TSTP Solution File: COM081_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM081_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 : n005.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 04:48:19 EDT 2024
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 331
% Syntax : Number of formulae : 802 ( 233 unt; 88 typ; 0 def)
% Number of atoms : 1800 ( 830 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1649 ( 563 ~; 548 |; 223 &)
% ( 172 <=>; 141 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 135 ( 68 >; 67 *; 0 +; 0 <<)
% Number of predicates : 140 ( 138 usr; 132 prp; 0-5 aty)
% Number of functors : 77 ( 77 usr; 7 con; 0-6 aty)
% Number of variables : 2116 (1888 !; 135 ?;2116 :)
% ( 93 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
fm: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
atom: $tType ).
tff(type_def_11,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_12,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(X1,fun(X0,X2)) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,X0)) ).
tff(func_def_4,type,
n_lists:
!>[X0: $tType] : ( ( nat * list(X0) ) > list(list(X0)) ) ).
tff(func_def_5,type,
product:
!>[X0: $tType,X1: $tType] : ( ( list(X0) * list(X1) ) > list(product_prod(X0,X1)) ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_8,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * list(X0) * list(X1) ) > list(X2) ) ).
tff(func_def_9,type,
concat:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
tff(func_def_10,type,
dropWhile:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_11,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) ) > fun(list(X1),X0) ) ).
tff(func_def_15,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_17,type,
map:
!>[X0: $tType,X1: $tType] : fun(fun(X0,X1),fun(list(X0),list(X1))) ).
tff(func_def_18,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_19,type,
remdups:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_20,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_21,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_22,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_23,type,
transpose:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
tff(func_def_24,type,
transpose_rel:
!>[X0: $tType] : fun(list(list(X0)),fun(list(list(X0)),bool)) ).
tff(func_def_25,type,
list_conj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_26,type,
list_disj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_27,type,
suc: nat > nat ).
tff(func_def_28,type,
i_Z: fun(atom,fun(list(int),bool)) ).
tff(func_def_29,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_30,type,
divisor: atom > int ).
tff(func_def_31,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_32,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
tff(func_def_33,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_34,type,
fFalse: bool ).
tff(func_def_35,type,
fTrue: bool ).
tff(func_def_36,type,
as: list(atom) ).
tff(func_def_37,type,
xs: list(int) ).
tff(func_def_38,type,
sK0: int > atom ).
tff(func_def_39,type,
sK1: int ).
tff(func_def_40,type,
sK2: int ).
tff(func_def_41,type,
sK3:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK4:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_43,type,
sK5:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_44,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_45,type,
sK7:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_46,type,
sK8:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
tff(func_def_47,type,
sK9:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
tff(func_def_48,type,
sK10: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_49,type,
sK11: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_50,type,
sK12:
!>[X0: $tType] : ( list(list(X0)) > list(X0) ) ).
tff(func_def_51,type,
sK13:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_52,type,
sK14:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_53,type,
sK15:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_54,type,
sK16:
!>[X0: $tType] : ( ( fun(X0,X0) * list(X0) ) > X0 ) ).
tff(func_def_55,type,
sK17:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_56,type,
sK18:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_57,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_58,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > list(X1) ) ).
tff(func_def_59,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > X0 ) ).
tff(func_def_60,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_61,type,
sK23:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * list(X0) ) > X0 ) ).
tff(func_def_62,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_63,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X1) * fun(X1,X0) ) > X1 ) ).
tff(func_def_64,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_65,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_66,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_67,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_68,type,
sK30:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_69,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_70,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_71,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_72,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
interpret:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(list(X1),bool)) * fm(X0) * list(X1) ) > $o ) ).
tff(pred_def_5,type,
accp:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * X0 ) > $o ) ).
tff(pred_def_6,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_7,type,
pp: bool > $o ).
tff(f1596,plain,
$false,
inference(avatar_sat_refutation,[],[f540,f545,f550,f555,f560,f565,f569,f573,f577,f582,f586,f590,f594,f598,f602,f606,f610,f614,f619,f623,f627,f631,f635,f639,f643,f647,f651,f663,f667,f671,f675,f680,f686,f690,f698,f702,f706,f710,f714,f721,f725,f730,f734,f741,f745,f749,f753,f757,f761,f765,f769,f773,f777,f781,f806,f810,f820,f824,f831,f835,f839,f843,f847,f851,f855,f880,f884,f888,f898,f910,f914,f918,f922,f926,f942,f946,f961,f976,f980,f985,f989,f1006,f1024,f1028,f1033,f1037,f1041,f1078,f1082,f1086,f1114,f1118,f1130,f1141,f1145,f1156,f1176,f1188,f1192,f1217,f1230,f1254,f1260,f1277,f1293,f1312,f1320,f1327,f1353,f1357,f1361,f1365,f1384,f1402,f1406,f1410,f1414,f1454,f1476,f1483,f1498,f1502,f1506,f1541,f1560,f1564,f1572,f1581,f1585,f1589,f1593]) ).
tff(f1593,plain,
( ~ spl35_1
| spl35_125 ),
inference(avatar_contradiction_clause,[],[f1590]) ).
tff(f1590,plain,
( $false
| ~ spl35_1
| spl35_125 ),
inference(resolution,[],[f1540,f539]) ).
tff(f539,plain,
( ! [X0: int] : member(atom,sK0(X0),set(atom,as))
| ~ spl35_1 ),
inference(avatar_component_clause,[],[f538]) ).
tff(f538,plain,
( spl35_1
<=> ! [X0: int] : member(atom,sK0(X0),set(atom,as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_1])]) ).
tff(f1540,plain,
( ~ member(atom,sK0(sK2),set(atom,as))
| spl35_125 ),
inference(avatar_component_clause,[],[f1538]) ).
tff(f1538,plain,
( spl35_125
<=> member(atom,sK0(sK2),set(atom,as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_125])]) ).
tff(f1589,plain,
spl35_131,
inference(avatar_split_clause,[],[f501,f1587]) ).
tff(f1587,plain,
( spl35_131
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK32(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_131])]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK32(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) )
| ! [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK32(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK31(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK31(X0,X1,X2,X3,X4,X5)),sK32(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f343,f344]) ).
tff(f344,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
=> ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK32(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK31(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK31(X0,X1,X2,X3,X4,X5)),sK32(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f343,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) )
| ! [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
inference(rectify,[],[f342]) ).
tff(f342,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) )
| ! [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
inference(nnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) )
<=> ? [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X1: $tType,X35: list(X1),X34: fun(X1,X0),X10: list(X0),X11: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X35) )
<=> ? [X47: X1,X48: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X48) = X10 )
& ( aa(X1,X0,X34,X47) = X11 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X47),X48) = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Cons__eq__map__conv) ).
tff(f1585,plain,
spl35_130,
inference(avatar_split_clause,[],[f498,f1583]) ).
tff(f1583,plain,
( spl35_130
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK30(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_130])]) ).
tff(f498,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK30(X0,X1,X2,X3,X4,X5)) = X2 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ),
inference(cnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK30(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK29(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK29(X0,X1,X2,X3,X4,X5)),sK30(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f262,f340]) ).
tff(f340,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
=> ( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK30(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK29(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK29(X0,X1,X2,X3,X4,X5)),sK30(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f262,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) )
=> ? [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X1: $tType,X0: $tType,X35: list(X0),X12: X0,X10: list(X1),X34: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X10) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X12),X35) )
=> ? [X49: X1,X50: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X50) = X35 )
& ( aa(X1,X0,X34,X49) = X12 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X49),X50) = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_map__eq__Cons__D) ).
tff(f1581,plain,
spl35_129,
inference(avatar_split_clause,[],[f495,f1579]) ).
tff(f1579,plain,
( spl35_129
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK28(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_129])]) ).
tff(f495,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK28(X0,X1,X2,X3,X4,X5)) = X4 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(cnf_transformation,[],[f339]) ).
tff(f339,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK28(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK27(X0,X1,X2,X3,X4,X5)),sK28(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f261,f338]) ).
tff(f338,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
=> ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),sK28(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK27(X0,X1,X2,X3,X4,X5)),sK28(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f261,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) )
=> ? [X6: X1,X7: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X1: $tType,X35: list(X1),X34: fun(X1,X0),X10: list(X0),X11: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X35) )
=> ? [X49: X1,X50: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X50) = X10 )
& ( aa(X1,X0,X34,X49) = X11 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X49),X50) = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Cons__eq__map__D) ).
tff(f1572,plain,
spl35_128,
inference(avatar_split_clause,[],[f457,f1570]) ).
tff(f1570,plain,
( spl35_128
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(list(X1))] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),concat(X1,X2)) = concat(X0,aa(list(list(X1)),list(list(X0)),aa(fun(list(X1),list(X0)),fun(list(list(X1)),list(list(X0))),map(list(X1),list(X0)),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_128])]) ).
tff(f457,plain,
! [X1: $tType,X0: $tType,X2: list(list(X1)),X3: fun(X1,X0)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),concat(X1,X2)) = concat(X0,aa(list(list(X1)),list(list(X0)),aa(fun(list(X1),list(X0)),fun(list(list(X1)),list(list(X0))),map(list(X1),list(X0)),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3)),X2)) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: $tType,X2: list(list(X1)),X3: fun(X1,X0)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),concat(X1,X2)) = concat(X0,aa(list(list(X1)),list(list(X0)),aa(fun(list(X1),list(X0)),fun(list(list(X1)),list(list(X0))),map(list(X1),list(X0)),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3)),X2)) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X1: $tType,X10: list(list(X1)),X34: fun(X1,X0)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),concat(X1,X10)) = concat(X0,aa(list(list(X1)),list(list(X0)),aa(fun(list(X1),list(X0)),fun(list(list(X1)),list(list(X0))),map(list(X1),list(X0)),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_map__concat) ).
tff(f1564,plain,
spl35_127,
inference(avatar_split_clause,[],[f439,f1562]) ).
tff(f1562,plain,
( spl35_127
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] :
( ( zipwith0(X0,X2,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),nil(X2)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2))),zipwith0(X0,X2,X1,X5,X3,nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_127])]) ).
tff(f439,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] :
( ( zipwith0(X0,X2,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),nil(X2)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2))),zipwith0(X0,X2,X1,X5,X3,nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),nil(X2)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2))),zipwith0(X0,X2,X1,X5,X3,nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f240]) ).
tff(f240,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),nil(X2)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2))),zipwith0(X0,X2,X1,X5,X3,nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),nil(X2)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2))),zipwith0(X0,X2,X1,X5,X3,nil(X2))) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X10: list(X1),X11: X1,X34: fun(X1,fun(X2,X0))] : ( zipwith0(X1,X2,X0,X34,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X11),X10),nil(X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X2,X0,aa(X1,fun(X2,X0),X34,X11),zero_zero(X2))),zipwith0(X1,X2,X0,X34,X10,nil(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I3_J) ).
tff(f1560,plain,
spl35_126,
inference(avatar_split_clause,[],[f438,f1558]) ).
tff(f1558,plain,
( spl35_126
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] :
( ( zipwith0(X0,X2,X1,X5,nil(X0),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X3)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4)),zipwith0(X0,X2,X1,X5,nil(X0),X3)) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_126])]) ).
tff(f438,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] :
( ( zipwith0(X0,X2,X1,X5,nil(X0),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X3)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4)),zipwith0(X0,X2,X1,X5,nil(X0),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,nil(X0),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X3)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4)),zipwith0(X0,X2,X1,X5,nil(X0),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,nil(X0),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X3)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4)),zipwith0(X0,X2,X1,X5,nil(X0),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X5,nil(X0),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X3)) = aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4)),zipwith0(X0,X2,X1,X5,nil(X0),X3)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X35: list(X2),X12: X2,X34: fun(X1,fun(X2,X0))] : ( zipwith0(X1,X2,X0,X34,nil(X1),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X12),X35)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X2,X0,aa(X1,fun(X2,X0),X34,zero_zero(X1)),X12)),zipwith0(X1,X2,X0,X34,nil(X1),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
tff(f1541,plain,
( ~ spl35_125
| ~ spl35_11
| ~ spl35_120 ),
inference(avatar_split_clause,[],[f1477,f1474,f584,f1538]) ).
tff(f584,plain,
( spl35_11
<=> ! [X0: int] : ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0(X0)),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_11])]) ).
tff(f1474,plain,
( spl35_120
<=> ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK2),xs)))
| ~ member(atom,X1,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_120])]) ).
