
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_122])]) ).
tff(f1361,plain,
( spl25_121
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_121])]) ).
tff(f1364,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),X0),var(X1))))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl25_87
| ~ spl25_121 ),
inference(forward_demodulation,[],[f1362,f1011]) ).
tff(f1362,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl25_121 ),
inference(avatar_component_clause,[],[f1361]) ).
tff(f1363,plain,
spl25_121,
inference(avatar_split_clause,[],[f402,f1361]) ).
tff(f402,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X2),var(X1)),X0))) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X50: nat,X49: nat,X26: dB] :
( pp(aa(dB,bool,it,X26))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X26),var(X49)),X50))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_subst__Var__IT) ).
tff(f1353,plain,
( spl25_120
| ~ spl25_87
| ~ spl25_119 ),
inference(avatar_split_clause,[],[f1349,f1345,f1010,f1351]) ).
tff(f1351,plain,
( spl25_120
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_120])]) ).
tff(f1345,plain,
( spl25_119
<=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_119])]) ).
tff(f1349,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(dB,dB,combc(dB,nat,dB,lift,X1),X2)),X1) = X2 )
| ~ spl25_87
| ~ spl25_119 ),
inference(forward_demodulation,[],[f1348,f1011]) ).
tff(f1348,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X1) = X2 )
| ~ spl25_87
| ~ spl25_119 ),
inference(forward_demodulation,[],[f1346,f1011]) ).
tff(f1346,plain,
( ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 )
| ~ spl25_119 ),
inference(avatar_component_clause,[],[f1345]) ).
tff(f1347,plain,
spl25_119,
inference(avatar_split_clause,[],[f394,f1345]) ).
tff(f394,plain,
! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X36: dB,X35: nat,X38: dB] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X38),X35)),X36),X35) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_subst__lift) ).
tff(f1343,plain,
( spl25_118
| ~ spl25_14
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f680,f673,f595,f1341]) ).
tff(f1341,plain,
( spl25_118
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_118])]) ).
tff(f680,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl25_14
| ~ spl25_29 ),
inference(resolution,[],[f674,f596]) ).
tff(f1339,plain,
spl25_117,
inference(avatar_split_clause,[],[f477,f1336]) ).
tff(f1336,plain,
( spl25_117
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),n),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_117])]) ).
tff(f477,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),n),as))),
inference(definition_unfolding,[],[f336,f323]) ).
tff(f336,plain,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),i),as))),
inference(cnf_transformation,[],[f86]) ).
tff(f86,axiom,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun1(nat,dB),subst,u),i),as))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85__096listsp_AIT_A_Imap_A_I_Ft_O_Alift_At_A0_J_A_Imap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_J_096) ).
tff(f1326,plain,
( spl25_116
| ~ spl25_87
| ~ spl25_115 ),
inference(avatar_split_clause,[],[f1322,f1318,f1010,f1324]) ).
tff(f1318,plain,
( spl25_115
<=> ! [X0: dB,X3: fun1(nat,type),X2: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_115])]) ).
tff(f1322,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X2))
| pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0) )
| ~ spl25_87
| ~ spl25_115 ),
inference(forward_demodulation,[],[f1321,f1011]) ).
tff(f1321,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,combc(dB,type,bool,typing(X3),X1),X0))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) )
| ~ spl25_87
| ~ spl25_115 ),
inference(forward_demodulation,[],[f1319,f1011]) ).
tff(f1319,plain,
( ! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) )
| ~ spl25_115 ),
inference(avatar_component_clause,[],[f1318]) ).
tff(f1320,plain,
spl25_115,
inference(avatar_split_clause,[],[f423,f1318]) ).
tff(f423,plain,
! [X2: dB,X3: fun1(nat,type),X0: dB,X1: type] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(flattening,[],[f228]) ).
tff(f228,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1))
| ~ beta(X2,X0)
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1)) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: dB,X1: type,X2: dB,X3: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X2),X1))
=> ( beta(X2,X0)
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X3),X0),X1)) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X70: dB,X4: type,X17: dB,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X17),X4))
=> ( beta(X17,X70)
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),X70),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_subject__reduction) ).
tff(f1313,plain,
( spl25_114
| ~ spl25_87
| ~ spl25_113 ),
inference(avatar_split_clause,[],[f1309,f1306,f1010,f1311]) ).
tff(f1311,plain,
( spl25_114
<=> ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| beta(X1,sK13(X0,X1,X2))
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_114])]) ).
tff(f1306,plain,
( spl25_113
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_113])]) ).
tff(f1309,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ~ beta(aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)
| beta(X1,sK13(X0,X1,X2))
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1) )
| ~ spl25_87
| ~ spl25_113 ),
inference(forward_demodulation,[],[f1307,f1011]) ).
tff(f1307,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) )
| ~ spl25_113 ),
inference(avatar_component_clause,[],[f1306]) ).
tff(f1308,plain,
spl25_113,
inference(avatar_split_clause,[],[f410,f1306]) ).
tff(f410,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(X1,sK13(X0,X1,X2))
| beta(X2,sK14(X0,X1,X2))
| sP2(X2,X0,X1)
| ~ beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1),X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1304,plain,
( spl25_112
| ~ spl25_87
| ~ spl25_111 ),
inference(avatar_split_clause,[],[f1300,f1297,f1010,f1302]) ).
tff(f1302,plain,
( spl25_112
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),zero_zero(nat)),X2) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_112])]) ).
tff(f1297,plain,
( spl25_111
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_111])]) ).
tff(f1300,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(dB,dB,combc(dB,nat,dB,aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),zero_zero(nat)),X2) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl25_87
| ~ spl25_111 ),
inference(forward_demodulation,[],[f1298,f1011]) ).
tff(f1298,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl25_111 ),
inference(avatar_component_clause,[],[f1297]) ).
tff(f1299,plain,
spl25_111,
inference(avatar_split_clause,[],[f405,f1297]) ).
tff(f405,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( ( abs(sK12(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f281,f282]) ).
tff(f282,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
=> ( ( abs(sK12(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,sK12(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f281,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f280]) ).
tff(f280,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
inference(nnf_transformation,[],[f258]) ).
tff(f1190,plain,
spl25_110,
inference(avatar_split_clause,[],[f465,f1188]) ).
