TSTP Solution File: COM034_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM034_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:10 EDT 2024
% Result : Theorem 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 344
% Syntax : Number of formulae : 962 ( 213 unt; 56 typ; 0 def)
% Number of atoms : 2051 ( 807 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1970 ( 825 ~; 790 |; 34 &)
% ( 198 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 47 ( 23 >; 24 *; 0 +; 0 <<)
% Number of predicates : 208 ( 206 usr; 188 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 11 con; 0-5 aty)
% Number of variables : 2524 (2481 !; 4 ?;2524 :)
% ( 39 !>; 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,
atom: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
div_mod:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_4,type,
succ: int > int ).
tff(func_def_5,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_6,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_7,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > 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_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_10,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_11,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_13,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_14,type,
c_PresArith_Oatom_OLe: ( int * list(int) ) > atom ).
tff(func_def_15,type,
atom_case:
!>[X0: $tType] : ( ( fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom ) > X0 ) ).
tff(func_def_16,type,
atom_rec:
!>[X0: $tType] : ( ( fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom ) > X0 ) ).
tff(func_def_17,type,
divisor: atom > int ).
tff(func_def_18,type,
hd_coeff: atom > int ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
a: atom ).
tff(func_def_23,type,
d: int ).
tff(func_def_24,type,
e: list(int) ).
tff(func_def_25,type,
i: int ).
tff(func_def_26,type,
j: int ).
tff(func_def_27,type,
ks: list(int) ).
tff(func_def_28,type,
ks1: list(int) ).
tff(func_def_29,type,
l: int ).
tff(func_def_30,type,
sK0: list(int) ).
tff(func_def_31,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f3198,plain,
$false,
inference(avatar_sat_refutation,[],[f463,f468,f473,f478,f483,f488,f493,f498,f503,f508,f513,f518,f523,f528,f533,f538,f543,f548,f553,f558,f562,f566,f570,f574,f579,f583,f588,f593,f601,f605,f611,f616,f622,f627,f632,f637,f641,f645,f649,f653,f657,f661,f665,f676,f692,f696,f700,f714,f718,f728,f733,f738,f742,f746,f750,f754,f758,f780,f784,f802,f806,f821,f825,f829,f833,f837,f848,f853,f857,f863,f867,f871,f875,f879,f883,f887,f891,f903,f907,f911,f915,f922,f926,f956,f961,f968,f972,f976,f995,f1000,f1005,f1013,f1017,f1030,f1035,f1039,f1043,f1063,f1067,f1071,f1078,f1082,f1086,f1090,f1094,f1103,f1107,f1116,f1121,f1139,f1148,f1153,f1158,f1179,f1185,f1215,f1221,f1225,f1229,f1233,f1237,f1261,f1276,f1281,f1291,f1299,f1303,f1344,f1348,f1352,f1392,f1396,f1400,f1446,f1451,f1455,f1459,f1463,f1467,f1471,f1475,f1555,f1559,f1591,f1595,f1599,f1604,f1608,f1612,f1683,f1695,f1745,f1785,f1789,f1793,f1857,f1861,f1865,f1869,f1873,f1877,f1881,f1885,f1889,f1893,f1897,f2376,f2380,f2384,f2452,f2456,f2460,f2464,f2525,f2542,f2546,f2629,f2696,f2700,f2704,f2850,f2854,f2858,f2973,f3071,f3075,f3079,f3135]) ).
tff(f3135,plain,
( spl2_31
| ~ spl2_186 ),
inference(avatar_contradiction_clause,[],[f3134]) ).
tff(f3134,plain,
( $false
| spl2_31
| ~ spl2_186 ),
inference(trivial_inequality_removal,[],[f3127]) ).
tff(f3127,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) )
| spl2_31
| ~ spl2_186 ),
inference(superposition,[],[f610,f3074]) ).
tff(f3074,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl2_186 ),
inference(avatar_component_clause,[],[f3073]) ).
tff(f3073,plain,
( spl2_186
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_186])]) ).
tff(f610,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d) )
| spl2_31 ),
inference(avatar_component_clause,[],[f608]) ).
tff(f608,plain,
( spl2_31
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
tff(f3079,plain,
( spl2_187
| ~ spl2_95
| ~ spl2_97 ),
inference(avatar_split_clause,[],[f1051,f1041,f1033,f3077]) ).
tff(f3077,plain,
( spl2_187
<=> ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X1)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_187])]) ).
tff(f1033,plain,
( spl2_95
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).
tff(f1041,plain,
( spl2_97
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).
tff(f1051,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X1)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0)),X1) )
| ~ spl2_95
| ~ spl2_97 ),
inference(superposition,[],[f1042,f1034]) ).
tff(f1034,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) )
| ~ spl2_95 ),
inference(avatar_component_clause,[],[f1033]) ).
tff(f1042,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) )
| ~ spl2_97 ),
inference(avatar_component_clause,[],[f1041]) ).
tff(f3075,plain,
( spl2_186
| ~ spl2_16
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f996,f993,f535,f3073]) ).
tff(f535,plain,
( spl2_16
<=> semiring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f993,plain,
( spl2_89
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
tff(f996,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_89 ),
inference(resolution,[],[f994,f537]) ).
tff(f537,plain,
( semiring_div(int)
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f535]) ).
tff(f994,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) )
| ~ spl2_89 ),
inference(avatar_component_clause,[],[f993]) ).
tff(f3071,plain,
( ~ spl2_185
| ~ spl2_28
| spl2_31
| ~ spl2_33
| ~ spl2_102
| ~ spl2_124
| ~ spl2_152
| ~ spl2_175
| ~ spl2_178 ),
inference(avatar_split_clause,[],[f2757,f2694,f2540,f1743,f1278,f1080,f619,f608,f590,f3068]) ).
tff(f3068,plain,
( spl2_185
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,sK0,e)),div_mod(int,j,d)),d) = div_mod(int,iprod(int,ks1,cons(int,i,e)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_185])]) ).
tff(f590,plain,
( spl2_28
<=> ( ks1 = cons(int,hd_coeff(a),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
tff(f619,plain,
( spl2_33
<=> ( div_mod(int,i,d) = div_mod(int,j,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
tff(f1080,plain,
( spl2_102
<=> ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_102])]) ).
tff(f1278,plain,
( spl2_124
<=> ( ks = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_124])]) ).
tff(f1743,plain,
( spl2_152
<=> ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_152])]) ).
tff(f2540,plain,
( spl2_175
<=> ! [X0: int,X3: list(int),X2: int,X1: list(int)] : ( iprod(int,cons(int,X0,X1),cons(int,X2,X3)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X2)),iprod(int,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_175])]) ).
tff(f2694,plain,
( spl2_178
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_178])]) ).
tff(f2757,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,sK0,e)),div_mod(int,j,d)),d) != div_mod(int,iprod(int,ks1,cons(int,i,e)),d) )
| ~ spl2_28
| spl2_31
| ~ spl2_33
| ~ spl2_102
| ~ spl2_124
| ~ spl2_152
| ~ spl2_175
| ~ spl2_178 ),
inference(forward_demodulation,[],[f2756,f592]) ).
tff(f592,plain,
( ( ks1 = cons(int,hd_coeff(a),sK0) )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f590]) ).
tff(f2756,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,sK0,e)),div_mod(int,j,d)),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),sK0),cons(int,i,e)),d) )
| spl2_31
| ~ spl2_33
| ~ spl2_102
| ~ spl2_124
| ~ spl2_152
| ~ spl2_175
| ~ spl2_178 ),
inference(forward_demodulation,[],[f2755,f2547]) ).
tff(f2547,plain,
( ! [X2: list(int),X0: int,X1: list(int)] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,X2)) = iprod(int,cons(int,hd_coeff(a),X1),cons(int,X0,X2)) )
| ~ spl2_102
| ~ spl2_175 ),
inference(superposition,[],[f2541,f1081]) ).
tff(f1081,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_102 ),
inference(avatar_component_clause,[],[f1080]) ).
tff(f2541,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int)] : ( iprod(int,cons(int,X0,X1),cons(int,X2,X3)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X2)),iprod(int,X1,X3)) )
| ~ spl2_175 ),
inference(avatar_component_clause,[],[f2540]) ).
tff(f2755,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,sK0,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,sK0,e)),div_mod(int,j,d)),d) )
| spl2_31
| ~ spl2_33
| ~ spl2_124
| ~ spl2_152
| ~ spl2_178 ),
inference(forward_demodulation,[],[f2754,f1280]) ).
tff(f1280,plain,
( ( ks = sK0 )
| ~ spl2_124 ),
inference(avatar_component_clause,[],[f1278]) ).
tff(f2754,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,ks,e)),div_mod(int,j,d)),d) )
| spl2_31
| ~ spl2_33
| ~ spl2_152
| ~ spl2_178 ),
inference(forward_demodulation,[],[f2753,f621]) ).
tff(f621,plain,
( ( div_mod(int,i,d) = div_mod(int,j,d) )
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f619]) ).
tff(f2753,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,ks,e)),div_mod(int,i,d)),d) )
| spl2_31
| ~ spl2_152
| ~ spl2_178 ),
inference(forward_demodulation,[],[f2727,f1744]) ).
tff(f1744,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1) )
| ~ spl2_152 ),
inference(avatar_component_clause,[],[f1743]) ).
tff(f2727,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),iprod(int,ks,e)),d) )
| spl2_31
| ~ spl2_178 ),
inference(superposition,[],[f610,f2695]) ).
tff(f2695,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2)),X2) )
| ~ spl2_178 ),
inference(avatar_component_clause,[],[f2694]) ).
tff(f2973,plain,
( spl2_184
| ~ spl2_60 ),
inference(avatar_split_clause,[],[f810,f800,f2971]) ).
tff(f2971,plain,
( spl2_184
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_184])]) ).
tff(f800,plain,
( spl2_60
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_60])]) ).
tff(f810,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) )
| ~ spl2_60 ),
inference(forward_demodulation,[],[f808,f801]) ).
tff(f801,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) )
| ~ spl2_60 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f808,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),div_mod(int,aa(int,int,times_times(int,X0),X1),X2)),X2) )
| ~ spl2_60 ),
inference(superposition,[],[f801,f801]) ).
tff(f2858,plain,
( spl2_183
| ~ spl2_43
| ~ spl2_109 ),
inference(avatar_split_clause,[],[f1128,f1119,f663,f2856]) ).
tff(f2856,plain,
( spl2_183
<=> ! [X2: int,X3: int,X0: int,X1: int,X8: list(int),X6: int,X7: int,X4: list(int),X5: list(int)] :
( ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != dvd(X6,X7,X8) )
| ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),aa(int,int,times_times(int,X2),X3)) = X7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_183])]) ).
tff(f663,plain,
( spl2_43
<=> ! [X2: int,X3: list(int),X4: int,X0: list(int),X5: int,X1: int] :
( ( X1 = X4 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
tff(f1119,plain,
( spl2_109
<=> ! [X2: int,X3: int,X4: list(int),X0: list(int),X5: int,X1: int] : ( asubst(X5,X4,dvd(X3,X2,cons(int,X1,X0))) = dvd(X3,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),aa(int,int,times_times(int,X1),X5)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X4)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_109])]) ).
tff(f1128,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X8: list(int),X6: int,X7: int,X4: list(int),X5: list(int)] :
( ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != dvd(X6,X7,X8) )
| ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),aa(int,int,times_times(int,X2),X3)) = X7 ) )
| ~ spl2_43
| ~ spl2_109 ),
inference(superposition,[],[f664,f1120]) ).
tff(f1120,plain,
( ! [X2: int,X3: int,X0: list(int),X1: int,X4: list(int),X5: int] : ( asubst(X5,X4,dvd(X3,X2,cons(int,X1,X0))) = dvd(X3,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),aa(int,int,times_times(int,X1),X5)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X4)),X0)) )
| ~ spl2_109 ),
inference(avatar_component_clause,[],[f1119]) ).
tff(f664,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( dvd(X2,X1,X0) != dvd(X5,X4,X3) )
| ( X1 = X4 ) )
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f663]) ).