tff(f1477,plain,
( ~ member(atom,sK0(sK2),set(atom,as))
| ~ spl35_11
| ~ spl35_120 ),
inference(resolution,[],[f1475,f585]) ).
tff(f585,plain,
( ! [X0: int] : ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0(X0)),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
| ~ spl35_11 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f1475,plain,
( ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK2),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ~ spl35_120 ),
inference(avatar_component_clause,[],[f1474]) ).
tff(f1506,plain,
spl35_124,
inference(avatar_split_clause,[],[f524,f1504]) ).
tff(f1504,plain,
( spl35_124
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X5: list(X1),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X5) )
| ( aa(X1,X0,X2,sK26(X0,X1,X2,X3,X5)) != aa(X1,X0,X3,sK26(X0,X1,X2,X3,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_124])]) ).
tff(f524,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X5) )
| ( aa(X1,X0,X2,sK26(X0,X1,X2,X3,X5)) != aa(X1,X0,X3,sK26(X0,X1,X2,X3,X5)) ) ),
inference(equality_resolution,[],[f492]) ).
tff(f492,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) )
| ( aa(X1,X0,X2,sK26(X0,X1,X2,X3,X4)) != aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4)) )
| ( X4 != X5 ) ),
inference(cnf_transformation,[],[f337]) ).
tff(f337,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) )
| ( ( aa(X1,X0,X2,sK26(X0,X1,X2,X3,X4)) != aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4)) )
& member(X1,sK26(X0,X1,X2,X3,X4),set(X1,X4)) )
| ( X4 != X5 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f260,f336]) ).
tff(f336,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ? [X6: X1] :
( ( aa(X1,X0,X2,X6) != aa(X1,X0,X3,X6) )
& member(X1,X6,set(X1,X4)) )
=> ( ( aa(X1,X0,X2,sK26(X0,X1,X2,X3,X4)) != aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4)) )
& member(X1,sK26(X0,X1,X2,X3,X4),set(X1,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f260,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) )
| ? [X6: X1] :
( ( aa(X1,X0,X2,X6) != aa(X1,X0,X3,X6) )
& member(X1,X6,set(X1,X4)) )
| ( X4 != X5 ) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) )
| ? [X6: X1] :
( ( aa(X1,X0,X2,X6) != aa(X1,X0,X3,X6) )
& member(X1,X6,set(X1,X4)) )
| ( X4 != X5 ) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( X4 = X5 )
=> ( ! [X6: X1] :
( member(X1,X6,set(X1,X4))
=> ( aa(X1,X0,X2,X6) = aa(X1,X0,X3,X6) ) )
=> ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) ) ) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X1: $tType,X0: $tType,X41: fun(X0,X1),X34: fun(X0,X1),X35: list(X0),X10: list(X0)] :
( ( X10 = X35 )
=> ( ! [X4: X0] :
( member(X0,X4,set(X0,X35))
=> ( aa(X0,X1,X34,X4) = aa(X0,X1,X41,X4) ) )
=> ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X34),X10) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X41),X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_map__cong) ).
tff(f1502,plain,
spl35_123,
inference(avatar_split_clause,[],[f486,f1500]) ).
tff(f1500,plain,
( spl35_123
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: list(X1),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| ( aa(X1,X0,X2,sK25(X0,X1,X2,X3,X4)) != aa(X1,X0,X4,sK25(X0,X1,X2,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_123])]) ).
tff(f486,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| ( aa(X1,X0,X2,sK25(X0,X1,X2,X3,X4)) != aa(X1,X0,X4,sK25(X0,X1,X2,X3,X4)) ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| ( ( aa(X1,X0,X2,sK25(X0,X1,X2,X3,X4)) != aa(X1,X0,X4,sK25(X0,X1,X2,X3,X4)) )
& member(X1,sK25(X0,X1,X2,X3,X4),set(X1,X3)) ) )
& ( ! [X6: X1] :
( ( aa(X1,X0,X2,X6) = aa(X1,X0,X4,X6) )
| ~ member(X1,X6,set(X1,X3)) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f333,f334]) ).
tff(f334,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ? [X5: X1] :
( ( aa(X1,X0,X2,X5) != aa(X1,X0,X4,X5) )
& member(X1,X5,set(X1,X3)) )
=> ( ( aa(X1,X0,X2,sK25(X0,X1,X2,X3,X4)) != aa(X1,X0,X4,sK25(X0,X1,X2,X3,X4)) )
& member(X1,sK25(X0,X1,X2,X3,X4),set(X1,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f333,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| ? [X5: X1] :
( ( aa(X1,X0,X2,X5) != aa(X1,X0,X4,X5) )
& member(X1,X5,set(X1,X3)) ) )
& ( ! [X6: X1] :
( ( aa(X1,X0,X2,X6) = aa(X1,X0,X4,X6) )
| ~ member(X1,X6,set(X1,X3)) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) ) ) ),
inference(rectify,[],[f332]) ).
tff(f332,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| ? [X5: X1] :
( ( aa(X1,X0,X2,X5) != aa(X1,X0,X4,X5) )
& member(X1,X5,set(X1,X3)) ) )
& ( ! [X5: X1] :
( ( aa(X1,X0,X2,X5) = aa(X1,X0,X4,X5) )
| ~ member(X1,X5,set(X1,X3)) )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) ) ) ),
inference(nnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
<=> ! [X5: X1] :
( ( aa(X1,X0,X2,X5) = aa(X1,X0,X4,X5) )
| ~ member(X1,X5,set(X1,X3)) ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
<=> ! [X5: X1] :
( member(X1,X5,set(X1,X3))
=> ( aa(X1,X0,X2,X5) = aa(X1,X0,X4,X5) ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType,X1: $tType,X41: fun(X1,X0),X10: list(X1),X34: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X10) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X41),X10) )
<=> ! [X32: X1] :
( member(X1,X32,set(X1,X10))
=> ( aa(X1,X0,X34,X32) = aa(X1,X0,X41,X32) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_map__eq__conv) ).
tff(f1498,plain,
spl35_122,
inference(avatar_split_clause,[],[f480,f1496]) ).
tff(f1496,plain,
( spl35_122
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X4: list(X1),X3: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| ( aa(X1,X0,X3,sK24(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_122])]) ).
tff(f480,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| ( aa(X1,X0,X3,sK24(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3,X4)) ) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| ( ( aa(X1,X0,X3,sK24(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3,X4)) )
& member(X1,sK24(X0,X1,X2,X3,X4),set(X1,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f257,f328]) ).
tff(f328,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ? [X5: X1] :
( ( aa(X1,X0,X3,X5) != aa(X1,X0,X2,X5) )
& member(X1,X5,set(X1,X4)) )
=> ( ( aa(X1,X0,X3,sK24(X0,X1,X2,X3,X4)) != aa(X1,X0,X2,sK24(X0,X1,X2,X3,X4)) )
& member(X1,sK24(X0,X1,X2,X3,X4),set(X1,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f257,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| ? [X5: X1] :
( ( aa(X1,X0,X3,X5) != aa(X1,X0,X2,X5) )
& member(X1,X5,set(X1,X4)) ) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ! [X5: X1] :
( member(X1,X5,set(X1,X4))
=> ( aa(X1,X0,X3,X5) = aa(X1,X0,X2,X5) ) )
=> ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X1: $tType,X0: $tType,X41: fun(X0,X1),X34: fun(X0,X1),X10: list(X0)] :
( ! [X4: X0] :
( member(X0,X4,set(X0,X10))
=> ( aa(X0,X1,X34,X4) = aa(X0,X1,X41,X4) ) )
=> ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X34),X10) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X41),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_map__ext) ).
tff(f1483,plain,
spl35_121,
inference(avatar_split_clause,[],[f484,f1481]) ).
tff(f1481,plain,
( spl35_121
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0),X6: X1] :
( ( aa(X1,X0,X2,X6) = aa(X1,X0,X4,X6) )
| ~ member(X1,X6,set(X1,X3))
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_121])]) ).
tff(f484,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X6: X1,X4: fun(X1,X0)] :
( ( aa(X1,X0,X2,X6) = aa(X1,X0,X4,X6) )
| ~ member(X1,X6,set(X1,X3))
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f1476,plain,
( ~ spl35_106
| spl35_120 ),
inference(avatar_split_clause,[],[f359,f1474,f1306]) ).
tff(f1306,plain,
( spl35_106
<=> ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_106])]) ).
tff(f359,plain,
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK2),xs)))
| ~ member(atom,X1,set(atom,as))
| ( lbounds(as) != nil(product_prod(int,list(int))) ) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
( ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK2),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ( lbounds(as) != nil(product_prod(int,list(int))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f214,f267]) ).
tff(f267,plain,
( ? [X0: int] :
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
| ~ member(atom,X1,set(atom,as)) )
=> ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK2),xs)))
| ~ member(atom,X1,set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
( ? [X0: int] :
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ( lbounds(as) != nil(product_prod(int,list(int))) ) ),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
( ( lbounds(as) = nil(product_prod(int,list(int))) )
=> ? [X0: int] :
! [X1: atom] :
( member(atom,X1,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs))) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
( ( lbounds(as) = nil(product_prod(int,list(int))) )
=> ? [X4: int] :
! [X5: atom] :
( member(atom,X5,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X5),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X4),xs))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096lbounds_Aas_A_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
tff(f1454,plain,
( ~ spl35_1
| spl35_115 ),
inference(avatar_contradiction_clause,[],[f1451]) ).
tff(f1451,plain,
( $false
| ~ spl35_1
| spl35_115 ),
inference(resolution,[],[f1383,f539]) ).
tff(f1383,plain,
( ~ member(atom,sK0(sK1),set(atom,as))
| spl35_115 ),
inference(avatar_component_clause,[],[f1381]) ).
tff(f1381,plain,
( spl35_115
<=> member(atom,sK0(sK1),set(atom,as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_115])]) ).
tff(f1414,plain,
spl35_119,
inference(avatar_split_clause,[],[f534,f1412]) ).
tff(f1412,plain,
( spl35_119
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X1)),sK14(X0,X1))))
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_119])]) ).
tff(f534,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X1)),sK14(X0,X1))))
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f433,f384]) ).
tff(f384,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X14: X0] : ( insert(X0,X14,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X14),nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_insert__Nil) ).
tff(f433,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X1)),sK14(X0,X1))))
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK15(X0,X1)),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( pp(aa(list(X0),bool,X1,X2))
| ( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X1)),sK14(X0,X1))))
& pp(aa(list(X0),bool,X1,sK14(X0,X1)))
& ( nil(X0) != sK14(X0,X1) ) )
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK15(X0,X1)),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f301,f303,f302]) ).
tff(f302,plain,
! [X0: $tType,X1: fun(list(X0),bool)] :
( ? [X3: X0,X4: list(X0)] :
( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4)))
& pp(aa(list(X0),bool,X1,X4))
& ( nil(X0) != X4 ) )
=> ( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X1)),sK14(X0,X1))))
& pp(aa(list(X0),bool,X1,sK14(X0,X1)))
& ( nil(X0) != sK14(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f303,plain,
! [X0: $tType,X1: fun(list(X0),bool)] :
( ? [X5: X0] : ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),nil(X0))))
=> ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK15(X0,X1)),nil(X0)))) ),
introduced(choice_axiom,[]) ).
tff(f301,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( pp(aa(list(X0),bool,X1,X2))
| ? [X3: X0,X4: list(X0)] :
( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4)))
& pp(aa(list(X0),bool,X1,X4))
& ( nil(X0) != X4 ) )
| ? [X5: X0] : ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(rectify,[],[f231]) ).
tff(f231,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( pp(aa(list(X0),bool,X1,X2))
| ? [X4: X0,X5: list(X0)] :
( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5)))
& pp(aa(list(X0),bool,X1,X5))
& ( nil(X0) != X5 ) )
| ? [X3: X0] : ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(flattening,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( pp(aa(list(X0),bool,X1,X2))
| ? [X4: X0,X5: list(X0)] :
( ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5)))
& pp(aa(list(X0),bool,X1,X5))
& ( nil(X0) != X5 ) )
| ? [X3: X0] : ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( ( nil(X0) != X2 )
=> ( ! [X3: X0] : pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))
=> ( ! [X4: X0,X5: list(X0)] :
( ( nil(X0) != X5 )
=> ( pp(aa(list(X0),bool,X1,X5))
=> pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5))) ) )
=> pp(aa(list(X0),bool,X1,X2)) ) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X27: fun(list(X0),bool),X10: list(X0)] :
( ( nil(X0) != X10 )
=> ( ! [X4: X0] : pp(aa(list(X0),bool,X27,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),nil(X0))))
=> ( ! [X4: X0,X29: list(X0)] :
( ( nil(X0) != X29 )
=> ( pp(aa(list(X0),bool,X27,X29))
=> pp(aa(list(X0),bool,X27,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X29))) ) )
=> pp(aa(list(X0),bool,X27,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_list__nonempty__induct) ).