tff(f465,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun1(X2,X1),X5: fun1(X2,fun1(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun1(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X81: X0,X82: fun1(X0,X1),X80: fun1(X0,fun1(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X80,X82),X81) = aa(X1,X2,aa(X0,fun1(X1,X2),X80,X81),aa(X0,X1,X82,X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1186,plain,
spl25_109,
inference(avatar_split_clause,[],[f464,f1184]) ).
tff(f464,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X5,X4,cons(X1,X3,X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun1(X1,X0),X5,X4),X3),X2) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X1: $tType,X63: list(X1),X5: X1,X60: X0,X64: fun1(X0,fun1(X1,X0))] : ( foldl(X0,X1,X64,X60,cons(X1,X5,X63)) = foldl(X0,X1,X64,aa(X1,X0,aa(X0,fun1(X1,X0),X64,X60),X5),X63) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_foldl__Cons) ).
tff(f1181,plain,
spl25_108,
inference(avatar_split_clause,[],[f463,f1179]) ).
tff(f463,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun1(X0,fun1(X1,X1))] : ( foldr(X0,X1,X5,cons(X0,X4,X3),X2) = aa(X1,X1,aa(X0,fun1(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X1: $tType,X0: $tType,X60: X0,X63: list(X1),X5: X1,X64: fun1(X1,fun1(X0,X0))] : ( foldr(X1,X0,X64,cons(X1,X5,X63),X60) = aa(X0,X0,aa(X1,fun1(X0,X0),X64,X5),foldr(X1,X0,X64,X63,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_foldr_Osimps_I2_J) ).
tff(f1177,plain,
spl25_107,
inference(avatar_split_clause,[],[f446,f1175]) ).
tff(f1175,plain,
( spl25_107
<=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_107])]) ).
tff(f446,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X0 = X2 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
inference(flattening,[],[f310]) ).
tff(f310,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: dB,X1: dB,X2: dB,X3: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X31: dB,X32: dB,X33: dB,X34: dB] :
( ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X34),X33) = aa(dB,dB,aa(dB,fun1(dB,dB),app,X32),X31) )
<=> ( ( X31 = X33 )
& ( X32 = X34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dB_Osimps_I2_J) ).
tff(f1173,plain,
spl25_106,
inference(avatar_split_clause,[],[f445,f1171]) ).
tff(f1171,plain,
( spl25_106
<=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_106])]) ).
tff(f445,plain,
! [X2: dB,X3: dB,X0: dB,X1: dB] :
( ( X1 = X3 )
| ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X3),X2) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f1169,plain,
spl25_105,
inference(avatar_split_clause,[],[f443,f1167]) ).
tff(f1167,plain,
( spl25_105
<=> ! [X2: type,X0: type,X1: type,X3: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_105])]) ).
tff(f443,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X0 = X2 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
inference(flattening,[],[f308]) ).
tff(f308,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: type,X1: type,X2: type,X3: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) = aa(type,type,aa(type,fun1(type,type),fun,X1),X0) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X9: type,X10: type,X11: type,X12: type] :
( ( aa(type,type,aa(type,fun1(type,type),fun,X12),X11) = aa(type,type,aa(type,fun1(type,type),fun,X10),X9) )
<=> ( ( X9 = X11 )
& ( X10 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_type_Osimps_I2_J) ).
tff(f1165,plain,
spl25_104,
inference(avatar_split_clause,[],[f442,f1163]) ).
tff(f442,plain,
! [X2: type,X3: type,X0: type,X1: type] :
( ( X1 = X3 )
| ( aa(type,type,aa(type,fun1(type,type),fun,X3),X2) != aa(type,type,aa(type,fun1(type,type),fun,X1),X0) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1161,plain,
( spl25_103
| ~ spl25_87
| ~ spl25_102 ),
inference(avatar_split_clause,[],[f1157,f1153,f1010,f1159]) ).
tff(f1159,plain,
( spl25_103
<=> ! [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,[spl25_103])]) ).
tff(f1153,plain,
( spl25_102
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_102])]) ).
tff(f1157,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) )
| ~ spl25_87
| ~ spl25_102 ),
inference(forward_demodulation,[],[f1156,f1011]) ).
tff(f1156,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,combc(dB,dB,dB,app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl25_87
| ~ spl25_102 ),
inference(forward_demodulation,[],[f1154,f1011]) ).
tff(f1154,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl25_102 ),
inference(avatar_component_clause,[],[f1153]) ).
tff(f1155,plain,
spl25_102,
inference(avatar_split_clause,[],[f401,f1153]) ).
tff(f401,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X0),aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X37: dB,X38: dB,X36: dB] :
( beta(X36,X38)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X36),X37),aa(dB,dB,aa(dB,fun1(dB,dB),app,X38),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_appL) ).
tff(f1151,plain,
( spl25_101
| ~ spl25_87
| ~ spl25_100 ),
inference(avatar_split_clause,[],[f1146,f1142,f1010,f1149]) ).
tff(f1149,plain,
( spl25_101
<=> ! [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,[spl25_101])]) ).
tff(f1142,plain,
( spl25_100
<=> ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_100])]) ).
tff(f1146,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) )
| ~ spl25_87
| ~ spl25_100 ),
inference(forward_demodulation,[],[f1145,f1011]) ).
tff(f1145,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))
| ~ beta(X2,X1) )
| ~ spl25_87
| ~ spl25_100 ),
inference(forward_demodulation,[],[f1143,f1011]) ).
tff(f1143,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) )
| ~ spl25_100 ),
inference(avatar_component_clause,[],[f1142]) ).
tff(f1144,plain,
spl25_100,
inference(avatar_split_clause,[],[f400,f1142]) ).
tff(f400,plain,
! [X2: dB,X0: dB,X1: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: dB,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X2),aa(dB,dB,aa(dB,fun1(dB,dB),app,X0),X1)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X37: dB,X38: dB,X36: dB] :
( beta(X36,X38)
=> beta(aa(dB,dB,aa(dB,fun1(dB,dB),app,X37),X36),aa(dB,dB,aa(dB,fun1(dB,dB),app,X37),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_appR) ).
tff(f1140,plain,
( spl25_99
| ~ spl25_87
| ~ spl25_98 ),
inference(avatar_split_clause,[],[f1136,f1132,f1010,f1138]) ).
tff(f1138,plain,
( spl25_99
<=> ! [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,[spl25_99])]) ).
tff(f1132,plain,
( spl25_98
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_98])]) ).
tff(f1136,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) )
| ~ spl25_87
| ~ spl25_98 ),
inference(forward_demodulation,[],[f1135,f1011]) ).
