TSTP Solution File: COM080_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM080_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Mon May 20 19:12:22 EDT 2024
% Result : Theorem 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 348
% Syntax : Number of formulae : 873 ( 255 unt; 74 typ; 0 def)
% Number of atoms : 1829 ( 682 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1618 ( 588 ~; 569 |; 127 &)
% ( 195 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 66 ( 43 >; 23 *; 0 +; 0 <<)
% Number of predicates : 169 ( 167 usr; 152 prp; 0-5 aty)
% Number of functors : 54 ( 54 usr; 13 con; 0-5 aty)
% Number of variables : 1705 (1597 !; 56 ?;1705 :)
% ( 52 !>; 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,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_1,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_4,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_5,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_9,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_11,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_13,type,
list_conj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_14,type,
list_disj:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_15,type,
map_fm:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fm(X0) ) > fm(X1) ) ).
tff(func_def_16,type,
neg:
!>[X0: $tType] : ( fm(X0) > fm(X0) ) ).
tff(func_def_17,type,
suc: nat > nat ).
tff(func_def_18,type,
i_Z: fun(atom,fun(list(int),bool)) ).
tff(func_def_19,type,
asubst: ( int * list(int) ) > fun(atom,atom) ).
tff(func_def_20,type,
divisor: atom > int ).
tff(func_def_21,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_22,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fTrue: bool ).
tff(func_def_26,type,
as: list(atom) ).
tff(func_def_27,type,
il: int ).
tff(func_def_28,type,
ksl: list(int) ).
tff(func_def_29,type,
m: int ).
tff(func_def_30,type,
xs: list(int) ).
tff(func_def_31,type,
sK0: atom ).
tff(func_def_32,type,
sK1: int ).
tff(func_def_33,type,
sK2: int ).
tff(func_def_34,type,
sK3: list(int) ).
tff(func_def_35,type,
sK4: int ).
tff(func_def_36,type,
sK5:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_37,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_38,type,
sK7:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_39,type,
sK8:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).
tff(func_def_41,type,
sK10:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK11:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_43,type,
sK12: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_44,type,
sK13: ( list(int) * list(fm(atom)) ) > fm(atom) ).
tff(func_def_45,type,
sK14:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_46,type,
sK15:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_47,type,
sK16:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_48,type,
sK17:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_49,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_13,type,
interpret:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(list(X1),bool)) * fm(X0) * list(X1) ) > $o ) ).
tff(pred_def_14,type,
qfree:
!>[X0: $tType] : ( fm(X0) > $o ) ).
tff(pred_def_15,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f1775,plain,
$false,
inference(avatar_sat_refutation,[],[f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f635,f640,f645,f650,f655,f660,f664,f669,f673,f677,f681,f685,f689,f693,f697,f701,f705,f709,f713,f719,f723,f727,f731,f735,f739,f743,f747,f751,f755,f761,f768,f773,f777,f783,f787,f791,f796,f802,f806,f810,f814,f830,f837,f841,f845,f849,f853,f858,f862,f866,f879,f883,f887,f891,f895,f899,f903,f935,f939,f943,f947,f951,f955,f959,f963,f967,f971,f993,f997,f1001,f1005,f1025,f1030,f1034,f1038,f1047,f1051,f1059,f1063,f1067,f1071,f1106,f1110,f1114,f1118,f1145,f1149,f1161,f1165,f1169,f1173,f1186,f1206,f1210,f1221,f1235,f1258,f1262,f1296,f1300,f1304,f1318,f1369,f1374,f1378,f1386,f1392,f1396,f1402,f1406,f1432,f1438,f1478,f1483,f1487,f1640,f1644,f1648,f1652,f1656,f1670,f1674,f1690,f1705,f1711,f1715,f1719,f1729,f1739,f1745,f1749,f1769,f1773,f1774]) ).
tff(f1774,plain,
( ~ spl19_1
| ~ spl19_126
| spl19_141 ),
inference(avatar_split_clause,[],[f1730,f1687,f1394,f547]) ).
tff(f547,plain,
( spl19_1
<=> member(atom,sK0,set(atom,as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
tff(f1394,plain,
( spl19_126
<=> ! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_126])]) ).
tff(f1687,plain,
( spl19_141
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_141])]) ).
tff(f1730,plain,
( ~ member(atom,sK0,set(atom,as))
| ~ spl19_126
| spl19_141 ),
inference(resolution,[],[f1689,f1395]) ).
tff(f1395,plain,
( ! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) )
| ~ spl19_126 ),
inference(avatar_component_clause,[],[f1394]) ).
tff(f1689,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs))
| spl19_141 ),
inference(avatar_component_clause,[],[f1687]) ).
tff(f1773,plain,
( spl19_151
| ~ spl19_89
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f1096,f1069,f1023,f1771]) ).
tff(f1771,plain,
( spl19_151
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) != times_times(nat,suc(X1),X0) )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_151])]) ).
tff(f1023,plain,
( spl19_89
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_89])]) ).
tff(f1069,plain,
( spl19_98
<=> ! [X0: nat,X1: nat] : ( times_times(nat,suc(X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),times_times(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_98])]) ).
tff(f1096,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero(nat) != times_times(nat,suc(X1),X0) )
| ( zero_zero(nat) = X0 ) )
| ~ spl19_89
| ~ spl19_98 ),
inference(superposition,[],[f1024,f1070]) ).
tff(f1070,plain,
( ! [X0: nat,X1: nat] : ( times_times(nat,suc(X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),times_times(nat,X1,X0)) )
| ~ spl19_98 ),
inference(avatar_component_clause,[],[f1069]) ).
tff(f1024,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) )
| ( zero_zero(nat) = X1 ) )
| ~ spl19_89 ),
inference(avatar_component_clause,[],[f1023]) ).
tff(f1769,plain,
( spl19_150
| ~ spl19_89
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f1082,f1065,f1023,f1767]) ).
tff(f1767,plain,
( spl19_150
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) != times_times(nat,X0,suc(X1)) )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_150])]) ).
tff(f1065,plain,
( spl19_97
<=> ! [X0: nat,X1: nat] : ( times_times(nat,X1,suc(X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),times_times(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_97])]) ).
tff(f1082,plain,
( ! [X0: nat,X1: nat] :
( ( zero_zero(nat) != times_times(nat,X0,suc(X1)) )
| ( zero_zero(nat) = X0 ) )
| ~ spl19_89
| ~ spl19_97 ),
inference(superposition,[],[f1024,f1066]) ).
tff(f1066,plain,
( ! [X0: nat,X1: nat] : ( times_times(nat,X1,suc(X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),times_times(nat,X1,X0)) )
| ~ spl19_97 ),
inference(avatar_component_clause,[],[f1065]) ).
tff(f1749,plain,
( spl19_149
| ~ spl19_97
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f1091,f1069,f1065,f1747]) ).
tff(f1747,plain,
( spl19_149
<=> ! [X0: nat] : ( times_times(nat,X0,suc(X0)) = times_times(nat,suc(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_149])]) ).
tff(f1091,plain,
( ! [X0: nat] : ( times_times(nat,X0,suc(X0)) = times_times(nat,suc(X0),X0) )
| ~ spl19_97
| ~ spl19_98 ),
inference(superposition,[],[f1070,f1066]) ).
tff(f1745,plain,
( spl19_148
| ~ spl19_27
| ~ spl19_69 ),
inference(avatar_split_clause,[],[f915,f881,f675,f1743]) ).
tff(f1743,plain,
( spl19_148
<=> ! [X0: $tType,X1: list(X0)] :
( ( sK11(X0,X1) != X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_148])]) ).
tff(f675,plain,
( spl19_27
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_27])]) ).
tff(f881,plain,
( spl19_69
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_69])]) ).
tff(f915,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( sK11(X0,X1) != X1 )
| ( nil(X0) = X1 ) )
| ~ spl19_27
| ~ spl19_69 ),
inference(superposition,[],[f676,f882]) ).
tff(f882,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 )
| ( nil(X0) = X1 ) )
| ~ spl19_69 ),
inference(avatar_component_clause,[],[f881]) ).
tff(f676,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 )
| ~ spl19_27 ),
inference(avatar_component_clause,[],[f675]) ).
tff(f1739,plain,
spl19_147,
inference(avatar_split_clause,[],[f410,f1737]) ).
tff(f1737,plain,
( spl19_147
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2)),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X2),X1)) )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_147])]) ).
tff(f410,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2)),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X2),X1)) )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2)),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X2),X1)) )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2)),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X2),X1)) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X21: list(X0),X8: list(X0),X10: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),X8)),X21) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X8),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list__add__assoc) ).
tff(f1729,plain,
spl19_146,
inference(avatar_split_clause,[],[f418,f1727]) ).
tff(f1727,plain,
( spl19_146
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_146])]) ).
tff(f418,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X42: X0,X31: X0,X32: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X32)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X42)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
tff(f1719,plain,
spl19_145,
inference(avatar_split_clause,[],[f483,f1717]) ).
tff(f1717,plain,
( spl19_145
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: X2,X7: fun(X0,fun(X2,X1)),X6: X0,X5: list(X0)] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_145])]) ).
tff(f483,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: X0,X7: fun(X0,fun(X2,X1)),X4: X2,X5: list(X0)] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: list(X0),X6: X0,X7: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f282]) ).
tff(f282,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: list(X0),X6: X0,X7: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X2),X4: X2,X5: list(X0),X6: X0,X7: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X40: list(X2),X25: X2,X12: list(X1),X24: X1,X41: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),cons(X1,X24,X12)),cons(X2,X25,X40)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X41,X24),X25),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),X12),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_zipwith0_Osimps_I2_J) ).
tff(f1715,plain,
spl19_144,
inference(avatar_split_clause,[],[f482,f1713]) ).
tff(f1713,plain,
( spl19_144
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),cons(X0,X4,X3)),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),X3),nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_144])]) ).
tff(f482,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),cons(X0,X4,X3)),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),X3),nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),cons(X0,X4,X3)),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),X3),nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f280]) ).
tff(f280,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),cons(X0,X4,X3)),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),X3),nil(X2))) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X0),X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),cons(X0,X4,X3)),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),X3),nil(X2))) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X12: list(X1),X24: X1,X41: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),cons(X1,X24,X12)),nil(X2)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X41,X24),zero_zero(X2)),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),X12),nil(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zipwith0_Osimps_I3_J) ).