tff(f1410,plain,
spl35_118,
inference(avatar_split_clause,[],[f525,f1408]) ).
tff(f1408,plain,
( spl35_118
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X5: list(X1),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X5) )
| member(X1,sK26(X0,X1,X2,X3,X5),set(X1,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_118])]) ).
tff(f525,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X5) )
| member(X1,sK26(X0,X1,X2,X3,X5),set(X1,X5)) ),
inference(equality_resolution,[],[f491]) ).
tff(f491,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1),X5: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X5) )
| member(X1,sK26(X0,X1,X2,X3,X4),set(X1,X4))
| ( X4 != X5 ) ),
inference(cnf_transformation,[],[f337]) ).
tff(f1406,plain,
spl35_117,
inference(avatar_split_clause,[],[f485,f1404]) ).
tff(f1404,plain,
( spl35_117
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: list(X1),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| member(X1,sK25(X0,X1,X2,X3,X4),set(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_117])]) ).
tff(f485,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X1),X4: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X4),X3) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X3) )
| member(X1,sK25(X0,X1,X2,X3,X4),set(X1,X3)) ),
inference(cnf_transformation,[],[f335]) ).
tff(f1402,plain,
spl35_116,
inference(avatar_split_clause,[],[f479,f1400]) ).
tff(f1400,plain,
( spl35_116
<=> ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X4: list(X1),X3: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| member(X1,sK24(X0,X1,X2,X3,X4),set(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_116])]) ).
tff(f479,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X4) )
| member(X1,sK24(X0,X1,X2,X3,X4),set(X1,X4)) ),
inference(cnf_transformation,[],[f329]) ).
tff(f1384,plain,
( ~ spl35_115
| ~ spl35_11
| ~ spl35_107 ),
inference(avatar_split_clause,[],[f1321,f1310,f584,f1381]) ).
tff(f1310,plain,
( spl35_107
<=> ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK1),xs)))
| ~ member(atom,X1,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_107])]) ).
tff(f1321,plain,
( ~ member(atom,sK0(sK1),set(atom,as))
| ~ spl35_11
| ~ spl35_107 ),
inference(resolution,[],[f1311,f585]) ).
tff(f1311,plain,
( ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK1),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ~ spl35_107 ),
inference(avatar_component_clause,[],[f1310]) ).
tff(f1365,plain,
spl35_114,
inference(avatar_split_clause,[],[f504,f1363]) ).
tff(f1363,plain,
( spl35_114
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK33(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_114])]) ).
tff(f504,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK33(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) )
| ! [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK34(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK33(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK33(X0,X1,X2,X3,X4,X5)),sK34(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f347,f348]) ).
tff(f348,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
=> ( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),sK34(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK33(X0,X1,X2,X3,X4,X5)) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK33(X0,X1,X2,X3,X4,X5)),sK34(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f347,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) )
| ! [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
inference(rectify,[],[f346]) ).
tff(f346,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) )
| ! [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X0: $tType,X35: list(X0),X12: X0,X10: list(X1),X34: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X10) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X12),X35) )
<=> ? [X47: X1,X48: list(X1)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X48) = X35 )
& ( aa(X1,X0,X34,X47) = X12 )
& ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X47),X48) = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_map__eq__Cons__conv) ).
tff(f1361,plain,
spl35_113,
inference(avatar_split_clause,[],[f500,f1359]) ).
tff(f1359,plain,
( spl35_113
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK31(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_113])]) ).
tff(f500,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK31(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(cnf_transformation,[],[f345]) ).
tff(f1357,plain,
spl35_112,
inference(avatar_split_clause,[],[f497,f1355]) ).
tff(f1355,plain,
( spl35_112
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK29(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_112])]) ).
tff(f497,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK29(X0,X1,X2,X3,X4,X5)) = X3 )
| ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X5),X4) ) ),
inference(cnf_transformation,[],[f341]) ).
tff(f1353,plain,
spl35_111,
inference(avatar_split_clause,[],[f494,f1351]) ).
tff(f1351,plain,
( spl35_111
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_111])]) ).
tff(f494,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X5 )
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) ) ),
inference(cnf_transformation,[],[f339]) ).
tff(f1327,plain,
spl35_110,
inference(avatar_split_clause,[],[f490,f1325]) ).
tff(f1325,plain,
( spl35_110
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0,X2: list(X1)] : ( list_rec(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_110])]) ).
tff(f490,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X1: $tType,X8: list(X1),X9: X1,X18: fun(X1,fun(list(X1),fun(X0,X0))),X19: X0] : ( list_rec(X0,X1,X19,X18,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X9),X8)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X18,X9),X8),list_rec(X0,X1,X19,X18,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list_Orecs_I2_J) ).
tff(f1320,plain,
( spl35_108
| ~ spl35_109
| ~ spl35_32
| ~ spl35_85 ),
inference(avatar_split_clause,[],[f1097,f1031,f678,f1317,f1314]) ).
tff(f1314,plain,
( spl35_108
<=> ! [X0: int] : ( aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as) = nil(atom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_108])]) ).
tff(f1317,plain,
( spl35_109
<=> ( remdups(atom,as) = nil(atom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_109])]) ).
tff(f678,plain,
( spl35_32
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_32])]) ).
tff(f1031,plain,
( spl35_85
<=> ! [X0: int] : ( remdups(atom,as) = remdups(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_85])]) ).
tff(f1097,plain,
( ! [X0: int] :
( ( remdups(atom,as) != nil(atom) )
| ( aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as) = nil(atom) ) )
| ~ spl35_32
| ~ spl35_85 ),
inference(superposition,[],[f679,f1032]) ).
tff(f1032,plain,
( ! [X0: int] : ( remdups(atom,as) = remdups(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) )
| ~ spl35_85 ),
inference(avatar_component_clause,[],[f1031]) ).
tff(f679,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != remdups(X0,X1) )
| ( nil(X0) = X1 ) )
| ~ spl35_32 ),
inference(avatar_component_clause,[],[f678]) ).
tff(f1312,plain,
( spl35_106
| spl35_107 ),
inference(avatar_split_clause,[],[f358,f1310,f1306]) ).
tff(f358,plain,
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK1),xs)))
| ~ member(atom,X1,set(atom,as))
| ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
( ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK1),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f213,f265]) ).
tff(f265,plain,
( ? [X0: int] :
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
| ~ member(atom,X1,set(atom,as)) )
=> ! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),sK1),xs)))
| ~ member(atom,X1,set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f213,plain,
( ? [X0: int] :
! [X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
| ~ member(atom,X1,set(atom,as)) )
| ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
( ( lbounds(as) != nil(product_prod(int,list(int))) )
=> ? [X0: int] :
! [X1: atom] :
( member(atom,X1,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs))) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( ( lbounds(as) != nil(product_prod(int,list(int))) )
=> ? [X4: int] :
! [X5: atom] :
( member(atom,X5,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X5),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X4),xs))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096lbounds_Aas_A_126_061_A_091_093_A_061_061_062_AEX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
tff(f1293,plain,
spl35_105,
inference(avatar_split_clause,[],[f456,f1291]) ).
tff(f1291,plain,
( spl35_105
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(X1)] : ( remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),remdups(X1,X2))) = remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_105])]) ).
tff(f456,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0)] : ( remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),remdups(X1,X2))) = remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2)) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] : ( remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),remdups(X1,X2))) = remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2)) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType,X1: $tType,X10: list(X1),X34: fun(X1,X0)] : ( remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),remdups(X1,X10))) = remdups(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_remdups__map__remdups) ).
tff(f1277,plain,
spl35_104,
inference(avatar_split_clause,[],[f430,f1275]) ).
tff(f1275,plain,
( spl35_104
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),remdups(X0,X1)) )
| member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_104])]) ).
tff(f430,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),remdups(X0,X1)) )
| member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),remdups(X0,X1)) )
| member(X0,X2,set(X0,X1)) )
& ( ( remdups(X0,X1) = remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| ~ member(X0,X2,set(X0,X1)) ) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ~ member(X0,X2,set(X0,X1))
=> ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),remdups(X0,X1)) ) )
& ( member(X0,X2,set(X0,X1))
=> ( remdups(X0,X1) = remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) ) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType,X10: list(X0),X11: X0] :
( ( ~ member(X0,X11,set(X0,X10))
=> ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),remdups(X0,X10)) ) )
& ( member(X0,X11,set(X0,X10))
=> ( remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10)) = remdups(X0,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_remdups_Osimps_I2_J) ).
tff(f1260,plain,
spl35_103,
inference(avatar_split_clause,[],[f462,f1258]) ).
tff(f1258,plain,
( spl35_103
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_103])]) ).
tff(f462,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: fun(X0,bool)] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| pp(aa(X0,bool,X3,X2)) )
& ( ( dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = dropWhile(X0,X3,X1) )
| ~ pp(aa(X0,bool,X3,X2)) ) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: fun(X0,bool)] :
( ( ~ pp(aa(X0,bool,X3,X2))
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) ) )
& ( pp(aa(X0,bool,X3,X2))
=> ( dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = dropWhile(X0,X3,X1) ) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X10: list(X0),X11: X0,X27: fun(X0,bool)] :
( ( ~ pp(aa(X0,bool,X27,X11))
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10) = dropWhile(X0,X27,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10)) ) )
& ( pp(aa(X0,bool,X27,X11))
=> ( dropWhile(X0,X27,X10) = dropWhile(X0,X27,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dropWhile_Osimps_I2_J) ).
tff(f1254,plain,
spl35_102,
inference(avatar_split_clause,[],[f437,f1252]) ).
tff(f1252,plain,
( spl35_102
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X0,fun(X2,X1)),X3: list(X2)] :
( ( zipwith0(X0,X2,X1,X4,nil(X0),X3) = aa(list(X2),list(X1),aa(fun(X2,X1),fun(list(X2),list(X1)),map(X2,X1),aa(X0,fun(X2,X1),X4,zero_zero(X0))),X3) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_102])]) ).
tff(f437,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: fun(X0,fun(X2,X1))] :
( ( zipwith0(X0,X2,X1,X4,nil(X0),X3) = aa(list(X2),list(X1),aa(fun(X2,X1),fun(list(X2),list(X1)),map(X2,X1),aa(X0,fun(X2,X1),X4,zero_zero(X0))),X3) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X4,nil(X0),X3) = aa(list(X2),list(X1),aa(fun(X2,X1),fun(list(X2),list(X1)),map(X2,X1),aa(X0,fun(X2,X1),X4,zero_zero(X0))),X3) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X4,nil(X0),X3) = aa(list(X2),list(X1),aa(fun(X2,X1),fun(list(X2),list(X1)),map(X2,X1),aa(X0,fun(X2,X1),X4,zero_zero(X0))),X3) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X2),X4: fun(X0,fun(X2,X1))] : ( zipwith0(X0,X2,X1,X4,nil(X0),X3) = aa(list(X2),list(X1),aa(fun(X2,X1),fun(list(X2),list(X1)),map(X2,X1),aa(X0,fun(X2,X1),X4,zero_zero(X0))),X3) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X35: list(X2),X34: fun(X1,fun(X2,X0))] : ( zipwith0(X1,X2,X0,X34,nil(X1),X35) = aa(list(X2),list(X0),aa(fun(X2,X0),fun(list(X2),list(X0)),map(X2,X0),aa(X1,fun(X2,X0),X34,zero_zero(X1))),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zipwith0__Nil) ).
tff(f1230,plain,
spl35_101,
inference(avatar_split_clause,[],[f489,f1228]) ).
tff(f1228,plain,
( spl35_101
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( aa(list(X1),X0,list_case(X0,X1,X5,X4),aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_101])]) ).
tff(f489,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,list_case(X0,X1,X5,X4),aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( aa(list(X1),X0,list_case(X0,X1,X5,X4),aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X1: $tType,X8: list(X1),X9: X1,X18: fun(X1,fun(list(X1),X0)),X19: X0] : ( aa(list(X1),X0,list_case(X0,X1,X19,X18),aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X9),X8)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X18,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list_Osimps_I5_J) ).
tff(f1217,plain,
spl35_100,
inference(avatar_split_clause,[],[f482,f1215]) ).