tff(f1135,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(dB,dB,combc(dB,nat,dB,lift,X0),X1))
| ~ beta(X2,X1) )
| ~ spl25_87
| ~ spl25_98 ),
inference(forward_demodulation,[],[f1133,f1011]) ).
tff(f1133,plain,
( ! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) )
| ~ spl25_98 ),
inference(avatar_component_clause,[],[f1132]) ).
tff(f1134,plain,
spl25_98,
inference(avatar_split_clause,[],[f399,f1132]) ).
tff(f399,plain,
! [X2: dB,X0: nat,X1: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X2),X0),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X49: nat,X36: dB,X26: dB] :
( beta(X26,X36)
=> beta(aa(nat,dB,aa(dB,fun1(nat,dB),lift,X26),X49),aa(nat,dB,aa(dB,fun1(nat,dB),lift,X36),X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_lift__preserves__beta) ).
tff(f1118,plain,
spl25_97,
inference(avatar_split_clause,[],[f433,f1116]) ).
tff(f1116,plain,
( spl25_97
<=> ! [X1: $tType,X0: $tType,X3: fun1(X1,X0),X2: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_97])]) ).
tff(f433,plain,
! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f235,f301]) ).
tff(f301,plain,
! [X1: $tType,X0: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f235,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: $tType,X2: fun1(X1,X0),X3: fun1(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,X68: fun1(X0,X1),X64: fun1(X0,X1)] :
( ! [X69: X0] : ( aa(X0,X1,X64,X69) = aa(X0,X1,X68,X69) )
=> ( X64 = X68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1114,plain,
( spl25_96
| ~ spl25_95 ),
inference(avatar_split_clause,[],[f1110,f1107,f1112]) ).
tff(f1112,plain,
( spl25_96
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,abs(sK8(X0)),cons(dB,sK9(X0),sK10(X0))) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_96])]) ).
tff(f1107,plain,
( spl25_95
<=> ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_95])]) ).
tff(f1110,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,abs(sK8(X0)),cons(dB,sK9(X0),sK10(X0))) = X0 )
| ~ sP0(X0) )
| ~ spl25_95 ),
inference(forward_demodulation,[],[f1108,f464]) ).
tff(f1108,plain,
( ! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) )
| ~ spl25_95 ),
inference(avatar_component_clause,[],[f1107]) ).
tff(f1109,plain,
spl25_95,
inference(avatar_split_clause,[],[f362,f1107]) ).
tff(f362,plain,
! [X0: dB] :
( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f1088,plain,
( spl25_94
| ~ spl25_87
| ~ spl25_93 ),
inference(avatar_split_clause,[],[f1083,f1079,f1010,f1085]) ).
tff(f1085,plain,
( spl25_94
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),t),foldl(dB,dB,app,var(n),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_94])]) ).
tff(f1079,plain,
( spl25_93
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),foldl(dB,dB,app,var(n),rs)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_93])]) ).
tff(f1083,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),t),foldl(dB,dB,app,var(n),rs)))
| ~ spl25_87
| ~ spl25_93 ),
inference(forward_demodulation,[],[f1081,f1011]) ).
tff(f1081,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),foldl(dB,dB,app,var(n),rs)),t))
| ~ spl25_93 ),
inference(avatar_component_clause,[],[f1079]) ).
tff(f1082,plain,
spl25_93,
inference(avatar_split_clause,[],[f476,f1079]) ).
tff(f476,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),foldl(dB,dB,app,var(n),rs)),t)),
inference(definition_unfolding,[],[f334,f323]) ).
tff(f334,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t)),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),foldl(dB,dB,app,var(n),rs)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_nT) ).
tff(f1077,plain,
spl25_92,
inference(avatar_split_clause,[],[f462,f1075]) ).
tff(f1075,plain,
( spl25_92
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun1(X1,fun1(list(X1),X0)),X3: X1,X2: list(X1)] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_92])]) ).
tff(f462,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun1(X1,fun1(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType,X1: $tType,X59: list(X1),X60: X1,X72: fun1(X1,fun1(list(X1),X0)),X73: X0] : ( list_case(X0,X1,X73,X72,cons(X1,X60,X59)) = aa(list(X1),X0,aa(X1,fun1(list(X1),X0),X72,X60),X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_list_Osimps_I5_J) ).
tff(f1069,plain,
( spl25_91
| ~ spl25_87
| ~ spl25_90 ),
inference(avatar_split_clause,[],[f1065,f1062,f1010,f1067]) ).
tff(f1067,plain,
( spl25_91
<=> ! [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,[spl25_91])]) ).
tff(f1062,plain,
( spl25_90
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_90])]) ).
tff(f1065,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)) )
| ~ spl25_87
| ~ spl25_90 ),
inference(forward_demodulation,[],[f1063,f1011]) ).
tff(f1063,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl25_90 ),
inference(avatar_component_clause,[],[f1062]) ).
tff(f1064,plain,
spl25_90,
inference(avatar_split_clause,[],[f383,f1062]) ).
tff(f383,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0))))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),var(X0)))) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X49: nat,X38: dB] :
( pp(aa(dB,bool,it,X38))
=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun1(dB,dB),app,X38),var(X49)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_app__Var__IT) ).
tff(f1058,plain,
( spl25_89
| ~ spl25_87
| ~ spl25_88 ),
inference(avatar_split_clause,[],[f1053,f1049,f1010,f1055]) ).
tff(f1055,plain,
( spl25_89
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(n),rs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_89])]) ).
tff(f1049,plain,
( spl25_88
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_88])]) ).
tff(f1053,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,ea,ia,t1)),t_a),foldl(dB,dB,app,var(n),rs)))
| ~ spl25_87
| ~ spl25_88 ),
inference(forward_demodulation,[],[f1051,f1011]) ).
tff(f1051,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a))
| ~ spl25_88 ),
inference(avatar_component_clause,[],[f1049]) ).
tff(f1052,plain,
spl25_88,
inference(avatar_split_clause,[],[f333,f1049]) ).
tff(f333,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
inference(cnf_transformation,[],[f70]) ).
tff(f70,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,ea,ia,t1)),foldl(dB,dB,app,var(n),rs)),t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Var_I2_J) ).
tff(f1012,plain,
spl25_87,
inference(avatar_split_clause,[],[f461,f1010]) ).
tff(f1008,plain,
spl25_86,
inference(avatar_split_clause,[],[f451,f1006]) ).
