TSTP Solution File: COM041_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM041_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 : n017.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 : Tue Apr 30 10:47:36 EDT 2024
% Result : Theorem 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 345
% Syntax : Number of formulae : 974 ( 219 unt; 56 typ; 0 def)
% Number of atoms : 2142 ( 838 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 2103 ( 879 ~; 844 |; 49 &)
% ( 198 <=>; 133 =>; 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 : 43 ( 21 >; 22 *; 0 +; 0 <<)
% Number of predicates : 205 ( 203 usr; 183 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 11 con; 0-5 aty)
% Number of variables : 2519 (2478 !; 4 ?;2519 :)
% ( 37 !>; 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,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_4,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
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,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_9,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_10,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_11,type,
c_PresArith_Oatom_OLe: ( int * list(int) ) > atom ).
tff(func_def_12,type,
nDvd: ( int * int * list(int) ) > atom ).
tff(func_def_13,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_14,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_15,type,
divisor: atom > int ).
tff(func_def_16,type,
hd_coeff: atom > int ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
a: atom ).
tff(func_def_21,type,
d: int ).
tff(func_def_22,type,
e: list(int) ).
tff(func_def_23,type,
i: int ).
tff(func_def_24,type,
j: int ).
tff(func_def_25,type,
ks: list(int) ).
tff(func_def_26,type,
ks1: list(int) ).
tff(func_def_27,type,
l: int ).
tff(func_def_28,type,
sK0: list(int) ).
tff(func_def_29,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,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comm_ring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_21,type,
pp: bool > $o ).
tff(f2582,plain,
$false,
inference(avatar_sat_refutation,[],[f498,f503,f508,f513,f518,f523,f528,f533,f538,f543,f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f612,f616,f620,f624,f628,f632,f637,f641,f646,f651,f658,f663,f669,f675,f679,f684,f688,f692,f696,f701,f705,f709,f713,f717,f721,f725,f738,f754,f758,f762,f766,f781,f785,f796,f800,f805,f810,f814,f818,f822,f826,f843,f848,f852,f865,f869,f873,f877,f881,f890,f895,f899,f903,f913,f917,f921,f925,f929,f933,f937,f941,f953,f957,f961,f965,f972,f976,f1001,f1006,f1012,f1016,f1022,f1028,f1032,f1036,f1045,f1049,f1062,f1066,f1071,f1075,f1079,f1083,f1099,f1103,f1107,f1111,f1115,f1124,f1128,f1132,f1142,f1146,f1168,f1173,f1190,f1194,f1208,f1213,f1218,f1246,f1253,f1257,f1261,f1265,f1286,f1294,f1309,f1313,f1327,f1331,f1346,f1350,f1390,f1394,f1398,f1420,f1439,f1443,f1456,f1460,f1464,f1468,f1472,f1512,f1516,f1540,f1544,f1548,f1601,f1611,f1658,f1662,f1666,f1714,f1718,f1726,f1730,f1777,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1841,f2281,f2310,f2314,f2348,f2352,f2438,f2442,f2510,f2514,f2575]) ).
tff(f2575,plain,
( ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(avatar_contradiction_clause,[],[f2574]) ).
tff(f2574,plain,
( $false
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(trivial_inequality_removal,[],[f2573]) ).
tff(f2573,plain,
( ( div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2572,f645]) ).
tff(f645,plain,
( ( ks1 = cons(int,hd_coeff(a),ks) )
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f643]) ).
tff(f643,plain,
( spl2_32
<=> ( ks1 = cons(int,hd_coeff(a),ks) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
tff(f2572,plain,
( ( div_mod(int,iprod(int,cons(int,hd_coeff(a),cons(int,hd_coeff(a),ks)),cons(int,i,cons(int,l,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2571,f2353]) ).
tff(f2353,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_107
| ~ spl2_177 ),
inference(superposition,[],[f2347,f1098]) ).
tff(f1098,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_107 ),
inference(avatar_component_clause,[],[f1097]) ).
tff(f1097,plain,
( spl2_107
<=> ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_107])]) ).
tff(f2347,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_177 ),
inference(avatar_component_clause,[],[f2346]) ).
tff(f2346,plain,
( spl2_177
<=> ! [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_177])]) ).
tff(f2571,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,cons(int,hd_coeff(a),ks),cons(int,l,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2570,f2353]) ).
tff(f2570,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),aa(int,int,aa(int,fun(int,int),plus_plus(int),l),iprod(int,ks,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2569,f1117]) ).
tff(f1117,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X2)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2)) )
| ~ spl2_18
| ~ spl2_109 ),
inference(resolution,[],[f1106,f582]) ).
tff(f582,plain,
( comm_semiring_1(int)
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f580]) ).
tff(f580,plain,
( spl2_18
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f1106,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(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)) ) )
| ~ spl2_109 ),
inference(avatar_component_clause,[],[f1105]) ).
tff(f1105,plain,
( spl2_109
<=> ! [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_109])]) ).
tff(f2569,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),ks1),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| ~ spl2_32
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2568,f645]) ).
tff(f2568,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) != div_mod(int,iprod(int,cons(int,hd_coeff(a),cons(int,hd_coeff(a),ks)),cons(int,i,cons(int,l,e))),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2567,f2353]) ).
tff(f2567,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,cons(int,hd_coeff(a),ks),cons(int,l,e))),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_107
| ~ spl2_109
| ~ spl2_155
| ~ spl2_177
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2566,f2353]) ).
tff(f2566,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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),aa(int,int,aa(int,fun(int,int),plus_plus(int),l),iprod(int,ks,e))),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_109
| ~ spl2_155
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2565,f1657]) ).
tff(f1657,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_155 ),
inference(avatar_component_clause,[],[f1656]) ).
tff(f1656,plain,
( spl2_155
<=> ! [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_155])]) ).
tff(f2565,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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),aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,ks,e)),l)),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_109
| ~ spl2_155
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2564,f2552]) ).
tff(f2552,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) )
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2523,f2509]) ).
tff(f2509,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_181 ),
inference(avatar_component_clause,[],[f2508]) ).
tff(f2508,plain,
( spl2_181
<=> ! [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_181])]) ).
tff(f2523,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2)),X2) )
| ~ spl2_181 ),
inference(superposition,[],[f2509,f2509]) ).
tff(f2564,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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),aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,ks,e)),div_mod(int,l,d))),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_109
| ~ spl2_155
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2563,f1657]) ).
tff(f2563,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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),aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),iprod(int,ks,e))),d) )
| ~ spl2_18
| spl2_57
| ~ spl2_109
| ~ spl2_181 ),
inference(forward_demodulation,[],[f2537,f1117]) ).
tff(f2537,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) )
| spl2_57
| ~ spl2_181 ),
inference(superposition,[],[f795,f2509]) ).
tff(f795,plain,
( ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d) )
| spl2_57 ),
inference(avatar_component_clause,[],[f793]) ).
tff(f793,plain,
( spl2_57
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
tff(f2514,plain,
( spl2_182
| ~ spl2_17
| ~ spl2_94 ),
inference(avatar_split_clause,[],[f1018,f1014,f575,f2512]) ).
tff(f2512,plain,
( spl2_182
<=> ! [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_182])]) ).
tff(f575,plain,
( spl2_17
<=> semiring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f1014,plain,
( spl2_94
<=> ! [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)),X2),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).
tff(f1018,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_17
| ~ spl2_94 ),
inference(resolution,[],[f1015,f577]) ).
tff(f577,plain,
( semiring_div(int)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f575]) ).
tff(f1015,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)),X2),X1) ) )
| ~ spl2_94 ),
inference(avatar_component_clause,[],[f1014]) ).
tff(f2510,plain,
( spl2_181
| ~ spl2_17
| ~ spl2_93 ),
inference(avatar_split_clause,[],[f1017,f1010,f575,f2508]) ).
tff(f1010,plain,
( spl2_93
<=> ! [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_93])]) ).
tff(f1017,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_17
| ~ spl2_93 ),
inference(resolution,[],[f1011,f577]) ).
tff(f1011,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_93 ),
inference(avatar_component_clause,[],[f1010]) ).
tff(f2442,plain,
( spl2_180
| ~ spl2_32
| ~ spl2_133 ),
inference(avatar_split_clause,[],[f1332,f1325,f643,f2440]) ).
tff(f2440,plain,
( spl2_180
<=> ! [X3: int,X4: int,X0: int,X5: list(int),X2: int,X1: list(int)] : ( nDvd(X3,X4,X5) != asubst(X0,X1,c_PresArith_Oatom_OLe(X2,ks1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_180])]) ).
tff(f1325,plain,
( spl2_133
<=> ! [X5: int,X3: list(int),X4: list(int),X2: int,X7: list(int),X0: int,X6: int,X1: int] : ( asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) != nDvd(X5,X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_133])]) ).
tff(f1332,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int),X4: int,X5: list(int)] : ( nDvd(X3,X4,X5) != asubst(X0,X1,c_PresArith_Oatom_OLe(X2,ks1)) )
| ~ spl2_32
| ~ spl2_133 ),
inference(superposition,[],[f1326,f645]) ).
tff(f1326,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X6: int,X7: list(int),X4: list(int),X5: int] : ( asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) != nDvd(X5,X6,X7) )
| ~ spl2_133 ),
inference(avatar_component_clause,[],[f1325]) ).
tff(f2438,plain,
( spl2_179
| ~ spl2_18
| ~ spl2_22
| ~ spl2_92 ),
inference(avatar_split_clause,[],[f1008,f1004,f600,f580,f2436]) ).
tff(f2436,plain,
( spl2_179
<=> ! [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_179])]) ).
tff(f600,plain,
( spl2_22
<=> ( one_one(int) = hd_coeff(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
tff(f1004,plain,
( spl2_92
<=> ! [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_92])]) ).
tff(f1008,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_18
| ~ spl2_22
| ~ spl2_92 ),
inference(forward_demodulation,[],[f1007,f602]) ).
tff(f602,plain,
( ( one_one(int) = hd_coeff(a) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f1007,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_18
| ~ spl2_92 ),
inference(resolution,[],[f1005,f582]) ).
tff(f1005,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_92 ),
inference(avatar_component_clause,[],[f1004]) ).
tff(f2352,plain,
( spl2_178
| ~ spl2_99 ),
inference(avatar_split_clause,[],[f1054,f1043,f2350]) ).