tff(f1711,plain,
spl19_143,
inference(avatar_split_clause,[],[f481,f1709]) ).
tff(f1709,plain,
( spl19_143
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),X3)) )
| ~ zero(X0)
| ~ zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_143])]) ).
tff(f481,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] :
( ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X2) )
=> ! [X3: list(X2),X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X5),nil(X0)),X3)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X40: list(X2),X25: X2,X41: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),nil(X1)),cons(X2,X25,X40)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X41,zero_zero(X1)),X25),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),nil(X1)),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J) ).
tff(f1705,plain,
spl19_142,
inference(avatar_split_clause,[],[f425,f1703]) ).
tff(f1703,plain,
( spl19_142
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_142])]) ).
tff(f425,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X1)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X4,X3)),cons(X0,X2,X1)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X1)) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X8: list(X0),X9: X0,X10: list(X0),X11: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X11,X10)),cons(X0,X9,X8)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X11),X9),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list__add__Cons) ).
tff(f1690,plain,
( ~ spl19_141
| spl19_48
| ~ spl19_139 ),
inference(avatar_split_clause,[],[f1675,f1668,f765,f1687]) ).
tff(f765,plain,
( spl19_48
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_48])]) ).
tff(f1668,plain,
( spl19_139
<=> ! [X0: list(int),X3: int,X2: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_139])]) ).
tff(f1675,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs))
| spl19_48
| ~ spl19_139 ),
inference(resolution,[],[f1669,f767]) ).
tff(f767,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
| spl19_48 ),
inference(avatar_component_clause,[],[f765]) ).
tff(f1669,plain,
( ! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) )
| ~ spl19_139 ),
inference(avatar_component_clause,[],[f1668]) ).
tff(f1674,plain,
spl19_140,
inference(avatar_split_clause,[],[f510,f1672]) ).
tff(f1672,plain,
( spl19_140
<=> ! [X0: list(int),X3: int,X2: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_140])]) ).
tff(f510,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) )
& ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X12: list(int),X13: atom,X14: list(int),X15: int] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X15,X14),X13)),X12))
<=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X13),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X15),iprod(int,X14,X12)),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IZ__asubst) ).
tff(f1670,plain,
spl19_139,
inference(avatar_split_clause,[],[f509,f1668]) ).
tff(f509,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
| ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ),
inference(cnf_transformation,[],[f349]) ).
tff(f1656,plain,
spl19_138,
inference(avatar_split_clause,[],[f417,f1654]) ).
tff(f1654,plain,
( spl19_138
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_138])]) ).
tff(f417,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)),X2) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X31: X0,X32: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X32)),X31) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31)),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
tff(f1652,plain,
spl19_137,
inference(avatar_split_clause,[],[f415,f1650]) ).
tff(f1650,plain,
( spl19_137
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_137])]) ).
tff(f415,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X42: X0,X31: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X42)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31)),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f1648,plain,
spl19_136,
inference(avatar_split_clause,[],[f414,f1646]) ).
tff(f1646,plain,
( spl19_136
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_136])]) ).
tff(f414,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1)) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X42: X0,X31: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X42)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f1644,plain,
( spl19_135
| ~ spl19_27
| ~ spl19_68 ),
inference(avatar_split_clause,[],[f909,f877,f675,f1642]) ).
tff(f1642,plain,
( spl19_135
<=> ! [X0: $tType,X1: list(X0)] :
( ( sK7(X0,X1) != X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_135])]) ).
tff(f877,plain,
( spl19_68
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_68])]) ).
tff(f909,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( sK7(X0,X1) != X1 )
| ( nil(X0) = X1 ) )
| ~ spl19_27
| ~ spl19_68 ),
inference(superposition,[],[f676,f878]) ).
tff(f878,plain,
( ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) )
| ~ spl19_68 ),
inference(avatar_component_clause,[],[f877]) ).
tff(f1640,plain,
spl19_134,
inference(avatar_split_clause,[],[f396,f1638]) ).
tff(f1638,plain,
( spl19_134
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_134])]) ).
tff(f396,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) )
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X31: X0,X32: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X32)),X31) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1487,plain,
spl19_133,
inference(avatar_split_clause,[],[f470,f1485]) ).
tff(f1485,plain,
( spl19_133
<=> ! [X2: nat,X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_133])]) ).
tff(f470,plain,
! [X2: nat,X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1)),X0) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: nat,X1: nat,X2: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1)),X0) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X55: nat,X56: nat,X57: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),X56)),X55) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X56),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__assoc) ).
tff(f1483,plain,
spl19_132,
inference(avatar_split_clause,[],[f469,f1481]) ).
tff(f1481,plain,
( spl19_132
<=> ! [X2: nat,X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_132])]) ).
tff(f469,plain,
! [X2: nat,X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: nat,X1: nat,X2: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X58: nat,X9: nat,X11: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X11),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X9),X58)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X9),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X11),X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__add__left__commute) ).
tff(f1478,plain,
spl19_131,
inference(avatar_split_clause,[],[f392,f1476]) ).
tff(f1476,plain,
( spl19_131
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: list(X0)] :
( ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_131])]) ).
tff(f392,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X21: list(X0),X8: list(X0),X10: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),X8),X21) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X10,X21)),iprod(X0,X8,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_iprod__left__add__distrib) ).
tff(f1438,plain,
spl19_130,
inference(avatar_split_clause,[],[f500,f1436]) ).
tff(f1436,plain,
( spl19_130
<=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: list(X0)] : ( list_size(X0,X3,cons(X0,X2,X1)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(X0,nat,X3,X2)),list_size(X0,X3,X1))),suc(zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_130])]) ).
tff(f500,plain,
! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: list(X0)] : ( list_size(X0,X3,cons(X0,X2,X1)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(X0,nat,X3,X2)),list_size(X0,X3,X1))),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: fun(X0,nat)] : ( list_size(X0,X3,cons(X0,X2,X1)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(X0,nat,X3,X2)),list_size(X0,X3,X1))),suc(zero_zero(nat))) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X18: list(X0),X13: X0,X59: fun(X0,nat)] : ( list_size(X0,X59,cons(X0,X13,X18)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),aa(X0,nat,X59,X13)),list_size(X0,X59,X18))),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_list_Osize_I2_J) ).
tff(f1432,plain,
spl19_129,
inference(avatar_split_clause,[],[f541,f1430]) ).
tff(f1430,plain,
( spl19_129
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1))))
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_129])]) ).
tff(f541,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1))))
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f477,f431]) ).
tff(f431,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X11: X0] : ( insert(X0,X11,nil(X0)) = cons(X0,X11,nil(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insert__Nil) ).
tff(f477,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1))))
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( pp(aa(list(X0),bool,X1,X2))
| ( ~ pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1))))
& pp(aa(list(X0),bool,X1,sK15(X0,X1)))
& ( nil(X0) != sK15(X0,X1) ) )
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f332,f334,f333]) ).
tff(f333,plain,
! [X0: $tType,X1: fun(list(X0),bool)] :
( ? [X3: X0,X4: list(X0)] :
( ~ pp(aa(list(X0),bool,X1,cons(X0,X3,X4)))
& pp(aa(list(X0),bool,X1,X4))
& ( nil(X0) != X4 ) )
=> ( ~ pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1))))
& pp(aa(list(X0),bool,X1,sK15(X0,X1)))
& ( nil(X0) != sK15(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f334,plain,
! [X0: $tType,X1: fun(list(X0),bool)] :
( ? [X5: X0] : ~ pp(aa(list(X0),bool,X1,cons(X0,X5,nil(X0))))
=> ~ pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))) ),
introduced(choice_axiom,[]) ).
tff(f332,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,cons(X0,X3,X4)))
& pp(aa(list(X0),bool,X1,X4))
& ( nil(X0) != X4 ) )
| ? [X5: X0] : ~ pp(aa(list(X0),bool,X1,cons(X0,X5,nil(X0))))
| ( nil(X0) = X2 ) ),
inference(rectify,[],[f273]) ).
tff(f273,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,cons(X0,X4,X5)))
& pp(aa(list(X0),bool,X1,X5))
& ( nil(X0) != X5 ) )
| ? [X3: X0] : ~ pp(aa(list(X0),bool,X1,cons(X0,X3,nil(X0))))
| ( nil(X0) = X2 ) ),
inference(flattening,[],[f272]) ).
tff(f272,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,cons(X0,X4,X5)))
& pp(aa(list(X0),bool,X1,X5))
& ( nil(X0) != X5 ) )
| ? [X3: X0] : ~ pp(aa(list(X0),bool,X1,cons(X0,X3,nil(X0))))
| ( nil(X0) = X2 ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: fun(list(X0),bool),X2: list(X0)] :
( ( nil(X0) != X2 )
=> ( ! [X3: X0] : pp(aa(list(X0),bool,X1,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,cons(X0,X4,X5))) ) )
=> pp(aa(list(X0),bool,X1,X2)) ) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X47: fun(list(X0),bool),X12: list(X0)] :
( ( nil(X0) != X12 )
=> ( ! [X22: X0] : pp(aa(list(X0),bool,X47,cons(X0,X22,nil(X0))))
=> ( ! [X22: X0,X60: list(X0)] :
( ( nil(X0) != X60 )
=> ( pp(aa(list(X0),bool,X47,X60))
=> pp(aa(list(X0),bool,X47,cons(X0,X22,X60))) ) )
=> pp(aa(list(X0),bool,X47,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list__nonempty__induct) ).
tff(f1406,plain,
spl19_128,
inference(avatar_split_clause,[],[f502,f1404]) ).
tff(f1404,plain,
( spl19_128
<=> ! [X0: list(int),X3: fm(atom),X2: int,X1: list(int)] :
( interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
| ~ interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0)
| ~ qfree(atom,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_128])]) ).