tff(f451,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun1(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType,X1: $tType,X63: list(X1),X5: X1,X64: fun1(X1,X0)] : ( map(X1,X0,X64,cons(X1,X5,X63)) = cons(X0,aa(X1,X0,X64,X5),map(X1,X0,X64,X63)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_map_Osimps_I2_J) ).
tff(f1000,plain,
( spl25_85
| ~ spl25_84 ),
inference(avatar_split_clause,[],[f996,f993,f998]) ).
tff(f993,plain,
( spl25_84
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_84])]) ).
tff(f996,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)) )
| ~ spl25_84 ),
inference(forward_demodulation,[],[f994,f461]) ).
tff(f994,plain,
( ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) )
| ~ spl25_84 ),
inference(avatar_component_clause,[],[f993]) ).
tff(f995,plain,
spl25_84,
inference(avatar_split_clause,[],[f382,f993]) ).
tff(f382,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X1),X0))) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X49: nat,X38: dB] :
( pp(aa(dB,bool,it,X38))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun1(nat,dB),lift,X38),X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_lift__IT) ).
tff(f991,plain,
( spl25_83
| ~ spl25_81 ),
inference(avatar_split_clause,[],[f982,f979,f989]) ).
tff(f989,plain,
( spl25_83
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_83])]) ).
tff(f979,plain,
( spl25_81
<=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_81])]) ).
tff(f982,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),combc(dB,dB,fun1(nat,dB),subst,X0),var(X1)),X1) = X0 )
| ~ spl25_81 ),
inference(forward_demodulation,[],[f980,f461]) ).
tff(f980,plain,
( ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 )
| ~ spl25_81 ),
inference(avatar_component_clause,[],[f979]) ).
tff(f987,plain,
( spl25_82
| ~ spl25_8
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f683,f673,f562,f984]) ).
tff(f984,plain,
( spl25_82
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_82])]) ).
tff(f683,plain,
( sP1(abs(ua))
| ~ spl25_8
| ~ spl25_29 ),
inference(resolution,[],[f674,f564]) ).
tff(f981,plain,
spl25_81,
inference(avatar_split_clause,[],[f373,f979]) ).
tff(f373,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X37: dB,X35: nat] : ( aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,var(X35)),X37),X35) = X37 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_subst__eq) ).
tff(f977,plain,
spl25_80,
inference(avatar_split_clause,[],[f357,f975]) ).
tff(f975,plain,
( spl25_80
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_80])]) ).
tff(f357,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,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,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) )
| ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f267,f269,f268]) ).
tff(f268,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f269,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f267,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,[],[f266]) ).
tff(f266,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,[],[f265]) ).
tff(f265,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,[],[f256]) ).
tff(f256,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(f971,plain,
( spl25_79
| ~ spl25_78 ),
inference(avatar_split_clause,[],[f967,f964,f969]) ).
tff(f964,plain,
( spl25_78
<=> ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_78])]) ).
tff(f967,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(X2),X0),var(X1)))
| ( aa(nat,type,X2,X1) = X0 ) )
| ~ spl25_78 ),
inference(forward_demodulation,[],[f965,f461]) ).
tff(f965,plain,
( ! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) )
| ~ spl25_78 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f966,plain,
spl25_78,
inference(avatar_split_clause,[],[f414,f964]) ).
tff(f414,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
| ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
=> ( aa(nat,type,X2,X1) = X0 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X4: type,X7: nat,X8: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X8),var(X7)),X4))
=> ( aa(nat,type,X8,X7) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_typing__elims_I1_J) ).
tff(f958,plain,
spl25_77,
inference(avatar_split_clause,[],[f419,f956]) ).
tff(f956,plain,
( spl25_77
<=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_77])]) ).
tff(f419,plain,
! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X3)),X2) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X40: list(dB),X55: nat,X17: dB,X39: dB] : ( foldl(dB,dB,app,var(X55),X40) != aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X39)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Abs__App__neq__Var__apps) ).
tff(f954,plain,
spl25_76,
inference(avatar_split_clause,[],[f355,f952]) ).
tff(f952,plain,
( spl25_76
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_76])]) ).
tff(f355,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f949,plain,
( spl25_75
| ~ spl25_9
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f682,f673,f567,f946]) ).
tff(f946,plain,
( spl25_75
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_75])]) ).
tff(f682,plain,
( sP1(abs(u))
| ~ spl25_9
| ~ spl25_29 ),
inference(resolution,[],[f674,f569]) ).
tff(f943,plain,
spl25_74,
inference(avatar_split_clause,[],[f440,f941]) ).
tff(f941,plain,
( spl25_74
<=> ! [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,[spl25_74])]) ).
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,[],[f307]) ).
tff(f307,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,[],[f306]) ).
tff(f306,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,[],[f179]) ).
tff(f179,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,[],[f53]) ).
tff(f53,axiom,
! [X40: list(dB),X55: nat,X54: list(dB),X56: nat] :
( ( foldl(dB,dB,app,var(X56),X54) = foldl(dB,dB,app,var(X55),X40) )
<=> ( ( X40 = X54 )
& ( X55 = X56 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Var__apps__eq__Var__apps__conv) ).
tff(f939,plain,
spl25_73,
inference(avatar_split_clause,[],[f437,f937]) ).
tff(f937,plain,
( spl25_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,[spl25_73])]) ).
tff(f437,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,[],[f305]) ).
tff(f305,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,[],[f304]) ).
tff(f304,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,[],[f178]) ).
tff(f178,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,[],[f52]) ).
tff(f52,axiom,
! [X40: list(dB),X39: dB,X54: list(dB),X41: dB] :
( ( foldl(dB,dB,app,abs(X41),X54) = foldl(dB,dB,app,abs(X39),X40) )
<=> ( ( X40 = X54 )
& ( X39 = X41 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Abs__apps__eq__Abs__apps__conv) ).
tff(f932,plain,
spl25_72,
inference(avatar_split_clause,[],[f511,f929]) ).
tff(f929,plain,
( spl25_72
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_72])]) ).
tff(f511,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),t1)),
inference(forward_demodulation,[],[f478,f332]) ).
tff(f332,plain,
aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)) = t1,
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)) = t1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_T) ).
tff(f478,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
inference(definition_unfolding,[],[f337,f323]) ).
tff(f337,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),var(n)),aa(type,type,aa(type,fun1(type,type),fun,t2),foldr(type,type,fun,ts,t)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_varT) ).