tff(f2350,plain,
( spl2_178
<=> ! [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_178])]) ).
tff(f1043,plain,
( spl2_99
<=> ! [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_99])]) ).
tff(f1054,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_99 ),
inference(equality_resolution,[],[f1044]) ).
tff(f1044,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_99 ),
inference(avatar_component_clause,[],[f1043]) ).
tff(f2348,plain,
( spl2_177
| ~ spl2_15
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f1002,f999,f565,f2346]) ).
tff(f565,plain,
( spl2_15
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f999,plain,
( spl2_91
<=> ! [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_91])]) ).
tff(f1002,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_15
| ~ spl2_91 ),
inference(resolution,[],[f1000,f567]) ).
tff(f567,plain,
( ring(int)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f565]) ).
tff(f1000,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_91 ),
inference(avatar_component_clause,[],[f999]) ).
tff(f2314,plain,
( spl2_176
| ~ spl2_23
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f990,f974,f605,f2312]) ).
tff(f2312,plain,
( spl2_176
<=> ! [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_rec(X0,X2,X3,X1,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_176])]) ).
tff(f605,plain,
( spl2_23
<=> ( a = nDvd(d,l,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
tff(f974,plain,
( spl2_90
<=> ! [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)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
tff(f990,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_rec(X0,X2,X3,X1,a) )
| ~ spl2_23
| ~ spl2_90 ),
inference(superposition,[],[f975,f607]) ).
tff(f607,plain,
( ( a = nDvd(d,l,ks1) )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f975,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)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1)) )
| ~ spl2_90 ),
inference(avatar_component_clause,[],[f974]) ).
tff(f2310,plain,
( spl2_175
| ~ spl2_23
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f977,f970,f605,f2308]) ).
tff(f2308,plain,
( spl2_175
<=> ! [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)),X3,d),l),ks1) = atom_case(X0,X1,X2,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_175])]) ).
tff(f970,plain,
( spl2_89
<=> ! [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)] : ( atom_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
tff(f977,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)),X3,d),l),ks1) = atom_case(X0,X1,X2,X3,a) )
| ~ spl2_23
| ~ spl2_89 ),
inference(superposition,[],[f971,f607]) ).
tff(f971,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) )
| ~ spl2_89 ),
inference(avatar_component_clause,[],[f970]) ).
tff(f2281,plain,
( spl2_174
| ~ spl2_68
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1095,f1081,f863,f2279]) ).
tff(f2279,plain,
( spl2_174
<=> ! [X2: int,X4: list(int),X0: int,X3: list(int),X1: int] : ( a != asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_174])]) ).
tff(f863,plain,
( spl2_68
<=> ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
tff(f1081,plain,
( spl2_106
<=> ! [X2: int,X4: int,X0: list(int),X3: list(int),X1: int] : ( asubst(X4,X3,c_PresArith_Oatom_OLe(X2,cons(int,X1,X0))) = c_PresArith_Oatom_OLe(minus_minus(int,X2,aa(int,int,times_times(int,X1),X4)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X3)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_106])]) ).
tff(f1095,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X4: list(int)] : ( a != asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) )
| ~ spl2_68
| ~ spl2_106 ),
inference(superposition,[],[f864,f1082]) ).
tff(f1082,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int] : ( asubst(X4,X3,c_PresArith_Oatom_OLe(X2,cons(int,X1,X0))) = c_PresArith_Oatom_OLe(minus_minus(int,X2,aa(int,int,times_times(int,X1),X4)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X3)),X0)) )
| ~ spl2_106 ),
inference(avatar_component_clause,[],[f1081]) ).
tff(f864,plain,
( ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) )
| ~ spl2_68 ),
inference(avatar_component_clause,[],[f863]) ).
tff(f1841,plain,
( spl2_173
| ~ spl2_63
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f989,f974,f820,f1839]) ).
tff(f1839,plain,
( spl2_173
<=> ! [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_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_173])]) ).
tff(f820,plain,
( spl2_63
<=> ! [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_63])]) ).
tff(f989,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_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_63
| ~ spl2_90 ),
inference(superposition,[],[f975,f821]) ).
tff(f821,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_63 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f1835,plain,
( spl2_172
| ~ spl2_64
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f988,f974,f824,f1833]) ).
tff(f1833,plain,
( spl2_172
<=> ! [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_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_172])]) ).
tff(f824,plain,
( spl2_64
<=> ! [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_64])]) ).
tff(f988,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_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_64
| ~ spl2_90 ),
inference(superposition,[],[f975,f825]) ).
tff(f825,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_64 ),
inference(avatar_component_clause,[],[f824]) ).
tff(f1831,plain,
( spl2_171
| ~ spl2_63
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f980,f970,f820,f1829]) ).
tff(f1829,plain,
( spl2_171
<=> ! [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,X7,X8,X1,nDvd(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_171])]) ).
tff(f980,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,X7,X8,X1,nDvd(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_63
| ~ spl2_89 ),
inference(superposition,[],[f971,f821]) ).
tff(f1827,plain,
( spl2_170
| ~ spl2_64
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f979,f970,f824,f1825]) ).
tff(f1825,plain,
( spl2_170
<=> ! [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,X7,X8,X1,nDvd(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_170])]) ).
tff(f979,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,X7,X8,X1,nDvd(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_64
| ~ spl2_89 ),
inference(superposition,[],[f971,f825]) ).
tff(f1823,plain,
( spl2_169
| ~ spl2_3
| ~ spl2_18
| ~ spl2_77
| ~ spl2_84 ),
inference(avatar_split_clause,[],[f949,f939,f911,f580,f505,f1821]) ).
tff(f1821,plain,
( spl2_169
<=> ! [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_169])]) ).
tff(f505,plain,
( spl2_3
<=> ab_semigroup_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f911,plain,
( spl2_77
<=> ! [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_77])]) ).
tff(f939,plain,
( spl2_84
<=> ! [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_84])]) ).
tff(f949,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_18
| ~ spl2_77
| ~ spl2_84 ),
inference(forward_demodulation,[],[f948,f942]) ).
tff(f942,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_77 ),
inference(resolution,[],[f912,f507]) ).
tff(f507,plain,
( ab_semigroup_mult(int)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f505]) ).
tff(f912,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_77 ),
inference(avatar_component_clause,[],[f911]) ).
tff(f948,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_18
| ~ spl2_84 ),
inference(resolution,[],[f940,f582]) ).
tff(f940,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_84 ),
inference(avatar_component_clause,[],[f939]) ).
tff(f1819,plain,
( spl2_168
| ~ spl2_18
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f946,f931,f580,f1817]) ).
tff(f1817,plain,
( spl2_168
<=> ! [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_168])]) ).
tff(f931,plain,
( spl2_82
<=> ! [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_82])]) ).
tff(f946,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_18
| ~ spl2_82 ),
inference(resolution,[],[f932,f582]) ).
tff(f932,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_82 ),
inference(avatar_component_clause,[],[f931]) ).
tff(f1815,plain,
( spl2_167
| ~ spl2_17
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f945,f923,f575,f1813]) ).
tff(f1813,plain,
( spl2_167
<=> ! [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_167])]) ).
tff(f923,plain,
( spl2_80
<=> ! [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_80])]) ).
tff(f945,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_17
| ~ spl2_80 ),
inference(resolution,[],[f924,f577]) ).
tff(f924,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_80 ),
inference(avatar_component_clause,[],[f923]) ).
tff(f1811,plain,
( spl2_166
| ~ spl2_17
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f944,f919,f575,f1809]) ).
tff(f1809,plain,
( spl2_166
<=> ! [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_166])]) ).
tff(f919,plain,
( spl2_79
<=> ! [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_79])]) ).
tff(f944,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_17
| ~ spl2_79 ),
inference(resolution,[],[f920,f577]) ).
tff(f920,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_79 ),
inference(avatar_component_clause,[],[f919]) ).
tff(f1807,plain,
( spl2_165
| ~ spl2_17
| ~ spl2_78 ),
inference(avatar_split_clause,[],[f943,f915,f575,f1805]) ).
tff(f1805,plain,
( spl2_165
<=> ! [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_165])]) ).
tff(f915,plain,
( spl2_78
<=> ! [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_78])]) ).
tff(f943,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_17
| ~ spl2_78 ),
inference(resolution,[],[f916,f577]) ).
tff(f916,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_78 ),
inference(avatar_component_clause,[],[f915]) ).
tff(f1803,plain,
( spl2_164
| ~ spl2_3
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f942,f911,f505,f1801]) ).
tff(f1801,plain,
( spl2_164
<=> ! [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_164])]) ).
tff(f1777,plain,
( spl2_163
| ~ spl2_23
| ~ spl2_147 ),
inference(avatar_split_clause,[],[f1667,f1470,f605,f1775]) ).
tff(f1775,plain,
( spl2_163
<=> ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_163])]) ).
tff(f1470,plain,
( spl2_147
<=> ! [X2: int,X0: int,X1: list(int),X3: int] : ( divisor(asubst(X0,X1,nDvd(X2,X3,ks1))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_147])]) ).
tff(f1667,plain,
( ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) )
| ~ spl2_23
| ~ spl2_147 ),
inference(superposition,[],[f1471,f607]) ).
tff(f1471,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,nDvd(X2,X3,ks1))) = X2 )
| ~ spl2_147 ),
inference(avatar_component_clause,[],[f1470]) ).
tff(f1730,plain,
( spl2_162
| ~ spl2_16
| ~ spl2_21
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f907,f901,f595,f570,f1728]) ).
tff(f1728,plain,
( spl2_162
<=> ! [X0: int,X3: list(int),X2: int,X1: list(int)] : ( minus_minus(list(int),cons(int,X0,X1),cons(int,X2,X3)) = cons(int,minus_minus(int,X0,X2),minus_minus(list(int),X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_162])]) ).
tff(f570,plain,
( spl2_16
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f595,plain,
( spl2_21
<=> cl_Groups_Ominus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
tff(f901,plain,
( spl2_76
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
tff(f907,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int)] :
( ~ zero(int)
| ( minus_minus(list(int),cons(int,X0,X1),cons(int,X2,X3)) = cons(int,minus_minus(int,X0,X2),minus_minus(list(int),X1,X3)) ) )
| ~ spl2_21
| ~ spl2_76 ),
inference(resolution,[],[f902,f597]) ).