tff(f502,plain,
! [X2: int,X3: fm(atom),X0: list(int),X1: list(int)] :
( interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
| ~ interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0)
| ~ qfree(atom,X3) ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: list(int),X1: list(int),X2: int,X3: fm(atom)] :
( ( ( interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
| ~ interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0) )
& ( interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0)
| ~ interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0)) ) )
| ~ qfree(atom,X3) ),
inference(nnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: list(int),X1: list(int),X2: int,X3: fm(atom)] :
( ( interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
<=> interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0) )
| ~ qfree(atom,X3) ),
inference(ennf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: list(int),X1: list(int),X2: int,X3: fm(atom)] :
( qfree(atom,X3)
=> ( interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
<=> interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X12: list(int),X14: list(int),X15: int,X49: fm(atom)] :
( qfree(atom,X49)
=> ( interpret(atom,int,i_Z,X49,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X15),iprod(int,X14,X12)),X12))
<=> interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X15,X14),X49),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_I__subst) ).
tff(f1402,plain,
spl19_127,
inference(avatar_split_clause,[],[f501,f1400]) ).
tff(f1400,plain,
( spl19_127
<=> ! [X0: list(int),X3: fm(atom),X2: int,X1: list(int)] :
( interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0)
| ~ interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
| ~ qfree(atom,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_127])]) ).
tff(f501,plain,
! [X2: int,X3: fm(atom),X0: list(int),X1: list(int)] :
( interpret(atom,int,i_Z,map_fm(atom,atom,asubst(X2,X1),X3),X0)
| ~ interpret(atom,int,i_Z,X3,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),iprod(int,X1,X0)),X0))
| ~ qfree(atom,X3) ),
inference(cnf_transformation,[],[f345]) ).
tff(f1396,plain,
spl19_126,
inference(avatar_split_clause,[],[f422,f1394]) ).
tff(f422,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
| ~ member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs)) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X4: atom] :
( member(atom,X4,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X4)),xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).
tff(f1392,plain,
spl19_125,
inference(avatar_split_clause,[],[f379,f1390]) ).
tff(f1390,plain,
( spl19_125
<=> ! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),sK2),sK4),sK3),X3)),xs))
| ~ member(atom,X3,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_125])]) ).
tff(f379,plain,
! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),sK2),sK4),sK3),X3)),xs))
| ~ member(atom,X3,set(atom,as)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),sK2),sK4),sK3),X3)),xs))
| ~ member(atom,X3,set(atom,as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f226,f296]) ).
tff(f296,plain,
( ? [X0: int,X1: list(int),X2: int] :
! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2),X1),X3)),xs))
| ~ member(atom,X3,set(atom,as)) )
=> ! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),sK2),sK4),sK3),X3)),xs))
| ~ member(atom,X3,set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f226,plain,
? [X0: int,X1: list(int),X2: int] :
! [X3: atom] :
( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2),X1),X3)),xs))
| ~ member(atom,X3,set(atom,as)) ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
~ ! [X0: int,X1: list(int),X2: int] :
~ ! [X3: atom] :
( member(atom,X3,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2),X1),X3)),xs)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
~ ! [X5: int,X6: list(int),X7: int] :
~ ! [X4: atom] :
( member(atom,X4,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),X5),X7),X6),X4)),xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_B_Bthesis_O_A_I_B_Bil_Aksl_Am_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1386,plain,
( spl19_123
| ~ spl19_124
| ~ spl19_28
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f818,f800,f679,f1383,f1380]) ).
tff(f1380,plain,
( spl19_123
<=> ! [X0: nat] : ( zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_123])]) ).
tff(f1383,plain,
( spl19_124
<=> ( zero_zero(nat) = suc(zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_124])]) ).
tff(f679,plain,
( spl19_28
<=> ! [X0: nat] : ( zero_zero(nat) = times_times(nat,X0,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_28])]) ).
tff(f800,plain,
( spl19_55
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X1 )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_55])]) ).
tff(f818,plain,
( ! [X0: nat] :
( ( zero_zero(nat) != suc(zero_zero(nat)) )
| ( zero_zero(nat) = X0 ) )
| ~ spl19_28
| ~ spl19_55 ),
inference(inner_rewriting,[],[f815]) ).
tff(f815,plain,
( ! [X0: nat] :
( ( zero_zero(nat) != suc(zero_zero(nat)) )
| ( suc(zero_zero(nat)) = X0 ) )
| ~ spl19_28
| ~ spl19_55 ),
inference(superposition,[],[f801,f680]) ).
tff(f680,plain,
( ! [X0: nat] : ( zero_zero(nat) = times_times(nat,X0,zero_zero(nat)) )
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f679]) ).
tff(f801,plain,
( ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) != times_times(nat,X1,X0) )
| ( suc(zero_zero(nat)) = X1 ) )
| ~ spl19_55 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f1378,plain,
spl19_122,
inference(avatar_split_clause,[],[f542,f1376]) ).
tff(f1376,plain,
( spl19_122
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK15(X0,X1)))
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_122])]) ).
tff(f542,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK15(X0,X1)))
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f476,f431]) ).
tff(f476,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| pp(aa(list(X0),bool,X1,sK15(X0,X1)))
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f1374,plain,
spl19_121,
inference(avatar_split_clause,[],[f543,f1372]) ).
tff(f1372,plain,
( spl19_121
<=> ! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK15(X0,X1) )
| ( nil(X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_121])]) ).
tff(f543,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( ~ pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0))))
| pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK15(X0,X1) )
| ( nil(X0) = X2 ) ),
inference(forward_demodulation,[],[f475,f431]) ).
tff(f475,plain,
! [X0: $tType,X2: list(X0),X1: fun(list(X0),bool)] :
( pp(aa(list(X0),bool,X1,X2))
| ( nil(X0) != sK15(X0,X1) )
| ~ pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0))))
| ( nil(X0) = X2 ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f1369,plain,
spl19_120,
inference(avatar_split_clause,[],[f393,f1367]) ).
tff(f1367,plain,
( spl19_120
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),times_times(X0,X4,X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_120])]) ).
tff(f393,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),times_times(X0,X4,X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),times_times(X0,X4,X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),times_times(X0,X4,X2)),iprod(X0,X3,X1)) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X8: list(X0),X9: X0,X10: list(X0),X11: X0] : ( iprod(X0,cons(X0,X11,X10),cons(X0,X9,X8)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),times_times(X0,X11,X9)),iprod(X0,X10,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_iprod__Cons) ).
tff(f1318,plain,
spl19_119,
inference(avatar_split_clause,[],[f480,f1316]) ).
tff(f1316,plain,
( spl19_119
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = aa(list(X0),list(X2),aa(list(X1),fun(list(X0),list(X2)),zipwith0(X1,X0,X2,X3),nil(X1)),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_119])]) ).
tff(f480,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = aa(list(X0),list(X2),aa(list(X1),fun(list(X0),list(X2)),zipwith0(X1,X0,X2,X3),nil(X1)),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = aa(list(X0),list(X2),aa(list(X1),fun(list(X0),list(X2)),zipwith0(X1,X0,X2,X3),nil(X1)),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(flattening,[],[f276]) ).
tff(f276,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = aa(list(X0),list(X2),aa(list(X1),fun(list(X0),list(X2)),zipwith0(X1,X0,X2,X3),nil(X1)),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X1) )
=> ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = aa(list(X0),list(X2),aa(list(X1),fun(list(X0),list(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) )
=> ! [X41: fun(X1,fun(X2,X0))] : ( nil(X0) = aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X41),nil(X1)),nil(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_zipwith0_Osimps_I1_J) ).
tff(f1304,plain,
spl19_118,
inference(avatar_split_clause,[],[f401,f1302]) ).
tff(f1302,plain,
( spl19_118
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_118])]) ).
tff(f401,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X31: X0,X32: X0,X26: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X32) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31) )
=> ( X31 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__imp__eq) ).
tff(f1300,plain,
spl19_117,
inference(avatar_split_clause,[],[f400,f1298]) ).
tff(f1298,plain,
( spl19_117
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_117])]) ).
tff(f400,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X3 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X31: X0,X26: X0,X32: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),X26) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X26) )
=> ( X31 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add__right__imp__eq) ).
tff(f1296,plain,
spl19_116,
inference(avatar_split_clause,[],[f397,f1294]) ).
tff(f1294,plain,
( spl19_116
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_116])]) ).
tff(f397,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) ) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X31: X0,X32: X0,X26: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X32) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31) )
=> ( X31 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__imp__eq) ).
tff(f1262,plain,
spl19_115,
inference(avatar_split_clause,[],[f497,f1260]) ).
tff(f1260,plain,
( spl19_115
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_115])]) ).
tff(f497,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ) ),
inference(nnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X51: nat,X53: nat,X52: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X52),X53) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X51),X53) )
<=> ( X51 = X52 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_nat__add__right__cancel) ).
tff(f1258,plain,
spl19_114,
inference(avatar_split_clause,[],[f495,f1256]) ).
tff(f1256,plain,
( spl19_114
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_114])]) ).
tff(f495,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X2),X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X51: nat,X52: nat,X53: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X53),X52) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X53),X51) )
<=> ( X51 = X52 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__cancel) ).
tff(f1235,plain,
spl19_113,
inference(avatar_split_clause,[],[f435,f1233]) ).
tff(f1233,plain,
( spl19_113
<=> ! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),suc(X1)),X0) = suc(aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_113])]) ).
tff(f435,plain,
! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),suc(X1)),X0) = suc(aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),suc(X1)),X0) = suc(aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0)) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X56: nat,X57: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),suc(X57)),X56) = suc(aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__Suc) ).
tff(f1221,plain,
spl19_112,
inference(avatar_split_clause,[],[f413,f1219]) ).
tff(f1219,plain,
( spl19_112
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_112])]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X31: X0,X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X26) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),X31) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f1210,plain,
spl19_111,
inference(avatar_split_clause,[],[f485,f1208]) ).
tff(f1208,plain,
( spl19_111
<=> ! [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,[spl19_111])]) ).
tff(f485,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,[],[f337]) ).
tff(f337,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])],[f285,f336]) ).
tff(f336,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(f285,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,[],[f284]) ).
tff(f284,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,[],[f223]) ).
tff(f223,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,[],[f205]) ).
tff(f205,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,[],[f70]) ).
tff(f70,axiom,
! [X0: $tType,X12: list(X0),X47: fun(X0,bool)] :
( list_ex1(X0,X47,X12)
<=> ? [X35: X0] :
( ! [X38: X0] :
( ( pp(aa(X0,bool,X47,X38))
& member(X0,X38,set(X0,X12)) )
=> ( X35 = X38 ) )
& pp(aa(X0,bool,X47,X35))
& member(X0,X35,set(X0,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list__ex1__iff) ).