tff(f924,plain,
( spl25_71
| ~ spl25_69 ),
inference(avatar_split_clause,[],[f915,f912,f922]) ).
tff(f912,plain,
( spl25_69
<=> ! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_69])]) ).
tff(f915,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(dB,bool,combc(dB,type,bool,typing(X2),aa(nat,type,X2,X1)),var(X1)))
| ~ spl25_69 ),
inference(forward_demodulation,[],[f913,f461]) ).
tff(f913,plain,
( ! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1)))
| ~ spl25_69 ),
inference(avatar_component_clause,[],[f912]) ).
tff(f920,plain,
( spl25_70
| ~ spl25_7
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f681,f673,f557,f917]) ).
tff(f917,plain,
( spl25_70
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_70])]) ).
tff(f681,plain,
( sP1(abs(t3))
| ~ spl25_7
| ~ spl25_29 ),
inference(resolution,[],[f674,f559]) ).
tff(f914,plain,
spl25_69,
inference(avatar_split_clause,[],[f496,f912]) ).
tff(f496,plain,
! [X2: fun1(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),aa(nat,type,X2,X1))),
inference(equality_resolution,[],[f403]) ).
tff(f403,plain,
! [X2: fun1(nat,type),X0: type,X1: nat] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0))
| ( aa(nat,type,X2,X1) != X0 ) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: type,X1: nat,X2: fun1(nat,type)] :
( ( aa(nat,type,X2,X1) = X0 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X2),var(X1)),X0)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X4: type,X5: nat,X6: fun1(nat,type)] :
( ( aa(nat,type,X6,X5) = X4 )
=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(X6),var(X5)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_typing_OVar) ).
tff(f910,plain,
spl25_68,
inference(avatar_split_clause,[],[f439,f908]) ).
tff(f908,plain,
( spl25_68
<=> ! [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,[spl25_68])]) ).
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,[],[f307]) ).
tff(f906,plain,
spl25_67,
inference(avatar_split_clause,[],[f436,f904]) ).
tff(f904,plain,
( spl25_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,[spl25_67])]) ).
tff(f436,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,[],[f305]) ).
tff(f902,plain,
spl25_66,
inference(avatar_split_clause,[],[f353,f900]) ).
tff(f900,plain,
( spl25_66
<=> ! [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,[spl25_66])]) ).
tff(f353,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,[],[f206]) ).
tff(f206,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,[],[f122]) ).
tff(f122,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,[],[f93]) ).
tff(f93,axiom,
! [X43: list(dB)] :
( listsp(dB,it,X43)
=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_lifts__IT) ).
tff(f898,plain,
spl25_65,
inference(avatar_split_clause,[],[f332,f895]) ).
tff(f891,plain,
( spl25_64
| ~ spl25_63 ),
inference(avatar_split_clause,[],[f886,f882,f888]) ).
tff(f888,plain,
( spl25_64
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),sK3),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_64])]) ).
tff(f882,plain,
( spl25_63
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_63])]) ).
tff(f886,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),sK3),a))
| ~ spl25_63 ),
inference(forward_demodulation,[],[f884,f461]) ).
tff(f884,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),sK3))
| ~ spl25_63 ),
inference(avatar_component_clause,[],[f882]) ).
tff(f885,plain,
spl25_63,
inference(avatar_split_clause,[],[f485,f882]) ).
tff(f485,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),sK3)),
inference(definition_unfolding,[],[f345,f323]) ).
tff(f345,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),sK3)),
inference(cnf_transformation,[],[f261]) ).
tff(f878,plain,
( spl25_62
| ~ spl25_60 ),
inference(avatar_split_clause,[],[f869,f865,f875]) ).
tff(f875,plain,
( spl25_62
<=> pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),t2),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_62])]) ).
tff(f865,plain,
( spl25_60
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_60])]) ).
tff(f869,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,n,t1)),t2),a))
| ~ spl25_60 ),
inference(forward_demodulation,[],[f867,f461]) ).
tff(f867,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),t2))
| ~ spl25_60 ),
inference(avatar_component_clause,[],[f865]) ).
tff(f873,plain,
( spl25_61
| ~ spl25_14
| ~ spl25_18 ),
inference(avatar_split_clause,[],[f645,f617,f595,f871]) ).
tff(f871,plain,
( spl25_61
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_61])]) ).
tff(f645,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl25_14
| ~ spl25_18 ),
inference(resolution,[],[f618,f596]) ).
tff(f868,plain,
spl25_60,
inference(avatar_split_clause,[],[f475,f865]) ).
tff(f475,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,n,t1)),a),t2)),
inference(definition_unfolding,[],[f331,f323]) ).
tff(f331,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),t2)),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,i,t1)),a),t2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_argT) ).
tff(f854,plain,
spl25_59,
inference(avatar_split_clause,[],[f416,f852]) ).
tff(f852,plain,
( spl25_59
<=> ! [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,[spl25_59])]) ).
tff(f416,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,[],[f292]) ).
tff(f292,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,[],[f164]) ).
tff(f164,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X39: dB,X43: list(dB),X41: dB] :
( ( foldl(dB,dB,app,X41,X43) = foldl(dB,dB,app,X39,X43) )
<=> ( X39 = X41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_apps__eq__tail__conv) ).
tff(f850,plain,
spl25_58,
inference(avatar_split_clause,[],[f398,f848]) ).
tff(f848,plain,
( spl25_58
<=> ! [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,[spl25_58])]) ).
tff(f398,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,[],[f213]) ).
tff(f213,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,[],[f152]) ).
tff(f152,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,[],[f97]) ).
tff(f97,axiom,
! [X40: list(dB),X39: dB,X41: dB] :
( beta(X41,X39)
=> beta(foldl(dB,dB,app,X41,X40),foldl(dB,dB,app,X39,X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_apps__preserves__beta) ).
tff(f846,plain,
spl25_57,
inference(avatar_split_clause,[],[f381,f844]) ).
tff(f381,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,[],[f210]) ).
tff(f210,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,[],[f137]) ).
tff(f137,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X55: nat,X54: list(dB)] :
( listsp(dB,it,X54)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X55),X54))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_IT_OVar) ).
tff(f838,plain,
( spl25_56
| ~ spl25_55 ),
inference(avatar_split_clause,[],[f834,f831,f836]) ).
tff(f836,plain,
( spl25_56
<=> ! [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,[spl25_56])]) ).