tff(f597,plain,
( cl_Groups_Ominus(int)
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f902,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ~ cl_Groups_Ominus(X0)
| ~ zero(X0)
| ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) ) )
| ~ spl2_76 ),
inference(avatar_component_clause,[],[f901]) ).
tff(f1726,plain,
( spl2_160
| ~ spl2_161
| ~ spl2_20
| ~ spl2_76 ),
inference(avatar_split_clause,[],[f906,f901,f590,f1723,f1720]) ).
tff(f1720,plain,
( spl2_160
<=> ! [X0: bool,X3: list(bool),X2: bool,X1: list(bool)] : ( minus_minus(list(bool),cons(bool,X0,X1),cons(bool,X2,X3)) = cons(bool,minus_minus(bool,X0,X2),minus_minus(list(bool),X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_160])]) ).
tff(f1723,plain,
( spl2_161
<=> zero(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_161])]) ).
tff(f590,plain,
( spl2_20
<=> cl_Groups_Ominus(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
tff(f906,plain,
( ! [X2: bool,X3: list(bool),X0: bool,X1: list(bool)] :
( ~ zero(bool)
| ( minus_minus(list(bool),cons(bool,X0,X1),cons(bool,X2,X3)) = cons(bool,minus_minus(bool,X0,X2),minus_minus(list(bool),X1,X3)) ) )
| ~ spl2_20
| ~ spl2_76 ),
inference(resolution,[],[f902,f592]) ).
tff(f592,plain,
( cl_Groups_Ominus(bool)
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f590]) ).
tff(f1718,plain,
( spl2_159
| ~ spl2_17
| ~ spl2_75 ),
inference(avatar_split_clause,[],[f905,f897,f575,f1716]) ).
tff(f1716,plain,
( spl2_159
<=> ! [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_159])]) ).
tff(f897,plain,
( spl2_75
<=> ! [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_75])]) ).
tff(f905,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_17
| ~ spl2_75 ),
inference(resolution,[],[f898,f577]) ).
tff(f898,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_75 ),
inference(avatar_component_clause,[],[f897]) ).
tff(f1714,plain,
( spl2_158
| ~ spl2_17
| ~ spl2_74 ),
inference(avatar_split_clause,[],[f904,f893,f575,f1712]) ).
tff(f1712,plain,
( spl2_158
<=> ! [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_158])]) ).
tff(f893,plain,
( spl2_74
<=> ! [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_74])]) ).
tff(f904,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_17
| ~ spl2_74 ),
inference(resolution,[],[f894,f577]) ).
tff(f894,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_74 ),
inference(avatar_component_clause,[],[f893]) ).
tff(f1666,plain,
( spl2_157
| ~ spl2_119 ),
inference(avatar_split_clause,[],[f1197,f1188,f1664]) ).
tff(f1664,plain,
( spl2_157
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X1,X1)),X2)),X3) = X3 )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_157])]) ).
tff(f1188,plain,
( spl2_119
<=> ! [X0: $tType,X5: X0,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,minus_minus(X0,X5,X2)),X4)),X3) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_119])]) ).
tff(f1197,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X1,X1)),X2)),X3) = X3 )
| ~ ring(X0) )
| ~ spl2_119 ),
inference(equality_resolution,[],[f1189]) ).
tff(f1189,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) = X1 )
| ~ ring(X0) )
| ~ spl2_119 ),
inference(avatar_component_clause,[],[f1188]) ).
tff(f1662,plain,
( spl2_156
| ~ spl2_34
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1089,f1081,f656,f1660]) ).
tff(f1660,plain,
( spl2_156
<=> ! [X2: int,X6: list(int),X4: list(int),X0: int,X3: list(int),X5: int,X1: int] :
( ( c_PresArith_Oatom_OLe(X5,X6) != asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) )
| ( minus_minus(int,X0,aa(int,int,times_times(int,X1),X2)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_156])]) ).
tff(f656,plain,
( spl2_34
<=> ! [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_34])]) ).
tff(f1089,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X6: list(int),X4: list(int),X5: int] :
( ( c_PresArith_Oatom_OLe(X5,X6) != asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) )
| ( minus_minus(int,X0,aa(int,int,times_times(int,X1),X2)) = X5 ) )
| ~ spl2_34
| ~ spl2_106 ),
inference(superposition,[],[f657,f1082]) ).
tff(f657,plain,
( ! [X2: list(int),X3: int,X0: list(int),X1: int] :
( ( c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2) )
| ( X1 = X3 ) )
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f1658,plain,
( spl2_155
| ~ spl2_18
| ~ spl2_73 ),
inference(avatar_split_clause,[],[f891,f888,f580,f1656]) ).
tff(f888,plain,
( spl2_73
<=> ! [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_73])]) ).
tff(f891,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_18
| ~ spl2_73 ),
inference(resolution,[],[f889,f582]) ).
tff(f889,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_73 ),
inference(avatar_component_clause,[],[f888]) ).
tff(f1611,plain,
( spl2_154
| ~ spl2_17
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f883,f871,f575,f1609]) ).
tff(f1609,plain,
( spl2_154
<=> ! [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_154])]) ).
tff(f871,plain,
( spl2_70
<=> ! [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)),X2),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
tff(f883,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_17
| ~ spl2_70 ),
inference(resolution,[],[f872,f577]) ).
tff(f872,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)),X2),X1) ) )
| ~ spl2_70 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f1601,plain,
( spl2_153
| ~ spl2_56
| ~ spl2_62 ),
inference(avatar_split_clause,[],[f829,f816,f783,f1599]) ).
tff(f1599,plain,
( spl2_153
<=> ! [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_153])]) ).
tff(f783,plain,
( spl2_56
<=> ! [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_56])]) ).
tff(f816,plain,
( spl2_62
<=> ! [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_62])]) ).
tff(f829,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_56
| ~ spl2_62 ),
inference(superposition,[],[f784,f817]) ).
tff(f817,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_62 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f784,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X1 = X3 ) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f783]) ).
tff(f1548,plain,
( spl2_152
| ~ spl2_37
| ~ spl2_66 ),
inference(avatar_split_clause,[],[f855,f846,f672,f1546]) ).
tff(f1546,plain,
( spl2_152
<=> ! [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_152])]) ).
tff(f672,plain,
( spl2_37
<=> ( div_mod(int,i,d) = div_mod(int,j,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
tff(f846,plain,
( spl2_66
<=> ! [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_66])]) ).
tff(f855,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_37
| ~ spl2_66 ),
inference(forward_demodulation,[],[f853,f847]) ).
tff(f847,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_66 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f853,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_37
| ~ spl2_66 ),
inference(superposition,[],[f847,f674]) ).
tff(f674,plain,
( ( div_mod(int,i,d) = div_mod(int,j,d) )
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f672]) ).
tff(f1544,plain,
( spl2_151
| ~ spl2_15
| ~ spl2_65 ),
inference(avatar_split_clause,[],[f844,f841,f565,f1542]) ).
tff(f1542,plain,
( spl2_151
<=> ! [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_151])]) ).
tff(f841,plain,
( spl2_65
<=> ! [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_65])]) ).
tff(f844,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_15
| ~ spl2_65 ),
inference(resolution,[],[f842,f567]) ).
tff(f842,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_65 ),
inference(avatar_component_clause,[],[f841]) ).
tff(f1540,plain,
( spl2_150
| ~ spl2_52
| ~ spl2_62 ),
inference(avatar_split_clause,[],[f831,f816,f756,f1538]) ).
tff(f1538,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) )
| ( aa(X1,X0,X2,X3) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_150])]) ).
tff(f756,plain,
( spl2_52
<=> ! [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_52])]) ).
tff(f831,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_52
| ~ spl2_62 ),
inference(superposition,[],[f757,f817]) ).
tff(f757,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X2 = X4 ) )
| ~ spl2_52 ),
inference(avatar_component_clause,[],[f756]) ).
tff(f1516,plain,
( spl2_149
| ~ spl2_17
| ~ spl2_61 ),
inference(avatar_split_clause,[],[f828,f812,f575,f1514]) ).
tff(f1514,plain,
( spl2_149
<=> ! [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_149])]) ).
tff(f812,plain,
( spl2_61
<=> ! [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_61])]) ).
tff(f828,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_17
| ~ spl2_61 ),
inference(resolution,[],[f813,f577]) ).
tff(f813,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_61 ),
inference(avatar_component_clause,[],[f812]) ).
tff(f1512,plain,
( spl2_148
| ~ spl2_17
| ~ spl2_60 ),
inference(avatar_split_clause,[],[f827,f808,f575,f1510]) ).
tff(f1510,plain,
( spl2_148
<=> ! [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_148])]) ).
tff(f808,plain,
( spl2_60
<=> ! [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_60])]) ).
tff(f827,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_17
| ~ spl2_60 ),
inference(resolution,[],[f809,f577]) ).
tff(f809,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_60 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f1472,plain,
( spl2_147
| ~ spl2_32
| ~ spl2_132 ),
inference(avatar_split_clause,[],[f1319,f1311,f643,f1470]) ).
tff(f1311,plain,
( spl2_132
<=> ! [X3: int,X4: list(int),X0: int,X5: list(int),X2: int,X1: int] : ( divisor(asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_132])]) ).
tff(f1319,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,nDvd(X2,X3,ks1))) = X2 )
| ~ spl2_32
| ~ spl2_132 ),
inference(superposition,[],[f1312,f645]) ).
tff(f1312,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X4: list(int),X5: list(int)] : ( divisor(asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5)))) = X0 )
| ~ spl2_132 ),
inference(avatar_component_clause,[],[f1311]) ).
tff(f1468,plain,
( spl2_146
| ~ spl2_89
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f987,f974,f970,f1466]) ).
tff(f1466,plain,
( spl2_146
<=> ! [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,X6,X1,nDvd(X2,X3,X4)) = atom_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_146])]) ).
tff(f987,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,X6,X1,nDvd(X2,X3,X4)) = atom_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_89
| ~ spl2_90 ),
inference(superposition,[],[f975,f971]) ).
tff(f1464,plain,
( spl2_145
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f986,f974,f1462]) ).
tff(f1462,plain,
( spl2_145
<=> ! [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,X6,X1,nDvd(X2,X3,X4)) = atom_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_145])]) ).
tff(f986,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,X6,X1,nDvd(X2,X3,X4)) = atom_rec(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_90 ),
inference(superposition,[],[f975,f975]) ).
tff(f1460,plain,
( spl2_144
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f978,f970,f1458]) ).