tff(f1206,plain,
spl19_110,
inference(avatar_split_clause,[],[f484,f1204]) ).
tff(f1204,plain,
( spl19_110
<=> ! [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,[spl19_110])]) ).
tff(f484,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,[],[f337]) ).
tff(f1186,plain,
spl19_109,
inference(avatar_split_clause,[],[f434,f1184]) ).
tff(f1184,plain,
( spl19_109
<=> ! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_109])]) ).
tff(f434,plain,
! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: nat,X1: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),X1) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X56: nat,X57: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),X56) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X56),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__add__commute) ).
tff(f1173,plain,
( spl19_108
| ~ spl19_29
| ~ spl19_60
| ~ spl19_98 ),
inference(avatar_split_clause,[],[f1100,f1069,f835,f683,f1171]) ).
tff(f1171,plain,
( spl19_108
<=> ! [X0: nat] : ( times_times(nat,suc(zero_zero(nat)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_108])]) ).
tff(f683,plain,
( spl19_29
<=> ! [X0: nat] : ( zero_zero(nat) = times_times(nat,zero_zero(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_29])]) ).
tff(f835,plain,
( spl19_60
<=> ! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_60])]) ).
tff(f1100,plain,
( ! [X0: nat] : ( times_times(nat,suc(zero_zero(nat)),X0) = X0 )
| ~ spl19_29
| ~ spl19_60
| ~ spl19_98 ),
inference(forward_demodulation,[],[f1090,f836]) ).
tff(f836,plain,
( ! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 )
| ~ spl19_60 ),
inference(avatar_component_clause,[],[f835]) ).
tff(f1090,plain,
( ! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = times_times(nat,suc(zero_zero(nat)),X0) )
| ~ spl19_29
| ~ spl19_98 ),
inference(superposition,[],[f1070,f684]) ).
tff(f684,plain,
( ! [X0: nat] : ( zero_zero(nat) = times_times(nat,zero_zero(nat),X0) )
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f683]) ).
tff(f1169,plain,
spl19_107,
inference(avatar_split_clause,[],[f506,f1167]) ).
tff(f1167,plain,
( spl19_107
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_107])]) ).
tff(f506,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f291,f346]) ).
tff(f346,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,sK18(X0,X1,X2,X3)) != aa(X1,X0,X2,sK18(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f291,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,[],[f217]) ).
tff(f217,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,X54: fun(X0,X1),X41: fun(X0,X1)] :
( ! [X22: X0] : ( aa(X0,X1,X41,X22) = aa(X0,X1,X54,X22) )
=> ( X41 = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f1165,plain,
spl19_106,
inference(avatar_split_clause,[],[f409,f1163]) ).
tff(f1163,plain,
( spl19_106
<=> ! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),nil(X0)),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_106])]) ).
tff(f409,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),nil(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),nil(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),nil(X0)),X1) = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X10: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),nil(X0)),X10) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__add__Nil) ).
tff(f1161,plain,
spl19_105,
inference(avatar_split_clause,[],[f408,f1159]) ).
tff(f1159,plain,
( spl19_105
<=> ! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X1),nil(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_105])]) ).
tff(f408,plain,
! [X0: $tType,X1: list(X0)] :
( ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X1),nil(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X1),nil(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X1),nil(X0)) = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X10: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),nil(X0)) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list__add__Nil2) ).
tff(f1149,plain,
spl19_104,
inference(avatar_split_clause,[],[f515,f1147]) ).
tff(f1147,plain,
( spl19_104
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_104])]) ).
tff(f515,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType,X1: $tType,X18: list(X1),X13: X1,X45: fun(X1,fun(list(X1),X0)),X46: X0] : ( list_case(X0,X1,X46,X45,cons(X1,X13,X18)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X45,X13),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_list_Osimps_I5_J) ).
tff(f1145,plain,
spl19_103,
inference(avatar_split_clause,[],[f486,f1143]) ).
tff(f1143,plain,
( spl19_103
<=> ! [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,[spl19_103])]) ).
tff(f486,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,[],[f337]) ).
tff(f1118,plain,
( spl19_102
| ~ spl19_28
| ~ spl19_60
| ~ spl19_97 ),
inference(avatar_split_clause,[],[f1085,f1065,f835,f679,f1116]) ).
tff(f1116,plain,
( spl19_102
<=> ! [X0: nat] : ( times_times(nat,X0,suc(zero_zero(nat))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_102])]) ).
tff(f1085,plain,
( ! [X0: nat] : ( times_times(nat,X0,suc(zero_zero(nat))) = X0 )
| ~ spl19_28
| ~ spl19_60
| ~ spl19_97 ),
inference(forward_demodulation,[],[f1076,f836]) ).
tff(f1076,plain,
( ! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = times_times(nat,X0,suc(zero_zero(nat))) )
| ~ spl19_28
| ~ spl19_97 ),
inference(superposition,[],[f1066,f680]) ).
tff(f1114,plain,
spl19_101,
inference(avatar_split_clause,[],[f511,f1112]) ).
tff(f1112,plain,
( spl19_101
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_101])]) ).
tff(f511,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X8: list(X0),X9: X0,X10: list(X0),X11: X0] : ( splice(X0,cons(X0,X11,X10),cons(X0,X9,X8)) = cons(X0,X11,cons(X0,X9,splice(X0,X10,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_splice_Osimps_I3_J) ).
tff(f1110,plain,
spl19_100,
inference(avatar_split_clause,[],[f459,f1108]) ).
tff(f1108,plain,
( spl19_100
<=> ! [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,[spl19_100])]) ).
tff(f459,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,[],[f329]) ).
tff(f329,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,sK13(X0,X1),X0)
& member(fm(atom),sK13(X0,X1),set(fm(atom),X1)) )
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f327,f328]) ).
tff(f328,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,sK13(X0,X1),X0)
& member(fm(atom),sK13(X0,X1),set(fm(atom),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f327,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,[],[f326]) ).
tff(f326,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,[],[f186]) ).
tff(f186,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,[],[f53]) ).
tff(f53,axiom,
! [X12: list(int),X34: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,X34),X12)
<=> ? [X35: fm(atom)] :
( interpret(atom,int,i_Z,X35,X12)
& member(fm(atom),X35,set(fm(atom),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Z_OI__list__disj) ).
tff(f1106,plain,
spl19_99,
inference(avatar_split_clause,[],[f454,f1104]) ).
tff(f1104,plain,
( spl19_99
<=> ! [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,[spl19_99])]) ).
tff(f454,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,[],[f325]) ).
tff(f325,plain,
! [X0: list(int),X1: list(fm(atom))] :
( ( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ( ~ interpret(atom,int,i_Z,sK12(X0,X1),X0)
& member(fm(atom),sK12(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,[sK12])],[f323,f324]) ).
tff(f324,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,sK12(X0,X1),X0)
& member(fm(atom),sK12(X0,X1),set(fm(atom),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f323,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,[],[f322]) ).
tff(f322,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,[],[f269]) ).
tff(f269,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,[],[f185]) ).
tff(f185,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,[],[f36]) ).
tff(f36,axiom,
! [X12: list(int),X34: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X34),X12)
<=> ! [X35: fm(atom)] :
( member(fm(atom),X35,set(fm(atom),X34))
=> interpret(atom,int,i_Z,X35,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Z_OI__list__conj) ).
tff(f1071,plain,
spl19_98,
inference(avatar_split_clause,[],[f433,f1069]) ).
tff(f433,plain,
! [X0: nat,X1: nat] : ( times_times(nat,suc(X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),times_times(nat,X1,X0)) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: nat,X1: nat] : ( times_times(nat,suc(X1),X0) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),times_times(nat,X1,X0)) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X56: nat,X57: nat] : ( times_times(nat,suc(X57),X56) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X56),times_times(nat,X57,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_mult__Suc) ).
tff(f1067,plain,
spl19_97,
inference(avatar_split_clause,[],[f432,f1065]) ).
tff(f432,plain,
! [X0: nat,X1: nat] : ( times_times(nat,X1,suc(X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),times_times(nat,X1,X0)) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: nat,X1: nat] : ( times_times(nat,X1,suc(X0)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),times_times(nat,X1,X0)) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X56: nat,X57: nat] : ( times_times(nat,X57,suc(X56)) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),times_times(nat,X57,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_mult__Suc__right) ).
tff(f1063,plain,
spl19_96,
inference(avatar_split_clause,[],[f424,f1061]) ).
tff(f1061,plain,
( spl19_96
<=> ! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_96])]) ).
tff(f424,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list__add__def) ).
tff(f1059,plain,
spl19_95,
inference(avatar_split_clause,[],[f384,f1057]) ).
tff(f1057,plain,
( spl19_95
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_95])]) ).
tff(f384,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X13: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X13),X13) )
<=> ( zero_zero(X0) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_double__eq__0__iff) ).
tff(f1051,plain,
spl19_94,
inference(avatar_split_clause,[],[f540,f1049]) ).
tff(f1049,plain,
( spl19_94
<=> ! [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,[spl19_94])]) ).
tff(f540,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,[],[f471,f431]) ).
tff(f471,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) )
& ( ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X2)
=> ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) ) )
& ( member(nat,zero_zero(nat),X2)
=> ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) ) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType,X24: X0,X48: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X48)
=> ( nil(X0) = sublist(X0,cons(X0,X24,nil(X0)),X48) ) )
& ( member(nat,zero_zero(nat),X48)
=> ( cons(X0,X24,nil(X0)) = sublist(X0,cons(X0,X24,nil(X0)),X48) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_sublist__singleton) ).
tff(f1047,plain,
spl19_93,
inference(avatar_split_clause,[],[f394,f1045]) ).
tff(f1045,plain,
( spl19_93
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) != X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_93])]) ).
tff(f394,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) != X2 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = X2 )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) != X2 ) ) )
| ~ semiri456707255roduct(X0) ),
inference(nnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = X2 )
<=> ( zero_zero(X0) = X1 ) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X1: X0,X2: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = X2 )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X13: X0,X20: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X20),X13) = X20 )
<=> ( zero_zero(X0) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__0__iff) ).