tff(f1215,plain,
( spl35_100
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_100])]) ).
tff(f482,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(flattening,[],[f330]) ).
tff(f330,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType,X6: list(X0),X7: X0,X8: list(X0),X9: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X9),X8) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X7),X6) )
<=> ( ( X6 = X8 )
& ( X7 = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_list_Oinject) ).
tff(f1192,plain,
spl35_99,
inference(avatar_split_clause,[],[f481,f1190]) ).
tff(f1190,plain,
( spl35_99
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_99])]) ).
tff(f481,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f1188,plain,
spl35_98,
inference(avatar_split_clause,[],[f473,f1186]) ).
tff(f1186,plain,
( spl35_98
<=> ! [X1: $tType,X0: $tType,X6: X1,X3: list(X0),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 )
| ( aa(X1,X0,X2,X6) != sK21(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_98])]) ).
tff(f473,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0),X6: X1] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 )
| ( aa(X1,X0,X2,X6) != sK21(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 )
| ( ! [X6: X1] : ( aa(X1,X0,X2,X6) != sK21(X0,X1,X2,X3) )
& member(X0,sK21(X0,X1,X2,X3),set(X0,X3)) ) )
& ( ! [X7: X0] :
( ( aa(X1,X0,X2,sK22(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,set(X0,X3)) )
| ! [X9: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X9) != X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f319,f322,f321,f320]) ).
tff(f320,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = X3 )
=> ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
tff(f321,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,set(X0,X3)) )
=> ( ! [X6: X1] : ( aa(X1,X0,X2,X6) != sK21(X0,X1,X2,X3) )
& member(X0,sK21(X0,X1,X2,X3),set(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f322,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X7: X0] :
( ? [X8: X1] : ( aa(X1,X0,X2,X8) = X7 )
=> ( aa(X1,X0,X2,sK22(X0,X1,X2,X7)) = X7 ) ),
introduced(choice_axiom,[]) ).
tff(f319,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ? [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = X3 )
| ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,set(X0,X3)) ) )
& ( ! [X7: X0] :
( ? [X8: X1] : ( aa(X1,X0,X2,X8) = X7 )
| ~ member(X0,X7,set(X0,X3)) )
| ! [X9: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X9) != X3 ) ) ),
inference(rectify,[],[f318]) ).
tff(f318,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ? [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = X3 )
| ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,set(X0,X3)) ) )
& ( ! [X5: X0] :
( ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 )
| ~ member(X0,X5,set(X0,X3)) )
| ! [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) != X3 ) ) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = X3 )
<=> ! [X5: X0] :
( ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 )
| ~ member(X0,X5,set(X0,X3)) ) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X4) = X3 )
<=> ! [X5: X0] :
( member(X0,X5,set(X0,X3))
=> ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 ) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X1: $tType,X0: $tType,X34: fun(X0,X1),X35: list(X1)] :
( ? [X45: list(X0)] : ( aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X34),X45) = X35 )
<=> ! [X32: X1] :
( member(X1,X32,set(X1,X35))
=> ? [X46: X0] : ( aa(X0,X1,X34,X46) = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ex__map__conv) ).
tff(f1176,plain,
spl35_97,
inference(avatar_split_clause,[],[f472,f1174]) ).
tff(f1174,plain,
( spl35_97
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X2: fun(X1,X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 )
| member(X0,sK21(X0,X1,X2,X3),set(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_97])]) ).
tff(f472,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),sK20(X0,X1,X2,X3)) = X3 )
| member(X0,sK21(X0,X1,X2,X3),set(X0,X3)) ),
inference(cnf_transformation,[],[f323]) ).
tff(f1156,plain,
( spl35_96
| ~ spl35_31
| ~ spl35_85 ),
inference(avatar_split_clause,[],[f1100,f1031,f673,f1154]) ).
tff(f1154,plain,
( spl35_96
<=> ! [X0: int] : ( set(atom,as) = set(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_96])]) ).
tff(f673,plain,
( spl35_31
<=> ! [X0: $tType,X1: list(X0)] : ( set(X0,X1) = set(X0,remdups(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_31])]) ).
tff(f1100,plain,
( ! [X0: int] : ( set(atom,as) = set(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) )
| ~ spl35_31
| ~ spl35_85 ),
inference(forward_demodulation,[],[f1098,f674]) ).
tff(f674,plain,
( ! [X0: $tType,X1: list(X0)] : ( set(X0,X1) = set(X0,remdups(X0,X1)) )
| ~ spl35_31 ),
inference(avatar_component_clause,[],[f673]) ).
tff(f1098,plain,
( ! [X0: int] : ( set(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) = set(atom,remdups(atom,as)) )
| ~ spl35_31
| ~ spl35_85 ),
inference(superposition,[],[f674,f1032]) ).
tff(f1145,plain,
spl35_95,
inference(avatar_split_clause,[],[f518,f1143]) ).
tff(f1143,plain,
( spl35_95
<=> ! [X1: $tType,X0: $tType,X7: X0,X9: list(X1),X2: fun(X1,X0)] :
( ( aa(X1,X0,X2,sK22(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,set(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_95])]) ).
tff(f518,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X9: list(X1),X7: X0] :
( ( aa(X1,X0,X2,sK22(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,set(X0,aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X9))) ),
inference(equality_resolution,[],[f471]) ).
tff(f471,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0),X9: list(X1),X7: X0] :
( ( aa(X1,X0,X2,sK22(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,set(X0,X3))
| ( aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X2),X9) != X3 ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f1141,plain,
spl35_94,
inference(avatar_split_clause,[],[f442,f1139]) ).
tff(f1139,plain,
( spl35_94
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| ( sK16(X0,X1,X2) != aa(X0,X0,X1,sK16(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_94])]) ).
tff(f442,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| ( sK16(X0,X1,X2) != aa(X0,X0,X1,sK16(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| ( ( sK16(X0,X1,X2) != aa(X0,X0,X1,sK16(X0,X1,X2)) )
& member(X0,sK16(X0,X1,X2),set(X0,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f244,f305]) ).
tff(f305,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ? [X3: X0] :
( ( aa(X0,X0,X1,X3) != X3 )
& member(X0,X3,set(X0,X2)) )
=> ( ( sK16(X0,X1,X2) != aa(X0,X0,X1,sK16(X0,X1,X2)) )
& member(X0,sK16(X0,X1,X2),set(X0,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f244,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| ? [X3: X0] :
( ( aa(X0,X0,X1,X3) != X3 )
& member(X0,X3,set(X0,X2)) ) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ! [X3: X0] :
( member(X0,X3,set(X0,X2))
=> ( aa(X0,X0,X1,X3) = X3 ) )
=> ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType,X34: fun(X0,X0),X10: list(X0)] :
( ! [X4: X0] :
( member(X0,X4,set(X0,X10))
=> ( aa(X0,X0,X34,X4) = X4 ) )
=> ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X34),X10) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_map__idI) ).
tff(f1130,plain,
spl35_93,
inference(avatar_split_clause,[],[f535,f1128]) ).
tff(f1128,plain,
( spl35_93
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK14(X0,X1)))
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_93])]) ).
tff(f535,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK14(X0,X1)))
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f432,f384]) ).
tff(f432,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK14(X0,X1)))
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK15(X0,X1)),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f1118,plain,
spl35_92,
inference(avatar_split_clause,[],[f386,f1116]) ).
tff(f1116,plain,
( spl35_92
<=> ! [X0: $tType,X1: list(X0)] : ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_92])]) ).
tff(f386,plain,
! [X0: $tType,X1: list(X0)] : ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: list(X0)] : ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType,X15: list(X0)] : ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,zero_zero(nat),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_n__lists_Osimps_I1_J) ).
tff(f1114,plain,
spl35_91,
inference(avatar_split_clause,[],[f536,f1112]) ).
tff(f1112,plain,
( spl35_91
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK14(X0,X1) )
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_91])]) ).
tff(f536,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK15(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK14(X0,X1) )
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f431,f384]) ).
tff(f431,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK14(X0,X1) )
| ~ pp(aa(list(X0),bool,X1,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK15(X0,X1)),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f1086,plain,
spl35_90,
inference(avatar_split_clause,[],[f461,f1084]) ).
tff(f1084,plain,
( spl35_90
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: list(X0)] :
( ( dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = dropWhile(X0,X3,X1) )
| ~ pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_90])]) ).
tff(f461,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: list(X0)] :
( ( dropWhile(X0,X3,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) = dropWhile(X0,X3,X1) )
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f248]) ).
tff(f1082,plain,
spl35_89,
inference(avatar_split_clause,[],[f441,f1080]) ).
tff(f1080,plain,
( spl35_89
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| member(X0,sK16(X0,X1,X2),set(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_89])]) ).
tff(f441,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),X1),X2) = X2 )
| member(X0,sK16(X0,X1,X2),set(X0,X2)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1078,plain,
spl35_88,
inference(avatar_split_clause,[],[f385,f1076]) ).
tff(f1076,plain,
( spl35_88
<=> ! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),X1)) = transpose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_88])]) ).
tff(f385,plain,
! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),X1)) = transpose(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),X1)) = transpose(X0,X1) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType,X40: list(list(X0))] : ( transpose(X0,aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),X40)) = transpose(X0,X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_transpose_Osimps_I2_J) ).
tff(f1041,plain,
spl35_87,
inference(avatar_split_clause,[],[f520,f1039]) ).
tff(f1039,plain,
( spl35_87
<=> ! [X0: $tType,X2: fun(X0,bool),X4: list(X0),X1: fun(X0,bool)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_87])]) ).
tff(f520,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) ),
inference(equality_resolution,[],[f477]) ).
tff(f477,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4)))
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ( ( ~ pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| ~ pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) )
& ( pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) )
& member(X0,sK23(X0,X1,X2,X4),set(X0,X4)) )
| ( X3 != X4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f325,f326]) ).
tff(f326,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X4: list(X0)] :
( ? [X5: X0] :
( ( ~ pp(aa(X0,bool,X1,X5))
| ~ pp(aa(X0,bool,X2,X5)) )
& ( pp(aa(X0,bool,X1,X5))
| pp(aa(X0,bool,X2,X5)) )
& member(X0,X5,set(X0,X4)) )
=> ( ( ~ pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| ~ pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) )
& ( pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) )
& member(X0,sK23(X0,X1,X2,X4),set(X0,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f325,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ? [X5: X0] :
( ( ~ pp(aa(X0,bool,X1,X5))
| ~ pp(aa(X0,bool,X2,X5)) )
& ( pp(aa(X0,bool,X1,X5))
| pp(aa(X0,bool,X2,X5)) )
& member(X0,X5,set(X0,X4)) )
| ( X3 != X4 ) ),
inference(flattening,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ? [X5: X0] :
( ( ~ pp(aa(X0,bool,X1,X5))
| ~ pp(aa(X0,bool,X2,X5)) )
& ( pp(aa(X0,bool,X1,X5))
| pp(aa(X0,bool,X2,X5)) )
& member(X0,X5,set(X0,X4)) )
| ( X3 != X4 ) ),
inference(nnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ? [X5: X0] :
( ( pp(aa(X0,bool,X2,X5))
<~> pp(aa(X0,bool,X1,X5)) )
& member(X0,X5,set(X0,X4)) )
| ( X3 != X4 ) ),
inference(flattening,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ? [X5: X0] :
( ( pp(aa(X0,bool,X2,X5))
<~> pp(aa(X0,bool,X1,X5)) )
& member(X0,X5,set(X0,X4)) )
| ( X3 != X4 ) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0),X4: list(X0)] :
( ( X3 = X4 )
=> ( ! [X5: X0] :
( member(X0,X5,set(X0,X4))
=> ( pp(aa(X0,bool,X2,X5))
<=> pp(aa(X0,bool,X1,X5)) ) )
=> ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) ) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X42: fun(X0,bool),X27: fun(X0,bool),X43: list(X0),X44: list(X0)] :
( ( X43 = X44 )
=> ( ! [X4: X0] :
( member(X0,X4,set(X0,X44))
=> ( pp(aa(X0,bool,X27,X4))
<=> pp(aa(X0,bool,X42,X4)) ) )
=> ( dropWhile(X0,X27,X44) = dropWhile(X0,X42,X43) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dropWhile__cong) ).
tff(f1037,plain,
spl35_86,
inference(avatar_split_clause,[],[f519,f1035]) ).
tff(f1035,plain,
( spl35_86
<=> ! [X0: $tType,X2: fun(X0,bool),X4: list(X0),X1: fun(X0,bool)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| ~ pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| ~ pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_86])]) ).