tff(f1458,plain,
( spl2_144
<=> ! [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,X6,X1,nDvd(X2,X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_144])]) ).
tff(f978,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,X6,X1,nDvd(X2,X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_89 ),
inference(superposition,[],[f971,f971]) ).
tff(f1456,plain,
( ~ spl2_19
| spl2_143
| ~ spl2_16
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f806,f803,f570,f1453,f585]) ).
tff(f585,plain,
( spl2_19
<=> cl_Groups_Oplus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f1453,plain,
( spl2_143
<=> ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_143])]) ).
tff(f803,plain,
( spl2_59
<=> ! [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_59])]) ).
tff(f806,plain,
( ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) )
| ~ cl_Groups_Oplus(int)
| ~ spl2_16
| ~ spl2_59 ),
inference(resolution,[],[f804,f572]) ).
tff(f572,plain,
( zero(int)
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f570]) ).
tff(f804,plain,
( ! [X0: $tType] :
( ~ zero(X0)
| ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ cl_Groups_Oplus(X0) )
| ~ spl2_59 ),
inference(avatar_component_clause,[],[f803]) ).
tff(f1443,plain,
( spl2_142
| ~ spl2_48
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f1155,f1144,f719,f1441]) ).
tff(f1441,plain,
( spl2_142
<=> ! [X2: int,X3: int,X0: int,X1: int,X8: list(int),X6: int,X7: int,X4: list(int),X5: list(int)] :
( ( asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5))) != nDvd(X6,X7,X8) )
| ( X0 = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_142])]) ).
tff(f719,plain,
( spl2_48
<=> ! [X3: list(int),X4: int,X0: list(int),X5: int,X2: int,X1: int] :
( ( X2 = X5 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
tff(f1144,plain,
( spl2_116
<=> ! [X2: int,X3: int,X4: list(int),X0: list(int),X5: int,X1: int] : ( asubst(X5,X4,nDvd(X3,X2,cons(int,X1,X0))) = nDvd(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_116])]) ).
tff(f1155,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,nDvd(X0,X1,cons(int,X2,X5))) != nDvd(X6,X7,X8) )
| ( X0 = X6 ) )
| ~ spl2_48
| ~ spl2_116 ),
inference(superposition,[],[f720,f1145]) ).
tff(f1145,plain,
( ! [X2: int,X3: int,X0: list(int),X1: int,X4: list(int),X5: int] : ( asubst(X5,X4,nDvd(X3,X2,cons(int,X1,X0))) = nDvd(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_116 ),
inference(avatar_component_clause,[],[f1144]) ).
tff(f720,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) )
| ( X2 = X5 ) )
| ~ spl2_48 ),
inference(avatar_component_clause,[],[f719]) ).
tff(f1439,plain,
( spl2_141
| ~ spl2_46
| ~ spl2_115 ),
inference(avatar_split_clause,[],[f1151,f1140,f711,f1437]) ).
tff(f1437,plain,
( spl2_141
<=> ! [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_141])]) ).
tff(f711,plain,
( spl2_46
<=> ! [X3: list(int),X4: int,X0: list(int),X5: int,X2: int,X1: int] :
( ( X2 = X5 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
tff(f1140,plain,
( spl2_115
<=> ! [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_115])]) ).
tff(f1151,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_46
| ~ spl2_115 ),
inference(superposition,[],[f712,f1141]) ).
tff(f1141,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_115 ),
inference(avatar_component_clause,[],[f1140]) ).
tff(f712,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( dvd(X5,X4,X3) != dvd(X2,X1,X0) )
| ( X2 = X5 ) )
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f1420,plain,
( spl2_140
| ~ spl2_32
| ~ spl2_131 ),
inference(avatar_split_clause,[],[f1314,f1307,f643,f1418]) ).
tff(f1418,plain,
( spl2_140
<=> ! [X2: int,X0: int,X1: list(int)] : ( hd_coeff(a) = divisor(asubst(X0,X1,c_PresArith_Oatom_OLe(X2,ks1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_140])]) ).
tff(f1307,plain,
( spl2_131
<=> ! [X2: int,X4: list(int),X0: int,X3: list(int),X1: int] : ( hd_coeff(a) = divisor(asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_131])]) ).
tff(f1314,plain,
( ! [X2: int,X0: int,X1: list(int)] : ( hd_coeff(a) = divisor(asubst(X0,X1,c_PresArith_Oatom_OLe(X2,ks1))) )
| ~ spl2_32
| ~ spl2_131 ),
inference(superposition,[],[f1308,f645]) ).
tff(f1308,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X4: list(int)] : ( hd_coeff(a) = divisor(asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4)))) )
| ~ spl2_131 ),
inference(avatar_component_clause,[],[f1307]) ).
tff(f1398,plain,
( spl2_139
| ~ spl2_63
| ~ spl2_64 ),
inference(avatar_split_clause,[],[f837,f824,f820,f1396]) ).
tff(f1396,plain,
( spl2_139
<=> ! [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_139])]) ).
tff(f837,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_63
| ~ spl2_64 ),
inference(superposition,[],[f825,f821]) ).
tff(f1394,plain,
( spl2_138
| ~ spl2_64 ),
inference(avatar_split_clause,[],[f836,f824,f1392]) ).
tff(f1392,plain,
( spl2_138
<=> ! [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_138])]) ).
tff(f836,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_64 ),
inference(superposition,[],[f825,f825]) ).
tff(f1390,plain,
( spl2_137
| ~ spl2_63 ),
inference(avatar_split_clause,[],[f834,f820,f1388]) ).
tff(f1388,plain,
( spl2_137
<=> ! [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_137])]) ).
tff(f834,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_63 ),
inference(superposition,[],[f821,f821]) ).
tff(f1350,plain,
( spl2_136
| ~ spl2_27
| ~ spl2_62 ),
inference(avatar_split_clause,[],[f833,f816,f622,f1348]) ).
tff(f1348,plain,
( spl2_136
<=> ! [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_136])]) ).
tff(f622,plain,
( spl2_27
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
tff(f833,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_27
| ~ spl2_62 ),
inference(superposition,[],[f623,f817]) ).
tff(f623,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f622]) ).
tff(f1346,plain,
( spl2_135
| ~ spl2_18
| ~ spl2_58 ),
inference(avatar_split_clause,[],[f801,f798,f580,f1344]) ).
tff(f1344,plain,
( spl2_135
<=> ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),X1) = aa(int,int,times_times(int,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_135])]) ).
tff(f798,plain,
( spl2_58
<=> ! [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_58])]) ).
tff(f801,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),X1) = aa(int,int,times_times(int,X1),X0) )
| ~ spl2_18
| ~ spl2_58 ),
inference(resolution,[],[f799,f582]) ).
tff(f799,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_58 ),
inference(avatar_component_clause,[],[f798]) ).
tff(f1331,plain,
( spl2_134
| ~ spl2_31
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f1154,f1144,f639,f1329]) ).
tff(f1329,plain,
( spl2_134
<=> ! [X5: list(int),X3: int,X4: list(int),X7: list(int),X0: int,X6: int,X2: int,X1: int] : ( asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5))) != c_PresArith_Oatom_OLe(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_134])]) ).
tff(f639,plain,
( spl2_31
<=> ! [X4: int,X0: list(int),X3: int,X2: list(int),X1: int] : ( c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
tff(f1154,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X6: int,X7: list(int),X4: list(int),X5: list(int)] : ( asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5))) != c_PresArith_Oatom_OLe(X6,X7) )
| ~ spl2_31
| ~ spl2_116 ),
inference(superposition,[],[f640,f1145]) ).
tff(f640,plain,
( ! [X2: list(int),X3: int,X0: list(int),X1: int,X4: int] : ( c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2) )
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f1327,plain,
( spl2_133
| ~ spl2_31
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1088,f1081,f639,f1325]) ).
tff(f1088,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X6: int,X7: list(int),X4: list(int),X5: int] : ( asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4))) != nDvd(X5,X6,X7) )
| ~ spl2_31
| ~ spl2_106 ),
inference(superposition,[],[f640,f1082]) ).
tff(f1313,plain,
( spl2_132
| ~ spl2_28
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f1153,f1144,f626,f1311]) ).
tff(f626,plain,
( spl2_28
<=> ! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
tff(f1153,plain,
( ! [X2: int,X3: int,X0: int,X1: int,X4: list(int),X5: list(int)] : ( divisor(asubst(X3,X4,nDvd(X0,X1,cons(int,X2,X5)))) = X0 )
| ~ spl2_28
| ~ spl2_116 ),
inference(superposition,[],[f627,f1145]) ).
tff(f627,plain,
( ! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f1309,plain,
( spl2_131
| ~ spl2_29
| ~ spl2_106 ),
inference(avatar_split_clause,[],[f1087,f1081,f630,f1307]) ).
tff(f630,plain,
( spl2_29
<=> ! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
tff(f1087,plain,
( ! [X2: int,X3: list(int),X0: int,X1: int,X4: list(int)] : ( hd_coeff(a) = divisor(asubst(X2,X3,c_PresArith_Oatom_OLe(X0,cons(int,X1,X4)))) )
| ~ spl2_29
| ~ spl2_106 ),
inference(superposition,[],[f631,f1082]) ).
tff(f631,plain,
( ! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) )
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f1294,plain,
( spl2_130
| ~ spl2_17
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f786,f779,f575,f1292]) ).
tff(f1292,plain,
( spl2_130
<=> ! [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_130])]) ).
tff(f779,plain,
( spl2_55
<=> ! [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_55])]) ).
tff(f786,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) )
| ~ spl2_17
| ~ spl2_55 ),
inference(resolution,[],[f780,f577]) ).
tff(f780,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_55 ),
inference(avatar_component_clause,[],[f779]) ).
tff(f1286,plain,
( spl2_129
| ~ spl2_33
| ~ spl2_127 ),
inference(avatar_split_clause,[],[f1280,f1259,f648,f1283]) ).
tff(f1283,plain,
( spl2_129
<=> ( ks = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_129])]) ).
tff(f648,plain,
( spl2_33
<=> ( ks1 = cons(int,hd_coeff(a),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
tff(f1259,plain,
( spl2_127
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_127])]) ).
tff(f1280,plain,
( ( ks = sK0 )
| ~ spl2_33
| ~ spl2_127 ),
inference(trivial_inequality_removal,[],[f1278]) ).