tff(f831,plain,
( spl25_55
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_55])]) ).
tff(f834,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl25_55 ),
inference(forward_demodulation,[],[f832,f461]) ).
tff(f832,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl25_55 ),
inference(avatar_component_clause,[],[f831]) ).
tff(f833,plain,
spl25_55,
inference(avatar_split_clause,[],[f375,f831]) ).
tff(f375,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X82: bool,X80: bool] :
( pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X80),X82))
| ~ pp(X82)
| ~ pp(X80) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f829,plain,
spl25_54,
inference(avatar_split_clause,[],[f358,f827]) ).
tff(f358,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f811,plain,
spl25_53,
inference(avatar_split_clause,[],[f418,f809]) ).
tff(f809,plain,
( spl25_53
<=> ! [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,[spl25_53])]) ).
tff(f418,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,[],[f165]) ).
tff(f165,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,[],[f60]) ).
tff(f60,axiom,
! [X40: list(dB),X41: dB,X43: list(dB),X55: nat] : ( foldl(dB,dB,app,var(X55),X43) != foldl(dB,dB,app,abs(X41),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Var__apps__neq__Abs__apps) ).
tff(f807,plain,
spl25_52,
inference(avatar_split_clause,[],[f397,f805]) ).
tff(f397,plain,
! [X0: $tType,X2: fun1(X0,bool),X1: X0] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: X0,X2: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X2))
| ~ pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: $tType,X62: X0,X80: fun1(X0,bool)] :
( pp(aa(fun1(X0,bool),bool,fEx(X0),X80))
| ~ pp(aa(X0,bool,X80,X62)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
tff(f800,plain,
spl25_51,
inference(avatar_split_clause,[],[f459,f798]) ).
tff(f459,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
inference(flattening,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X57: list(X0),X58: X0,X59: list(X0),X60: X0] :
( ( cons(X0,X60,X59) = cons(X0,X58,X57) )
<=> ( ( X57 = X59 )
& ( X58 = X60 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_list_Oinject) ).
tff(f796,plain,
spl25_50,
inference(avatar_split_clause,[],[f392,f794]) ).
tff(f392,plain,
! [X2: nat,X0: dB,X1: dB] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: dB,X1: dB,X2: nat] : ( aa(dB,dB,aa(dB,fun1(dB,dB),app,X1),X0) != var(X2) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X45: dB,X46: dB,X21: nat] : ( var(X21) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X46),X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_dB_Osimps_I4_J) ).
tff(f792,plain,
spl25_49,
inference(avatar_split_clause,[],[f390,f790]) ).
tff(f390,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X2),X1) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X20: dB,X47: dB,X48: dB] : ( abs(X20) != aa(dB,dB,aa(dB,fun1(dB,dB),app,X48),X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_dB_Osimps_I8_J) ).
tff(f787,plain,
( spl25_48
| ~ spl25_47 ),
inference(avatar_split_clause,[],[f783,f780,f785]) ).
tff(f785,plain,
( spl25_48
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_48])]) ).
tff(f780,plain,
( spl25_47
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_47])]) ).
tff(f783,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl25_47 ),
inference(forward_demodulation,[],[f781,f461]) ).
tff(f781,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) )
| ~ spl25_47 ),
inference(avatar_component_clause,[],[f780]) ).
tff(f782,plain,
spl25_47,
inference(avatar_split_clause,[],[f377,f780]) ).
tff(f377,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X82: bool,X80: bool] :
( pp(X80)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X80),X82)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f777,plain,
( spl25_46
| ~ spl25_45 ),
inference(avatar_split_clause,[],[f773,f770,f775]) ).
tff(f775,plain,
( spl25_46
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_46])]) ).
tff(f770,plain,
( spl25_45
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_45])]) ).
tff(f773,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl25_45 ),
inference(forward_demodulation,[],[f771,f461]) ).
tff(f771,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) )
| ~ spl25_45 ),
inference(avatar_component_clause,[],[f770]) ).
tff(f772,plain,
spl25_45,
inference(avatar_split_clause,[],[f376,f770]) ).
tff(f376,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X82: bool,X80: bool] :
( pp(X82)
| ~ pp(aa(bool,bool,aa(bool,fun1(bool,bool),fconj,X80),X82)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f768,plain,
spl25_44,
inference(avatar_split_clause,[],[f356,f766]) ).
tff(f766,plain,
( spl25_44
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_44])]) ).
tff(f356,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f756,plain,
spl25_43,
inference(avatar_split_clause,[],[f487,f753]) ).
tff(f753,plain,
( spl25_43
<=> pp(aa(list(type),bool,typings(shift(type,e,n,t1),as),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_43])]) ).
tff(f487,plain,
pp(aa(list(type),bool,typings(shift(type,e,n,t1),as),sK4)),
inference(definition_unfolding,[],[f347,f323]) ).
tff(f347,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),sK4)),
inference(cnf_transformation,[],[f263]) ).
tff(f751,plain,
spl25_42,
inference(avatar_split_clause,[],[f474,f748]) ).
tff(f474,plain,
pp(aa(list(type),bool,typings(shift(type,e,n,t1),as),ts)),
inference(definition_unfolding,[],[f330,f323]) ).
tff(f330,plain,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
pp(aa(list(type),bool,typings(shift(type,e,i,t1),as),ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_argsT) ).
tff(f746,plain,
spl25_41,
inference(avatar_split_clause,[],[f458,f744]) ).
tff(f458,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f742,plain,
spl25_40,
inference(avatar_split_clause,[],[f354,f740]) ).
tff(f354,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X26: dB] :
( pp(aa(dB,bool,it,X26))
=> pp(aa(dB,bool,it,abs(X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Lambda) ).
tff(f737,plain,
( spl25_39
| ~ spl25_37 ),
inference(avatar_split_clause,[],[f727,f723,f734]) ).
tff(f723,plain,
( spl25_37
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_37])]) ).
tff(f727,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(e),t1),u))
| ~ spl25_37 ),
inference(forward_demodulation,[],[f725,f461]) ).
tff(f725,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t1))
| ~ spl25_37 ),
inference(avatar_component_clause,[],[f723]) ).
tff(f732,plain,
( spl25_38
| ~ spl25_8
| ~ spl25_18 ),
inference(avatar_split_clause,[],[f648,f617,f562,f729]) ).
tff(f729,plain,
( spl25_38
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_38])]) ).