tff(f519,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| ~ pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| ~ pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4))) ),
inference(equality_resolution,[],[f478]) ).
tff(f478,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| ~ pp(aa(X0,bool,X1,sK23(X0,X1,X2,X4)))
| ~ pp(aa(X0,bool,X2,sK23(X0,X1,X2,X4)))
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f1033,plain,
( spl35_85
| ~ spl35_1
| ~ spl35_82 ),
inference(avatar_split_clause,[],[f1017,f1004,f538,f1031]) ).
tff(f1004,plain,
( spl35_82
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( remdups(X0,X1) = remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| ~ member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_82])]) ).
tff(f1017,plain,
( ! [X0: int] : ( remdups(atom,as) = remdups(atom,aa(list(atom),list(atom),aa(atom,fun(list(atom),list(atom)),cons(atom),sK0(X0)),as)) )
| ~ spl35_1
| ~ spl35_82 ),
inference(resolution,[],[f1005,f539]) ).
tff(f1005,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] :
( ~ member(X0,X2,set(X0,X1))
| ( remdups(X0,X1) = remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) ) )
| ~ spl35_82 ),
inference(avatar_component_clause,[],[f1004]) ).
tff(f1028,plain,
spl35_84,
inference(avatar_split_clause,[],[f507,f1026]) ).
tff(f1026,plain,
( spl35_84
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,list(X1))] : ( nil(X1) = concat(X1,aa(list(X0),list(list(X1)),aa(fun(X0,list(X1)),fun(list(X0),list(list(X1))),map(X0,list(X1)),X2),nil(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_84])]) ).
tff(f507,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,list(X1))] : ( nil(X1) = concat(X1,aa(list(X0),list(list(X1)),aa(fun(X0,list(X1)),fun(list(X0),list(list(X1))),map(X0,list(X1)),X2),nil(X0))) ),
inference(definition_unfolding,[],[f415,f454]) ).
tff(f454,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,list(X0))] : ( maps(X1,X0,X3,X2) = concat(X0,aa(list(X1),list(list(X0)),aa(fun(X1,list(X0)),fun(list(X1),list(list(X0))),map(X1,list(X0)),X3),X2)) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,list(X0))] : ( maps(X1,X0,X3,X2) = concat(X0,aa(list(X1),list(list(X0)),aa(fun(X1,list(X0)),fun(list(X1),list(list(X0))),map(X1,list(X0)),X3),X2)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $tType,X1: $tType,X10: list(X1),X34: fun(X1,list(X0))] : ( maps(X1,X0,X34,X10) = concat(X0,aa(list(X1),list(list(X0)),aa(fun(X1,list(X0)),fun(list(X1),list(list(X0))),map(X1,list(X0)),X34),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_maps__def) ).
tff(f415,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,list(X1))] : ( nil(X1) = maps(X0,X1,X2,nil(X0)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,list(X1))] : ( nil(X1) = maps(X0,X1,X2,nil(X0)) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X1: $tType,X0: $tType,X34: fun(X1,list(X0))] : ( nil(X0) = maps(X1,X0,X34,nil(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_maps__simps_I2_J) ).
tff(f1024,plain,
spl35_83,
inference(avatar_split_clause,[],[f465,f1022]) ).
tff(f1022,plain,
( spl35_83
<=> ! [X0: $tType,X3: X0,X2: X0,X1: list(X0)] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_83])]) ).
tff(f465,plain,
! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1))) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1))) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1))) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)))
=> ( member(X0,X3,set(X0,X1))
| ( X2 = X3 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType,X10: list(X0),X11: X0,X12: X0] :
( member(X0,X12,set(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10)))
=> ( member(X0,X12,set(X0,X10))
| ( X11 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_set__ConsD) ).
tff(f1006,plain,
spl35_82,
inference(avatar_split_clause,[],[f429,f1004]) ).
tff(f429,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( remdups(X0,X1) = remdups(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1)) )
| ~ member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f989,plain,
spl35_81,
inference(avatar_split_clause,[],[f467,f987]) ).
tff(f987,plain,
( spl35_81
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(X1)] :
( ( nil(X1) = X2 )
| ( nil(X0) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_81])]) ).
tff(f467,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X1) = X2 )
| ( nil(X0) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) ) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( ( nil(X0) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) )
| ( nil(X1) != X2 ) )
& ( ( nil(X1) = X2 )
| ( nil(X0) != aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) ) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X0) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X3),X2) )
<=> ( nil(X1) = X2 ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X1: $tType,X10: list(X1),X34: fun(X1,X0)] :
( ( nil(X0) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),X10) )
<=> ( nil(X1) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Nil__is__map__conv) ).
tff(f985,plain,
spl35_80,
inference(avatar_split_clause,[],[f428,f983]) ).
tff(f983,plain,
( spl35_80
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) )
| member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_80])]) ).
tff(f428,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) )
| member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ( insert(X0,X2,X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) )
| member(X0,X2,set(X0,X1)) )
& ( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ~ member(X0,X2,set(X0,X1))
=> ( insert(X0,X2,X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) ) )
& ( member(X0,X2,set(X0,X1))
=> ( insert(X0,X2,X1) = X1 ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType,X10: list(X0),X11: X0] :
( ( ~ member(X0,X11,set(X0,X10))
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),X10) = insert(X0,X11,X10) ) )
& ( member(X0,X11,set(X0,X10))
=> ( insert(X0,X11,X10) = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_List_Oinsert__def) ).
tff(f980,plain,
spl35_79,
inference(avatar_split_clause,[],[f391,f978]) ).
tff(f978,plain,
( spl35_79
<=> ! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK6(X0,X1)),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_79])]) ).
tff(f391,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK6(X0,X1)),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 ) )
& ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK6(X0,X1)),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f275,f276]) ).
tff(f276,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X4: X0,X5: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X1 )
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK6(X0,X1)),sK7(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f275,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 ) )
& ( ? [X4: X0,X5: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(rectify,[],[f274]) ).
tff(f274,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 ) )
& ( ? [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
<=> ? [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X10: list(X0)] :
( ( nil(X0) != X10 )
<=> ? [X23: X0,X24: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X23),X24) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_neq__Nil__conv) ).
tff(f976,plain,
spl35_78,
inference(avatar_split_clause,[],[f389,f974]) ).
tff(f974,plain,
( spl35_78
<=> ! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK4(X0,X1)),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_78])]) ).
tff(f389,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK4(X0,X1)),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK4(X0,X1)),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f221,f272]) ).
tff(f272,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 )
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK4(X0,X1)),sK5(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f221,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 )
| ( nil(X0) = X1 ) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
=> ~ ! [X2: X0,X3: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType,X20: list(X0)] :
( ( nil(X0) != X20 )
=> ~ ! [X21: X0,X22: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X21),X22) != X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_Oexhaust) ).
tff(f961,plain,
spl35_77,
inference(avatar_split_clause,[],[f488,f959]) ).
tff(f959,plain,
( spl35_77
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_77])]) ).
tff(f488,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X59: X0,X60: X1,X61: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),combc(X0,X1,X2,X61),X60),X59) = aa(X1,X2,aa(X0,fun(X1,X2),X61,X59),X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f946,plain,
spl35_76,
inference(avatar_split_clause,[],[f444,f944]) ).
tff(f944,plain,
( spl35_76
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: list(X0)] :
( list_ex1(X0,X2,X1)
| pp(aa(X0,bool,X2,sK17(X0,X1,X2,X3)))
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_76])]) ).
tff(f444,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0)] :
( list_ex1(X0,X2,X1)
| pp(aa(X0,bool,X2,sK17(X0,X1,X2,X3)))
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( list_ex1(X0,X2,X1)
| ! [X3: X0] :
( ( ( sK17(X0,X1,X2,X3) != X3 )
& pp(aa(X0,bool,X2,sK17(X0,X1,X2,X3)))
& member(X0,sK17(X0,X1,X2,X3),set(X0,X1)) )
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f246,f307]) ).
tff(f307,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool),X3: X0] :
( ? [X4: X0] :
( ( X3 != X4 )
& pp(aa(X0,bool,X2,X4))
& member(X0,X4,set(X0,X1)) )
=> ( ( sK17(X0,X1,X2,X3) != X3 )
& pp(aa(X0,bool,X2,sK17(X0,X1,X2,X3)))
& member(X0,sK17(X0,X1,X2,X3),set(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f246,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( list_ex1(X0,X2,X1)
| ! [X3: X0] :
( ? [X4: X0] :
( ( X3 != X4 )
& pp(aa(X0,bool,X2,X4))
& member(X0,X4,set(X0,X1)) )
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( list_ex1(X0,X2,X1)
| ! [X3: X0] :
( ? [X4: X0] :
( ( X3 != X4 )
& pp(aa(X0,bool,X2,X4))
& member(X0,X4,set(X0,X1)) )
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ! [X4: X0] :
( ( pp(aa(X0,bool,X2,X4))
& member(X0,X4,set(X0,X1)) )
=> ( X3 = X4 ) )
& pp(aa(X0,bool,X2,X3))
& member(X0,X3,set(X0,X1)) )
=> list_ex1(X0,X2,X1) ),
inference(unused_predicate_definition_removal,[],[f171]) ).
tff(f171,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( list_ex1(X0,X2,X1)
<=> ? [X3: X0] :
( ! [X4: X0] :
( ( pp(aa(X0,bool,X2,X4))
& member(X0,X4,set(X0,X1)) )
=> ( X3 = X4 ) )
& pp(aa(X0,bool,X2,X3))
& member(X0,X3,set(X0,X1)) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X10: list(X0),X27: fun(X0,bool)] :
( list_ex1(X0,X27,X10)
<=> ? [X32: X0] :
( ! [X23: X0] :
( ( pp(aa(X0,bool,X27,X23))
& member(X0,X23,set(X0,X10)) )
=> ( X23 = X32 ) )
& pp(aa(X0,bool,X27,X32))
& member(X0,X32,set(X0,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list__ex1__iff) ).
tff(f942,plain,
spl35_75,
inference(avatar_split_clause,[],[f443,f940]) ).
tff(f940,plain,
( spl35_75
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: list(X0)] :
( list_ex1(X0,X2,X1)
| member(X0,sK17(X0,X1,X2,X3),set(X0,X1))
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_75])]) ).
tff(f443,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0)] :
( list_ex1(X0,X2,X1)
| member(X0,sK17(X0,X1,X2,X3),set(X0,X1))
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f926,plain,
spl35_74,
inference(avatar_split_clause,[],[f466,f924]) ).
tff(f924,plain,
( spl35_74
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_74])]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f253,f314]) ).
tff(f314,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK19(X0,X1,X2,X3)) != aa(X1,X0,X2,sK19(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f253,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X41: fun(X0,X1),X34: fun(X0,X1)] :
( ! [X4: X0] : ( aa(X0,X1,X34,X4) = aa(X0,X1,X41,X4) )
=> ( X34 = X41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f922,plain,
spl35_73,
inference(avatar_split_clause,[],[f422,f920]) ).
tff(f920,plain,
( spl35_73
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X2),nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_73])]) ).
tff(f422,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X2),nil(X0)) ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = aa(list(X0),list(X1),aa(fun(X0,X1),fun(list(X0),list(X1)),map(X0,X1),X2),nil(X0)) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X1: $tType,X0: $tType,X34: fun(X1,X0)] : ( nil(X0) = aa(list(X1),list(X0),aa(fun(X1,X0),fun(list(X1),list(X0)),map(X1,X0),X34),nil(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_map_Osimps_I1_J) ).
tff(f918,plain,
spl35_72,
inference(avatar_split_clause,[],[f384,f916]) ).
tff(f916,plain,
( spl35_72
<=> ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_72])]) ).
tff(f914,plain,
spl35_71,
inference(avatar_split_clause,[],[f445,f912]) ).
tff(f912,plain,
( spl35_71
<=> ! [X0: $tType,X3: X0,X2: fun(X0,bool),X1: list(X0)] :
( list_ex1(X0,X2,X1)
| ( sK17(X0,X1,X2,X3) != X3 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_71])]) ).
tff(f445,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0)] :
( list_ex1(X0,X2,X1)
| ( sK17(X0,X1,X2,X3) != X3 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f910,plain,
spl35_70,
inference(avatar_split_clause,[],[f383,f908]) ).
tff(f908,plain,
( spl35_70
<=> ! [X0: $tType,X1: list(X0)] : ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),combi(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_70])]) ).