tff(f1278,plain,
( ( ks1 != ks1 )
| ( ks = sK0 )
| ~ spl2_33
| ~ spl2_127 ),
inference(superposition,[],[f1260,f650]) ).
tff(f650,plain,
( ( ks1 = cons(int,hd_coeff(a),sK0) )
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f648]) ).
tff(f1260,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_127 ),
inference(avatar_component_clause,[],[f1259]) ).
tff(f1265,plain,
( spl2_128
| ~ spl2_33
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f788,f783,f648,f1263]) ).
tff(f1263,plain,
( spl2_128
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_128])]) ).
tff(f788,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) )
| ~ spl2_33
| ~ spl2_56 ),
inference(superposition,[],[f784,f650]) ).
tff(f1261,plain,
( spl2_127
| ~ spl2_32
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f787,f783,f643,f1259]) ).
tff(f787,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_32
| ~ spl2_56 ),
inference(superposition,[],[f784,f645]) ).
tff(f1257,plain,
( spl2_126
| ~ spl2_32
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f769,f756,f643,f1255]) ).
tff(f1255,plain,
( spl2_126
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_126])]) ).
tff(f769,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) )
| ~ spl2_32
| ~ spl2_52 ),
inference(superposition,[],[f757,f645]) ).
tff(f1253,plain,
( spl2_125
| ~ spl2_13
| ~ spl2_22
| ~ spl2_51 ),
inference(avatar_split_clause,[],[f768,f752,f600,f555,f1251]) ).
tff(f1251,plain,
( spl2_125
<=> ! [X0: list(int)] : ( map(int,int,times_times(int,hd_coeff(a)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_125])]) ).
tff(f555,plain,
( spl2_13
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f752,plain,
( spl2_51
<=> ! [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_51])]) ).
tff(f768,plain,
( ! [X0: list(int)] : ( map(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_13
| ~ spl2_22
| ~ spl2_51 ),
inference(forward_demodulation,[],[f767,f602]) ).
tff(f767,plain,
( ! [X0: list(int)] : ( map(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl2_13
| ~ spl2_51 ),
inference(resolution,[],[f753,f557]) ).
tff(f557,plain,
( monoid_mult(int)
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f555]) ).
tff(f753,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ monoid_mult(X0)
| ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f752]) ).
tff(f1246,plain,
spl2_124,
inference(avatar_split_clause,[],[f363,f1244]) ).
tff(f1244,plain,
( spl2_124
<=> ! [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_124])]) ).
tff(f363,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,[],[f233]) ).
tff(f233,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,[],[f136]) ).
tff(f136,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,[],[f13]) ).
tff(f13,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/sandbox2/benchmark/theBenchmark.p',fact_12_list__add__assoc) ).
tff(f1218,plain,
spl2_123,
inference(avatar_split_clause,[],[f429,f1216]) ).
tff(f1216,plain,
( spl2_123
<=> ! [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_123])]) ).
tff(f429,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,[],[f293]) ).
tff(f293,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,[],[f194]) ).
tff(f194,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,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X23: 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),X23)) = 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),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
tff(f1213,plain,
spl2_122,
inference(avatar_split_clause,[],[f365,f1211]) ).
tff(f1211,plain,
( spl2_122
<=> ! [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_122])]) ).
tff(f365,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,[],[f235]) ).
tff(f235,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,[],[f138]) ).
tff(f138,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,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( semiring(X0)
=> ! [X12: X0,X4: X0,X54: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X54)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X54)),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)),X54)),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_combine__common__factor) ).
tff(f1208,plain,
spl2_121,
inference(avatar_split_clause,[],[f443,f1206]) ).
tff(f1206,plain,
( spl2_121
<=> ! [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_121])]) ).
tff(f443,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,[],[f306]) ).
tff(f306,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,[],[f305]) ).
tff(f305,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,[],[f207]) ).
tff(f207,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,[],[f30]) ).
tff(f30,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X25: list(X2),X26: X2,X27: list(X1),X28: X1,X29: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X29),cons(X1,X28,X27)),cons(X2,X26,X25)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X29,X28),X26),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X29),X27),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zipwith0_Osimps_I2_J) ).
tff(f1194,plain,
spl2_120,
inference(avatar_split_clause,[],[f433,f1192]) ).
tff(f1192,plain,
( spl2_120
<=> ! [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_120])]) ).
tff(f433,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,[],[f301]) ).
tff(f301,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,[],[f300]) ).
tff(f300,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,[],[f197]) ).
tff(f197,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,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X10: list(X0),X30: X0,X11: list(X0),X31: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X31,X11)),cons(X0,X30,X10)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X30),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_list__add__Cons) ).
tff(f1190,plain,
spl2_119,
inference(avatar_split_clause,[],[f386,f1188]) ).
tff(f386,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) != X1 ) )
& ( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) = X1 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) ) ) )
| ~ ring(X0) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
<=> ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) = X1 ) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
<=> ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) = X1 ) ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X43: X0,X7: X0,X6: X0,X60: X0,X8: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X8),X60)),X6) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X7),X60)),X43) )
<=> ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X8,X7)),X60)),X6) = X43 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_eq__add__iff1) ).
tff(f1173,plain,
spl2_118,
inference(avatar_split_clause,[],[f479,f1171]) ).
tff(f1171,plain,
( spl2_118
<=> ! [X0: $tType,X3: X0,X4: X0,X5: X0,X2: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_118])]) ).
tff(f479,plain,
! [X0: $tType,X2: X0,X3: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3)) )
| ~ ring(X0) ),
inference(equality_resolution,[],[f387]) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X4)),X3) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X4)),X1) )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,minus_minus(X0,X5,X2)),X4)),X3) != X1 )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1168,plain,
spl2_117,
inference(avatar_split_clause,[],[f368,f1166]) ).
tff(f1166,plain,
( spl2_117
<=> ! [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_117])]) ).
tff(f368,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,[],[f312]) ).
tff(f312,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,[],[f311]) ).
tff(f311,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,[],[f238]) ).
tff(f238,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,[],[f141]) ).
tff(f141,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,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X45: X0,X28: X0,X26: X0,X46: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X46),X26)),aa(X0,X0,times_times(X0,X28),X45)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X46),X45)),aa(X0,X0,times_times(X0,X28),X26)) )
<=> ( ( X26 = X45 )
| ( X28 = X46 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_crossproduct__eq) ).
tff(f1146,plain,
spl2_116,
inference(avatar_split_clause,[],[f460,f1144]) ).
tff(f460,plain,
! [X2: int,X3: int,X0: list(int),X1: int,X4: list(int),X5: int] : ( asubst(X5,X4,nDvd(X3,X2,cons(int,X1,X0))) = nDvd(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,[],[f219]) ).
tff(f219,plain,
! [X0: list(int),X1: int,X2: int,X3: int,X4: list(int),X5: int] : ( asubst(X5,X4,nDvd(X3,X2,cons(int,X1,X0))) = nDvd(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,[],[f87]) ).
tff(f87,axiom,
! [X55: list(int),X57: int,X56: int,X43: int,X58: list(int),X59: int] : ( asubst(X59,X58,nDvd(X43,X56,cons(int,X57,X55))) = nDvd(X43,aa(int,int,aa(int,fun(int,int),plus_plus(int),X56),aa(int,int,times_times(int,X57),X59)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X57),X58)),X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_asubst_Osimps_I3_J) ).
tff(f1142,plain,
spl2_115,
inference(avatar_split_clause,[],[f459,f1140]) ).
tff(f459,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,[],[f218]) ).
tff(f218,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,[],[f93]) ).
tff(f93,axiom,
! [X55: list(int),X57: int,X56: int,X43: int,X58: list(int),X59: int] : ( asubst(X59,X58,dvd(X43,X56,cons(int,X57,X55))) = dvd(X43,aa(int,int,aa(int,fun(int,int),plus_plus(int),X56),aa(int,int,times_times(int,X57),X59)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X57),X58)),X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I2_J) ).
tff(f1132,plain,
( spl2_114
| ~ spl2_23
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f775,f764,f605,f1130]) ).
tff(f1130,plain,
( spl2_114
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( ks1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_114])]) ).
tff(f764,plain,
( spl2_54
<=> ! [X2: int,X4: int,X0: list(int),X5: int,X3: list(int),X1: int] :
( ( X0 = X3 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
tff(f775,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( ks1 = X2 ) )
| ~ spl2_23
| ~ spl2_54 ),
inference(superposition,[],[f765,f607]) ).
tff(f765,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) )
| ( X0 = X3 ) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f1128,plain,
spl2_113,
inference(avatar_split_clause,[],[f474,f1126]) ).
tff(f1126,plain,
( spl2_113
<=> ! [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_113])]) ).
tff(f474,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,[],[f369]) ).
tff(f369,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,[],[f312]) ).
tff(f1124,plain,
spl2_112,
inference(avatar_split_clause,[],[f407,f1122]) ).
tff(f1122,plain,
( spl2_112
<=> ! [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_112])]) ).
tff(f407,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,[],[f271]) ).
tff(f271,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,[],[f270]) ).
tff(f270,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,[],[f172]) ).
tff(f172,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,[],[f18]) ).
tff(f18,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/sandbox2/benchmark/theBenchmark.p',fact_17_mod__add__cong) ).
tff(f1115,plain,
spl2_111,
inference(avatar_split_clause,[],[f425,f1113]) ).
tff(f1113,plain,
( spl2_111
<=> ! [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_111])]) ).
tff(f425,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,[],[f289]) ).
tff(f289,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,[],[f190]) ).
tff(f190,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,[],[f26]) ).
tff(f26,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/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
tff(f1111,plain,
spl2_110,
inference(avatar_split_clause,[],[f423,f1109]) ).
tff(f1109,plain,
( spl2_110
<=> ! [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_110])]) ).
tff(f423,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,[],[f287]) ).
tff(f287,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,[],[f188]) ).
tff(f188,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,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X23: 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),X23)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f1107,plain,
spl2_109,
inference(avatar_split_clause,[],[f422,f1105]) ).
tff(f422,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,[],[f286]) ).
tff(f286,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,[],[f187]) ).
tff(f187,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,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X23: 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),X23)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f1103,plain,
spl2_108,
inference(avatar_split_clause,[],[f362,f1101]) ).
tff(f1101,plain,
( spl2_108
<=> ! [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_108])]) ).
tff(f362,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,[],[f232]) ).
tff(f232,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,[],[f135]) ).