tff(f648,plain,
( sP1(ua)
| ~ spl25_8
| ~ spl25_18 ),
inference(resolution,[],[f618,f564]) ).
tff(f726,plain,
spl25_37,
inference(avatar_split_clause,[],[f329,f723]) ).
tff(f329,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t1)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_uT) ).
tff(f720,plain,
( spl25_36
| ~ spl25_35 ),
inference(avatar_split_clause,[],[f715,f711,f717]) ).
tff(f711,plain,
( spl25_35
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_35])]) ).
tff(f715,plain,
( pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t1),ua))
| ~ spl25_35 ),
inference(forward_demodulation,[],[f713,f461]) ).
tff(f713,plain,
( pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t1))
| ~ spl25_35 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f714,plain,
spl25_35,
inference(avatar_split_clause,[],[f328,f711]) ).
tff(f328,plain,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t1)),
inference(cnf_transformation,[],[f72]) ).
tff(f72,axiom,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Var_I4_J) ).
tff(f709,plain,
spl25_34,
inference(avatar_split_clause,[],[f492,f707]) ).
tff(f707,plain,
( spl25_34
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_34])]) ).
tff(f492,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f359]) ).
tff(f359,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,[],[f270]) ).
tff(f704,plain,
spl25_33,
inference(avatar_split_clause,[],[f506,f702]) ).
tff(f506,plain,
! [X0: $tType,X2: fun1(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1 ),
inference(equality_resolution,[],[f452]) ).
tff(f452,plain,
! [X0: $tType,X2: fun1(nat,X0),X3: nat,X1: X0,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: X0,X2: fun1(nat,X0),X3: nat,X4: nat] :
( ( X3 = X4 )
=> ( aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType,X4: X0,X8: fun1(nat,X0),X15: nat,X7: nat] :
( ( X7 = X15 )
=> ( aa(nat,X0,shift(X0,X8,X7,X4),X15) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_shift__eq) ).
tff(f700,plain,
spl25_32,
inference(avatar_split_clause,[],[f406,f698]) ).
tff(f698,plain,
( spl25_32
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK12(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_32])]) ).
tff(f406,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK12(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f283]) ).
tff(f696,plain,
( spl25_31
| ~ spl25_9
| ~ spl25_18 ),
inference(avatar_split_clause,[],[f647,f617,f567,f693]) ).
tff(f693,plain,
( spl25_31
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_31])]) ).
tff(f647,plain,
( sP1(u)
| ~ spl25_9
| ~ spl25_18 ),
inference(resolution,[],[f618,f569]) ).
tff(f689,plain,
spl25_30,
inference(avatar_split_clause,[],[f379,f687]) ).
tff(f379,plain,
! [X0: dB,X1: dB] :
( ( abs(sK11(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: dB,X1: dB] :
( ( beta(X1,sK11(X0,X1))
& ( abs(sK11(X0,X1)) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f209,f276]) ).
tff(f276,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
=> ( beta(X1,sK11(X0,X1))
& ( abs(sK11(X0,X1)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f209,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),X0)
=> ~ ! [X2: dB] :
( ( abs(X2) = X0 )
=> ~ beta(X1,X2) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X36: dB,X26: dB] :
( beta(abs(X26),X36)
=> ~ ! [X71: dB] :
( ( abs(X71) = X36 )
=> ~ beta(X26,X71) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_beta__cases_I2_J) ).
tff(f675,plain,
spl25_29,
inference(avatar_split_clause,[],[f491,f673]) ).
tff(f491,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f360]) ).
tff(f360,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f270]) ).
tff(f671,plain,
spl25_28,
inference(avatar_split_clause,[],[f380,f669]) ).
tff(f380,plain,
! [X0: dB,X1: dB] :
( beta(X1,sK11(X0,X1))
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f667,plain,
spl25_27,
inference(avatar_split_clause,[],[f372,f665]) ).
tff(f665,plain,
( spl25_27
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_27])]) ).
tff(f372,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X67: list(X0)] : ( map(X0,X0,combi(X0),X67) = X67 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_map__ident) ).
tff(f663,plain,
spl25_26,
inference(avatar_split_clause,[],[f364,f661]) ).
tff(f364,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f659,plain,
( spl25_25
| ~ spl25_7
| ~ spl25_18 ),
inference(avatar_split_clause,[],[f646,f617,f557,f656]) ).
tff(f656,plain,
( spl25_25
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_25])]) ).
tff(f646,plain,
( sP1(t3)
| ~ spl25_7
| ~ spl25_18 ),
inference(resolution,[],[f618,f559]) ).
tff(f644,plain,
spl25_24,
inference(avatar_split_clause,[],[f386,f642]) ).
tff(f642,plain,
( spl25_24
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_24])]) ).
tff(f386,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X13: nat,X14: nat] :
( ( var(X14) = var(X13) )
<=> ( X13 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_dB_Osimps_I1_J) ).
tff(f640,plain,
spl25_23,
inference(avatar_split_clause,[],[f384,f638]) ).
tff(f638,plain,
( spl25_23
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_23])]) ).
tff(f384,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X18: dB,X19: dB] :
( ( abs(X19) = abs(X18) )
<=> ( X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I3_J) ).
tff(f636,plain,
spl25_22,
inference(avatar_split_clause,[],[f378,f634]) ).
tff(f378,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: dB,X1: dB] :
( beta(X1,X0)
=> beta(abs(X1),abs(X0)) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X38: dB,X36: dB] :
( beta(X36,X38)
=> beta(abs(X36),abs(X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_abs) ).
tff(f632,plain,
spl25_21,
inference(avatar_split_clause,[],[f371,f630]) ).
tff(f371,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X80: X0] : ( aa(X0,X0,combi(X0),X80) = X80 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f628,plain,
( ~ spl25_20
| ~ spl25_12
| ~ spl25_15 ),
inference(avatar_split_clause,[],[f603,f599,f586,f625]) ).
tff(f625,plain,
( spl25_20
<=> ( as = rs ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_20])]) ).
tff(f603,plain,
( ( as != rs )
| ~ spl25_12
| ~ spl25_15 ),
inference(superposition,[],[f600,f588]) ).
tff(f623,plain,
spl25_19,
inference(avatar_split_clause,[],[f367,f621]) ).
tff(f367,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f124,f256,f255]) ).
tff(f124,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,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X1),X2),zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(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,[],[f98]) ).