tff(f383,plain,
! [X0: $tType,X1: list(X0)] : ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),combi(X0)),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: list(X0)] : ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),combi(X0)),X1) = X1 ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X13: list(X0)] : ( aa(list(X0),list(X0),aa(fun(X0,X0),fun(list(X0),list(X0)),map(X0,X0),combi(X0)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_map__ident) ).
tff(f898,plain,
( spl35_69
| ~ spl35_16
| ~ spl35_27 ),
inference(avatar_split_clause,[],[f659,f649,f604,f896]) ).
tff(f896,plain,
( spl35_69
<=> ! [X0: bool] :
( ~ pp(X0)
| member(bool,X0,combi(bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_69])]) ).
tff(f604,plain,
( spl35_16
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_16])]) ).
tff(f649,plain,
( spl35_27
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_27])]) ).
tff(f659,plain,
( ! [X0: bool] :
( ~ pp(X0)
| member(bool,X0,combi(bool)) )
| ~ spl35_16
| ~ spl35_27 ),
inference(superposition,[],[f650,f605]) ).
tff(f605,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl35_16 ),
inference(avatar_component_clause,[],[f604]) ).
tff(f650,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| member(X0,X2,X1) )
| ~ spl35_27 ),
inference(avatar_component_clause,[],[f649]) ).
tff(f888,plain,
spl35_68,
inference(avatar_split_clause,[],[f411,f886]) ).
tff(f886,plain,
( spl35_68
<=> ! [X0: $tType,X1: list(list(X0)),X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1))
| ( nil(list(X0)) != transpose(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_68])]) ).
tff(f411,plain,
! [X0: $tType,X3: list(X0),X1: list(list(X0))] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1))
| ( nil(list(X0)) != transpose(X0,X1) ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(list(X0)) = transpose(X0,X1) )
| ( ( nil(X0) != sK12(X0,X1) )
& member(list(X0),sK12(X0,X1),set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(list(X0)) != transpose(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f298,f299]) ).
tff(f299,plain,
! [X0: $tType,X1: list(list(X0))] :
( ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) )
=> ( ( nil(X0) != sK12(X0,X1) )
& member(list(X0),sK12(X0,X1),set(list(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f298,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(list(X0)) = transpose(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(list(X0)) != transpose(X0,X1) ) ) ),
inference(rectify,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(list(X0)) = transpose(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) )
| ( nil(list(X0)) != transpose(X0,X1) ) ) ),
inference(nnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
<=> ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) ) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
<=> ! [X2: list(X0)] :
( member(list(X0),X2,set(list(X0),X1))
=> ( nil(X0) = X2 ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType,X10: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X10) )
<=> ! [X32: list(X0)] :
( member(list(X0),X32,set(list(X0),X10))
=> ( nil(X0) = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_transpose__empty) ).
tff(f884,plain,
spl35_67,
inference(avatar_split_clause,[],[f410,f882]) ).
tff(f882,plain,
( spl35_67
<=> ! [X2: fm(atom),X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_67])]) ).
tff(f410,plain,
! [X2: fm(atom),X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
| ! [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ) )
& ( ( interpret(atom,int,i_Z,sK11(X0,X1),X0)
& member(fm(atom),sK11(X0,X1),set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f294,f295]) ).
tff(f295,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ? [X3: fm(atom)] :
( interpret(atom,int,i_Z,X3,X0)
& member(fm(atom),X3,set(fm(atom),X1)) )
=> ( interpret(atom,int,i_Z,sK11(X0,X1),X0)
& member(fm(atom),sK11(X0,X1),set(fm(atom),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f294,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
| ! [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ) )
& ( ? [X3: fm(atom)] :
( interpret(atom,int,i_Z,X3,X0)
& member(fm(atom),X3,set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
inference(rectify,[],[f293]) ).
tff(f293,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
| ! [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ) )
& ( ? [X2: fm(atom)] :
( interpret(atom,int,i_Z,X2,X0)
& member(fm(atom),X2,set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
inference(nnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,X1),X0)
<=> ? [X2: fm(atom)] :
( interpret(atom,int,i_Z,X2,X0)
& member(fm(atom),X2,set(fm(atom),X1)) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X10: list(int),X31: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,X31),X10)
<=> ? [X32: fm(atom)] :
( interpret(atom,int,i_Z,X32,X10)
& member(fm(atom),X32,set(fm(atom),X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Z_OI__list__disj) ).
tff(f880,plain,
spl35_66,
inference(avatar_split_clause,[],[f405,f878]) ).
tff(f878,plain,
( spl35_66
<=> ! [X0: list(int),X1: list(fm(atom)),X3: fm(atom)] :
( interpret(atom,int,i_Z,X3,X0)
| ~ member(fm(atom),X3,set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_conj(atom,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_66])]) ).
tff(f405,plain,
! [X3: fm(atom),X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,X3,X0)
| ~ member(fm(atom),X3,set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_conj(atom,X1),X0) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ( ~ interpret(atom,int,i_Z,sK10(X0,X1),X0)
& member(fm(atom),sK10(X0,X1),set(fm(atom),X1)) ) )
& ( ! [X3: fm(atom)] :
( interpret(atom,int,i_Z,X3,X0)
| ~ member(fm(atom),X3,set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_conj(atom,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f290,f291]) ).
tff(f291,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ? [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
& member(fm(atom),X2,set(fm(atom),X1)) )
=> ( ~ interpret(atom,int,i_Z,sK10(X0,X1),X0)
& member(fm(atom),sK10(X0,X1),set(fm(atom),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f290,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ? [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
& member(fm(atom),X2,set(fm(atom),X1)) ) )
& ( ! [X3: fm(atom)] :
( interpret(atom,int,i_Z,X3,X0)
| ~ member(fm(atom),X3,set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_conj(atom,X1),X0) ) ),
inference(rectify,[],[f289]) ).
tff(f289,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ? [X2: fm(atom)] :
( ~ interpret(atom,int,i_Z,X2,X0)
& member(fm(atom),X2,set(fm(atom),X1)) ) )
& ( ! [X2: fm(atom)] :
( interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_conj(atom,X1),X0) ) ),
inference(nnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
<=> ! [X2: fm(atom)] :
( interpret(atom,int,i_Z,X2,X0)
| ~ member(fm(atom),X2,set(fm(atom),X1)) ) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
<=> ! [X2: fm(atom)] :
( member(fm(atom),X2,set(fm(atom),X1))
=> interpret(atom,int,i_Z,X2,X0) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X10: list(int),X31: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X31),X10)
<=> ! [X32: fm(atom)] :
( member(fm(atom),X32,set(fm(atom),X31))
=> interpret(atom,int,i_Z,X32,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Z_OI__list__conj) ).
tff(f855,plain,
( spl35_65
| ~ spl35_16
| ~ spl35_26 ),
inference(avatar_split_clause,[],[f657,f645,f604,f853]) ).
tff(f853,plain,
( spl35_65
<=> ! [X0: bool] :
( pp(X0)
| ~ member(bool,X0,combi(bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_65])]) ).
tff(f645,plain,
( spl35_26
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_26])]) ).
tff(f657,plain,
( ! [X0: bool] :
( pp(X0)
| ~ member(bool,X0,combi(bool)) )
| ~ spl35_16
| ~ spl35_26 ),
inference(superposition,[],[f646,f605]) ).
tff(f646,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) )
| ~ spl35_26 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f851,plain,
spl35_64,
inference(avatar_split_clause,[],[f533,f849]) ).
tff(f849,plain,
( spl35_64
<=> ! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_64])]) ).
tff(f533,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ),
inference(forward_demodulation,[],[f425,f384]) ).
tff(f425,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ( nil(X0) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) )
& ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X2)
=> ( nil(X0) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) ) )
& ( member(nat,zero_zero(nat),X2)
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) ) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X11: X0,X33: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X33)
=> ( nil(X0) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),nil(X0)),X33) ) )
& ( member(nat,zero_zero(nat),X33)
=> ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),nil(X0)) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X11),nil(X0)),X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_sublist__singleton) ).
tff(f847,plain,
spl35_63,
inference(avatar_split_clause,[],[f521,f845]) ).
tff(f845,plain,
( spl35_63
<=> ! [X0: $tType,X2: fun(X0,bool),X4: list(X0),X1: fun(X0,bool)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| member(X0,sK23(X0,X1,X2,X4),set(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_63])]) ).
tff(f521,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X4) )
| member(X0,sK23(X0,X1,X2,X4),set(X0,X4)) ),
inference(equality_resolution,[],[f476]) ).
tff(f476,plain,
! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool),X4: list(X0)] :
( ( dropWhile(X0,X2,X4) = dropWhile(X0,X1,X3) )
| member(X0,sK23(X0,X1,X2,X4),set(X0,X4))
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f843,plain,
spl35_62,
inference(avatar_split_clause,[],[f512,f841]) ).
tff(f841,plain,
( spl35_62
<=> ! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_62])]) ).
tff(f512,plain,
! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) ),
inference(equality_resolution,[],[f392]) ).
tff(f392,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( nil(X0) != X1 )
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1 ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f839,plain,
spl35_61,
inference(avatar_split_clause,[],[f487,f837]) ).
tff(f837,plain,
( spl35_61
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_61])]) ).
tff(f487,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(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,X59: X0,X60: fun(X0,X1),X61: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X61,X60),X59) = aa(X1,X2,X61,aa(X0,X1,X60,X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f835,plain,
spl35_60,
inference(avatar_split_clause,[],[f448,f833]) ).
tff(f833,plain,
( spl35_60
<=> ! [X0: $tType,X4: X0,X2: fun(X0,bool),X1: list(X0)] :
( pp(aa(X0,bool,X2,X4))
| ~ member(X0,X4,set(X0,X1))
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_60])]) ).
tff(f448,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0),X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ member(X0,X4,set(X0,X1))
| ( nil(X0) != dropWhile(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ( ~ pp(aa(X0,bool,X2,sK18(X0,X1,X2)))
& member(X0,sK18(X0,X1,X2),set(X0,X1)) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ member(X0,X4,set(X0,X1)) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f311,f312]) ).
tff(f312,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& member(X0,X3,set(X0,X1)) )
=> ( ~ pp(aa(X0,bool,X2,sK18(X0,X1,X2)))
& member(X0,sK18(X0,X1,X2),set(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f311,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& member(X0,X3,set(X0,X1)) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ member(X0,X4,set(X0,X1)) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(rectify,[],[f310]) ).
tff(f310,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& member(X0,X3,set(X0,X1)) ) )
& ( ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
<=> ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ member(X0,X3,set(X0,X1)) ) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
<=> ! [X3: X0] :
( member(X0,X3,set(X0,X1))
=> pp(aa(X0,bool,X2,X3)) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X10: list(X0),X27: fun(X0,bool)] :
( ( nil(X0) = dropWhile(X0,X27,X10) )
<=> ! [X32: X0] :
( member(X0,X32,set(X0,X10))
=> pp(aa(X0,bool,X27,X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dropWhile__eq__Nil__conv) ).
tff(f831,plain,
spl35_59,
inference(avatar_split_clause,[],[f395,f829]) ).
tff(f829,plain,
( spl35_59
<=> ! [X0: $tType,X1: list(list(X0)),X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1))
| ( nil(X0) != concat(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_59])]) ).
tff(f395,plain,
! [X0: $tType,X3: list(X0),X1: list(list(X0))] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1))
| ( nil(X0) != concat(X0,X1) ) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ( ( nil(X0) != sK8(X0,X1) )
& member(list(X0),sK8(X0,X1),set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f280,f281]) ).
tff(f281,plain,
! [X0: $tType,X1: list(list(X0))] :
( ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) )
=> ( ( nil(X0) != sK8(X0,X1) )
& member(list(X0),sK8(X0,X1),set(list(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(rectify,[],[f279]) ).
tff(f279,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(nnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
<=> ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) ) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
<=> ! [X2: list(X0)] :
( member(list(X0),X2,set(list(X0),X1))
=> ( nil(X0) = X2 ) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType,X51: list(list(X0))] :
( ( nil(X0) = concat(X0,X51) )
<=> ! [X32: list(X0)] :
( member(list(X0),X32,set(list(X0),X51))
=> ( nil(X0) = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Nil__eq__concat__conv) ).
tff(f824,plain,
spl35_58,
inference(avatar_split_clause,[],[f418,f822]) ).
tff(f822,plain,
( spl35_58
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_58])]) ).
tff(f418,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),X2) != X2 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X14: X0,X15: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X14),X15) != X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_not__Cons__self) ).