tff(f135,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,[],[f17]) ).
tff(f17,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/sandbox2/benchmark/theBenchmark.p',fact_16_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1099,plain,
( spl2_107
| ~ spl2_12
| ~ spl2_22
| ~ spl2_40 ),
inference(avatar_split_clause,[],[f729,f686,f600,f550,f1097]) ).
tff(f550,plain,
( spl2_12
<=> comm_monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f686,plain,
( spl2_40
<=> ! [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_40])]) ).
tff(f729,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_12
| ~ spl2_22
| ~ spl2_40 ),
inference(forward_demodulation,[],[f728,f602]) ).
tff(f728,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl2_12
| ~ spl2_40 ),
inference(resolution,[],[f687,f552]) ).
tff(f552,plain,
( comm_monoid_mult(int)
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f550]) ).
tff(f687,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f686]) ).
tff(f1083,plain,
spl2_106,
inference(avatar_split_clause,[],[f453,f1081]) ).
tff(f453,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int] : ( asubst(X4,X3,c_PresArith_Oatom_OLe(X2,cons(int,X1,X0))) = c_PresArith_Oatom_OLe(minus_minus(int,X2,aa(int,int,times_times(int,X1),X4)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X3)),X0)) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int] : ( asubst(X4,X3,c_PresArith_Oatom_OLe(X2,cons(int,X1,X0))) = c_PresArith_Oatom_OLe(minus_minus(int,X2,aa(int,int,times_times(int,X1),X4)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X1),X3)),X0)) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X55: list(int),X57: int,X56: int,X58: list(int),X59: int] : ( asubst(X59,X58,c_PresArith_Oatom_OLe(X56,cons(int,X57,X55))) = c_PresArith_Oatom_OLe(minus_minus(int,X56,aa(int,int,times_times(int,X57),X59)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X57),X58)),X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_asubst_Osimps_I1_J) ).
tff(f1079,plain,
spl2_105,
inference(avatar_split_clause,[],[f420,f1077]) ).
tff(f1077,plain,
( spl2_105
<=> ! [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_105])]) ).
tff(f420,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,[],[f284]) ).
tff(f284,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,[],[f185]) ).
tff(f185,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,[],[f57]) ).
tff(f57,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/sandbox2/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
tff(f1075,plain,
spl2_104,
inference(avatar_split_clause,[],[f419,f1073]) ).
tff(f1073,plain,
( spl2_104
<=> ! [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_104])]) ).
tff(f419,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,[],[f283]) ).
tff(f283,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,[],[f184]) ).
tff(f184,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,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X42: X0,X30: X0,X31: X0] : ( aa(X0,X0,times_times(X0,X31),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X30),X42)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X31),X30)),aa(X0,X0,times_times(X0,X31),X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
tff(f1071,plain,
spl2_103,
inference(avatar_split_clause,[],[f361,f1069]) ).
tff(f1069,plain,
( spl2_103
<=> ! [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_103])]) ).
tff(f361,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,[],[f231]) ).
tff(f231,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,[],[f134]) ).
tff(f134,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,[],[f84]) ).
tff(f84,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/sandbox2/benchmark/theBenchmark.p',fact_83_comm__semiring__class_Odistrib) ).
tff(f1066,plain,
spl2_102,
inference(avatar_split_clause,[],[f384,f1064]) ).
tff(f1064,plain,
( spl2_102
<=> ! [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_102])]) ).
tff(f384,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,[],[f248]) ).
tff(f248,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,[],[f151]) ).
tff(f151,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,[],[f8]) ).
tff(f8,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/sandbox2/benchmark/theBenchmark.p',fact_7_iprod__left__add__distrib) ).
tff(f1062,plain,
( spl2_101
| ~ spl2_12
| ~ spl2_22
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f727,f682,f600,f550,f1060]) ).
tff(f1060,plain,
( spl2_101
<=> ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_101])]) ).
tff(f682,plain,
( spl2_39
<=> ! [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_39])]) ).
tff(f727,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 )
| ~ spl2_12
| ~ spl2_22
| ~ spl2_39 ),
inference(forward_demodulation,[],[f726,f602]) ).
tff(f726,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),one_one(int)) = X0 )
| ~ spl2_12
| ~ spl2_39 ),
inference(resolution,[],[f683,f552]) ).
tff(f683,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) )
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f682]) ).
tff(f1049,plain,
spl2_100,
inference(avatar_split_clause,[],[f428,f1047]) ).
tff(f1047,plain,
( spl2_100
<=> ! [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_100])]) ).
tff(f428,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,[],[f292]) ).
tff(f292,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,[],[f193]) ).
tff(f193,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,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X38: X0,X39: X0,X40: X0,X41: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X41),X40)),aa(X0,X0,times_times(X0,X39),X38)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X41),X39)),aa(X0,X0,times_times(X0,X40),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
tff(f1045,plain,
spl2_99,
inference(avatar_split_clause,[],[f406,f1043]) ).
tff(f406,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,[],[f269]) ).
tff(f269,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,[],[f268]) ).
tff(f268,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,[],[f171]) ).
tff(f171,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,[],[f66]) ).
tff(f66,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/sandbox2/benchmark/theBenchmark.p',fact_65_mod__mult__cong) ).
tff(f1036,plain,
spl2_98,
inference(avatar_split_clause,[],[f414,f1034]) ).
tff(f1034,plain,
( spl2_98
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).
tff(f414,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,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),X1),one_one(X0))),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0,X44: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X44) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X44),aa(X0,X0,times_times(X0,X5),X44)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
tff(f1032,plain,
spl2_97,
inference(avatar_split_clause,[],[f413,f1030]) ).
tff(f1030,plain,
( spl2_97
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X44: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X44)),X44) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
tff(f1028,plain,
spl2_96,
inference(avatar_split_clause,[],[f359,f1026]) ).
tff(f1026,plain,
( spl2_96
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( minus_minus(X0,aa(X0,X0,times_times(X0,X2),X2),aa(X0,X0,times_times(X0,X1),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)),minus_minus(X0,X2,X1)) )
| ~ comm_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
tff(f359,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( minus_minus(X0,aa(X0,X0,times_times(X0,X2),X2),aa(X0,X0,times_times(X0,X1),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)),minus_minus(X0,X2,X1)) )
| ~ comm_ring(X0) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( minus_minus(X0,aa(X0,X0,times_times(X0,X2),X2),aa(X0,X0,times_times(X0,X1),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)),minus_minus(X0,X2,X1)) )
| ~ comm_ring(X0) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType] :
( comm_ring(X0)
=> ! [X1: X0,X2: X0] : ( minus_minus(X0,aa(X0,X0,times_times(X0,X2),X2),aa(X0,X0,times_times(X0,X1),X1)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)),minus_minus(X0,X2,X1)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType] :
( comm_ring(X0)
=> ! [X30: X0,X31: X0] : ( minus_minus(X0,aa(X0,X0,times_times(X0,X31),X31),aa(X0,X0,times_times(X0,X30),X30)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X31),X30)),minus_minus(X0,X31,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_square__diff__square__factored) ).
tff(f1022,plain,
spl2_95,
inference(avatar_split_clause,[],[f405,f1020]) ).
tff(f1020,plain,
( spl2_95
<=> ! [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_95])]) ).
tff(f405,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,[],[f267]) ).
tff(f267,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,[],[f170]) ).
tff(f170,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,[],[f11]) ).
tff(f11,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/sandbox2/benchmark/theBenchmark.p',fact_10_mod__add__eq) ).
tff(f1016,plain,
spl2_94,
inference(avatar_split_clause,[],[f403,f1014]) ).
tff(f403,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)),X2),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,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)),X2),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,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)),X2),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)),X4),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mod__add__left__eq) ).
tff(f1012,plain,
spl2_93,
inference(avatar_split_clause,[],[f401,f1010]) ).
tff(f401,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,[],[f263]) ).
tff(f263,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,[],[f166]) ).
tff(f166,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,[],[f9]) ).
tff(f9,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/sandbox2/benchmark/theBenchmark.p',fact_8_mod__add__right__eq) ).
tff(f1006,plain,
spl2_92,
inference(avatar_split_clause,[],[f410,f1004]) ).
tff(f410,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,[],[f274]) ).
tff(f274,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,[],[f175]) ).
tff(f175,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,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X44: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X44),X44) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f1001,plain,
spl2_91,
inference(avatar_split_clause,[],[f385,f999]) ).
tff(f385,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,[],[f249]) ).
tff(f249,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,[],[f152]) ).
tff(f152,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,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X10: list(X0),X30: X0,X11: list(X0),X31: X0] : ( iprod(X0,cons(X0,X31,X11),cons(X0,X30,X10)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X31),X30)),iprod(X0,X11,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_iprod__Cons) ).
tff(f976,plain,
spl2_90,
inference(avatar_split_clause,[],[f470,f974]) ).
tff(f470,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)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,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)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X18: list(int),X19: int,X20: int,X33: fun(int,fun(int,fun(list(int),X0))),X34: fun(int,fun(int,fun(list(int),X0))),X35: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X33,X20),X19),X18) = atom_rec(X0,X35,X34,X33,nDvd(X20,X19,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_atom_Orecs_I3_J) ).
tff(f972,plain,
spl2_89,
inference(avatar_split_clause,[],[f469,f970]) ).
tff(f469,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X18: list(int),X19: int,X20: int,X33: fun(int,fun(int,fun(list(int),X0))),X34: fun(int,fun(int,fun(list(int),X0))),X35: fun(int,fun(list(int),X0))] : ( atom_case(X0,X35,X34,X33,nDvd(X20,X19,X18)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X33,X20),X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_atom_Osimps_I12_J) ).
tff(f965,plain,
spl2_88,
inference(avatar_split_clause,[],[f378,f963]) ).
tff(f963,plain,
( spl2_88
<=> ! [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_88])]) ).
tff(f378,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,[],[f244]) ).
tff(f244,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,[],[f147]) ).
tff(f147,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,[],[f14]) ).
tff(f14,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/sandbox2/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
tff(f961,plain,
spl2_87,
inference(avatar_split_clause,[],[f377,f959]) ).
tff(f959,plain,
( spl2_87
<=> ! [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_87])]) ).
tff(f377,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,[],[f243]) ).
tff(f243,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,[],[f146]) ).
tff(f146,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,[],[f16]) ).