tff(f2854,plain,
( spl2_182
| ~ spl2_55
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f789,f782,f748,f2852]) ).
tff(f2852,plain,
( spl2_182
<=> ! [X0: $tType,X5: $tType,X6: X5,X4: list(X0),X7: fun(X0,fun(list(X0),X5)),X3: list(X0),X2: X0,X1: X0] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,X1),cons(X0,X2,splice(X0,X3,X4))) = list_case(X5,X0,X6,X7,splice(X0,cons(X0,X1,X3),cons(X0,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_182])]) ).
tff(f748,plain,
( spl2_55
<=> ! [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,[spl2_55])]) ).
tff(f782,plain,
( spl2_59
<=> ! [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,[spl2_59])]) ).
tff(f789,plain,
( ! [X5: $tType,X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: X5,X7: fun(X0,fun(list(X0),X5)),X4: list(X0)] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,X1),cons(X0,X2,splice(X0,X3,X4))) = list_case(X5,X0,X6,X7,splice(X0,cons(X0,X1,X3),cons(X0,X2,X4))) )
| ~ spl2_55
| ~ spl2_59 ),
inference(superposition,[],[f783,f749]) ).
tff(f749,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))) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f783,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) )
| ~ spl2_59 ),
inference(avatar_component_clause,[],[f782]) ).
tff(f2850,plain,
( spl2_181
| ~ spl2_54
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f788,f782,f744,f2848]) ).
tff(f2848,plain,
( spl2_181
<=> ! [X1: $tType,X0: $tType,X5: $tType,X6: X5,X4: list(X1),X7: fun(X0,fun(list(X0),X5)),X3: X1,X2: fun(X1,X0)] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,aa(X1,X0,X2,X3)),map(X1,X0,X2,X4)) = list_case(X5,X0,X6,X7,map(X1,X0,X2,cons(X1,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_181])]) ).
tff(f744,plain,
( spl2_54
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
tff(f788,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: X5,X7: fun(X0,fun(list(X0),X5)),X4: list(X1)] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,aa(X1,X0,X2,X3)),map(X1,X0,X2,X4)) = list_case(X5,X0,X6,X7,map(X1,X0,X2,cons(X1,X3,X4))) )
| ~ spl2_54
| ~ spl2_59 ),
inference(superposition,[],[f783,f745]) ).
tff(f745,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f2704,plain,
( spl2_180
| ~ spl2_20
| ~ spl2_169 ),
inference(avatar_split_clause,[],[f2521,f2382,f555,f2702]) ).
tff(f2702,plain,
( spl2_180
<=> ! [X2: int,X0: int,X1: list(int),X3: list(int)] : ( c_PresArith_Oatom_OLe(X0,X1) != asubst(X2,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_180])]) ).
tff(f555,plain,
( spl2_20
<=> ( a = dvd(d,l,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
tff(f2382,plain,
( spl2_169
<=> ! [X5: list(int),X4: int,X0: int,X3: int,X2: int,X1: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,dvd(X2,X3,ks1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_169])]) ).
tff(f2521,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int)] : ( c_PresArith_Oatom_OLe(X0,X1) != asubst(X2,X3,a) )
| ~ spl2_20
| ~ spl2_169 ),
inference(superposition,[],[f2383,f557]) ).
tff(f557,plain,
( ( a = dvd(d,l,ks1) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f555]) ).
tff(f2383,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int),X4: int,X5: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,dvd(X2,X3,ks1)) )
| ~ spl2_169 ),
inference(avatar_component_clause,[],[f2382]) ).
tff(f2700,plain,
( spl2_179
| ~ spl2_16
| ~ spl2_87 ),
inference(avatar_split_clause,[],[f978,f970,f535,f2698]) ).
tff(f2698,plain,
( spl2_179
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_179])]) ).
tff(f970,plain,
( spl2_87
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
tff(f978,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),X1),X2) )
| ~ spl2_16
| ~ spl2_87 ),
inference(resolution,[],[f971,f537]) ).
tff(f971,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) ) )
| ~ spl2_87 ),
inference(avatar_component_clause,[],[f970]) ).
tff(f2696,plain,
( spl2_178
| ~ spl2_16
| ~ spl2_86 ),
inference(avatar_split_clause,[],[f977,f966,f535,f2694]) ).
tff(f966,plain,
( spl2_86
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
tff(f977,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_86 ),
inference(resolution,[],[f967,f537]) ).
tff(f967,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) ) )
| ~ spl2_86 ),
inference(avatar_component_clause,[],[f966]) ).
tff(f2629,plain,
( spl2_177
| ~ spl2_17
| ~ spl2_19
| ~ spl2_85 ),
inference(avatar_split_clause,[],[f964,f959,f550,f540,f2627]) ).
tff(f2627,plain,
( spl2_177
<=> ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),hd_coeff(a)),hd_coeff(a))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_177])]) ).
tff(f540,plain,
( spl2_17
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f550,plain,
( spl2_19
<=> ( one_one(int) = hd_coeff(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f959,plain,
( spl2_85
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
tff(f964,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),hd_coeff(a)),hd_coeff(a))),X0) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_85 ),
inference(forward_demodulation,[],[f963,f552]) ).
tff(f552,plain,
( ( one_one(int) = hd_coeff(a) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f550]) ).
tff(f963,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),X0) )
| ~ spl2_17
| ~ spl2_85 ),
inference(resolution,[],[f960,f542]) ).
tff(f542,plain,
( comm_semiring_1(int)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f540]) ).
tff(f960,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X1) ) )
| ~ spl2_85 ),
inference(avatar_component_clause,[],[f959]) ).
tff(f2546,plain,
( spl2_176
| ~ spl2_92 ),
inference(avatar_split_clause,[],[f1022,f1011,f2544]) ).
tff(f2544,plain,
( spl2_176
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,aa(X0,X0,times_times(X0,X4),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X4),X3),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_176])]) ).
tff(f1011,plain,
( spl2_92
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).
tff(f1022,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( div_mod(X0,X1,X2) != div_mod(X0,X3,X2) )
| ( div_mod(X0,aa(X0,X0,times_times(X0,X4),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X4),X3),X2) )
| ~ semiring_div(X0) )
| ~ spl2_92 ),
inference(equality_resolution,[],[f1012]) ).
tff(f1012,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ~ semiring_div(X0) )
| ~ spl2_92 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f2542,plain,
( spl2_175
| ~ spl2_12
| ~ spl2_84 ),
inference(avatar_split_clause,[],[f957,f954,f515,f2540]) ).
tff(f515,plain,
( spl2_12
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f954,plain,
( spl2_84
<=> ! [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),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_84])]) ).
tff(f957,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int)] : ( iprod(int,cons(int,X0,X1),cons(int,X2,X3)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X2)),iprod(int,X1,X3)) )
| ~ spl2_12
| ~ spl2_84 ),
inference(resolution,[],[f955,f517]) ).
tff(f517,plain,
( ring(int)
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f515]) ).
tff(f955,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ~ ring(X0)
| ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) ) )
| ~ spl2_84 ),
inference(avatar_component_clause,[],[f954]) ).
tff(f2525,plain,
( spl2_174
| ~ spl2_59
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f988,f974,f782,f2523]) ).
tff(f2523,plain,
( spl2_174
<=> ! [X1: $tType,X0: $tType,X5: fun(X1,X1),X3: X0,X4: list(X0),X6: X1,X2: fun(X0,fun(list(X0),fun(X1,X1)))] : ( list_rec(X1,X0,X6,X2,cons(X0,X3,X4)) = aa(X1,X1,list_case(fun(X1,X1),X0,X5,X2,cons(X0,X3,X4)),list_rec(X1,X0,X6,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_174])]) ).
tff(f974,plain,
( spl2_88
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0,X2: list(X1)] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).
tff(f988,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X0,X6: X1,X4: list(X0),X5: fun(X1,X1)] : ( list_rec(X1,X0,X6,X2,cons(X0,X3,X4)) = aa(X1,X1,list_case(fun(X1,X1),X0,X5,X2,cons(X0,X3,X4)),list_rec(X1,X0,X6,X2,X4)) )
| ~ spl2_59
| ~ spl2_88 ),
inference(superposition,[],[f975,f783]) ).
tff(f975,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) )
| ~ spl2_88 ),
inference(avatar_component_clause,[],[f974]) ).
tff(f2464,plain,
( spl2_173
| ~ spl2_56
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f985,f974,f752,f2462]) ).
tff(f2462,plain,
( spl2_173
<=> ! [X0: $tType,X2: int,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X1: fun(int,fun(list(int),fun(X0,X0)))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_case(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_173])]) ).
tff(f752,plain,
( spl2_56
<=> ! [X0: $tType,X3: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0)),X2: int,X1: list(int)] : ( atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
tff(f985,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(X0,X0))),X6: X0,X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X5: fun(int,fun(int,fun(list(int),fun(X0,X0))))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_case(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) )
| ~ spl2_56
| ~ spl2_88 ),
inference(superposition,[],[f975,f753]) ).
tff(f753,plain,
( ! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f752]) ).
tff(f2460,plain,
( spl2_172
| ~ spl2_57
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f984,f974,f756,f2458]) ).
tff(f2458,plain,
( spl2_172
<=> ! [X0: $tType,X2: int,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X1: fun(int,fun(list(int),fun(X0,X0)))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_rec(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_172])]) ).
tff(f756,plain,
( spl2_57
<=> ! [X0: $tType,X5: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X3: fun(int,fun(int,fun(list(int),X0))),X2: int,X1: list(int)] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
tff(f984,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(X0,X0))),X6: X0,X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X5: fun(int,fun(int,fun(list(int),fun(X0,X0))))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_rec(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) )
| ~ spl2_57
| ~ spl2_88 ),
inference(superposition,[],[f975,f757]) ).
tff(f757,plain,
( ! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) )
| ~ spl2_57 ),
inference(avatar_component_clause,[],[f756]) ).
tff(f2456,plain,
( spl2_171
| ~ spl2_20
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f944,f924,f555,f2454]) ).
tff(f2454,plain,
( spl2_171
<=> ! [X0: $tType,X3: fun(int,fun(int,fun(list(int),X0))),X2: fun(int,fun(list(int),X0)),X1: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X1,d),l),ks1) = atom_case(X0,X2,X1,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_171])]) ).
tff(f924,plain,
( spl2_83
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X3: int,X2: int,X1: list(int)] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_83])]) ).
tff(f944,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X1,d),l),ks1) = atom_case(X0,X2,X1,X3,a) )
| ~ spl2_20
| ~ spl2_83 ),
inference(superposition,[],[f925,f557]) ).
tff(f925,plain,
( ! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) )
| ~ spl2_83 ),
inference(avatar_component_clause,[],[f924]) ).
tff(f2452,plain,
( spl2_170
| ~ spl2_20
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f927,f920,f555,f2450]) ).
tff(f2450,plain,
( spl2_170
<=> ! [X0: $tType,X3: fun(int,fun(int,fun(list(int),X0))),X2: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X2,d),l),ks1) = atom_rec(X0,X1,X2,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_170])]) ).
tff(f920,plain,
( spl2_82
<=> ! [X0: $tType,X3: int,X4: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0))),X2: int,X1: list(int)] : ( atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_82])]) ).
tff(f927,plain,
( ! [X0: $tType,X2: fun(int,fun(int,fun(list(int),X0))),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X2,d),l),ks1) = atom_rec(X0,X1,X2,X3,a) )
| ~ spl2_20
| ~ spl2_82 ),
inference(superposition,[],[f921,f557]) ).
tff(f921,plain,
( ! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) )
| ~ spl2_82 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f2384,plain,
( spl2_169
| ~ spl2_27
| ~ spl2_125 ),
inference(avatar_split_clause,[],[f1292,f1289,f585,f2382]) ).
tff(f585,plain,
( spl2_27
<=> ( ks1 = cons(int,hd_coeff(a),ks) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
tff(f1289,plain,
( spl2_125
<=> ! [X5: list(int),X3: int,X4: list(int),X7: list(int),X0: int,X6: int,X2: int,X1: int] : ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != c_PresArith_Oatom_OLe(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_125])]) ).