tff(f1038,plain,
spl19_92,
inference(avatar_split_clause,[],[f516,f1036]) ).
tff(f1036,plain,
( spl19_92
<=> ! [X0: $tType] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_92])]) ).
tff(f516,plain,
! [X0: $tType] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f385]) ).
tff(f385,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1034,plain,
spl19_91,
inference(avatar_split_clause,[],[f461,f1032]) ).
tff(f1032,plain,
( spl19_91
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_91])]) ).
tff(f461,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ) ),
inference(flattening,[],[f330]) ).
tff(f330,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ) ),
inference(nnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X51: nat,X52: nat] :
( ( zero_zero(nat) = aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X52),X51) )
<=> ( ( zero_zero(nat) = X51 )
& ( zero_zero(nat) = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__is__0) ).
tff(f1030,plain,
( ~ spl19_90
| ~ spl19_43
| spl19_48 ),
inference(avatar_split_clause,[],[f769,f765,f741,f1027]) ).
tff(f1027,plain,
( spl19_90
<=> member(list(int),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs),aa(atom,fun(list(int),bool),i_Z,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_90])]) ).
tff(f741,plain,
( spl19_43
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_43])]) ).
tff(f769,plain,
( ~ member(list(int),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs),aa(atom,fun(list(int),bool),i_Z,sK0))
| ~ spl19_43
| spl19_48 ),
inference(resolution,[],[f767,f742]) ).
tff(f742,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) )
| ~ spl19_43 ),
inference(avatar_component_clause,[],[f741]) ).
tff(f1025,plain,
spl19_89,
inference(avatar_split_clause,[],[f460,f1023]) ).
tff(f460,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f1005,plain,
spl19_88,
inference(avatar_split_clause,[],[f505,f1003]) ).
tff(f1003,plain,
( spl19_88
<=> ! [X0: $tType,X3: X0,X2: X0,X1: list(X0)] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,cons(X0,X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_88])]) ).
tff(f505,plain,
! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,cons(X0,X2,X1))) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,cons(X0,X2,X1))) ),
inference(flattening,[],[f289]) ).
tff(f289,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,X1))
| ( X2 = X3 )
| ~ member(X0,X3,set(X0,cons(X0,X2,X1))) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
( member(X0,X3,set(X0,cons(X0,X2,X1)))
=> ( member(X0,X3,set(X0,X1))
| ( X2 = X3 ) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType,X12: list(X0),X24: X0,X25: X0] :
( member(X0,X25,set(X0,cons(X0,X24,X12)))
=> ( member(X0,X25,set(X0,X12))
| ( X24 = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_set__ConsD) ).
tff(f1001,plain,
spl19_87,
inference(avatar_split_clause,[],[f457,f999]) ).
tff(f999,plain,
( spl19_87
<=> ! [X0: list(int),X1: list(fm(atom))] :
( member(fm(atom),sK13(X0,X1),set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_87])]) ).
tff(f457,plain,
! [X0: list(int),X1: list(fm(atom))] :
( member(fm(atom),sK13(X0,X1),set(fm(atom),X1))
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ),
inference(cnf_transformation,[],[f329]) ).
tff(f997,plain,
spl19_86,
inference(avatar_split_clause,[],[f455,f995]) ).
tff(f995,plain,
( spl19_86
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| member(fm(atom),sK12(X0,X1),set(fm(atom),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_86])]) ).
tff(f455,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| member(fm(atom),sK12(X0,X1),set(fm(atom),X1)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f993,plain,
spl19_85,
inference(avatar_split_clause,[],[f437,f991]) ).
tff(f991,plain,
( spl19_85
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_85])]) ).
tff(f437,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) != X1 ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) != X1 ) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: nat,X1: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X1),X0) = X1 )
=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X56: nat,X57: nat] :
( ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),X56) = X57 )
=> ( zero_zero(nat) = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__eq__self__zero) ).
tff(f971,plain,
spl19_84,
inference(avatar_split_clause,[],[f539,f969]) ).
tff(f969,plain,
( spl19_84
<=> ! [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,[spl19_84])]) ).
tff(f539,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,[],[f472,f431]) ).
tff(f472,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f270]) ).
tff(f967,plain,
spl19_83,
inference(avatar_split_clause,[],[f518,f965]) ).
tff(f965,plain,
( spl19_83
<=> ! [X0: $tType,X2: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_83])]) ).
tff(f518,plain,
! [X0: $tType,X2: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ),
inference(equality_resolution,[],[f395]) ).
tff(f395,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1) = X2 )
| ( zero_zero(X0) != X1 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f302]) ).
tff(f963,plain,
( spl19_82
| ~ spl19_36
| ~ spl19_53 ),
inference(avatar_split_clause,[],[f797,f789,f711,f961]) ).
tff(f961,plain,
( spl19_82
<=> ! [X0: $tType,X1: X0] : ( nil(X0) != insert(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_82])]) ).
tff(f711,plain,
( spl19_36
<=> ! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_36])]) ).
tff(f789,plain,
( spl19_53
<=> ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_53])]) ).
tff(f797,plain,
( ! [X0: $tType,X1: X0] : ( nil(X0) != insert(X0,X1,nil(X0)) )
| ~ spl19_36
| ~ spl19_53 ),
inference(superposition,[],[f712,f790]) ).
tff(f790,plain,
( ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) )
| ~ spl19_53 ),
inference(avatar_component_clause,[],[f789]) ).
tff(f712,plain,
( ! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) )
| ~ spl19_36 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f959,plain,
spl19_81,
inference(avatar_split_clause,[],[f412,f957]) ).
tff(f957,plain,
( spl19_81
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_81])]) ).
tff(f412,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X26) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
tff(f955,plain,
spl19_80,
inference(avatar_split_clause,[],[f411,f953]) ).
tff(f953,plain,
( spl19_80
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_80])]) ).
tff(f411,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),zero_zero(X0)) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
tff(f951,plain,
spl19_79,
inference(avatar_split_clause,[],[f407,f949]) ).
tff(f949,plain,
( spl19_79
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_79])]) ).
tff(f407,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X26) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__0__left) ).
tff(f947,plain,
spl19_78,
inference(avatar_split_clause,[],[f406,f945]) ).
tff(f945,plain,
( spl19_78
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_78])]) ).
tff(f406,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),zero_zero(X0)) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_add__0__right) ).
tff(f943,plain,
spl19_77,
inference(avatar_split_clause,[],[f399,f941]) ).
tff(f941,plain,
( spl19_77
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_77])]) ).
tff(f399,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X26) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__0) ).
tff(f939,plain,
spl19_76,
inference(avatar_split_clause,[],[f398,f937]) ).
tff(f937,plain,
( spl19_76
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_76])]) ).
tff(f398,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X26: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X26),zero_zero(X0)) = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add_Ocomm__neutral) ).
tff(f935,plain,
spl19_75,
inference(avatar_split_clause,[],[f390,f933]) ).
tff(f933,plain,
( spl19_75
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| member(X0,sK5(X0,X2),set(X0,X2))
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_75])]) ).
tff(f390,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| member(X0,sK5(X0,X2),set(X0,X2))
| ~ ring(X0) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( ( zero_zero(X0) != sK5(X0,X2) )
& member(X0,sK5(X0,X2),set(X0,X2)) ) )
| ~ ring(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f231,f300]) ).
tff(f300,plain,
! [X0: $tType,X2: list(X0)] :
( ? [X3: X0] :
( ( zero_zero(X0) != X3 )
& member(X0,X3,set(X0,X2)) )
=> ( ( zero_zero(X0) != sK5(X0,X2) )
& member(X0,sK5(X0,X2),set(X0,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f231,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,[],[f136]) ).
tff(f136,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,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X12: list(X0),X33: list(X0)] :
( ! [X22: X0] :
( member(X0,X22,set(X0,X33))
=> ( zero_zero(X0) = X22 ) )
=> ( zero_zero(X0) = iprod(X0,X33,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_iprod0__if__coeffs0) ).
tff(f903,plain,
spl19_74,
inference(avatar_split_clause,[],[f492,f901]) ).
tff(f901,plain,
( spl19_74
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( X0 = X2 )
| ( times_times(nat,X2,X1) != times_times(nat,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_74])]) ).
tff(f492,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( X0 = X2 )
| ( times_times(nat,X2,X1) != times_times(nat,X0,X1) ) ),
inference(cnf_transformation,[],[f342]) ).
tff(f342,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( times_times(nat,X2,X1) = times_times(nat,X0,X1) )
| ( ( zero_zero(nat) != X1 )
& ( X0 != X2 ) ) )
& ( ( zero_zero(nat) = X1 )
| ( X0 = X2 )
| ( times_times(nat,X2,X1) != times_times(nat,X0,X1) ) ) ),
inference(flattening,[],[f341]) ).
tff(f341,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( times_times(nat,X2,X1) = times_times(nat,X0,X1) )
| ( ( zero_zero(nat) != X1 )
& ( X0 != X2 ) ) )
& ( ( zero_zero(nat) = X1 )
| ( X0 = X2 )
| ( times_times(nat,X2,X1) != times_times(nat,X0,X1) ) ) ),
inference(nnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( times_times(nat,X2,X1) = times_times(nat,X0,X1) )
<=> ( ( zero_zero(nat) = X1 )
| ( X0 = X2 ) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X51: nat,X53: nat,X52: nat] :
( ( times_times(nat,X52,X53) = times_times(nat,X51,X53) )
<=> ( ( zero_zero(nat) = X53 )
| ( X51 = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__cancel2) ).
tff(f899,plain,
spl19_73,
inference(avatar_split_clause,[],[f489,f897]) ).
tff(f897,plain,
( spl19_73
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero(nat) = X2 )
| ( X0 = X1 )
| ( times_times(nat,X2,X1) != times_times(nat,X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_73])]) ).
tff(f489,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( zero_zero(nat) = X2 )
| ( X0 = X1 )
| ( times_times(nat,X2,X1) != times_times(nat,X2,X0) ) ),
inference(cnf_transformation,[],[f340]) ).
tff(f340,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( times_times(nat,X2,X1) = times_times(nat,X2,X0) )
| ( ( zero_zero(nat) != X2 )
& ( X0 != X1 ) ) )
& ( ( zero_zero(nat) = X2 )
| ( X0 = X1 )
| ( times_times(nat,X2,X1) != times_times(nat,X2,X0) ) ) ),
inference(flattening,[],[f339]) ).