tff(f16,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/sandbox2/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
tff(f957,plain,
spl2_86,
inference(avatar_split_clause,[],[f364,f955]) ).
tff(f955,plain,
( spl2_86
<=> ! [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_86])]) ).
tff(f364,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,[],[f234]) ).
tff(f234,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,[],[f137]) ).
tff(f137,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,[],[f15]) ).
tff(f15,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/sandbox2/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
tff(f953,plain,
( spl2_85
| ~ spl2_23
| ~ spl2_49 ),
inference(avatar_split_clause,[],[f748,f723,f605,f951]) ).
tff(f951,plain,
( spl2_85
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( l = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
tff(f723,plain,
( spl2_49
<=> ! [X2: int,X3: list(int),X4: int,X0: list(int),X5: int,X1: int] :
( ( X1 = X4 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
tff(f748,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( l = X1 ) )
| ~ spl2_23
| ~ spl2_49 ),
inference(superposition,[],[f724,f607]) ).
tff(f724,plain,
( ! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) )
| ( X1 = X4 ) )
| ~ spl2_49 ),
inference(avatar_component_clause,[],[f723]) ).
tff(f941,plain,
spl2_84,
inference(avatar_split_clause,[],[f418,f939]) ).
tff(f418,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,[],[f282]) ).
tff(f282,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,[],[f183]) ).
tff(f183,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,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X39: X0,X40: X0,X41: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X41),X40)),X39) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X41),X39)),X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
tff(f937,plain,
spl2_83,
inference(avatar_split_clause,[],[f416,f935]) ).
tff(f935,plain,
( spl2_83
<=> ! [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_83])]) ).
tff(f416,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,[],[f280]) ).
tff(f280,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,[],[f181]) ).
tff(f181,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,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X38: X0,X39: X0,X41: X0] : ( aa(X0,X0,times_times(X0,X41),aa(X0,X0,times_times(X0,X39),X38)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X41),X39)),X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f933,plain,
spl2_82,
inference(avatar_split_clause,[],[f415,f931]) ).
tff(f415,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,[],[f279]) ).
tff(f279,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,[],[f180]) ).
tff(f180,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,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X38: X0,X39: X0,X41: X0] : ( aa(X0,X0,times_times(X0,X41),aa(X0,X0,times_times(X0,X39),X38)) = aa(X0,X0,times_times(X0,X39),aa(X0,X0,times_times(X0,X41),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f929,plain,
( spl2_81
| ~ spl2_23
| ~ spl2_48 ),
inference(avatar_split_clause,[],[f745,f719,f605,f927]) ).
tff(f927,plain,
( spl2_81
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( d = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
tff(f745,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( d = X0 ) )
| ~ spl2_23
| ~ spl2_48 ),
inference(superposition,[],[f720,f607]) ).
tff(f925,plain,
spl2_80,
inference(avatar_split_clause,[],[f400,f923]) ).
tff(f400,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,[],[f262]) ).
tff(f262,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,[],[f165]) ).
tff(f165,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,[],[f68]) ).
tff(f68,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/sandbox2/benchmark/theBenchmark.p',fact_67_mod__mult__mult2) ).
tff(f921,plain,
spl2_79,
inference(avatar_split_clause,[],[f399,f919]) ).
tff(f399,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,[],[f261]) ).
tff(f261,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,[],[f164]) ).
tff(f164,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,[],[f69]) ).
tff(f69,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/sandbox2/benchmark/theBenchmark.p',fact_68_mod__mult__mult1) ).
tff(f917,plain,
spl2_78,
inference(avatar_split_clause,[],[f398,f915]) ).
tff(f398,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,[],[f260]) ).
tff(f260,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,[],[f163]) ).
tff(f163,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,[],[f70]) ).
tff(f70,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/sandbox2/benchmark/theBenchmark.p',fact_69_mod__mult__eq) ).
tff(f913,plain,
spl2_77,
inference(avatar_split_clause,[],[f360,f911]) ).
tff(f360,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,[],[f230]) ).
tff(f230,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,[],[f133]) ).
tff(f133,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,[],[f54]) ).
tff(f54,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/sandbox2/benchmark/theBenchmark.p',fact_53_ab__semigroup__mult__class_Omult__ac_I1_J) ).
tff(f903,plain,
spl2_76,
inference(avatar_split_clause,[],[f434,f901]) ).
tff(f434,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(flattening,[],[f302]) ).
tff(f302,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) )
| ~ zero(X0)
| ~ cl_Groups_Ominus(X0) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Ominus(X0) )
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( minus_minus(list(X0),cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,minus_minus(X0,X4,X2),minus_minus(list(X0),X3,X1)) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Ominus(X0) )
=> ! [X10: list(X0),X30: X0,X11: list(X0),X31: X0] : ( minus_minus(list(X0),cons(X0,X31,X11),cons(X0,X30,X10)) = cons(X0,minus_minus(X0,X31,X30),minus_minus(list(X0),X11,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_list__diff__Cons__Cons) ).
tff(f899,plain,
spl2_75,
inference(avatar_split_clause,[],[f397,f897]) ).
tff(f397,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,[],[f259]) ).
tff(f259,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,[],[f162]) ).
tff(f162,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,[],[f43]) ).
tff(f43,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/sandbox2/benchmark/theBenchmark.p',fact_42_mod__mult__self2) ).
tff(f895,plain,
spl2_74,
inference(avatar_split_clause,[],[f396,f893]) ).
tff(f396,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,[],[f258]) ).
tff(f258,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,[],[f161]) ).
tff(f161,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,[],[f42]) ).
tff(f42,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/sandbox2/benchmark/theBenchmark.p',fact_41_mod__mult__self1) ).
tff(f890,plain,
spl2_73,
inference(avatar_split_clause,[],[f412,f888]) ).
tff(f412,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,[],[f276]) ).
tff(f276,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,[],[f177]) ).
tff(f177,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,[],[f33]) ).
tff(f33,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/sandbox2/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f881,plain,
spl2_72,
inference(avatar_split_clause,[],[f446,f879]) ).
tff(f879,plain,
( spl2_72
<=> ! [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_72])]) ).
tff(f446,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,[],[f321]) ).
tff(f321,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,[],[f209]) ).
tff(f209,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,[],[f86]) ).
tff(f86,axiom,
! [X27: list(int),X8: atom,X55: list(int),X56: int] :
( i_Z(asubst(X56,X55,X8),X27)
<=> i_Z(X8,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X56),iprod(int,X55,X27)),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_IZ__asubst) ).
tff(f877,plain,
spl2_71,
inference(avatar_split_clause,[],[f445,f875]) ).
tff(f875,plain,
( spl2_71
<=> ! [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_71])]) ).
tff(f445,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,[],[f321]) ).
tff(f873,plain,
spl2_70,
inference(avatar_split_clause,[],[f394,f871]) ).
tff(f394,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)),X2),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,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),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,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),X2),X1) ) ),
inference(rectify,[],[f71]) ).
tff(f71,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)),X4),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mod__mult__left__eq) ).
tff(f869,plain,
spl2_69,
inference(avatar_split_clause,[],[f393,f867]) ).
tff(f867,plain,
( spl2_69
<=> ! [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_69])]) ).
tff(f393,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,[],[f255]) ).
tff(f255,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,[],[f158]) ).
tff(f158,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,[],[f72]) ).
tff(f72,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/sandbox2/benchmark/theBenchmark.p',fact_71_mod__mult__right__eq) ).
tff(f865,plain,
( spl2_68
| ~ spl2_23
| ~ spl2_31 ),
inference(avatar_split_clause,[],[f652,f639,f605,f863]) ).
tff(f652,plain,
( ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) )
| ~ spl2_23
| ~ spl2_31 ),
inference(superposition,[],[f640,f607]) ).
tff(f852,plain,
spl2_67,
inference(avatar_split_clause,[],[f444,f850]) ).
tff(f850,plain,
( spl2_67
<=> ! [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_67])]) ).
tff(f444,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,[],[f320]) ).
tff(f320,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])],[f307,f319]) ).
tff(f319,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(f307,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,[],[f208]) ).
tff(f208,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,X47: fun(X0,X1),X29: fun(X0,X1)] :
( ! [X48: X0] : ( aa(X0,X1,X29,X48) = aa(X0,X1,X47,X48) )
=> ( X29 = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f848,plain,
spl2_66,
inference(avatar_split_clause,[],[f441,f846]) ).
tff(f441,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,[],[f205]) ).
tff(f205,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,[],[f74]) ).
tff(f74,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/sandbox2/benchmark/theBenchmark.p',fact_73_zmod__zmult1__eq) ).
tff(f843,plain,
spl2_65,
inference(avatar_split_clause,[],[f383,f841]) ).
tff(f383,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,[],[f247]) ).
tff(f247,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,[],[f150]) ).
tff(f150,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,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X25: list(X0),X27: list(X0),X28: X0] : ( iprod(X0,map(X0,X0,times_times(X0,X28),X27),X25) = aa(X0,X0,times_times(X0,X28),iprod(X0,X27,X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_iprod__assoc) ).
tff(f826,plain,
spl2_64,
inference(avatar_split_clause,[],[f458,f824]) ).
tff(f458,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,[],[f217]) ).
tff(f217,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,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X18: list(int),X37: int,X33: fun(int,fun(int,fun(list(int),X0))),X34: fun(int,fun(int,fun(list(int),X0))),X35: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X35,X37),X18) = atom_rec(X0,X35,X34,X33,c_PresArith_Oatom_OLe(X37,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_atom_Orecs_I1_J) ).
tff(f822,plain,
spl2_63,
inference(avatar_split_clause,[],[f457,f820]) ).
tff(f457,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,[],[f216]) ).
tff(f216,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,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType,X18: list(int),X37: int,X33: fun(int,fun(int,fun(list(int),X0))),X34: fun(int,fun(int,fun(list(int),X0))),X35: fun(int,fun(list(int),X0))] : ( atom_case(X0,X35,X34,X33,c_PresArith_Oatom_OLe(X37,X18)) = aa(list(int),X0,aa(int,fun(list(int),X0),X35,X37),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_atom_Osimps_I10_J) ).
tff(f818,plain,
spl2_62,
inference(avatar_split_clause,[],[f452,f816]) ).
tff(f452,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,[],[f213]) ).