tff(f1292,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int),X4: int,X5: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,dvd(X2,X3,ks1)) )
| ~ spl2_27
| ~ spl2_125 ),
inference(superposition,[],[f1290,f587]) ).
tff(f587,plain,
( ( ks1 = cons(int,hd_coeff(a),ks) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f585]) ).
tff(f1290,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X6: int,X7: list(int),X4: list(int),X5: list(int)] : ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != c_PresArith_Oatom_OLe(X6,X7) )
| ~ spl2_125 ),
inference(avatar_component_clause,[],[f1289]) ).
tff(f2380,plain,
( spl2_168
| ~ spl2_59
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f943,f924,f782,f2378]) ).
tff(f2378,plain,
( spl2_168
<=> ! [X0: $tType,X5: X0,X6: fun(int,fun(list(int),X0)),X4: list(int),X7: fun(int,fun(int,fun(list(int),X0))),X3: int,X2: int,X1: fun(int,fun(int,fun(list(int),X0)))] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_case(X0,X6,X1,X7,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_168])]) ).
tff(f943,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X7: fun(int,fun(int,fun(list(int),X0))),X4: list(int),X5: X0] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_case(X0,X6,X1,X7,dvd(X2,X3,X4)) )
| ~ spl2_59
| ~ spl2_83 ),
inference(superposition,[],[f925,f783]) ).
tff(f2376,plain,
( spl2_167
| ~ spl2_59
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f931,f920,f782,f2374]) ).
tff(f2374,plain,
( spl2_167
<=> ! [X0: $tType,X5: X0,X6: fun(int,fun(list(int),X0)),X4: list(int),X7: fun(int,fun(int,fun(list(int),X0))),X3: int,X2: int,X1: fun(int,fun(int,fun(list(int),X0)))] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_rec(X0,X6,X1,X7,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_167])]) ).
tff(f931,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X7: fun(int,fun(int,fun(list(int),X0))),X4: list(int),X5: X0] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_rec(X0,X6,X1,X7,dvd(X2,X3,X4)) )
| ~ spl2_59
| ~ spl2_82 ),
inference(superposition,[],[f921,f783]) ).
tff(f1897,plain,
( spl2_166
| ~ spl2_56
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f942,f924,f752,f1895]) ).
tff(f1895,plain,
( spl2_166
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_166])]) ).
tff(f942,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) )
| ~ spl2_56
| ~ spl2_83 ),
inference(superposition,[],[f925,f753]) ).
tff(f1893,plain,
( spl2_165
| ~ spl2_57
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f941,f924,f756,f1891]) ).
tff(f1891,plain,
( spl2_165
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_165])]) ).
tff(f941,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) )
| ~ spl2_57
| ~ spl2_83 ),
inference(superposition,[],[f925,f757]) ).
tff(f1889,plain,
( spl2_164
| ~ spl2_56
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f930,f920,f752,f1887]) ).
tff(f1887,plain,
( spl2_164
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) = atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_164])]) ).
tff(f930,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) = atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) )
| ~ spl2_56
| ~ spl2_82 ),
inference(superposition,[],[f921,f753]) ).
tff(f1885,plain,
( spl2_163
| ~ spl2_57
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f929,f920,f756,f1883]) ).
tff(f1883,plain,
( spl2_163
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) = atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_163])]) ).
tff(f929,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) = atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) )
| ~ spl2_57
| ~ spl2_82 ),
inference(superposition,[],[f921,f757]) ).
tff(f1881,plain,
( spl2_162
| ~ spl2_3
| ~ spl2_17
| ~ spl2_70
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f899,f885,f861,f540,f470,f1879]) ).
tff(f1879,plain,
( spl2_162
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) = aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_162])]) ).
tff(f470,plain,
( spl2_3
<=> ab_semigroup_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f861,plain,
( spl2_70
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
tff(f885,plain,
( spl2_76
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X1)),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
tff(f899,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) = aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X2),X1)) )
| ~ spl2_3
| ~ spl2_17
| ~ spl2_70
| ~ spl2_76 ),
inference(forward_demodulation,[],[f898,f892]) ).
tff(f892,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) )
| ~ spl2_3
| ~ spl2_70 ),
inference(resolution,[],[f862,f472]) ).
tff(f472,plain,
( ab_semigroup_mult(int)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f470]) ).
tff(f862,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_mult(X0)
| ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) ) )
| ~ spl2_70 ),
inference(avatar_component_clause,[],[f861]) ).
tff(f898,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X2)),X1) )
| ~ spl2_17
| ~ spl2_76 ),
inference(resolution,[],[f886,f542]) ).
tff(f886,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X1)),X2) ) )
| ~ spl2_76 ),
inference(avatar_component_clause,[],[f885]) ).
tff(f1877,plain,
( spl2_161
| ~ spl2_17
| ~ spl2_74 ),
inference(avatar_split_clause,[],[f896,f877,f540,f1875]) ).
tff(f1875,plain,
( spl2_161
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,X1),aa(int,int,times_times(int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_161])]) ).
tff(f877,plain,
( spl2_74
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).
tff(f896,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,X1),aa(int,int,times_times(int,X0),X2)) )
| ~ spl2_17
| ~ spl2_74 ),
inference(resolution,[],[f878,f542]) ).
tff(f878,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,X2),aa(X0,X0,times_times(X0,X3),X1)) ) )
| ~ spl2_74 ),
inference(avatar_component_clause,[],[f877]) ).
tff(f1873,plain,
( spl2_160
| ~ spl2_16
| ~ spl2_73 ),
inference(avatar_split_clause,[],[f895,f873,f535,f1871]) ).
tff(f1871,plain,
( spl2_160
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,div_mod(int,X0,X1)),X2) = div_mod(int,aa(int,int,times_times(int,X0),X2),aa(int,int,times_times(int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_160])]) ).
tff(f873,plain,
( spl2_73
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_73])]) ).
tff(f895,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,div_mod(int,X0,X1)),X2) = div_mod(int,aa(int,int,times_times(int,X0),X2),aa(int,int,times_times(int,X1),X2)) )
| ~ spl2_16
| ~ spl2_73 ),
inference(resolution,[],[f874,f537]) ).
tff(f874,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) ) )
| ~ spl2_73 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f1869,plain,
( spl2_159
| ~ spl2_16
| ~ spl2_72 ),
inference(avatar_split_clause,[],[f894,f869,f535,f1867]) ).
tff(f1867,plain,
( spl2_159
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),div_mod(int,X1,X2)) = div_mod(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_159])]) ).
tff(f869,plain,
( spl2_72
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_72])]) ).
tff(f894,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),div_mod(int,X1,X2)) = div_mod(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) )
| ~ spl2_16
| ~ spl2_72 ),
inference(resolution,[],[f870,f537]) ).
tff(f870,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) ) )
| ~ spl2_72 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f1865,plain,
( spl2_158
| ~ spl2_20
| ~ spl2_147 ),
inference(avatar_split_clause,[],[f1739,f1602,f555,f1863]) ).
tff(f1863,plain,
( spl2_158
<=> ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_158])]) ).
tff(f1602,plain,
( spl2_147
<=> ! [X2: int,X0: int,X1: list(int),X3: int] : ( divisor(asubst(X0,X1,dvd(X2,X3,ks1))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_147])]) ).
tff(f1739,plain,
( ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) )
| ~ spl2_20
| ~ spl2_147 ),
inference(superposition,[],[f1603,f557]) ).
tff(f1603,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,dvd(X2,X3,ks1))) = X2 )
| ~ spl2_147 ),
inference(avatar_component_clause,[],[f1602]) ).
tff(f1861,plain,
( spl2_157
| ~ spl2_16
| ~ spl2_71 ),
inference(avatar_split_clause,[],[f893,f865,f535,f1859]) ).
tff(f1859,plain,
( spl2_157
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_157])]) ).
tff(f865,plain,
( spl2_71
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_71])]) ).
tff(f893,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_71 ),
inference(resolution,[],[f866,f537]) ).
tff(f866,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) )
| ~ spl2_71 ),
inference(avatar_component_clause,[],[f865]) ).
tff(f1857,plain,
( spl2_156
| ~ spl2_3
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f892,f861,f470,f1855]) ).
tff(f1855,plain,
( spl2_156
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_156])]) ).
tff(f1793,plain,
( spl2_155
| ~ spl2_16
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f859,f855,f535,f1791]) ).
tff(f1791,plain,
( spl2_155
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X2),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_155])]) ).
tff(f855,plain,
( spl2_69
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X3,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).
tff(f859,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X2),X1)),X1) )
| ~ spl2_16
| ~ spl2_69 ),
inference(resolution,[],[f856,f537]) ).
tff(f856,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X3,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X1) ) )
| ~ spl2_69 ),
inference(avatar_component_clause,[],[f855]) ).
tff(f1789,plain,
( spl2_154
| ~ spl2_16
| ~ spl2_68 ),
inference(avatar_split_clause,[],[f858,f851,f535,f1787]) ).
tff(f1787,plain,
( spl2_154
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_154])]) ).
tff(f851,plain,
( spl2_68
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,X3,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
tff(f858,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X2)),X1) )
| ~ spl2_16
| ~ spl2_68 ),
inference(resolution,[],[f852,f537]) ).
tff(f852,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X3,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X2) ) )
| ~ spl2_68 ),
inference(avatar_component_clause,[],[f851]) ).
tff(f1785,plain,
( spl2_153
| ~ spl2_49
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f766,f748,f716,f1783]) ).
tff(f1783,plain,
( spl2_153
<=> ! [X0: $tType,X5: X0,X6: list(X0),X4: list(X0),X3: list(X0),X2: X0,X1: X0] :
( ( cons(X0,X5,X6) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ( cons(X0,X2,splice(X0,X3,X4)) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_153])]) ).
tff(f716,plain,
( spl2_49
<=> ! [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,[spl2_49])]) ).
tff(f766,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: list(X0),X4: list(X0),X5: X0] :
( ( cons(X0,X5,X6) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ( cons(X0,X2,splice(X0,X3,X4)) = X6 ) )
| ~ spl2_49
| ~ spl2_55 ),
inference(superposition,[],[f717,f749]) ).
tff(f717,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X1 = X3 ) )
| ~ spl2_49 ),
inference(avatar_component_clause,[],[f716]) ).
tff(f1745,plain,
( spl2_152
| ~ spl2_17
| ~ spl2_67 ),
inference(avatar_split_clause,[],[f849,f846,f540,f1743]) ).
tff(f846,plain,
( spl2_67
<=> ! [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,[spl2_67])]) ).
tff(f849,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1) )
| ~ spl2_17
| ~ spl2_67 ),
inference(resolution,[],[f847,f542]) ).
tff(f847,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(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) ) )
| ~ spl2_67 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f1695,plain,
( spl2_151
| ~ spl2_16
| ~ spl2_64 ),
inference(avatar_split_clause,[],[f839,f827,f535,f1693]) ).
tff(f1693,plain,
( spl2_151
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_151])]) ).
tff(f827,plain,
( spl2_64
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
tff(f839,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),X1),X2) )
| ~ spl2_16
| ~ spl2_64 ),
inference(resolution,[],[f828,f537]) ).
tff(f828,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) ) )
| ~ spl2_64 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f1683,plain,
( spl2_150
| ~ spl2_49
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f761,f744,f716,f1681]) ).
tff(f1681,plain,
( spl2_150
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: list(X1),X2: fun(X1,X0),X6: list(X0),X3: X1] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( map(X1,X0,X2,X4) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_150])]) ).
tff(f761,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( map(X1,X0,X2,X4) = X6 ) )
| ~ spl2_49
| ~ spl2_54 ),
inference(superposition,[],[f717,f745]) ).
tff(f1612,plain,
( spl2_149
| ~ spl2_33
| ~ spl2_60 ),
inference(avatar_split_clause,[],[f809,f800,f619,f1610]) ).
tff(f1610,plain,
( spl2_149
<=> ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),i),d) = div_mod(int,aa(int,int,times_times(int,X0),j),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_149])]) ).