tff(f820,plain,
spl35_57,
inference(avatar_split_clause,[],[f412,f818]) ).
tff(f818,plain,
( spl35_57
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
| member(list(X0),sK12(X0,X1),set(list(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_57])]) ).
tff(f412,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
| member(list(X0),sK12(X0,X1),set(list(X0),X1)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f810,plain,
spl35_56,
inference(avatar_split_clause,[],[f408,f808]) ).
tff(f808,plain,
( spl35_56
<=> ! [X0: list(int),X1: list(fm(atom))] :
( member(fm(atom),sK11(X0,X1),set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_56])]) ).
tff(f408,plain,
! [X0: list(int),X1: list(fm(atom))] :
( member(fm(atom),sK11(X0,X1),set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f806,plain,
spl35_55,
inference(avatar_split_clause,[],[f406,f804]) ).
tff(f804,plain,
( spl35_55
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| member(fm(atom),sK10(X0,X1),set(fm(atom),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_55])]) ).
tff(f406,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| member(fm(atom),sK10(X0,X1),set(fm(atom),X1)) ),
inference(cnf_transformation,[],[f292]) ).
tff(f781,plain,
spl35_54,
inference(avatar_split_clause,[],[f532,f779]) ).
tff(f779,plain,
( spl35_54
<=> ! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_54])]) ).
tff(f532,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ),
inference(forward_demodulation,[],[f426,f384]) ).
tff(f426,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f227]) ).
tff(f777,plain,
spl35_53,
inference(avatar_split_clause,[],[f450,f775]) ).
tff(f775,plain,
( spl35_53
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| ~ pp(aa(X0,bool,X2,sK18(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_53])]) ).
tff(f450,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| ~ pp(aa(X0,bool,X2,sK18(X0,X1,X2))) ),
inference(cnf_transformation,[],[f313]) ).
tff(f773,plain,
spl35_52,
inference(avatar_split_clause,[],[f449,f771]) ).
tff(f771,plain,
( spl35_52
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| member(X0,sK18(X0,X1,X2),set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_52])]) ).
tff(f449,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| member(X0,sK18(X0,X1,X2),set(X0,X1)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f769,plain,
spl35_51,
inference(avatar_split_clause,[],[f436,f767]) ).
tff(f767,plain,
( spl35_51
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_51])]) ).
tff(f436,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(flattening,[],[f234]) ).
tff(f234,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X1) )
=> ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X2: $tType,X1: $tType,X0: $tType] :
( ( zero(X2)
& zero(X1) )
=> ! [X34: fun(X1,fun(X2,X0))] : ( nil(X0) = zipwith0(X1,X2,X0,X34,nil(X1),nil(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zipwith0_Osimps_I1_J) ).
tff(f765,plain,
spl35_50,
inference(avatar_split_clause,[],[f399,f763]) ).
tff(f763,plain,
( spl35_50
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| member(list(X0),sK9(X0,X1),set(list(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_50])]) ).
tff(f399,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| member(list(X0),sK9(X0,X1),set(list(X0),X1)) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ( ( nil(X0) != sK9(X0,X1) )
& member(list(X0),sK9(X0,X1),set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f284,f285]) ).
tff(f285,plain,
! [X0: $tType,X1: list(list(X0))] :
( ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) )
=> ( ( nil(X0) != sK9(X0,X1) )
& member(list(X0),sK9(X0,X1),set(list(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f284,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X3: list(X0)] :
( ( nil(X0) = X3 )
| ~ member(list(X0),X3,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(rectify,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( ( nil(X0) = concat(X0,X1) )
| ? [X2: list(X0)] :
( ( nil(X0) != X2 )
& member(list(X0),X2,set(list(X0),X1)) ) )
& ( ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) )
| ( nil(X0) != concat(X0,X1) ) ) ),
inference(nnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
<=> ! [X2: list(X0)] :
( ( nil(X0) = X2 )
| ~ member(list(X0),X2,set(list(X0),X1)) ) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
<=> ! [X2: list(X0)] :
( member(list(X0),X2,set(list(X0),X1))
=> ( nil(X0) = X2 ) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X51: list(list(X0))] :
( ( nil(X0) = concat(X0,X51) )
<=> ! [X32: list(X0)] :
( member(list(X0),X32,set(list(X0),X51))
=> ( nil(X0) = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_concat__eq__Nil__conv) ).
tff(f761,plain,
spl35_49,
inference(avatar_split_clause,[],[f396,f759]) ).
tff(f759,plain,
( spl35_49
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| member(list(X0),sK8(X0,X1),set(list(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_49])]) ).
tff(f396,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| member(list(X0),sK8(X0,X1),set(list(X0),X1)) ),
inference(cnf_transformation,[],[f282]) ).
tff(f757,plain,
spl35_48,
inference(avatar_split_clause,[],[f369,f755]) ).
tff(f755,plain,
( spl35_48
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| member(X0,sK3(X0,X2),set(X0,X2))
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_48])]) ).
tff(f369,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| member(X0,sK3(X0,X2),set(X0,X2))
| ~ ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( ( zero_zero(X0) != sK3(X0,X2) )
& member(X0,sK3(X0,X2),set(X0,X2)) ) )
| ~ ring(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f217,f269]) ).
tff(f269,plain,
! [X0: $tType,X2: list(X0)] :
( ? [X3: X0] :
( ( zero_zero(X0) != X3 )
& member(X0,X3,set(X0,X2)) )
=> ( ( zero_zero(X0) != sK3(X0,X2) )
& member(X0,sK3(X0,X2),set(X0,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f217,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ? [X3: X0] :
( ( zero_zero(X0) != X3 )
& member(X0,X3,set(X0,X2)) ) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0)] :
( ! [X3: X0] :
( member(X0,X3,set(X0,X2))
=> ( zero_zero(X0) = X3 ) )
=> ( zero_zero(X0) = iprod(X0,X2,X1) ) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X10: list(X0),X39: list(X0)] :
( ! [X4: X0] :
( member(X0,X4,set(X0,X39))
=> ( zero_zero(X0) = X4 ) )
=> ( zero_zero(X0) = iprod(X0,X39,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_iprod0__if__coeffs0) ).
tff(f753,plain,
( spl35_47
| ~ spl35_35
| ~ spl35_38 ),
inference(avatar_split_clause,[],[f726,f708,f696,f751]) ).
tff(f751,plain,
( spl35_47
<=> ! [X0: int] : ( remdups(atom,as) = insert(atom,sK0(X0),remdups(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_47])]) ).
tff(f696,plain,
( spl35_35
<=> ! [X0: int] : ( as = insert(atom,sK0(X0),as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_35])]) ).
tff(f708,plain,
( spl35_38
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_38])]) ).
tff(f726,plain,
( ! [X0: int] : ( remdups(atom,as) = insert(atom,sK0(X0),remdups(atom,as)) )
| ~ spl35_35
| ~ spl35_38 ),
inference(superposition,[],[f709,f697]) ).
tff(f697,plain,
( ! [X0: int] : ( as = insert(atom,sK0(X0),as) )
| ~ spl35_35 ),
inference(avatar_component_clause,[],[f696]) ).
tff(f709,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) )
| ~ spl35_38 ),
inference(avatar_component_clause,[],[f708]) ).
tff(f749,plain,
spl35_46,
inference(avatar_split_clause,[],[f413,f747]) ).
tff(f747,plain,
( spl35_46
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
| ( nil(X0) != sK12(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_46])]) ).
tff(f413,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(list(X0)) = transpose(X0,X1) )
| ( nil(X0) != sK12(X0,X1) ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f745,plain,
spl35_45,
inference(avatar_split_clause,[],[f409,f743]) ).
tff(f743,plain,
( spl35_45
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,sK11(X0,X1),X0)
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_45])]) ).
tff(f409,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,sK11(X0,X1),X0)
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f741,plain,
spl35_44,
inference(avatar_split_clause,[],[f407,f739]) ).
tff(f739,plain,
( spl35_44
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,sK10(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_44])]) ).
tff(f407,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f292]) ).
tff(f734,plain,
spl35_43,
inference(avatar_split_clause,[],[f463,f732]) ).
tff(f732,plain,
( spl35_43
<=> ! [X0: $tType,X3: X0,X2: list(X0),X1: fun(nat,bool)] :
( ~ member(X0,X3,set(X0,sublist(X0,X2,X1)))
| member(X0,X3,set(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_43])]) ).
tff(f463,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: fun(nat,bool)] :
( ~ member(X0,X3,set(X0,sublist(X0,X2,X1)))
| member(X0,X3,set(X0,X2)) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType,X1: fun(nat,bool),X2: list(X0),X3: X0] :
( ~ member(X0,X3,set(X0,sublist(X0,X2,X1)))
| member(X0,X3,set(X0,X2)) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: fun(nat,bool),X2: list(X0),X3: X0] :
( ~ member(X0,X3,set(X0,X2))
=> ~ member(X0,X3,set(X0,sublist(X0,X2,X1))) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X36: fun(nat,bool),X10: list(X0),X11: X0] :
( ~ member(X0,X11,set(X0,X10))
=> ~ member(X0,X11,set(X0,sublist(X0,X10,X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_notin__set__sublistI) ).
tff(f730,plain,
spl35_42,
inference(avatar_split_clause,[],[f453,f728]) ).
tff(f728,plain,
( spl35_42
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_42])]) ).
tff(f453,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3 ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X1: $tType,X0: $tType,X60: X1,X61: X0] : ( aa(X1,X0,aa(X0,fun(X1,X0),combk(X0,X1),X61),X60) = X61 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f725,plain,
spl35_41,
inference(avatar_split_clause,[],[f388,f723]) ).
tff(f723,plain,
( spl35_41
<=> ! [X0: $tType,X1: nat] :
( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_41])]) ).
tff(f388,plain,
! [X0: $tType,X1: nat] :
( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: nat] :
( ( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) )
& ( ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) != X1 ) ) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType,X1: nat] :
( ( ( zero_zero(nat) != X1 )
=> ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) ) )
& ( ( zero_zero(nat) = X1 )
=> ( aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) = n_lists(X0,X1,nil(X0)) ) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType,X37: nat] :
( ( ( zero_zero(nat) != X37 )
=> ( n_lists(X0,X37,nil(X0)) = nil(list(X0)) ) )
& ( ( zero_zero(nat) = X37 )
=> ( n_lists(X0,X37,nil(X0)) = aa(list(list(X0)),list(list(X0)),aa(list(X0),fun(list(list(X0)),list(list(X0))),cons(list(X0)),nil(X0)),nil(list(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_n__lists__Nil) ).
tff(f721,plain,
spl35_40,
inference(avatar_split_clause,[],[f370,f719]) ).
tff(f719,plain,
( spl35_40
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK3(X0,X2) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_40])]) ).
tff(f370,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK3(X0,X2) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f714,plain,
spl35_39,
inference(avatar_split_clause,[],[f417,f712]) ).
tff(f712,plain,
( spl35_39
<=> ! [X1: $tType,X0: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_39])]) ).
tff(f417,plain,
! [X1: $tType,X0: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X1: $tType,X0: $tType,X30: list(X1)] : ( product(X0,X1,nil(X0),X30) = nil(product_prod(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_product_Osimps_I1_J) ).
tff(f710,plain,
spl35_38,
inference(avatar_split_clause,[],[f416,f708]) ).
tff(f416,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X15: list(X0),X14: X0] : ( insert(X0,X14,remdups(X0,X15)) = remdups(X0,insert(X0,X14,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_insert__remdups) ).
tff(f706,plain,
spl35_37,
inference(avatar_split_clause,[],[f400,f704]) ).
tff(f704,plain,
( spl35_37
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| ( nil(X0) != sK9(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_37])]) ).
tff(f400,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| ( nil(X0) != sK9(X0,X1) ) ),
inference(cnf_transformation,[],[f286]) ).
tff(f702,plain,
spl35_36,
inference(avatar_split_clause,[],[f397,f700]) ).
tff(f700,plain,
( spl35_36
<=> ! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| ( nil(X0) != sK8(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_36])]) ).
tff(f397,plain,
! [X0: $tType,X1: list(list(X0))] :
( ( nil(X0) = concat(X0,X1) )
| ( nil(X0) != sK8(X0,X1) ) ),
inference(cnf_transformation,[],[f282]) ).
tff(f698,plain,
( spl35_35
| ~ spl35_1
| ~ spl35_33 ),
inference(avatar_split_clause,[],[f691,f684,f538,f696]) ).
tff(f684,plain,
( spl35_33
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_33])]) ).