tff(f339,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( times_times(nat,X2,X1) = times_times(nat,X2,X0) )
| ( ( zero_zero(nat) != X2 )
& ( X0 != X1 ) ) )
& ( ( zero_zero(nat) = X2 )
| ( X0 = X1 )
| ( times_times(nat,X2,X1) != times_times(nat,X2,X0) ) ) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( times_times(nat,X2,X1) = times_times(nat,X2,X0) )
<=> ( ( zero_zero(nat) = X2 )
| ( X0 = X1 ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X51: nat,X52: nat,X53: nat] :
( ( times_times(nat,X53,X52) = times_times(nat,X53,X51) )
<=> ( ( zero_zero(nat) = X53 )
| ( X51 = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__cancel1) ).
tff(f895,plain,
spl19_72,
inference(avatar_split_clause,[],[f474,f893]) ).
tff(f893,plain,
( spl19_72
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_72])]) ).
tff(f474,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,set(X0,X1)) )
& ( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ~ member(X0,X2,set(X0,X1))
=> ( cons(X0,X2,X1) = insert(X0,X2,X1) ) )
& ( member(X0,X2,set(X0,X1))
=> ( insert(X0,X2,X1) = X1 ) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X12: list(X0),X24: X0] :
( ( ~ member(X0,X24,set(X0,X12))
=> ( cons(X0,X24,X12) = insert(X0,X24,X12) ) )
& ( member(X0,X24,set(X0,X12))
=> ( insert(X0,X24,X12) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_List_Oinsert__def) ).
tff(f891,plain,
spl19_71,
inference(avatar_split_clause,[],[f458,f889]) ).
tff(f889,plain,
( spl19_71
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,sK13(X0,X1),X0)
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_71])]) ).
tff(f458,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,sK13(X0,X1),X0)
| ~ interpret(atom,int,i_Z,list_disj(atom,X1),X0) ),
inference(cnf_transformation,[],[f329]) ).
tff(f887,plain,
spl19_70,
inference(avatar_split_clause,[],[f456,f885]) ).
tff(f885,plain,
( spl19_70
<=> ! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,sK12(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_70])]) ).
tff(f456,plain,
! [X0: list(int),X1: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,X1),X0)
| ~ interpret(atom,int,i_Z,sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f883,plain,
spl19_69,
inference(avatar_split_clause,[],[f442,f881]) ).
tff(f442,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ( cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f313,f314]) ).
tff(f314,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X4: X0,X5: list(X0)] : ( cons(X0,X4,X5) = X1 )
=> ( cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f313,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ? [X4: X0,X5: list(X0)] : ( cons(X0,X4,X5) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(rectify,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
<=> ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType,X12: list(X0)] :
( ( nil(X0) != X12 )
<=> ? [X38: X0,X39: list(X0)] : ( cons(X0,X38,X39) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_neq__Nil__conv) ).
tff(f879,plain,
spl19_68,
inference(avatar_split_clause,[],[f436,f877]) ).
tff(f436,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f265,f306]) ).
tff(f306,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
=> ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f265,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
| ( nil(X0) = X1 ) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
=> ~ ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X9: list(X0)] :
( ( nil(X0) != X9 )
=> ~ ! [X36: X0,X37: list(X0)] : ( cons(X0,X36,X37) != X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_list_Oexhaust) ).
tff(f866,plain,
spl19_67,
inference(avatar_split_clause,[],[f503,f864]) ).
tff(f864,plain,
( spl19_67
<=> ! [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,[spl19_67])]) ).
tff(f503,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,[],[f287]) ).
tff(f287,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,[],[f214]) ).
tff(f214,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,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X50: fun(nat,bool),X12: list(X0),X24: X0] :
( ~ member(X0,X24,set(X0,X12))
=> ~ member(X0,X24,set(X0,sublist(X0,X12,X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_notin__set__sublistI) ).
tff(f862,plain,
spl19_66,
inference(avatar_split_clause,[],[f448,f860]) ).
tff(f860,plain,
( spl19_66
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != times_times(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_66])]) ).
tff(f448,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != times_times(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = times_times(nat,X1,X0) )
| ( ( zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1 ) ) )
& ( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != times_times(nat,X1,X0) ) ) ),
inference(flattening,[],[f318]) ).
tff(f318,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = times_times(nat,X1,X0) )
| ( ( zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1 ) ) )
& ( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != times_times(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = times_times(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X51: nat,X52: nat] :
( ( zero_zero(nat) = times_times(nat,X52,X51) )
<=> ( ( zero_zero(nat) = X51 )
| ( zero_zero(nat) = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mult__is__0) ).
tff(f858,plain,
( spl19_65
| ~ spl19_1
| ~ spl19_57 ),
inference(avatar_split_clause,[],[f823,f808,f547,f855]) ).
tff(f855,plain,
( spl19_65
<=> ( as = insert(atom,sK0,as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_65])]) ).
tff(f808,plain,
( spl19_57
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_57])]) ).
tff(f823,plain,
( ( as = insert(atom,sK0,as) )
| ~ spl19_1
| ~ spl19_57 ),
inference(resolution,[],[f809,f549]) ).
tff(f549,plain,
( member(atom,sK0,set(atom,as))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f547]) ).
tff(f809,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] :
( ~ member(X0,X2,set(X0,X1))
| ( insert(X0,X2,X1) = X1 ) )
| ~ spl19_57 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f853,plain,
spl19_64,
inference(avatar_split_clause,[],[f440,f851]) ).
tff(f851,plain,
( spl19_64
<=> ! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| member(fm(X0),sK9(X0,X1),set(fm(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_64])]) ).
tff(f440,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| member(fm(X0),sK9(X0,X1),set(fm(X0),X1)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| ( ~ qfree(X0,sK9(X0,X1))
& member(fm(X0),sK9(X0,X1),set(fm(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f268,f310]) ).
tff(f310,plain,
! [X0: $tType,X1: list(fm(X0))] :
( ? [X2: fm(X0)] :
( ~ qfree(X0,X2)
& member(fm(X0),X2,set(fm(X0),X1)) )
=> ( ~ qfree(X0,sK9(X0,X1))
& member(fm(X0),sK9(X0,X1),set(fm(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f268,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| ? [X2: fm(X0)] :
( ~ qfree(X0,X2)
& member(fm(X0),X2,set(fm(X0),X1)) ) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: list(fm(X0))] :
( ! [X2: fm(X0)] :
( member(fm(X0),X2,set(fm(X0),X1))
=> qfree(X0,X2) )
=> qfree(X0,list_disj(X0,X1)) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X34: list(fm(X0))] :
( ! [X22: fm(X0)] :
( member(fm(X0),X22,set(fm(X0),X34))
=> qfree(X0,X22) )
=> qfree(X0,list_disj(X0,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_qfree__list__disj) ).
tff(f849,plain,
spl19_63,
inference(avatar_split_clause,[],[f438,f847]) ).
tff(f847,plain,
( spl19_63
<=> ! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| member(fm(X0),sK8(X0,X1),set(fm(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_63])]) ).
tff(f438,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| member(fm(X0),sK8(X0,X1),set(fm(X0),X1)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| ( ~ qfree(X0,sK8(X0,X1))
& member(fm(X0),sK8(X0,X1),set(fm(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f267,f308]) ).
tff(f308,plain,
! [X0: $tType,X1: list(fm(X0))] :
( ? [X2: fm(X0)] :
( ~ qfree(X0,X2)
& member(fm(X0),X2,set(fm(X0),X1)) )
=> ( ~ qfree(X0,sK8(X0,X1))
& member(fm(X0),sK8(X0,X1),set(fm(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f267,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| ? [X2: fm(X0)] :
( ~ qfree(X0,X2)
& member(fm(X0),X2,set(fm(X0),X1)) ) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType,X1: list(fm(X0))] :
( ! [X2: fm(X0)] :
( member(fm(X0),X2,set(fm(X0),X1))
=> qfree(X0,X2) )
=> qfree(X0,list_conj(X0,X1)) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X34: list(fm(X0))] :
( ! [X22: fm(X0)] :
( member(fm(X0),X22,set(fm(X0),X34))
=> qfree(X0,X22) )
=> qfree(X0,list_conj(X0,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_qfree__list__conj) ).
tff(f845,plain,
spl19_62,
inference(avatar_split_clause,[],[f391,f843]) ).
tff(f843,plain,
( spl19_62
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK5(X0,X2) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_62])]) ).
tff(f391,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK5(X0,X2) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f301]) ).
tff(f841,plain,
spl19_61,
inference(avatar_split_clause,[],[f383,f839]) ).
tff(f839,plain,
( spl19_61
<=> ! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_61])]) ).
tff(f383,plain,
! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X56: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X56) = X56 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_plus__nat_Oadd__0) ).
tff(f837,plain,
spl19_60,
inference(avatar_split_clause,[],[f382,f835]) ).
tff(f382,plain,
! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X57: nat] : ( aa(nat,nat,aa(nat,fun(nat,nat),plus_plus(nat),X57),zero_zero(nat)) = X57 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat_Oadd__0__right) ).
tff(f830,plain,
spl19_59,
inference(avatar_split_clause,[],[f513,f828]) ).
tff(f828,plain,
( spl19_59
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X1 = X3 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_59])]) ).
tff(f513,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f351]) ).
tff(f351,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
inference(flattening,[],[f350]) ).
tff(f350,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
inference(nnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( cons(X0,X4,X3) = cons(X0,X2,X1) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X16: list(X0),X17: X0,X18: list(X0),X13: X0] :
( ( cons(X0,X13,X18) = cons(X0,X17,X16) )
<=> ( ( X16 = X18 )
& ( X13 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list_Oinject) ).
tff(f814,plain,
spl19_58,
inference(avatar_split_clause,[],[f512,f812]) ).
tff(f812,plain,
( spl19_58
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_58])]) ).
tff(f512,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( cons(X0,X4,X3) != cons(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f351]) ).
tff(f810,plain,
spl19_57,
inference(avatar_split_clause,[],[f473,f808]) ).
tff(f473,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,set(X0,X1)) ),
inference(cnf_transformation,[],[f271]) ).