tff(f809,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),i),d) = div_mod(int,aa(int,int,times_times(int,X0),j),d) )
| ~ spl2_33
| ~ spl2_60 ),
inference(forward_demodulation,[],[f807,f801]) ).
tff(f807,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),i),d) = div_mod(int,aa(int,int,times_times(int,X0),div_mod(int,j,d)),d) )
| ~ spl2_33
| ~ spl2_60 ),
inference(superposition,[],[f801,f621]) ).
tff(f1608,plain,
( spl2_148
| ~ spl2_28
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f787,f782,f590,f1606]) ).
tff(f1606,plain,
( spl2_148
<=> ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( list_case(X0,int,X1,X2,ks1) = aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_148])]) ).
tff(f787,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( list_case(X0,int,X1,X2,ks1) = aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),sK0) )
| ~ spl2_28
| ~ spl2_59 ),
inference(superposition,[],[f783,f592]) ).
tff(f1604,plain,
( spl2_147
| ~ spl2_27
| ~ spl2_123 ),
inference(avatar_split_clause,[],[f1282,f1274,f585,f1602]) ).
tff(f1274,plain,
( spl2_123
<=> ! [X3: int,X4: list(int),X0: int,X5: list(int),X2: int,X1: int] : ( divisor(asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_123])]) ).
tff(f1282,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,dvd(X2,X3,ks1))) = X2 )
| ~ spl2_27
| ~ spl2_123 ),
inference(superposition,[],[f1275,f587]) ).
tff(f1275,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X4: list(int),X5: list(int)] : ( divisor(asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5)))) = X0 )
| ~ spl2_123 ),
inference(avatar_component_clause,[],[f1274]) ).
tff(f1599,plain,
( spl2_146
| ~ spl2_27
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f786,f782,f585,f1597]) ).
tff(f1597,plain,
( spl2_146
<=> ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),ks) = list_case(X0,int,X1,X2,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_146])]) ).
tff(f786,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),ks) = list_case(X0,int,X1,X2,ks1) )
| ~ spl2_27
| ~ spl2_59 ),
inference(superposition,[],[f783,f587]) ).
tff(f1595,plain,
( spl2_145
| ~ spl2_12
| ~ spl2_58 ),
inference(avatar_split_clause,[],[f785,f778,f515,f1593]) ).
tff(f1593,plain,
( spl2_145
<=> ! [X2: list(int),X0: int,X1: list(int)] : ( iprod(int,map(int,int,times_times(int,X0),X1),X2) = aa(int,int,times_times(int,X0),iprod(int,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_145])]) ).
tff(f778,plain,
( spl2_58
<=> ! [X0: $tType,X3: X0,X2: list(X0),X1: list(X0)] :
( ( iprod(X0,map(X0,X0,times_times(X0,X3),X2),X1) = aa(X0,X0,times_times(X0,X3),iprod(X0,X2,X1)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).
tff(f785,plain,
( ! [X2: list(int),X0: int,X1: list(int)] : ( iprod(int,map(int,int,times_times(int,X0),X1),X2) = aa(int,int,times_times(int,X0),iprod(int,X1,X2)) )
| ~ spl2_12
| ~ spl2_58 ),
inference(resolution,[],[f779,f517]) ).
tff(f779,plain,
( ! [X0: $tType,X2: list(X0),X3: X0,X1: list(X0)] :
( ~ ring(X0)
| ( iprod(X0,map(X0,X0,times_times(X0,X3),X2),X1) = aa(X0,X0,times_times(X0,X3),iprod(X0,X2,X1)) ) )
| ~ spl2_58 ),
inference(avatar_component_clause,[],[f778]) ).
tff(f1591,plain,
( spl2_144
| ~ spl2_46
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f763,f744,f694,f1589]) ).
tff(f1589,plain,
( spl2_144
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: list(X1),X2: fun(X1,X0),X6: list(X0),X3: X1] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_144])]) ).
tff(f694,plain,
( spl2_46
<=> ! [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,[spl2_46])]) ).
tff(f763,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X6: list(X0),X4: list(X1),X5: X0] :
( ( map(X1,X0,X2,cons(X1,X3,X4)) != cons(X0,X5,X6) )
| ( aa(X1,X0,X2,X3) = X5 ) )
| ~ spl2_46
| ~ spl2_54 ),
inference(superposition,[],[f695,f745]) ).
tff(f695,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X2 = X4 ) )
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f694]) ).
tff(f1559,plain,
( spl2_143
| ~ spl2_16
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f760,f740,f535,f1557]) ).
tff(f1557,plain,
( spl2_143
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_143])]) ).
tff(f740,plain,
( spl2_53
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
tff(f760,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X1) )
| ~ spl2_16
| ~ spl2_53 ),
inference(resolution,[],[f741,f537]) ).
tff(f741,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) ) )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f1555,plain,
( spl2_142
| ~ spl2_16
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f759,f736,f535,f1553]) ).
tff(f1553,plain,
( spl2_142
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_142])]) ).
tff(f736,plain,
( spl2_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
tff(f759,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0),X1) )
| ~ spl2_16
| ~ spl2_52 ),
inference(resolution,[],[f737,f537]) ).
tff(f737,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) ) )
| ~ spl2_52 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f1475,plain,
( spl2_141
| ~ spl2_82
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f940,f924,f920,f1473]) ).
tff(f1473,plain,
( spl2_141
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_141])]) ).
tff(f940,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) )
| ~ spl2_82
| ~ spl2_83 ),
inference(superposition,[],[f925,f921]) ).
tff(f1471,plain,
( spl2_140
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f939,f924,f1469]) ).
tff(f1469,plain,
( spl2_140
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_case(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_140])]) ).
tff(f939,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_case(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_case(X0,X7,X1,X8,dvd(X2,X3,X4)) )
| ~ spl2_83 ),
inference(superposition,[],[f925,f925]) ).
tff(f1467,plain,
( spl2_139
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f928,f920,f1465]) ).
tff(f1465,plain,
( spl2_139
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_139])]) ).
tff(f928,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X5,X1,X6,dvd(X2,X3,X4)) = atom_rec(X0,X7,X1,X8,dvd(X2,X3,X4)) )
| ~ spl2_82 ),
inference(superposition,[],[f921,f921]) ).
tff(f1463,plain,
( spl2_138
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f795,f782,f1461]) ).
tff(f1461,plain,
( spl2_138
<=> ! [X1: $tType,X0: $tType,X5: X1,X6: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_138])]) ).
tff(f795,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4)) )
| ~ spl2_59 ),
inference(superposition,[],[f783,f783]) ).
tff(f1459,plain,
( spl2_137
| ~ spl2_22
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f770,f748,f564,f1457]) ).
tff(f1457,plain,
( spl2_137
<=> ! [X0: $tType,X4: list(X0),X3: list(X0),X2: X0,X1: X0] : ( cons(X0,X2,splice(X0,X3,X4)) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_137])]) ).
tff(f564,plain,
( spl2_22
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
tff(f770,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X4: list(X0)] : ( cons(X0,X2,splice(X0,X3,X4)) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ~ spl2_22
| ~ spl2_55 ),
inference(superposition,[],[f565,f749]) ).
tff(f565,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f1455,plain,
( spl2_136
| ~ spl2_46
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f768,f748,f694,f1453]) ).
tff(f1453,plain,
( spl2_136
<=> ! [X0: $tType,X5: X0,X6: list(X0),X4: list(X0),X3: list(X0),X2: X0,X1: X0] :
( ( cons(X0,X5,X6) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ( X1 = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_136])]) ).
tff(f768,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: list(X0),X4: list(X0),X5: X0] :
( ( cons(X0,X5,X6) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ( X1 = X5 ) )
| ~ spl2_46
| ~ spl2_55 ),
inference(superposition,[],[f695,f749]) ).
tff(f1451,plain,
( ~ spl2_135
| spl2_117
| ~ spl2_124 ),
inference(avatar_split_clause,[],[f1353,f1278,f1218,f1448]) ).
tff(f1448,plain,
( spl2_135
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,sK0,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,sK0,e)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_135])]) ).
tff(f1218,plain,
( spl2_117
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_117])]) ).
tff(f1353,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,sK0,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,sK0,e)),d) )
| spl2_117
| ~ spl2_124 ),
inference(superposition,[],[f1220,f1280]) ).
tff(f1220,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) )
| spl2_117 ),
inference(avatar_component_clause,[],[f1218]) ).
tff(f1446,plain,
( ~ spl2_18
| spl2_134
| ~ spl2_15
| ~ spl2_51 ),
inference(avatar_split_clause,[],[f734,f731,f530,f1443,f545]) ).
tff(f545,plain,
( spl2_18
<=> cl_Groups_Oplus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f1443,plain,
( spl2_134
<=> ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_134])]) ).
tff(f530,plain,
( spl2_15
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f731,plain,
( spl2_51
<=> ! [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,[spl2_51])]) ).
tff(f734,plain,
( ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) )
| ~ cl_Groups_Oplus(int)
| ~ spl2_15
| ~ spl2_51 ),
inference(resolution,[],[f732,f532]) ).
tff(f532,plain,
( zero(int)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f530]) ).
tff(f732,plain,
( ! [X0: $tType] :
( ~ zero(X0)
| ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ cl_Groups_Oplus(X0) )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f731]) ).
tff(f1400,plain,
( spl2_133
| ~ spl2_42
| ~ spl2_109 ),
inference(avatar_split_clause,[],[f1126,f1119,f659,f1398]) ).
tff(f1398,plain,
( spl2_133
<=> ! [X2: int,X3: int,X0: int,X1: int,X8: list(int),X6: int,X7: int,X4: list(int),X5: list(int)] :
( ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != dvd(X6,X7,X8) )
| ( X0 = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_133])]) ).
tff(f659,plain,
( spl2_42
<=> ! [X3: list(int),X4: int,X0: list(int),X5: int,X2: int,X1: int] :
( ( X2 = X5 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
tff(f1126,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X8: list(int),X6: int,X7: int,X4: list(int),X5: list(int)] :
( ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != dvd(X6,X7,X8) )
| ( X0 = X6 ) )
| ~ spl2_42
| ~ spl2_109 ),
inference(superposition,[],[f660,f1120]) ).
tff(f660,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( dvd(X2,X1,X0) != dvd(X5,X4,X3) )
| ( X2 = X5 ) )
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f659]) ).
tff(f1396,plain,
( spl2_132
| ~ spl2_56
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f794,f782,f752,f1394]) ).
tff(f1394,plain,
( spl2_132
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X6: X0,X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_132])]) ).
tff(f794,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: X0,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) )
| ~ spl2_56
| ~ spl2_59 ),
inference(superposition,[],[f783,f753]) ).
tff(f1392,plain,
( spl2_131
| ~ spl2_57
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f793,f782,f756,f1390]) ).
tff(f1390,plain,
( spl2_131
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X6: X0,X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_131])]) ).
tff(f793,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: X0,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) )
| ~ spl2_57
| ~ spl2_59 ),
inference(superposition,[],[f783,f757]) ).
tff(f1352,plain,
( spl2_130
| ~ spl2_56
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f774,f756,f752,f1350]) ).
tff(f1350,plain,
( spl2_130
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_rec(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_130])]) ).
tff(f774,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_rec(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) )
| ~ spl2_56
| ~ spl2_57 ),
inference(superposition,[],[f757,f753]) ).
tff(f1348,plain,
( spl2_129
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f773,f756,f1346]) ).
tff(f1346,plain,
( spl2_129
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_rec(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_129])]) ).
tff(f773,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_rec(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) )
| ~ spl2_57 ),
inference(superposition,[],[f757,f757]) ).
tff(f1344,plain,
( spl2_128
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f771,f752,f1342]) ).
tff(f1342,plain,
( spl2_128
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_case(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_128])]) ).
tff(f771,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_case(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) )
| ~ spl2_56 ),
inference(superposition,[],[f753,f753]) ).
tff(f1303,plain,
( spl2_127
| ~ spl2_22
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f765,f744,f564,f1301]) ).