tff(f691,plain,
( ! [X0: int] : ( as = insert(atom,sK0(X0),as) )
| ~ spl35_1
| ~ spl35_33 ),
inference(resolution,[],[f685,f539]) ).
tff(f685,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] :
( ~ member(X0,X2,set(X0,X1))
| ( insert(X0,X2,X1) = X1 ) )
| ~ spl35_33 ),
inference(avatar_component_clause,[],[f684]) ).
tff(f690,plain,
spl35_34,
inference(avatar_split_clause,[],[f452,f688]) ).
tff(f688,plain,
( spl35_34
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: fun(X0,fun(list(X0),X1))] : ( aa(list(X0),X1,list_case(X1,X0,X3,X2),nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_34])]) ).
tff(f452,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( aa(list(X0),X1,list_case(X1,X0,X3,X2),nil(X0)) = X3 ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( aa(list(X0),X1,list_case(X1,X0,X3,X2),nil(X0)) = X3 ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X1: $tType,X0: $tType,X18: fun(X1,fun(list(X1),X0)),X19: X0] : ( aa(list(X1),X0,list_case(X0,X1,X19,X18),nil(X1)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list_Osimps_I4_J) ).
tff(f686,plain,
spl35_33,
inference(avatar_split_clause,[],[f427,f684]) ).
tff(f427,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f680,plain,
spl35_32,
inference(avatar_split_clause,[],[f401,f678]) ).
tff(f401,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) = remdups(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ) ),
inference(nnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = remdups(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X11: list(X0)] :
( ( nil(X0) = remdups(X0,X11) )
<=> ( nil(X0) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_remdups__eq__nil__iff) ).
tff(f675,plain,
spl35_31,
inference(avatar_split_clause,[],[f382,f673]) ).
tff(f382,plain,
! [X0: $tType,X1: list(X0)] : ( set(X0,X1) = set(X0,remdups(X0,X1)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: list(X0)] : ( set(X0,X1) = set(X0,remdups(X0,X1)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X10: list(X0)] : ( set(X0,X10) = set(X0,remdups(X0,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_set__remdups) ).
tff(f671,plain,
( spl35_30
| ~ spl35_11
| ~ spl35_26 ),
inference(avatar_split_clause,[],[f656,f645,f584,f669]) ).
tff(f669,plain,
( spl35_30
<=> ! [X0: int] : ~ member(list(int),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs),aa(atom,fun(list(int),bool),i_Z,sK0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_30])]) ).
tff(f656,plain,
( ! [X0: int] : ~ member(list(int),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs),aa(atom,fun(list(int),bool),i_Z,sK0(X0)))
| ~ spl35_11
| ~ spl35_26 ),
inference(resolution,[],[f646,f585]) ).
tff(f667,plain,
spl35_29,
inference(avatar_split_clause,[],[f373,f665]) ).
tff(f665,plain,
( spl35_29
<=> ! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_29])]) ).
tff(f373,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> ( zero_zero(int) != divisor(X0) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X13: atom] :
( member(atom,X13,set(atom,as))
=> ( divisor(X13) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_norm) ).
tff(f663,plain,
spl35_28,
inference(avatar_split_clause,[],[f366,f661]) ).
tff(f661,plain,
( spl35_28
<=> ! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_28])]) ).
tff(f366,plain,
! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ),
inference(cnf_transformation,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_transpose_Osimps_I1_J) ).
tff(f651,plain,
spl35_27,
inference(avatar_split_clause,[],[f447,f649]) ).
tff(f447,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X33: fun(X0,bool),X11: X0] :
( member(X0,X11,X33)
<=> pp(aa(X0,bool,X33,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f647,plain,
spl35_26,
inference(avatar_split_clause,[],[f446,f645]) ).
tff(f446,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f309]) ).
tff(f643,plain,
spl35_25,
inference(avatar_split_clause,[],[f381,f641]) ).
tff(f641,plain,
( spl35_25
<=> ! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_25])]) ).
tff(f381,plain,
! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X15: list(X0)] : ( remdups(X0,X15) = remdups(X0,remdups(X0,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_remdups__remdups) ).
tff(f639,plain,
spl35_24,
inference(avatar_split_clause,[],[f368,f637]) ).
tff(f637,plain,
( spl35_24
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_24])]) ).
tff(f368,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X28: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X28) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_iprod__Nil) ).
tff(f635,plain,
spl35_23,
inference(avatar_split_clause,[],[f367,f633]) ).
tff(f633,plain,
( spl35_23
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_23])]) ).
tff(f367,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X15: list(X0)] : ( zero_zero(X0) = iprod(X0,X15,nil(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_iprod__Nil2) ).
tff(f631,plain,
spl35_22,
inference(avatar_split_clause,[],[f451,f629]) ).
tff(f629,plain,
( spl35_22
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_22])]) ).
tff(f451,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X1: $tType,X0: $tType,X18: fun(X1,fun(list(X1),fun(X0,X0))),X19: X0] : ( list_rec(X0,X1,X19,X18,nil(X1)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_list_Orecs_I1_J) ).
tff(f627,plain,
spl35_21,
inference(avatar_split_clause,[],[f380,f625]) ).
tff(f625,plain,
( spl35_21
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_21])]) ).
tff(f380,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType,X27: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X27,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dropWhile_Osimps_I1_J) ).
tff(f623,plain,
spl35_20,
inference(avatar_split_clause,[],[f379,f621]) ).
tff(f621,plain,
( spl35_20
<=> ! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_20])]) ).
tff(f379,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X33: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sublist__nil) ).
tff(f619,plain,
spl35_19,
inference(avatar_split_clause,[],[f365,f617]) ).
tff(f617,plain,
( spl35_19
<=> ! [X0: $tType] : ( nil(X0) = concat(X0,nil(list(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_19])]) ).
tff(f365,plain,
! [X0: $tType] : ( nil(X0) = concat(X0,nil(list(X0))) ),
inference(cnf_transformation,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] : ( nil(X0) = concat(X0,nil(list(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_concat_Osimps_I1_J) ).
tff(f614,plain,
spl35_18,
inference(avatar_split_clause,[],[f414,f612]) ).
tff(f612,plain,
( spl35_18
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_18])]) ).
tff(f414,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X52: atom,X53: list(int),X54: int] : ( divisor(asubst(X54,X53,X52)) = divisor(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_divisor__asubst) ).
tff(f610,plain,
spl35_17,
inference(avatar_split_clause,[],[f390,f608]) ).
tff(f608,plain,
( spl35_17
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_17])]) ).
tff(f390,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X20: nat,X14: nat] :
( ( suc(X14) = suc(X20) )
=> ( X14 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Suc__inject) ).
tff(f606,plain,
spl35_16,
inference(avatar_split_clause,[],[f378,f604]) ).
tff(f378,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: $tType,X61: X0] : ( aa(X0,X0,combi(X0),X61) = X61 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f602,plain,
spl35_15,
inference(avatar_split_clause,[],[f377,f600]) ).
tff(f600,plain,
( spl35_15
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_15])]) ).
tff(f377,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType,X28: list(X0)] : ( splice(X0,nil(X0),X28) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_splice_Osimps_I1_J) ).
tff(f598,plain,
spl35_14,
inference(avatar_split_clause,[],[f376,f596]) ).
tff(f596,plain,
( spl35_14
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_14])]) ).
tff(f376,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(cnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X15: list(X0)] : ( splice(X0,X15,nil(X0)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_splice__Nil2) ).
tff(f594,plain,
spl35_13,
inference(avatar_split_clause,[],[f375,f592]) ).
tff(f592,plain,
( spl35_13
<=> ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_13])]) ).
tff(f375,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType,X38: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X38,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_list_Osize_I1_J) ).
tff(f590,plain,
spl35_12,
inference(avatar_split_clause,[],[f364,f588]) ).
tff(f588,plain,
( spl35_12
<=> ! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_12])]) ).
tff(f364,plain,
! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_remdups_Osimps_I1_J) ).
tff(f586,plain,
spl35_11,
inference(avatar_split_clause,[],[f351,f584]) ).
tff(f351,plain,
! [X0: int] : ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0(X0)),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs))),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: int] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0(X0)),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
& member(atom,sK0(X0),set(atom,as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f212,f263]) ).
tff(f263,plain,
! [X0: int] :
( ? [X1: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
& member(atom,X1,set(atom,as)) )
=> ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0(X0)),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
& member(atom,sK0(X0),set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f212,plain,
! [X0: int] :
? [X1: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs)))
& member(atom,X1,set(atom,as)) ),
inference(ennf_transformation,[],[f110]) ).
tff(f110,plain,
~ ? [X0: int] :
! [X1: atom] :
( member(atom,X1,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X0),xs))) ),
inference(rectify,[],[f109]) ).
tff(f109,negated_conjecture,
~ ? [X13: int] :
! [X62: atom] :
( member(atom,X62,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X62),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X13),xs))) ),
inference(negated_conjecture,[],[f108]) ).
tff(f108,conjecture,
? [X13: int] :
! [X62: atom] :
( member(atom,X62,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X62),aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X13),xs))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f582,plain,
spl35_10,
inference(avatar_split_clause,[],[f357,f579]) ).
tff(f579,plain,
( spl35_10
<=> interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_10])]) ).
tff(f357,plain,
interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096) ).
tff(f577,plain,
spl35_9,
inference(avatar_split_clause,[],[f374,f575]) ).
tff(f575,plain,
( spl35_9
<=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_9])]) ).
tff(f374,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X27: fun(X0,bool)] : ~ list_ex1(X0,X27,nil(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).
tff(f573,plain,
spl35_8,
inference(avatar_split_clause,[],[f362,f571]) ).
tff(f571,plain,
( spl35_8
<=> ! [X0: nat] : ( zero_zero(nat) != suc(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_8])]) ).
tff(f362,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X58: nat] : ( zero_zero(nat) != suc(X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Zero__neq__Suc) ).
tff(f569,plain,
spl35_7,
inference(avatar_split_clause,[],[f360,f567]) ).
tff(f567,plain,
( spl35_7
<=> ! [X0: nat] : ( suc(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_7])]) ).
tff(f360,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X37: nat] : ( suc(X37) != X37 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Suc__n__not__n) ).
tff(f565,plain,
spl35_6,
inference(avatar_split_clause,[],[f356,f562]) ).
tff(f562,plain,
( spl35_6
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_6])]) ).
tff(f356,plain,
pp(fTrue),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f560,plain,
spl35_5,
inference(avatar_split_clause,[],[f355,f557]) ).
tff(f557,plain,
( spl35_5
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_5])]) ).
tff(f355,plain,
zero(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f555,plain,
spl35_4,
inference(avatar_split_clause,[],[f354,f552]) ).
tff(f552,plain,
( spl35_4
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_4])]) ).
tff(f354,plain,
zero(nat),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f550,plain,
spl35_3,
inference(avatar_split_clause,[],[f353,f547]) ).
tff(f547,plain,
( spl35_3
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_3])]) ).
tff(f353,plain,
ring(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f545,plain,
~ spl35_2,
inference(avatar_split_clause,[],[f352,f542]) ).
tff(f542,plain,
( spl35_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_2])]) ).
tff(f352,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f540,plain,
spl35_1,
inference(avatar_split_clause,[],[f350,f538]) ).
tff(f350,plain,
! [X0: int] : member(atom,sK0(X0),set(atom,as)),
inference(cnf_transformation,[],[f264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM081_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 21:24:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (12109)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (12112)WARNING: value z3 for option sas not known
% 0.13/0.38 % (12112)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)
% 0.13/0.38 % (12113)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (12111)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (12116)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)
% 0.13/0.38 % (12115)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)
% 0.13/0.38 % (12114)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)
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38 % (12116)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (12110)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % Exception at run slice level
% 0.13/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.40 % (12117)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.40 % (12118)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)
% 0.13/0.40 % (12117)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40 % Exception at run slice level
% 0.13/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% (12118)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40
% 0.13/0.41 % (12119)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.19/0.42 % (12120)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.19/0.46 % (12114)First to succeed.
% 0.19/0.48 % (12114)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12109"
% 0.19/0.48 % (12114)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (12114)------------------------------
% 0.19/0.49 % (12114)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.49 % (12114)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (12114)Memory used [KB]: 2055
% 0.19/0.49 % (12114)Time elapsed: 0.103 s
% 0.19/0.49 % (12114)Instructions burned: 204 (million)
% 0.19/0.49 % (12109)Success in time 0.129 s
%------------------------------------------------------------------------------