tff(f806,plain,
spl19_56,
inference(avatar_split_clause,[],[f452,f804]) ).
tff(f804,plain,
( spl19_56
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_56])]) ).
tff(f452,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: nat,X1: nat] :
( ( ( suc(zero_zero(nat)) = times_times(nat,X1,X0) )
| ( suc(zero_zero(nat)) != X0 )
| ( suc(zero_zero(nat)) != X1 ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ) ),
inference(flattening,[],[f320]) ).
tff(f320,plain,
! [X0: nat,X1: nat] :
( ( ( suc(zero_zero(nat)) = times_times(nat,X1,X0) )
| ( suc(zero_zero(nat)) != X0 )
| ( suc(zero_zero(nat)) != X1 ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = times_times(nat,X1,X0) )
<=> ( ( suc(zero_zero(nat)) = X0 )
& ( suc(zero_zero(nat)) = X1 ) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X51: nat,X52: nat] :
( ( suc(zero_zero(nat)) = times_times(nat,X52,X51) )
<=> ( ( suc(zero_zero(nat)) = X51 )
& ( suc(zero_zero(nat)) = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult__eq__1__iff) ).
tff(f802,plain,
spl19_55,
inference(avatar_split_clause,[],[f451,f800]) ).
tff(f451,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X1 )
| ( suc(zero_zero(nat)) != times_times(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f321]) ).
tff(f796,plain,
spl19_54,
inference(avatar_split_clause,[],[f528,f793]) ).
tff(f793,plain,
( spl19_54
<=> ( suc(zero_zero(nat)) = times_times(nat,suc(zero_zero(nat)),suc(zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_54])]) ).
tff(f528,plain,
suc(zero_zero(nat)) = times_times(nat,suc(zero_zero(nat)),suc(zero_zero(nat))),
inference(equality_resolution,[],[f527]) ).
tff(f527,plain,
! [X1: nat] :
( ( suc(zero_zero(nat)) = times_times(nat,X1,suc(zero_zero(nat))) )
| ( suc(zero_zero(nat)) != X1 ) ),
inference(equality_resolution,[],[f453]) ).
tff(f453,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = times_times(nat,X1,X0) )
| ( suc(zero_zero(nat)) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ),
inference(cnf_transformation,[],[f321]) ).
tff(f791,plain,
spl19_53,
inference(avatar_split_clause,[],[f431,f789]) ).
tff(f787,plain,
( spl19_52
| ~ spl19_4
| ~ spl19_40 ),
inference(avatar_split_clause,[],[f757,f729,f562,f785]) ).
tff(f785,plain,
( spl19_52
<=> ! [X0: list(int)] : ( zero_zero(int) = iprod(int,nil(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_52])]) ).
tff(f562,plain,
( spl19_4
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
tff(f729,plain,
( spl19_40
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_40])]) ).
tff(f757,plain,
( ! [X0: list(int)] : ( zero_zero(int) = iprod(int,nil(int),X0) )
| ~ spl19_4
| ~ spl19_40 ),
inference(resolution,[],[f730,f564]) ).
tff(f564,plain,
( ring(int)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f730,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = iprod(X0,nil(X0),X1) ) )
| ~ spl19_40 ),
inference(avatar_component_clause,[],[f729]) ).
tff(f783,plain,
~ spl19_51,
inference(avatar_split_clause,[],[f377,f780]) ).
tff(f780,plain,
( spl19_51
<=> ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_51])]) ).
tff(f377,plain,
lbounds(as) != nil(product_prod(int,list(int))),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
lbounds(as) != nil(product_prod(int,list(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096lbounds_Aas_A_126_061_A_091_093_096) ).
tff(f777,plain,
spl19_50,
inference(avatar_split_clause,[],[f467,f775]) ).
tff(f775,plain,
( spl19_50
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(aa(atom,atom,asubst(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_50])]) ).
tff(f467,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(aa(atom,atom,asubst(X2,X1),X0)) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(X0) = divisor(aa(atom,atom,asubst(X2,X1),X0)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X26: atom,X27: list(int),X28: int] : ( divisor(aa(atom,atom,asubst(X28,X27),X26)) = divisor(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divisor__asubst) ).
tff(f773,plain,
spl19_49,
inference(avatar_split_clause,[],[f421,f771]) ).
tff(f771,plain,
( spl19_49
<=> ! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_49])]) ).
tff(f421,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: atom] :
( member(atom,X0,set(atom,as))
=> ( zero_zero(int) != divisor(X0) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X4: atom] :
( member(atom,X4,set(atom,as))
=> ( divisor(X4) != zero_zero(int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_norm) ).
tff(f768,plain,
~ spl19_48,
inference(avatar_split_clause,[],[f353,f765]) ).
tff(f353,plain,
~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,sK0,set(atom,as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f224,f292]) ).
tff(f292,plain,
( ? [X0: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,X0,set(atom,as)) )
=> ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,sK0,set(atom,as)) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
? [X0: atom] :
( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
& member(atom,X0,set(atom,as)) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
~ ! [X0: atom] :
( member(atom,X0,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
inference(rectify,[],[f124]) ).
tff(f124,negated_conjecture,
~ ! [X22: atom] :
( member(atom,X22,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
inference(negated_conjecture,[],[f123]) ).
tff(f123,conjecture,
! [X22: atom] :
( member(atom,X22,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f761,plain,
( spl19_47
| ~ spl19_4
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f756,f725,f562,f759]) ).
tff(f759,plain,
( spl19_47
<=> ! [X0: list(int)] : ( zero_zero(int) = iprod(int,X0,nil(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_47])]) ).
tff(f725,plain,
( spl19_39
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_39])]) ).
tff(f756,plain,
( ! [X0: list(int)] : ( zero_zero(int) = iprod(int,X0,nil(int)) )
| ~ spl19_4
| ~ spl19_39 ),
inference(resolution,[],[f726,f564]) ).
tff(f726,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = iprod(X0,X1,nil(X0)) ) )
| ~ spl19_39 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f755,plain,
spl19_46,
inference(avatar_split_clause,[],[f508,f753]) ).
tff(f753,plain,
( spl19_46
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fm(X1)] :
( qfree(X0,map_fm(X1,X0,X3,X2))
| ~ qfree(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_46])]) ).
tff(f508,plain,
! [X1: $tType,X0: $tType,X2: fm(X1),X3: fun(X1,X0)] :
( qfree(X0,map_fm(X1,X0,X3,X2))
| ~ qfree(X1,X2) ),
inference(cnf_transformation,[],[f348]) ).
tff(f348,plain,
! [X0: $tType,X1: $tType,X2: fm(X1),X3: fun(X1,X0)] :
( ( qfree(X0,map_fm(X1,X0,X3,X2))
| ~ qfree(X1,X2) )
& ( qfree(X1,X2)
| ~ qfree(X0,map_fm(X1,X0,X3,X2)) ) ),
inference(nnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType,X1: $tType,X2: fm(X1),X3: fun(X1,X0)] :
( qfree(X0,map_fm(X1,X0,X3,X2))
<=> qfree(X1,X2) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X1: $tType,X49: fm(X1),X41: fun(X1,X0)] :
( qfree(X0,map_fm(X1,X0,X41,X49))
<=> qfree(X1,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_qfree__map__fm) ).
tff(f751,plain,
spl19_45,
inference(avatar_split_clause,[],[f507,f749]) ).
tff(f749,plain,
( spl19_45
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fm(X1)] :
( qfree(X1,X2)
| ~ qfree(X0,map_fm(X1,X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_45])]) ).
tff(f507,plain,
! [X1: $tType,X0: $tType,X2: fm(X1),X3: fun(X1,X0)] :
( qfree(X1,X2)
| ~ qfree(X0,map_fm(X1,X0,X3,X2)) ),
inference(cnf_transformation,[],[f348]) ).
tff(f747,plain,
spl19_44,
inference(avatar_split_clause,[],[f488,f745]) ).
tff(f745,plain,
( spl19_44
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_44])]) ).
tff(f488,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f338]) ).
tff(f338,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,[],[f206]) ).
tff(f206,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,X48: fun(X0,bool),X24: X0] :
( member(X0,X24,X48)
<=> pp(aa(X0,bool,X48,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f743,plain,
spl19_43,
inference(avatar_split_clause,[],[f487,f741]) ).
tff(f487,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f338]) ).
tff(f739,plain,
spl19_42,
inference(avatar_split_clause,[],[f441,f737]) ).
tff(f737,plain,
( spl19_42
<=> ! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| ~ qfree(X0,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_42])]) ).
tff(f441,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_disj(X0,X1))
| ~ qfree(X0,sK9(X0,X1)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f735,plain,
spl19_41,
inference(avatar_split_clause,[],[f439,f733]) ).
tff(f733,plain,
( spl19_41
<=> ! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| ~ qfree(X0,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_41])]) ).
tff(f439,plain,
! [X0: $tType,X1: list(fm(X0))] :
( qfree(X0,list_conj(X0,X1))
| ~ qfree(X0,sK8(X0,X1)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f731,plain,
spl19_40,
inference(avatar_split_clause,[],[f389,f729]) ).
tff(f389,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X8: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_iprod__Nil) ).
tff(f727,plain,
spl19_39,
inference(avatar_split_clause,[],[f388,f725]) ).
tff(f388,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X10: list(X0)] : ( zero_zero(X0) = iprod(X0,X10,nil(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_iprod__Nil2) ).
tff(f723,plain,
spl19_38,
inference(avatar_split_clause,[],[f499,f721]) ).
tff(f721,plain,
( spl19_38
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_38])]) ).
tff(f499,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X1: $tType,X0: $tType,X45: fun(X1,fun(list(X1),X0)),X46: X0] : ( list_case(X0,X1,X46,X45,nil(X1)) = X46 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list_Osimps_I4_J) ).
tff(f719,plain,
spl19_37,
inference(avatar_split_clause,[],[f430,f717]) ).
tff(f717,plain,
( spl19_37
<=> ! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_37])]) ).
tff(f430,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType,X48: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_sublist__nil) ).
tff(f713,plain,
spl19_36,
inference(avatar_split_clause,[],[f523,f711]) ).
tff(f523,plain,
! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ),
inference(equality_resolution,[],[f443]) ).