tff(f1301,plain,
( spl2_127
<=> ! [X1: $tType,X0: $tType,X4: list(X1),X3: X1,X2: fun(X1,X0)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_127])]) ).
tff(f765,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: X1,X4: list(X1)] : ( map(X1,X0,X2,X4) != map(X1,X0,X2,cons(X1,X3,X4)) )
| ~ spl2_22
| ~ spl2_54 ),
inference(superposition,[],[f565,f745]) ).
tff(f1299,plain,
( spl2_126
| ~ spl2_17
| ~ spl2_50 ),
inference(avatar_split_clause,[],[f729,f726,f540,f1297]) ).
tff(f1297,plain,
( spl2_126
<=> ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X1),X0) = aa(int,int,times_times(int,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_126])]) ).
tff(f726,plain,
( spl2_50
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
tff(f729,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X1),X0) = aa(int,int,times_times(int,X0),X1) )
| ~ spl2_17
| ~ spl2_50 ),
inference(resolution,[],[f727,f542]) ).
tff(f727,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) ) )
| ~ spl2_50 ),
inference(avatar_component_clause,[],[f726]) ).
tff(f1291,plain,
( spl2_125
| ~ spl2_26
| ~ spl2_109 ),
inference(avatar_split_clause,[],[f1125,f1119,f581,f1289]) ).
tff(f581,plain,
( spl2_26
<=> ! [X2: int,X4: int,X0: list(int),X3: list(int),X1: int] : ( dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
tff(f1125,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X6: int,X7: list(int),X4: list(int),X5: list(int)] : ( asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5))) != c_PresArith_Oatom_OLe(X6,X7) )
| ~ spl2_26
| ~ spl2_109 ),
inference(superposition,[],[f582,f1120]) ).
tff(f582,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int] : ( dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f581]) ).
tff(f1281,plain,
( spl2_124
| ~ spl2_28
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f1250,f1231,f590,f1278]) ).
tff(f1231,plain,
( spl2_120
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_120])]) ).
tff(f1250,plain,
( ( ks = sK0 )
| ~ spl2_28
| ~ spl2_120 ),
inference(trivial_inequality_removal,[],[f1247]) ).
tff(f1247,plain,
( ( ks1 != ks1 )
| ( ks = sK0 )
| ~ spl2_28
| ~ spl2_120 ),
inference(superposition,[],[f1232,f592]) ).
tff(f1232,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_120 ),
inference(avatar_component_clause,[],[f1231]) ).
tff(f1276,plain,
( spl2_123
| ~ spl2_23
| ~ spl2_109 ),
inference(avatar_split_clause,[],[f1124,f1119,f568,f1274]) ).
tff(f568,plain,
( spl2_23
<=> ! [X2: int,X0: list(int),X1: int] : ( divisor(dvd(X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
tff(f1124,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X4: list(int),X5: list(int)] : ( divisor(asubst(X3,X4,dvd(X0,X1,cons(int,X2,X5)))) = X0 )
| ~ spl2_23
| ~ spl2_109 ),
inference(superposition,[],[f569,f1120]) ).
tff(f569,plain,
( ! [X2: int,X0: list(int),X1: int] : ( divisor(dvd(X2,X1,X0)) = X2 )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f568]) ).
tff(f1261,plain,
( spl2_122
| ~ spl2_16
| ~ spl2_48 ),
inference(avatar_split_clause,[],[f719,f712,f535,f1259]) ).
tff(f1259,plain,
( spl2_122
<=> ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_122])]) ).
tff(f712,plain,
( spl2_48
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
tff(f719,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) )
| ~ spl2_16
| ~ spl2_48 ),
inference(resolution,[],[f713,f537]) ).
tff(f713,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) ) )
| ~ spl2_48 ),
inference(avatar_component_clause,[],[f712]) ).
tff(f1237,plain,
( spl2_121
| ~ spl2_28
| ~ spl2_49 ),
inference(avatar_split_clause,[],[f721,f716,f590,f1235]) ).
tff(f1235,plain,
( spl2_121
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_121])]) ).
tff(f721,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) )
| ~ spl2_28
| ~ spl2_49 ),
inference(superposition,[],[f717,f592]) ).
tff(f1233,plain,
( spl2_120
| ~ spl2_27
| ~ spl2_49 ),
inference(avatar_split_clause,[],[f720,f716,f585,f1231]) ).
tff(f720,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_27
| ~ spl2_49 ),
inference(superposition,[],[f717,f587]) ).
tff(f1229,plain,
( spl2_119
| ~ spl2_27
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f703,f694,f585,f1227]) ).
tff(f1227,plain,
( spl2_119
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_119])]) ).
tff(f703,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) )
| ~ spl2_27
| ~ spl2_46 ),
inference(superposition,[],[f695,f587]) ).
tff(f1225,plain,
( spl2_118
| ~ spl2_13
| ~ spl2_19
| ~ spl2_45 ),
inference(avatar_split_clause,[],[f702,f690,f550,f520,f1223]) ).
tff(f1223,plain,
( spl2_118
<=> ! [X0: list(int)] : ( map(int,int,times_times(int,hd_coeff(a)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_118])]) ).
tff(f520,plain,
( spl2_13
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f690,plain,
( spl2_45
<=> ! [X0: $tType,X1: list(X0)] :
( ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
tff(f702,plain,
( ! [X0: list(int)] : ( map(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_13
| ~ spl2_19
| ~ spl2_45 ),
inference(forward_demodulation,[],[f701,f552]) ).
tff(f701,plain,
( ! [X0: list(int)] : ( map(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl2_13
| ~ spl2_45 ),
inference(resolution,[],[f691,f522]) ).
tff(f522,plain,
( monoid_mult(int)
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f520]) ).
tff(f691,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ monoid_mult(X0)
| ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl2_45 ),
inference(avatar_component_clause,[],[f690]) ).
tff(f1221,plain,
( ~ spl2_117
| ~ spl2_16
| ~ spl2_89
| spl2_116 ),
inference(avatar_split_clause,[],[f1216,f1212,f993,f535,f1218]) ).
tff(f1212,plain,
( spl2_116
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,j,d)),div_mod(int,iprod(int,ks,e),d)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_116])]) ).
tff(f1216,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) )
| ~ spl2_16
| ~ spl2_89
| spl2_116 ),
inference(forward_demodulation,[],[f1214,f996]) ).
tff(f1214,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,j,d)),div_mod(int,iprod(int,ks,e),d)),d) )
| spl2_116 ),
inference(avatar_component_clause,[],[f1212]) ).
tff(f1215,plain,
( ~ spl2_116
| spl2_31
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f623,f619,f608,f1212]) ).
tff(f623,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,j,d)),div_mod(int,iprod(int,ks,e),d)),d) )
| spl2_31
| ~ spl2_33 ),
inference(superposition,[],[f610,f621]) ).
tff(f1185,plain,
spl2_115,
inference(avatar_split_clause,[],[f341,f1183]) ).
tff(f1183,plain,
( spl2_115
<=> ! [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,[spl2_115])]) ).
tff(f341,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,[],[f224]) ).
tff(f224,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,[],[f131]) ).
tff(f131,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,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X9: list(X0),X10: list(X0),X11: 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)),X11),X10)),X9) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_list__add__assoc) ).
tff(f1179,plain,
spl2_114,
inference(avatar_split_clause,[],[f403,f1177]) ).
tff(f1177,plain,
( spl2_114
<=> ! [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,[spl2_114])]) ).
tff(f403,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,[],[f282]) ).
tff(f282,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,[],[f187]) ).
tff(f187,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,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
tff(f1158,plain,
spl2_113,
inference(avatar_split_clause,[],[f343,f1156]) ).
tff(f1156,plain,
( spl2_113
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X3)),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),X3)),X1) )
| ~ semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_113])]) ).
tff(f343,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,times_times(X0,X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X3)),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),X3)),X1) )
| ~ semiring(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,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,times_times(X0,X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X3)),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),X3)),X1) )
| ~ semiring(X0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType] :
( semiring(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X3)),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X2)),X3)),X1) ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType] :
( semiring(X0)
=> ! [X12: X0,X4: X0,X42: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X42)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X42)),X12)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X42)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_combine__common__factor) ).
tff(f1153,plain,
spl2_112,
inference(avatar_split_clause,[],[f416,f1151]) ).
tff(f1151,plain,
( spl2_112
<=> ! [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,[spl2_112])]) ).
tff(f416,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,[],[f290]) ).
tff(f290,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,[],[f289]) ).
tff(f289,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,[],[f199]) ).
tff(f199,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,[],[f35]) ).
tff(f35,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X27: list(X2),X28: X2,X29: list(X1),X30: X1,X31: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X31),cons(X1,X30,X29)),cons(X2,X28,X27)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X31,X30),X28),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X31),X29),X27)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_zipwith0_Osimps_I2_J) ).
tff(f1148,plain,
spl2_111,
inference(avatar_split_clause,[],[f406,f1146]) ).
tff(f1146,plain,
( spl2_111
<=> ! [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,[spl2_111])]) ).
tff(f406,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,[],[f288]) ).
tff(f288,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,[],[f287]) ).
tff(f287,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,[],[f189]) ).
tff(f189,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,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X25,X11)),cons(X0,X24,X10)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X25),X24),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list__add__Cons) ).
tff(f1139,plain,
spl2_110,
inference(avatar_split_clause,[],[f346,f1137]) ).
tff(f1137,plain,
( spl2_110
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( X2 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_110])]) ).
tff(f346,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( X1 = X3 )
| ( X2 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,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,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ( ( X1 != X3 )
& ( X2 != X4 ) ) )
& ( ( X1 = X3 )
| ( X2 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) ) ) )
| ~ semiri456707255roduct(X0) ),
inference(flattening,[],[f295]) ).
tff(f295,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,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ( ( X1 != X3 )
& ( X2 != X4 ) ) )
& ( ( X1 = X3 )
| ( X2 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) ) ) )
| ~ semiri456707255roduct(X0) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,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,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
<=> ( ( X1 = X3 )
| ( X2 = X4 ) ) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
<=> ( ( X1 = X3 )
| ( X2 = X4 ) ) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X39: X0,X30: X0,X28: X0,X40: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X40),X28)),aa(X0,X0,times_times(X0,X30),X39)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X40),X39)),aa(X0,X0,times_times(X0,X30),X28)) )
<=> ( ( X28 = X39 )
| ( X30 = X40 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_crossproduct__eq) ).
tff(f1121,plain,
spl2_109,
inference(avatar_split_clause,[],[f434,f1119]) ).
tff(f434,plain,
! [X2: int,X3: int,X0: list(int),X1: int,X4: list(int),X5: int] : ( asubst(X5,X4,dvd(X3,X2,cons(int,X1,X0))) = dvd(X3,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),aa(int,int,times_times(int,X1),X5)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X4)),X0)) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: list(int),X1: int,X2: int,X3: int,X4: list(int),X5: int] : ( asubst(X5,X4,dvd(X3,X2,cons(int,X1,X0))) = dvd(X3,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),aa(int,int,times_times(int,X1),X5)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X4)),X0)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X59: list(int),X60: int,X61: int,X38: int,X62: list(int),X63: int] : ( asubst(X63,X62,dvd(X38,X61,cons(int,X60,X59))) = dvd(X38,aa(int,int,aa(int,fun(int,int),plus_plus(int),X61),aa(int,int,times_times(int,X60),X63)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X60),X62)),X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_asubst_Osimps_I2_J) ).
tff(f1116,plain,
( spl2_108
| ~ spl2_20
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f708,f698,f555,f1114]) ).
tff(f1114,plain,
( spl2_108
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( ks1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_108])]) ).
tff(f698,plain,
( spl2_47
<=> ! [X2: int,X4: int,X0: list(int),X5: int,X3: list(int),X1: int] :
( ( X0 = X3 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
tff(f708,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( ks1 = X2 ) )
| ~ spl2_20
| ~ spl2_47 ),
inference(superposition,[],[f699,f557]) ).