tff(f98,axiom,
! [X60: dB] :
( pp(aa(dB,bool,it,X60))
<=> ( ? [X76: dB,X77: dB,X78: list(dB)] :
( pp(aa(dB,bool,it,X77))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun1(nat,dB),aa(dB,fun1(dB,fun1(nat,dB)),subst,X76),X77),zero_zero(nat)),X78)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun1(dB,dB),app,abs(X76)),X77),X78) = X60 ) )
| ? [X76: dB] :
( pp(aa(dB,bool,it,X76))
& ( abs(X76) = X60 ) )
| ? [X74: list(dB),X75: nat] :
( listsp(dB,it,X74)
& ( foldl(dB,dB,app,var(X75),X74) = X60 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_IT_Osimps) ).
tff(f619,plain,
spl25_18,
inference(avatar_split_clause,[],[f366,f617]) ).
tff(f366,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f614,plain,
( ~ spl25_17
| spl25_16 ),
inference(avatar_split_clause,[],[f609,f605,f611]) ).
tff(f605,plain,
( spl25_16
<=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_16])]) ).
tff(f609,plain,
( ~ pp(aa(dB,bool,combc(dB,type,bool,typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),foldr(type,type,fun,ts,t)),var(zero_zero(nat))))
| spl25_16 ),
inference(forward_demodulation,[],[f607,f461]) ).
tff(f607,plain,
( ~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t)))
| spl25_16 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f608,plain,
~ spl25_16,
inference(avatar_split_clause,[],[f318,f605]) ).
tff(f318,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(flattening,[],[f114]) ).
tff(f114,negated_conjecture,
~ pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
inference(negated_conjecture,[],[f113]) ).
tff(f113,conjecture,
pp(aa(type,bool,aa(dB,fun1(type,bool),typing(shift(type,e,zero_zero(nat),foldr(type,type,fun,ts,t))),var(zero_zero(nat))),foldr(type,type,fun,ts,t))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f601,plain,
spl25_15,
inference(avatar_split_clause,[],[f388,f599]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType,X61: list(X0),X62: X0] : ( cons(X0,X62,X61) != X61 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not__Cons__self2) ).
tff(f597,plain,
spl25_14,
inference(avatar_split_clause,[],[f349,f595]) ).
tff(f349,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X22: nat] : pp(aa(dB,bool,it,var(X22))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Var__IT) ).
tff(f593,plain,
( spl25_13
| spl25_1
| ~ spl25_11 ),
inference(avatar_split_clause,[],[f580,f576,f530,f591]) ).
tff(f591,plain,
( spl25_13
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_13])]) ).
tff(f530,plain,
( spl25_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).
tff(f580,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl25_1
| ~ spl25_11 ),
inference(superposition,[],[f532,f577]) ).
tff(f532,plain,
( ~ pp(fFalse)
| spl25_1 ),
inference(avatar_component_clause,[],[f530]) ).
tff(f589,plain,
spl25_12,
inference(avatar_split_clause,[],[f327,f586]) ).
tff(f327,plain,
rs = cons(dB,a,as),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
rs = cons(dB,a,as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Cons) ).
tff(f578,plain,
spl25_11,
inference(avatar_split_clause,[],[f350,f576]) ).
tff(f350,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X80: bool] :
( ( fFalse = X80 )
| ( fTrue = X80 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f574,plain,
spl25_10,
inference(avatar_split_clause,[],[f348,f572]) ).
tff(f572,plain,
( spl25_10
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_10])]) ).
tff(f348,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X21: nat] : ( zero_zero(nat) = dB_size(var(X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dB_Osize_I1_J) ).
tff(f570,plain,
spl25_9,
inference(avatar_split_clause,[],[f326,f567]) ).
tff(f326,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_uIT) ).
tff(f565,plain,
spl25_8,
inference(avatar_split_clause,[],[f325,f562]) ).
tff(f325,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Var_I3_J) ).
tff(f560,plain,
spl25_7,
inference(avatar_split_clause,[],[f324,f557]) ).
tff(f324,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
tff(f555,plain,
spl25_6,
inference(avatar_split_clause,[],[f369,f553]) ).
tff(f553,plain,
( spl25_6
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_6])]) ).
tff(f369,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X20: dB,X21: nat] : ( var(X21) != abs(X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dB_Osimps_I6_J) ).
tff(f551,plain,
spl25_5,
inference(avatar_split_clause,[],[f368,f549]) ).
tff(f368,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X38: dB,X49: nat] : ~ beta(var(X49),X38),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_beta__cases_I1_J) ).
tff(f547,plain,
spl25_4,
inference(avatar_split_clause,[],[f361,f545]) ).
tff(f545,plain,
( spl25_4
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_4])]) ).
tff(f361,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f543,plain,
spl25_3,
inference(avatar_split_clause,[],[f322,f540]) ).
tff(f540,plain,
( spl25_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
tff(f322,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f538,plain,
spl25_2,
inference(avatar_split_clause,[],[f321,f535]) ).
tff(f535,plain,
( spl25_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).
tff(f321,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f533,plain,
~ spl25_1,
inference(avatar_split_clause,[],[f319,f530]) ).
tff(f319,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : LCL813_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Fri May 3 13:45:09 EDT 2024
% 0.09/0.27 % CPUTime :
% 0.12/0.27 % (7874)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.29 % (7886)WARNING: value z3 for option sas not known
% 0.12/0.29 % (7885)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.29 % (7887)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.29 % (7886)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.29 % (7890)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.29 % (7888)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.29 % (7889)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.29 % (7884)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.29 % Exception at run slice level
% 0.12/0.29 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.29 % (7890)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.29 % Exception at run slice level
% 0.12/0.29 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.29 % Exception at run slice level
% 0.12/0.29 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.30 % (7904)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.30 % (7905)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.12/0.30 % (7906)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.12/0.30 % (7904)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.30 % Exception at run slice level
% 0.12/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.31 % (7905)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.31 % (7910)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.12/0.41 % (7888)First to succeed.
% 0.12/0.44 % (7888)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7874"
% 0.12/0.44 % (7888)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (7888)------------------------------
% 0.12/0.45 % (7888)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.45 % (7888)Termination reason: Refutation
% 0.12/0.45
% 0.12/0.45 % (7888)Memory used [KB]: 2598
% 0.12/0.45 % (7888)Time elapsed: 0.151 s
% 0.12/0.45 % (7888)Instructions burned: 286 (million)
% 0.12/0.45 % (7874)Success in time 0.166 s
%------------------------------------------------------------------------------