tff(f443,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( nil(X0) != X1 )
| ( cons(X0,X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f709,plain,
spl19_35,
inference(avatar_split_clause,[],[f447,f707]) ).
tff(f707,plain,
( spl19_35
<=> ! [X0: $tType,X1: fm(X0)] :
( qfree(X0,neg(X0,X1))
| ~ qfree(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_35])]) ).
tff(f447,plain,
! [X0: $tType,X1: fm(X0)] :
( qfree(X0,neg(X0,X1))
| ~ qfree(X0,X1) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: fm(X0)] :
( ( qfree(X0,neg(X0,X1))
| ~ qfree(X0,X1) )
& ( qfree(X0,X1)
| ~ qfree(X0,neg(X0,X1)) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: fm(X0)] :
( qfree(X0,neg(X0,X1))
<=> qfree(X0,X1) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType,X49: fm(X0)] :
( qfree(X0,neg(X0,X49))
<=> qfree(X0,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_qfree__neg) ).
tff(f705,plain,
spl19_34,
inference(avatar_split_clause,[],[f446,f703]) ).
tff(f703,plain,
( spl19_34
<=> ! [X0: $tType,X1: fm(X0)] :
( qfree(X0,X1)
| ~ qfree(X0,neg(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_34])]) ).
tff(f446,plain,
! [X0: $tType,X1: fm(X0)] :
( qfree(X0,X1)
| ~ qfree(X0,neg(X0,X1)) ),
inference(cnf_transformation,[],[f317]) ).
tff(f701,plain,
spl19_33,
inference(avatar_split_clause,[],[f444,f699]) ).
tff(f699,plain,
( spl19_33
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_33])]) ).
tff(f444,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: nat,X1: nat] :
( ( ( suc(X0) = suc(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X61: nat,X62: nat] :
( ( suc(X62) = suc(X61) )
<=> ( X61 = X62 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat_Oinject) ).
tff(f697,plain,
spl19_32,
inference(avatar_split_clause,[],[f429,f695]) ).
tff(f695,plain,
( spl19_32
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_32])]) ).
tff(f429,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType,X8: list(X0)] : ( splice(X0,nil(X0),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_splice_Osimps_I1_J) ).
tff(f693,plain,
spl19_31,
inference(avatar_split_clause,[],[f428,f691]) ).
tff(f691,plain,
( spl19_31
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_31])]) ).
tff(f428,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X10: list(X0)] : ( splice(X0,X10,nil(X0)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_splice__Nil2) ).
tff(f689,plain,
spl19_30,
inference(avatar_split_clause,[],[f427,f687]) ).
tff(f687,plain,
( spl19_30
<=> ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_30])]) ).
tff(f427,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType,X59: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X59,nil(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_list_Osize_I1_J) ).
tff(f685,plain,
spl19_29,
inference(avatar_split_clause,[],[f381,f683]) ).
tff(f381,plain,
! [X0: nat] : ( zero_zero(nat) = times_times(nat,zero_zero(nat),X0) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: nat] : ( zero_zero(nat) = times_times(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X56: nat] : ( zero_zero(nat) = times_times(nat,zero_zero(nat),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult__0) ).
tff(f681,plain,
spl19_28,
inference(avatar_split_clause,[],[f380,f679]) ).
tff(f380,plain,
! [X0: nat] : ( zero_zero(nat) = times_times(nat,X0,zero_zero(nat)) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: nat] : ( zero_zero(nat) = times_times(nat,X0,zero_zero(nat)) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X57: nat] : ( zero_zero(nat) = times_times(nat,X57,zero_zero(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult__0__right) ).
tff(f677,plain,
spl19_27,
inference(avatar_split_clause,[],[f463,f675]) ).
tff(f463,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( cons(X0,X1,X2) != X2 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X11: X0,X10: list(X0)] : ( cons(X0,X11,X10) != X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__Cons__self) ).
tff(f673,plain,
spl19_26,
inference(avatar_split_clause,[],[f423,f671]) ).
tff(f671,plain,
( spl19_26
<=> ! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_26])]) ).
tff(f423,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( ( cl_Groups_Oplus(X0)
& zero(X0) )
=> cl_Groups_Oplus(list(X0)) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X63: $tType] :
( ( cl_Groups_Oplus(X63)
& zero(X63) )
=> cl_Groups_Oplus(list(X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
tff(f669,plain,
spl19_25,
inference(avatar_split_clause,[],[f376,f666]) ).
tff(f666,plain,
( spl19_25
<=> interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
tff(f376,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/sandbox/benchmark/theBenchmark.p',fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096) ).
tff(f664,plain,
spl19_24,
inference(avatar_split_clause,[],[f426,f662]) ).
tff(f662,plain,
( spl19_24
<=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
tff(f426,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X47: fun(X0,bool)] : ~ list_ex1(X0,X47,nil(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_list__ex1__simps_I1_J) ).
tff(f660,plain,
spl19_23,
inference(avatar_split_clause,[],[f375,f657]) ).
tff(f657,plain,
( spl19_23
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
tff(f375,plain,
pp(fTrue),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f655,plain,
spl19_22,
inference(avatar_split_clause,[],[f374,f652]) ).
tff(f652,plain,
( spl19_22
<=> cl_Groups_Oplus(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
tff(f374,plain,
cl_Groups_Oplus(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
cl_Groups_Oplus(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oplus) ).
tff(f650,plain,
spl19_21,
inference(avatar_split_clause,[],[f373,f647]) ).
tff(f647,plain,
( spl19_21
<=> cl_Groups_Oplus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
tff(f373,plain,
cl_Groups_Oplus(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
cl_Groups_Oplus(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
tff(f645,plain,
spl19_20,
inference(avatar_split_clause,[],[f372,f642]) ).
tff(f642,plain,
( spl19_20
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
tff(f372,plain,
zero(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f640,plain,
spl19_19,
inference(avatar_split_clause,[],[f371,f637]) ).
tff(f637,plain,
( spl19_19
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
tff(f371,plain,
zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f635,plain,
spl19_18,
inference(avatar_split_clause,[],[f370,f632]) ).
tff(f632,plain,
( spl19_18
<=> comm_semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
tff(f370,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
tff(f630,plain,
spl19_17,
inference(avatar_split_clause,[],[f369,f627]) ).
tff(f627,plain,
( spl19_17
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
tff(f369,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f625,plain,
spl19_16,
inference(avatar_split_clause,[],[f368,f622]) ).
tff(f622,plain,
( spl19_16
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
tff(f368,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
tff(f620,plain,
spl19_15,
inference(avatar_split_clause,[],[f367,f617]) ).
tff(f617,plain,
( spl19_15
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
tff(f367,plain,
monoid_add(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f615,plain,
spl19_14,
inference(avatar_split_clause,[],[f366,f612]) ).
tff(f612,plain,
( spl19_14
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
tff(f366,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
tff(f610,plain,
spl19_13,
inference(avatar_split_clause,[],[f365,f607]) ).
tff(f607,plain,
( spl19_13
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
tff(f365,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f605,plain,
spl19_12,
inference(avatar_split_clause,[],[f364,f602]) ).
tff(f602,plain,
( spl19_12
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
tff(f364,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
tff(f600,plain,
spl19_11,
inference(avatar_split_clause,[],[f363,f597]) ).
tff(f597,plain,
( spl19_11
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
tff(f363,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f595,plain,
spl19_10,
inference(avatar_split_clause,[],[f362,f592]) ).
tff(f592,plain,
( spl19_10
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
tff(f362,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
tff(f590,plain,
spl19_9,
inference(avatar_split_clause,[],[f361,f587]) ).
tff(f587,plain,
( spl19_9
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
tff(f361,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
tff(f585,plain,
spl19_8,
inference(avatar_split_clause,[],[f360,f582]) ).
tff(f582,plain,
( spl19_8
<=> semiri456707255roduct(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
tff(f360,plain,
semiri456707255roduct(nat),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f580,plain,
spl19_7,
inference(avatar_split_clause,[],[f359,f577]) ).
tff(f577,plain,
( spl19_7
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
tff(f359,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f575,plain,
spl19_6,
inference(avatar_split_clause,[],[f358,f572]) ).
tff(f572,plain,
( spl19_6
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
tff(f358,plain,
semiri456707255roduct(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f570,plain,
spl19_5,
inference(avatar_split_clause,[],[f357,f567]) ).
tff(f567,plain,
( spl19_5
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
tff(f357,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f565,plain,
spl19_4,
inference(avatar_split_clause,[],[f356,f562]) ).
tff(f356,plain,
ring(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f560,plain,
spl19_3,
inference(avatar_split_clause,[],[f355,f557]) ).
tff(f557,plain,
( spl19_3
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
tff(f355,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f555,plain,
~ spl19_2,
inference(avatar_split_clause,[],[f354,f552]) ).
tff(f552,plain,
( spl19_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
tff(f354,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f550,plain,
spl19_1,
inference(avatar_split_clause,[],[f352,f547]) ).
tff(f352,plain,
member(atom,sK0,set(atom,as)),
inference(cnf_transformation,[],[f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM080_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n006.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 : Sun May 19 10:12:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (19296)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (19297)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/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
% 0.20/0.38 % (19299)WARNING: value z3 for option sas not known
% 0.20/0.38 % (19298)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 % (19299)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)
% 0.20/0.38 % (19301)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)
% 0.20/0.38 % (19302)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)
% 0.20/0.38 % (19303)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)
% 0.20/0.38 % (19300)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39 % (19303)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (19304)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.39 % (19304)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.40 % (19307)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.40 % (19305)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.41 % (19306)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.41 % (19305)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.44 % (19301)First to succeed.
% 0.20/0.46 % (19301)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19296"
% 0.20/0.46 % (19301)Refutation found. Thanks to Tanya!
% 0.20/0.46 % SZS status Theorem for theBenchmark
% 0.20/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (19301)------------------------------
% 0.20/0.47 % (19301)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.47 % (19301)Termination reason: Refutation
% 0.20/0.47
% 0.20/0.47 % (19301)Memory used [KB]: 1742
% 0.20/0.47 % (19301)Time elapsed: 0.080 s
% 0.20/0.47 % (19301)Instructions burned: 137 (million)
% 0.20/0.47 % (19296)Success in time 0.106 s
%------------------------------------------------------------------------------