tff(f699,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( dvd(X2,X1,X0) != dvd(X5,X4,X3) )
| ( X0 = X3 ) )
| ~ spl2_47 ),
inference(avatar_component_clause,[],[f698]) ).
tff(f1107,plain,
spl2_107,
inference(avatar_split_clause,[],[f444,f1105]) ).
tff(f1105,plain,
( spl2_107
<=> ! [X0: $tType,X4: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X4),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X4),X3)) )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_107])]) ).
tff(f444,plain,
! [X0: $tType,X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X4),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X4),X3)) )
| ~ semiri456707255roduct(X0) ),
inference(equality_resolution,[],[f347]) ).
tff(f347,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,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ( X2 != X4 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f1103,plain,
spl2_106,
inference(avatar_split_clause,[],[f381,f1101]) ).
tff(f1101,plain,
( spl2_106
<=> ! [X0: $tType,X2: X0,X4: X0,X3: X0,X5: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_106])]) ).
tff(f381,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,X5,X4) = div_mod(X0,X3,X4) )
=> ( ( div_mod(X0,X2,X4) = div_mod(X0,X1,X4) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X2),X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X4) ) ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X13: X0,X4: X0,X14: X0,X12: X0,X5: X0] :
( ( div_mod(X0,X5,X12) = div_mod(X0,X14,X12) )
=> ( ( div_mod(X0,X4,X12) = div_mod(X0,X13,X12) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X14),X13),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mod__add__cong) ).
tff(f1094,plain,
spl2_105,
inference(avatar_split_clause,[],[f399,f1092]) ).
tff(f1092,plain,
( spl2_105
<=> ! [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,[spl2_105])]) ).
tff(f399,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,[],[f278]) ).
tff(f278,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,[],[f183]) ).
tff(f183,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,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
tff(f1090,plain,
spl2_104,
inference(avatar_split_clause,[],[f397,f1088]) ).
tff(f1088,plain,
( spl2_104
<=> ! [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,[spl2_104])]) ).
tff(f397,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,[],[f276]) ).
tff(f276,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,[],[f181]) ).
tff(f181,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,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f1086,plain,
spl2_103,
inference(avatar_split_clause,[],[f396,f1084]) ).
tff(f1084,plain,
( spl2_103
<=> ! [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,[spl2_103])]) ).
tff(f396,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,[],[f275]) ).
tff(f275,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,[],[f180]) ).
tff(f180,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,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f1082,plain,
( spl2_102
| ~ spl2_11
| ~ spl2_19
| ~ spl2_37 ),
inference(avatar_split_clause,[],[f669,f639,f550,f510,f1080]) ).
tff(f510,plain,
( spl2_11
<=> comm_monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f639,plain,
( spl2_37
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
tff(f669,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_11
| ~ spl2_19
| ~ spl2_37 ),
inference(forward_demodulation,[],[f668,f552]) ).
tff(f668,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl2_11
| ~ spl2_37 ),
inference(resolution,[],[f640,f512]) ).
tff(f512,plain,
( comm_monoid_mult(int)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f510]) ).
tff(f640,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f1078,plain,
spl2_101,
inference(avatar_split_clause,[],[f340,f1076]) ).
tff(f1076,plain,
( spl2_101
<=> ! [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,[spl2_101])]) ).
tff(f340,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,[],[f223]) ).
tff(f223,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,[],[f130]) ).
tff(f130,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,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1071,plain,
spl2_100,
inference(avatar_split_clause,[],[f394,f1069]) ).
tff(f1069,plain,
( spl2_100
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_100])]) ).
tff(f394,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X12)),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
tff(f1067,plain,
spl2_99,
inference(avatar_split_clause,[],[f393,f1065]) ).
tff(f1065,plain,
( spl2_99
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(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),aa(X0,X0,times_times(X0,X3),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_99])]) ).
tff(f393,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(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),aa(X0,X0,times_times(X0,X3),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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),aa(X0,X0,times_times(X0,X3),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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),aa(X0,X0,times_times(X0,X3),X2)),aa(X0,X0,times_times(X0,X3),X1)) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X37: X0,X24: X0,X25: X0] : ( aa(X0,X0,times_times(X0,X25),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X24),X37)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X25),X24)),aa(X0,X0,times_times(X0,X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
tff(f1063,plain,
spl2_98,
inference(avatar_split_clause,[],[f339,f1061]) ).
tff(f1061,plain,
( spl2_98
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).
tff(f339,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring(X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring(X0) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType] :
( comm_semiring(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(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,times_times(X0,X3),X1)),aa(X0,X0,times_times(X0,X2),X1)) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType] :
( comm_semiring(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X12)),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__class_Odistrib) ).
tff(f1043,plain,
spl2_97,
inference(avatar_split_clause,[],[f415,f1041]) ).
tff(f415,plain,
! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: int,X1: int,X2: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X48: int,X49: int,X50: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X50),X49)),X48) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X50),X48)),aa(int,int,times_times(int,X49),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_int__distrib_I1_J) ).
tff(f1039,plain,
( spl2_96
| ~ spl2_11
| ~ spl2_19
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f667,f630,f550,f510,f1037]) ).
tff(f1037,plain,
( spl2_96
<=> ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
tff(f630,plain,
( spl2_35
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
tff(f667,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 )
| ~ spl2_11
| ~ spl2_19
| ~ spl2_35 ),
inference(forward_demodulation,[],[f666,f552]) ).
tff(f666,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),one_one(int)) = X0 )
| ~ spl2_11
| ~ spl2_35 ),
inference(resolution,[],[f631,f512]) ).
tff(f631,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) )
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f1035,plain,
spl2_95,
inference(avatar_split_clause,[],[f414,f1033]) ).
tff(f414,plain,
! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: int,X1: int,X2: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X49: int,X50: int,X48: int] : ( aa(int,int,times_times(int,X48),aa(int,int,aa(int,fun(int,int),plus_plus(int),X50),X49)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X48),X50)),aa(int,int,times_times(int,X48),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_int__distrib_I2_J) ).
tff(f1030,plain,
spl2_94,
inference(avatar_split_clause,[],[f356,f1028]) ).
tff(f1028,plain,
( spl2_94
<=> ! [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,[spl2_94])]) ).
tff(f356,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,[],[f235]) ).
tff(f235,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,[],[f142]) ).
tff(f142,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,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X9: list(X0),X10: list(X0),X11: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10),X9) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X11,X9)),iprod(X0,X10,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_iprod__left__add__distrib) ).
tff(f1017,plain,
spl2_93,
inference(avatar_split_clause,[],[f402,f1015]) ).
tff(f1015,plain,
( spl2_93
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).
tff(f402,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X2)),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X4),X2)),aa(X0,X0,times_times(X0,X3),X1)) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X35: X0,X36: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X35)),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),aa(X0,X0,times_times(X0,X35),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
tff(f1013,plain,
spl2_92,
inference(avatar_split_clause,[],[f380,f1011]) ).
tff(f380,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) )
| ( div_mod(X0,X2,X4) != div_mod(X0,X1,X4) )
| ( div_mod(X0,X5,X4) != div_mod(X0,X3,X4) ) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( div_mod(X0,X5,X4) = div_mod(X0,X3,X4) )
=> ( ( div_mod(X0,X2,X4) = div_mod(X0,X1,X4) )
=> ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X2),X4) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X4) ) ) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X13: X0,X4: X0,X14: X0,X12: X0,X5: X0] :
( ( div_mod(X0,X5,X12) = div_mod(X0,X14,X12) )
=> ( ( div_mod(X0,X4,X12) = div_mod(X0,X13,X12) )
=> ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X4),X12) = div_mod(X0,aa(X0,X0,times_times(X0,X14),X13),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_mod__mult__cong) ).
tff(f1005,plain,
spl2_91,
inference(avatar_split_clause,[],[f388,f1003]) ).
tff(f1003,plain,
( spl2_91
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X32: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X32) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X32)),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
tff(f1000,plain,
spl2_90,
inference(avatar_split_clause,[],[f387,f998]) ).
tff(f998,plain,
( spl2_90
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0,X32: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),aa(X0,X0,times_times(X0,X5),X32)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
tff(f995,plain,
spl2_89,
inference(avatar_split_clause,[],[f379,f993]) ).
tff(f379,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X5,X12)),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mod__add__eq) ).
tff(f976,plain,
spl2_88,
inference(avatar_split_clause,[],[f433,f974]) ).
tff(f433,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X1: $tType,X19: list(X1),X8: X1,X46: fun(X1,fun(list(X1),fun(X0,X0))),X47: X0] : ( list_rec(X0,X1,X47,X46,cons(X1,X8,X19)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X46,X8),X19),list_rec(X0,X1,X47,X46,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list_Orecs_I2_J) ).
tff(f972,plain,
spl2_87,
inference(avatar_split_clause,[],[f377,f970]) ).
tff(f377,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X5,X12)),X4),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zmod__simps_I1_J) ).
tff(f968,plain,
spl2_86,
inference(avatar_split_clause,[],[f375,f966]) ).
tff(f375,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_mod__add__right__eq) ).
tff(f961,plain,
spl2_85,
inference(avatar_split_clause,[],[f384,f959]) ).
tff(f384,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X1) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X32: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),X32) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f956,plain,
spl2_84,
inference(avatar_split_clause,[],[f357,f954]) ).
tff(f357,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),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,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),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,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),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( iprod(X0,cons(X0,X25,X11),cons(X0,X24,X10)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X25),X24)),iprod(X0,X11,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_iprod__Cons) ).
tff(f926,plain,
spl2_83,
inference(avatar_split_clause,[],[f440,f924]) ).
tff(f440,plain,
! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType,X1: list(int),X2: int,X3: int,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X19: list(int),X20: int,X21: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X46,X21),X20),X19) = atom_case(X0,X47,X46,X45,dvd(X21,X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atom_Osimps_I11_J) ).
tff(f922,plain,
spl2_82,
inference(avatar_split_clause,[],[f439,f920]) ).
tff(f439,plain,
! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: list(int),X2: int,X3: int,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X19: list(int),X20: int,X21: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X47,X46,X45,dvd(X21,X20,X19)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X46,X21),X20),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_atom_Orecs_I2_J) ).
tff(f915,plain,
( spl2_81
| ~ spl2_20
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f686,f663,f555,f913]) ).
tff(f913,plain,
( spl2_81
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( l = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
tff(f686,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( l = X1 ) )
| ~ spl2_20
| ~ spl2_43 ),
inference(superposition,[],[f664,f557]) ).
tff(f911,plain,
spl2_80,
inference(avatar_split_clause,[],[f359,f909]) ).
tff(f909,plain,
( spl2_80
<=> ! [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,[spl2_80])]) ).
tff(f359,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,[],[f238]) ).
tff(f238,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,[],[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),X1),X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X5: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X5) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X5) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__right__imp__eq) ).
tff(f907,plain,
spl2_79,
inference(avatar_split_clause,[],[f358,f905]) ).
tff(f905,plain,
( spl2_79
<=> ! [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,[spl2_79])]) ).
tff(f358,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,[],[f237]) ).
tff(f237,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,[],[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),X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__left__imp__eq) ).
tff(f903,plain,
spl2_78,
inference(avatar_split_clause,[],[f342,f901]) ).
tff(f901,plain,
( spl2_78
<=> ! [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,[spl2_78])]) ).
tff(f342,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,[],[f225]) ).
tff(f225,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,[],[f132]) ).
tff(f132,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,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__imp__eq) ).
tff(f891,plain,
( spl2_77
| ~ spl2_20
| ~ spl2_42 ),
inference(avatar_split_clause,[],[f683,f659,f555,f889]) ).
tff(f889,plain,
( spl2_77
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( d = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_77])]) ).
tff(f683,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != dvd(X0,X1,X2) )
| ( d = X0 ) )
| ~ spl2_20
| ~ spl2_42 ),
inference(superposition,[],[f660,f557]) ).
tff(f887,plain,
spl2_76,
inference(avatar_split_clause,[],[f392,f885]) ).
tff(f392,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X1)),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X1)),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X1)),X2) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X34: X0,X35: X0,X36: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X35)),X34) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
tff(f883,plain,
spl2_75,
inference(avatar_split_clause,[],[f390,f881]) ).
tff(f881,plain,
( spl2_75
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
tff(f390,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X36: X0] : ( aa(X0,X0,times_times(X0,X36),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f879,plain,
spl2_74,
inference(avatar_split_clause,[],[f389,f877]) ).
tff(f389,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,times_times(X0,X2),aa(X0,X0,times_times(X0,X3),X1)) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X36: X0] : ( aa(X0,X0,times_times(X0,X36),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,X34),aa(X0,X0,times_times(X0,X36),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f875,plain,
spl2_73,
inference(avatar_split_clause,[],[f374,f873]) ).
tff(f374,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X1),X2)) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X12),aa(X0,X0,times_times(X0,X4),X12)) = aa(X0,X0,times_times(X0,div_mod(X0,X5,X4)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_mod__mult__mult2) ).
tff(f871,plain,
spl2_72,
inference(avatar_split_clause,[],[f373,f869]) ).
tff(f373,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)) = div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),aa(X0,X0,times_times(X0,X3),X1)) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X5: X0,X12: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X12),X5),aa(X0,X0,times_times(X0,X12),X4)) = aa(X0,X0,times_times(X0,X12),div_mod(X0,X5,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mod__mult__mult1) ).
tff(f867,plain,
spl2_71,
inference(avatar_split_clause,[],[f372,f865]) ).
tff(f372,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X4),X12) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X5,X12)),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mod__mult__eq) ).
tff(f863,plain,
spl2_70,
inference(avatar_split_clause,[],[f338,f861]) ).
tff(f338,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) )
| ~ ab_semigroup_mult(X0) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType] :
( ab_semigroup_mult(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X3),X2)),X1) = aa(X0,X0,times_times(X0,X3),aa(X0,X0,times_times(X0,X2),X1)) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( ab_semigroup_mult(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X5),X4)),X12) = aa(X0,X0,times_times(X0,X5),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ab__semigroup__mult__class_Omult__ac_I1_J) ).
tff(f857,plain,
spl2_69,
inference(avatar_split_clause,[],[f371,f855]) ).
tff(f371,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,X3,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X1) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,times_times(X0,X12),X4)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_mod__mult__self1) ).
tff(f853,plain,
spl2_68,
inference(avatar_split_clause,[],[f370,f851]) ).
tff(f370,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,X3,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,X3,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,times_times(X0,X2),X1)),X2) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,times_times(X0,X4),X12)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_mod__mult__self2) ).
tff(f848,plain,
spl2_67,
inference(avatar_split_clause,[],[f386,f846]) ).
tff(f386,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,[],[f265]) ).
tff(f265,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,[],[f170]) ).
tff(f170,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,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X5) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f837,plain,
spl2_66,
inference(avatar_split_clause,[],[f419,f835]) ).
tff(f835,plain,
( spl2_66
<=> ! [X0: list(int),X3: int,X2: list(int),X1: atom] :
( i_Z(asubst(X3,X2,X1),X0)
| ~ 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,[spl2_66])]) ).
tff(f419,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( i_Z(asubst(X3,X2,X1),X0)
| ~ 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,[],[f303]) ).
tff(f303,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( ( i_Z(asubst(X3,X2,X1),X0)
| ~ i_Z(X1,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)) )
& ( i_Z(X1,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))
| ~ i_Z(asubst(X3,X2,X1),X0) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: list(int),X1: atom,X2: list(int),X3: int] :
( i_Z(asubst(X3,X2,X1),X0)
<=> i_Z(X1,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X29: list(int),X8: atom,X59: list(int),X61: int] :
( i_Z(asubst(X61,X59,X8),X29)
<=> i_Z(X8,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X61),iprod(int,X59,X29)),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_IZ__asubst) ).
tff(f833,plain,
spl2_65,
inference(avatar_split_clause,[],[f418,f831]) ).
tff(f831,plain,
( spl2_65
<=> ! [X0: list(int),X3: int,X2: list(int),X1: atom] :
( i_Z(X1,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))
| ~ i_Z(asubst(X3,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).
tff(f418,plain,
! [X2: list(int),X3: int,X0: list(int),X1: atom] :
( i_Z(X1,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))
| ~ i_Z(asubst(X3,X2,X1),X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f829,plain,
spl2_64,
inference(avatar_split_clause,[],[f368,f827]) ).
tff(f368,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X4),X12) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X5,X12)),X4),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_zmod__simps_I4_J) ).
tff(f825,plain,
( spl2_63
| ~ spl2_20
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f594,f581,f555,f823]) ).
tff(f823,plain,
( spl2_63
<=> ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).
tff(f594,plain,
( ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) )
| ~ spl2_20
| ~ spl2_26 ),
inference(superposition,[],[f582,f557]) ).
tff(f821,plain,
spl2_62,
inference(avatar_split_clause,[],[f367,f819]) ).
tff(f819,plain,
( spl2_62
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_62])]) ).
tff(f367,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,X3),div_mod(X0,X2,X1)),X1) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X4),X12) = div_mod(X0,aa(X0,X0,times_times(X0,X5),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mod__mult__right__eq) ).
tff(f806,plain,
spl2_61,
inference(avatar_split_clause,[],[f417,f804]) ).
tff(f804,plain,
( spl2_61
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK1(X0,X1,X2,X3)) != aa(X1,X0,X2,sK1(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).
tff(f417,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK1(X0,X1,X2,X3)) != aa(X1,X0,X2,sK1(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK1(X0,X1,X2,X3)) != aa(X1,X0,X2,sK1(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f291,f301]) ).
tff(f301,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,sK1(X0,X1,X2,X3)) != aa(X1,X0,X2,sK1(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,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X43: fun(X0,X1),X31: fun(X0,X1)] :
( ! [X44: X0] : ( aa(X0,X1,X31,X44) = aa(X0,X1,X43,X44) )
=> ( X31 = X43 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f802,plain,
spl2_60,
inference(avatar_split_clause,[],[f412,f800]) ).
tff(f412,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int,X2: int] : ( div_mod(int,aa(int,int,times_times(int,X2),div_mod(int,X1,X0)),X0) = div_mod(int,aa(int,int,times_times(int,X2),X1),X0) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X12: int,X4: int,X5: int] : ( div_mod(int,aa(int,int,times_times(int,X5),div_mod(int,X4,X12)),X12) = div_mod(int,aa(int,int,times_times(int,X5),X4),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zmod__zmult1__eq) ).
tff(f784,plain,
spl2_59,
inference(avatar_split_clause,[],[f432,f782]) ).
tff(f432,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,[],[f210]) ).
tff(f210,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,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X1: $tType,X19: list(X1),X8: X1,X46: fun(X1,fun(list(X1),X0)),X47: X0] : ( list_case(X0,X1,X47,X46,cons(X1,X8,X19)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X46,X8),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_list_Osimps_I5_J) ).
tff(f780,plain,
spl2_58,
inference(avatar_split_clause,[],[f355,f778]) ).
tff(f355,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: list(X0)] :
( ( iprod(X0,map(X0,X0,times_times(X0,X3),X2),X1) = aa(X0,X0,times_times(X0,X3),iprod(X0,X2,X1)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: X0] : ( iprod(X0,map(X0,X0,times_times(X0,X3),X2),X1) = aa(X0,X0,times_times(X0,X3),iprod(X0,X2,X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: X0] : ( iprod(X0,map(X0,X0,times_times(X0,X3),X2),X1) = aa(X0,X0,times_times(X0,X3),iprod(X0,X2,X1)) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X27: list(X0),X29: list(X0),X30: X0] : ( iprod(X0,map(X0,X0,times_times(X0,X30),X29),X27) = aa(X0,X0,times_times(X0,X30),iprod(X0,X29,X27)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_iprod__assoc) ).
tff(f758,plain,
spl2_57,
inference(avatar_split_clause,[],[f431,f756]) ).
tff(f431,plain,
! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: list(int),X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType,X19: list(int),X52: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X47,X52),X19) = atom_rec(X0,X47,X46,X45,c_PresArith_Oatom_OLe(X52,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_atom_Orecs_I1_J) ).
tff(f754,plain,
spl2_56,
inference(avatar_split_clause,[],[f430,f752]) ).
tff(f430,plain,
! [X0: $tType,X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X1: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: list(int),X2: int,X3: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(list(int),X0))] : ( atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType,X19: list(int),X52: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( atom_case(X0,X47,X46,X45,c_PresArith_Oatom_OLe(X52,X19)) = aa(list(int),X0,aa(int,fun(list(int),X0),X47,X52),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_atom_Osimps_I10_J) ).
tff(f750,plain,
spl2_55,
inference(avatar_split_clause,[],[f426,f748]) ).
tff(f426,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,[],[f206]) ).
tff(f206,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,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType,X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( splice(X0,cons(X0,X25,X11),cons(X0,X24,X10)) = cons(X0,X25,cons(X0,X24,splice(X0,X11,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_splice_Osimps_I3_J) ).
tff(f746,plain,
spl2_54,
inference(avatar_split_clause,[],[f425,f744]) ).
tff(f425,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType,X1: $tType,X29: list(X1),X30: X1,X31: fun(X1,X0)] : ( map(X1,X0,X31,cons(X1,X30,X29)) = cons(X0,aa(X1,X0,X31,X30),map(X1,X0,X31,X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map_Osimps_I2_J) ).
tff(f742,plain,
spl2_53,
inference(avatar_split_clause,[],[f366,f740]) ).
tff(f366,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X4) = div_mod(X0,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_mod__add__self2) ).
tff(f738,plain,
spl2_52,
inference(avatar_split_clause,[],[f365,f736]) ).
tff(f365,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X5: X0,X4: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X5),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_mod__add__self1) ).
tff(f733,plain,
spl2_51,
inference(avatar_split_clause,[],[f405,f731]) ).
tff(f405,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,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_20_list__add__def) ).
tff(f728,plain,
spl2_50,
inference(avatar_split_clause,[],[f385,f726]) ).
tff(f385,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,X5),X4) = aa(X0,X0,times_times(X0,X4),X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f718,plain,
spl2_49,
inference(avatar_split_clause,[],[f428,f716]) ).
tff(f428,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,[],[f307]) ).
tff(f307,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,[],[f306]) ).
tff(f306,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,[],[f207]) ).
tff(f207,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,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType,X16: list(X0),X41: X0,X19: list(X0),X8: X0] :
( ( cons(X0,X8,X19) = cons(X0,X41,X16) )
<=> ( ( X16 = X19 )
& ( X8 = X41 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_list_Oinject) ).
tff(f714,plain,
spl2_48,
inference(avatar_split_clause,[],[f364,f712]) ).
tff(f364,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0] : ( div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,div_mod(X0,X5,X4),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_mod__mod__trivial) ).
tff(f700,plain,
spl2_47,
inference(avatar_split_clause,[],[f437,f698]) ).
tff(f437,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X0 = X3 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
inference(flattening,[],[f308]) ).
tff(f308,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
<=> ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) ) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X16: list(int),X17: int,X18: int,X19: list(int),X20: int,X21: int] :
( ( dvd(X21,X20,X19) = dvd(X18,X17,X16) )
<=> ( ( X16 = X19 )
& ( X17 = X20 )
& ( X18 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_atom_Osimps_I2_J) ).
tff(f696,plain,
spl2_46,
inference(avatar_split_clause,[],[f427,f694]) ).
tff(f427,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,[],[f307]) ).
tff(f692,plain,
spl2_45,
inference(avatar_split_clause,[],[f354,f690]) ).
tff(f354,plain,
! [X0: $tType,X1: list(X0)] :
( ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X29: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X29) = X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_scale1) ).
tff(f676,plain,
( ~ spl2_44
| ~ spl2_22
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f596,f590,f564,f673]) ).
tff(f673,plain,
( spl2_44
<=> ( ks1 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
tff(f596,plain,
( ( ks1 != sK0 )
| ~ spl2_22
| ~ spl2_28 ),
inference(superposition,[],[f565,f592]) ).
tff(f665,plain,
spl2_43,
inference(avatar_split_clause,[],[f436,f663]) ).
tff(f436,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X1 = X4 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f661,plain,
spl2_42,
inference(avatar_split_clause,[],[f435,f659]) ).
tff(f435,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X2 = X5 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f657,plain,
spl2_41,
inference(avatar_split_clause,[],[f383,f655]) ).
tff(f655,plain,
( spl2_41
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
tff(f383,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
tff(f653,plain,
spl2_40,
inference(avatar_split_clause,[],[f382,f651]) ).
tff(f651,plain,
( spl2_40
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
tff(f382,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f649,plain,
spl2_39,
inference(avatar_split_clause,[],[f353,f647]) ).
tff(f647,plain,
( spl2_39
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
tff(f353,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mult__1__left) ).
tff(f645,plain,
spl2_38,
inference(avatar_split_clause,[],[f352,f643]) ).
tff(f643,plain,
( spl2_38
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
tff(f352,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mult__1__right) ).
tff(f641,plain,
spl2_37,
inference(avatar_split_clause,[],[f345,f639]) ).
tff(f345,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mult__1) ).
tff(f637,plain,
( ~ spl2_36
| ~ spl2_22
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f595,f585,f564,f634]) ).
tff(f634,plain,
( spl2_36
<=> ( ks = ks1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
tff(f595,plain,
( ( ks != ks1 )
| ~ spl2_22
| ~ spl2_27 ),
inference(superposition,[],[f565,f587]) ).
tff(f632,plain,
spl2_35,
inference(avatar_split_clause,[],[f344,f630]) ).
tff(f344,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mult_Ocomm__neutral) ).
tff(f627,plain,
spl2_34,
inference(avatar_split_clause,[],[f421,f625]) ).
tff(f625,plain,
( spl2_34
<=> ! [X2: list(int),X0: list(int),X1: int,X3: int] :
( ( X0 = X2 )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
tff(f421,plain,
! [X2: list(int),X3: int,X0: list(int),X1: int] :
( ( X0 = X2 )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( ( c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ) ),
inference(flattening,[],[f304]) ).
tff(f304,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( ( c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int] :
( ( c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X16: list(int),X51: int,X19: list(int),X52: int] :
( ( c_PresArith_Oatom_OLe(X52,X19) = c_PresArith_Oatom_OLe(X51,X16) )
<=> ( ( X16 = X19 )
& ( X51 = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_atom_Osimps_I1_J) ).
tff(f622,plain,
( spl2_33
| ~ spl2_29
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f617,f613,f598,f619]) ).
tff(f598,plain,
( spl2_29
<=> ( d = divisor(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
tff(f613,plain,
( spl2_32
<=> ( div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
tff(f617,plain,
( ( div_mod(int,i,d) = div_mod(int,j,d) )
| ~ spl2_29
| ~ spl2_32 ),
inference(forward_demodulation,[],[f615,f600]) ).
tff(f600,plain,
( ( d = divisor(a) )
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f598]) ).
tff(f615,plain,
( ( div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)) )
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f613]) ).
tff(f616,plain,
spl2_32,
inference(avatar_split_clause,[],[f332,f613]) ).
tff(f332,plain,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_assms_I3_J) ).
tff(f611,plain,
~ spl2_31,
inference(avatar_split_clause,[],[f310,f608]) ).
tff(f310,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(flattening,[],[f120]) ).
tff(f120,negated_conjecture,
( ~ div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d) ),
inference(negated_conjecture,[],[f119]) ).
tff(f119,conjecture,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f605,plain,
spl2_30,
inference(avatar_split_clause,[],[f420,f603]) ).
tff(f603,plain,
( spl2_30
<=> ! [X0: list(int),X3: int,X2: list(int),X1: int] :
( ( X1 = X3 )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
tff(f420,plain,
! [X2: list(int),X3: int,X0: list(int),X1: int] :
( ( X1 = X3 )
| ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f601,plain,
( spl2_29
| ~ spl2_20
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f575,f568,f555,f598]) ).
tff(f575,plain,
( ( d = divisor(a) )
| ~ spl2_20
| ~ spl2_23 ),
inference(superposition,[],[f569,f557]) ).
tff(f593,plain,
spl2_28,
inference(avatar_split_clause,[],[f457,f590]) ).
tff(f457,plain,
ks1 = cons(int,hd_coeff(a),sK0),
inference(forward_demodulation,[],[f334,f329]) ).
tff(f329,plain,
one_one(int) = hd_coeff(a),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
one_one(int) = hd_coeff(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_assms_I2_J) ).
tff(f334,plain,
ks1 = cons(int,one_one(int),sK0),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
ks1 = cons(int,one_one(int),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f219,f292]) ).
tff(f292,plain,
( ? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) )
=> ( ks1 = cons(int,one_one(int),sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f219,plain,
? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) ),
inference(ennf_transformation,[],[f122]) ).
tff(f122,plain,
~ ! [X0: list(int)] : ( ks1 != cons(int,one_one(int),X0) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
~ ! [X26: list(int)] : ( ks1 != cons(int,one_one(int),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__096_B_Bthesis_O_A_I_B_Bks_H_O_Aks_A_061_A1_A_D_Aks_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f588,plain,
spl2_27,
inference(avatar_split_clause,[],[f456,f585]) ).
tff(f456,plain,
ks1 = cons(int,hd_coeff(a),ks),
inference(forward_demodulation,[],[f331,f329]) ).
tff(f331,plain,
ks1 = cons(int,one_one(int),ks),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
ks1 = cons(int,one_one(int),ks),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__096ks_A_061_A1_A_D_Aks_H_096) ).
tff(f583,plain,
spl2_26,
inference(avatar_split_clause,[],[f423,f581]) ).
tff(f423,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int] : ( dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int] : ( dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X55: list(int),X56: int,X57: int,X53: list(int),X54: int] : ( dvd(X57,X56,X55) != c_PresArith_Oatom_OLe(X54,X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_atom_Osimps_I4_J) ).
tff(f579,plain,
spl2_25,
inference(avatar_split_clause,[],[f411,f577]) ).
tff(f577,plain,
( spl2_25
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
tff(f411,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X5: atom,X22: list(int),X23: int] : ( divisor(asubst(X23,X22,X5)) = divisor(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_divisor__asubst) ).
tff(f574,plain,
spl2_24,
inference(avatar_split_clause,[],[f458,f572]) ).
tff(f572,plain,
( spl2_24
<=> ! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
tff(f458,plain,
! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(forward_demodulation,[],[f407,f329]) ).
tff(f407,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X22: list(int),X23: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X23,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_divisor_Osimps_I1_J) ).
tff(f570,plain,
spl2_23,
inference(avatar_split_clause,[],[f410,f568]) ).
tff(f410,plain,
! [X2: int,X0: list(int),X1: int] : ( divisor(dvd(X2,X1,X0)) = X2 ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: list(int),X1: int,X2: int] : ( divisor(dvd(X2,X1,X0)) = X2 ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X22: list(int),X23: int,X15: int] : ( divisor(dvd(X15,X23,X22)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_divisor_Osimps_I2_J) ).
tff(f566,plain,
spl2_22,
inference(avatar_split_clause,[],[f408,f564]) ).
tff(f408,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( cons(X0,X1,X2) != X2 ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X25: X0,X11: list(X0)] : ( cons(X0,X25,X11) != X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_not__Cons__self) ).
tff(f562,plain,
spl2_21,
inference(avatar_split_clause,[],[f404,f560]) ).
tff(f560,plain,
( spl2_21
<=> ! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
tff(f404,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType] :
( ( cl_Groups_Oplus(X0)
& zero(X0) )
=> cl_Groups_Oplus(list(X0)) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X64: $tType] :
( ( cl_Groups_Oplus(X64)
& zero(X64) )
=> cl_Groups_Oplus(list(X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
tff(f558,plain,
spl2_20,
inference(avatar_split_clause,[],[f330,f555]) ).
tff(f330,plain,
a = dvd(d,l,ks1),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
a = dvd(d,l,ks1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Dvd) ).
tff(f553,plain,
spl2_19,
inference(avatar_split_clause,[],[f329,f550]) ).
tff(f548,plain,
spl2_18,
inference(avatar_split_clause,[],[f328,f545]) ).
tff(f328,plain,
cl_Groups_Oplus(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
cl_Groups_Oplus(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
tff(f543,plain,
spl2_17,
inference(avatar_split_clause,[],[f327,f540]) ).
tff(f327,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(f538,plain,
spl2_16,
inference(avatar_split_clause,[],[f326,f535]) ).
tff(f326,plain,
semiring_div(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_div(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f533,plain,
spl2_15,
inference(avatar_split_clause,[],[f325,f530]) ).
tff(f325,plain,
zero(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f528,plain,
spl2_14,
inference(avatar_split_clause,[],[f324,f525]) ).
tff(f525,plain,
( spl2_14
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f324,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f523,plain,
spl2_13,
inference(avatar_split_clause,[],[f323,f520]) ).
tff(f323,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f518,plain,
spl2_12,
inference(avatar_split_clause,[],[f322,f515]) ).
tff(f322,plain,
ring(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f513,plain,
spl2_11,
inference(avatar_split_clause,[],[f321,f510]) ).
tff(f321,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
tff(f508,plain,
spl2_10,
inference(avatar_split_clause,[],[f320,f505]) ).
tff(f505,plain,
( spl2_10
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f320,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(f503,plain,
spl2_9,
inference(avatar_split_clause,[],[f319,f500]) ).
tff(f500,plain,
( spl2_9
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f319,plain,
pp(fTrue),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f498,plain,
spl2_8,
inference(avatar_split_clause,[],[f318,f495]) ).
tff(f495,plain,
( spl2_8
<=> comm_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f318,plain,
comm_semiring(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
comm_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
tff(f493,plain,
spl2_7,
inference(avatar_split_clause,[],[f317,f490]) ).
tff(f490,plain,
( spl2_7
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f317,plain,
semiring(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
tff(f488,plain,
spl2_6,
inference(avatar_split_clause,[],[f316,f485]) ).
tff(f485,plain,
( spl2_6
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f316,plain,
one(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f483,plain,
spl2_5,
inference(avatar_split_clause,[],[f315,f480]) ).
tff(f480,plain,
( spl2_5
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f315,plain,
monoid_add(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f478,plain,
spl2_4,
inference(avatar_split_clause,[],[f314,f475]) ).
tff(f475,plain,
( spl2_4
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f314,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f473,plain,
spl2_3,
inference(avatar_split_clause,[],[f313,f470]) ).
tff(f313,plain,
ab_semigroup_mult(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
tff(f468,plain,
spl2_2,
inference(avatar_split_clause,[],[f312,f465]) ).
tff(f465,plain,
( spl2_2
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f312,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f463,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f311,f460]) ).
tff(f460,plain,
( spl2_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f311,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM034_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 21:24:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (32296)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (32299)WARNING: value z3 for option sas not known
% 0.15/0.39 % (32297)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (32298)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (32300)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (32301)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)
% 0.15/0.39 % (32299)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)
% 0.15/0.39 % (32302)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)
% 0.15/0.39 % (32303)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)
% 0.15/0.39 % (32303)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % (32306)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)
% 0.22/0.41 % (32305)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)
% 0.22/0.41 % (32304)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (32305)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (32304)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % Exception at run slice level
% 0.22/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % (32307)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)
% 0.22/0.54 % (32301)First to succeed.
% 0.22/0.55 % (32301)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32296"
% 0.22/0.55 % (32301)Refutation found. Thanks to Tanya!
% 0.22/0.55 % SZS status Theorem for theBenchmark
% 0.22/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.56 % (32301)------------------------------
% 0.22/0.56 % (32301)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.56 % (32301)Termination reason: Refutation
% 0.22/0.56
% 0.22/0.56 % (32301)Memory used [KB]: 2931
% 0.22/0.56 % (32301)Time elapsed: 0.163 s
% 0.22/0.56 % (32301)Instructions burned: 355 (million)
% 0.22/0.56 % (32296)Success in time 0.18 s
%------------------------------------------------------------------------------