tff(f213,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,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X1: $tType,X27: list(X1),X28: X1,X29: fun(X1,X0)] : ( map(X1,X0,X29,cons(X1,X28,X27)) = cons(X0,aa(X1,X0,X29,X28),map(X1,X0,X29,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_map_Osimps_I2_J) ).
tff(f814,plain,
spl2_61,
inference(avatar_split_clause,[],[f392,f812]) ).
tff(f392,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,[],[f254]) ).
tff(f254,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,[],[f157]) ).
tff(f157,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,[],[f1]) ).
tff(f1,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/sandbox2/benchmark/theBenchmark.p',fact_0_mod__add__self2) ).
tff(f810,plain,
spl2_60,
inference(avatar_split_clause,[],[f391,f808]) ).
tff(f391,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,[],[f253]) ).
tff(f253,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,[],[f156]) ).
tff(f156,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,[],[f2]) ).
tff(f2,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/sandbox2/benchmark/theBenchmark.p',fact_1_mod__add__self1) ).
tff(f805,plain,
spl2_59,
inference(avatar_split_clause,[],[f432,f803]) ).
tff(f432,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f298]) ).
tff(f298,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_list__add__def) ).
tff(f800,plain,
spl2_58,
inference(avatar_split_clause,[],[f411,f798]) ).
tff(f411,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,[],[f275]) ).
tff(f275,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,[],[f176]) ).
tff(f176,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,[],[f53]) ).
tff(f53,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/sandbox2/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f796,plain,
~ spl2_57,
inference(avatar_split_clause,[],[f330,f793]) ).
tff(f330,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
inference(flattening,[],[f125]) ).
tff(f125,negated_conjecture,
( ~ div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d) ),
inference(negated_conjecture,[],[f124]) ).
tff(f124,conjecture,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),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,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f785,plain,
spl2_56,
inference(avatar_split_clause,[],[f455,f783]) ).
tff(f455,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,[],[f325]) ).
tff(f325,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,[],[f324]) ).
tff(f324,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,[],[f215]) ).
tff(f215,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,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType,X15: list(X0),X32: X0,X18: list(X0),X8: X0] :
( ( cons(X0,X8,X18) = cons(X0,X32,X15) )
<=> ( ( X15 = X18 )
& ( X8 = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_list_Oinject) ).
tff(f781,plain,
spl2_55,
inference(avatar_split_clause,[],[f390,f779]) ).
tff(f390,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,[],[f252]) ).
tff(f252,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,[],[f155]) ).
tff(f155,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/sandbox2/benchmark/theBenchmark.p',fact_3_mod__mod__trivial) ).
tff(f766,plain,
spl2_54,
inference(avatar_split_clause,[],[f467,f764]) ).
tff(f467,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X0 = X3 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( nDvd(X2,X1,X0) = nDvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ) ),
inference(flattening,[],[f328]) ).
tff(f328,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( nDvd(X2,X1,X0) = nDvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ) ),
inference(nnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( nDvd(X2,X1,X0) = nDvd(X5,X4,X3) )
<=> ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X15: list(int),X16: int,X17: int,X18: list(int),X19: int,X20: int] :
( ( nDvd(X20,X19,X18) = nDvd(X17,X16,X15) )
<=> ( ( X15 = X18 )
& ( X16 = X19 )
& ( X17 = X20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_atom_Osimps_I3_J) ).
tff(f762,plain,
spl2_53,
inference(avatar_split_clause,[],[f463,f760]) ).
tff(f760,plain,
( spl2_53
<=> ! [X5: int,X4: int,X0: list(int),X3: list(int),X2: int,X1: int] :
( ( X0 = X3 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
tff(f463,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X0 = X3 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X5,X4,X3) = dvd(X2,X1,X0) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ) ),
inference(flattening,[],[f326]) ).
tff(f326,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X5,X4,X3) = dvd(X2,X1,X0) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ) ),
inference(nnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( dvd(X5,X4,X3) = dvd(X2,X1,X0) )
<=> ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X15: list(int),X16: int,X17: int,X18: list(int),X19: int,X20: int] :
( ( dvd(X20,X19,X18) = dvd(X17,X16,X15) )
<=> ( ( X15 = X18 )
& ( X16 = X19 )
& ( X17 = X20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_atom_Osimps_I2_J) ).
tff(f758,plain,
spl2_52,
inference(avatar_split_clause,[],[f454,f756]) ).
tff(f454,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,[],[f325]) ).
tff(f754,plain,
spl2_51,
inference(avatar_split_clause,[],[f376,f752]) ).
tff(f376,plain,
! [X0: $tType,X1: list(X0)] :
( ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X27: list(X0)] : ( map(X0,X0,times_times(X0,one_one(X0)),X27) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_scale1) ).
tff(f738,plain,
( ~ spl2_50
| ~ spl2_27
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f654,f648,f622,f735]) ).
tff(f735,plain,
( spl2_50
<=> ( ks1 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
tff(f654,plain,
( ( ks1 != sK0 )
| ~ spl2_27
| ~ spl2_33 ),
inference(superposition,[],[f623,f650]) ).
tff(f725,plain,
spl2_49,
inference(avatar_split_clause,[],[f466,f723]) ).
tff(f466,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X1 = X4 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f329]) ).
tff(f721,plain,
spl2_48,
inference(avatar_split_clause,[],[f465,f719]) ).
tff(f465,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X2 = X5 )
| ( nDvd(X2,X1,X0) != nDvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f329]) ).
tff(f717,plain,
spl2_47,
inference(avatar_split_clause,[],[f462,f715]) ).
tff(f715,plain,
( spl2_47
<=> ! [X2: int,X4: int,X0: list(int),X3: list(int),X5: int,X1: int] :
( ( X1 = X4 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
tff(f462,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X1 = X4 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f713,plain,
spl2_46,
inference(avatar_split_clause,[],[f461,f711]) ).
tff(f461,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X2 = X5 )
| ( dvd(X5,X4,X3) != dvd(X2,X1,X0) ) ),
inference(cnf_transformation,[],[f327]) ).
tff(f709,plain,
spl2_45,
inference(avatar_split_clause,[],[f409,f707]) ).
tff(f707,plain,
( spl2_45
<=> ! [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_45])]) ).
tff(f409,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
tff(f705,plain,
spl2_44,
inference(avatar_split_clause,[],[f408,f703]) ).
tff(f703,plain,
( spl2_44
<=> ! [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_44])]) ).
tff(f408,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f701,plain,
( ~ spl2_43
| ~ spl2_27
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f653,f643,f622,f698]) ).
tff(f698,plain,
( spl2_43
<=> ( ks1 = ks ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
tff(f653,plain,
( ( ks1 != ks )
| ~ spl2_27
| ~ spl2_32 ),
inference(superposition,[],[f623,f645]) ).
tff(f696,plain,
spl2_42,
inference(avatar_split_clause,[],[f375,f694]) ).
tff(f694,plain,
( spl2_42
<=> ! [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_42])]) ).
tff(f375,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__1__left) ).
tff(f692,plain,
spl2_41,
inference(avatar_split_clause,[],[f374,f690]) ).
tff(f690,plain,
( spl2_41
<=> ! [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_41])]) ).
tff(f374,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__1__right) ).
tff(f688,plain,
spl2_40,
inference(avatar_split_clause,[],[f367,f686]) ).
tff(f367,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__1) ).
tff(f684,plain,
spl2_39,
inference(avatar_split_clause,[],[f366,f682]) ).
tff(f366,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mult_Ocomm__neutral) ).
tff(f679,plain,
spl2_38,
inference(avatar_split_clause,[],[f448,f677]) ).
tff(f677,plain,
( spl2_38
<=> ! [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_38])]) ).
tff(f448,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,[],[f323]) ).
tff(f323,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,[],[f322]) ).
tff(f322,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,[],[f210]) ).
tff(f210,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,[],[f41]) ).
tff(f41,axiom,
! [X15: list(int),X36: int,X18: list(int),X37: int] :
( ( c_PresArith_Oatom_OLe(X37,X18) = c_PresArith_Oatom_OLe(X36,X15) )
<=> ( ( X15 = X18 )
& ( X36 = X37 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_atom_Osimps_I1_J) ).
tff(f675,plain,
( spl2_37
| ~ spl2_35
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f670,f666,f660,f672]) ).
tff(f660,plain,
( spl2_35
<=> ( d = divisor(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
tff(f666,plain,
( spl2_36
<=> ( div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
tff(f670,plain,
( ( div_mod(int,i,d) = div_mod(int,j,d) )
| ~ spl2_35
| ~ spl2_36 ),
inference(forward_demodulation,[],[f668,f662]) ).
tff(f662,plain,
( ( d = divisor(a) )
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f660]) ).
tff(f668,plain,
( ( div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)) )
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f666]) ).
tff(f669,plain,
spl2_36,
inference(avatar_split_clause,[],[f355,f666]) ).
tff(f355,plain,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms_I3_J) ).
tff(f663,plain,
( spl2_35
| ~ spl2_23
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f633,f626,f605,f660]) ).
tff(f633,plain,
( ( d = divisor(a) )
| ~ spl2_23
| ~ spl2_28 ),
inference(superposition,[],[f627,f607]) ).
tff(f658,plain,
spl2_34,
inference(avatar_split_clause,[],[f447,f656]) ).
tff(f447,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,[],[f323]) ).
tff(f651,plain,
spl2_33,
inference(avatar_split_clause,[],[f492,f648]) ).
tff(f492,plain,
ks1 = cons(int,hd_coeff(a),sK0),
inference(forward_demodulation,[],[f356,f352]) ).
tff(f352,plain,
one_one(int) = hd_coeff(a),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
one_one(int) = hd_coeff(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_assms_I2_J) ).
tff(f356,plain,
ks1 = cons(int,one_one(int),sK0),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
ks1 = cons(int,one_one(int),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f227,f308]) ).
tff(f308,plain,
( ? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) )
=> ( ks1 = cons(int,one_one(int),sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f227,plain,
? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
~ ! [X0: list(int)] : ( ks1 != cons(int,one_one(int),X0) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
~ ! [X24: list(int)] : ( ks1 != cons(int,one_one(int),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__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(f646,plain,
spl2_32,
inference(avatar_split_clause,[],[f491,f643]) ).
tff(f491,plain,
ks1 = cons(int,hd_coeff(a),ks),
inference(forward_demodulation,[],[f354,f352]) ).
tff(f354,plain,
ks1 = cons(int,one_one(int),ks),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
ks1 = cons(int,one_one(int),ks),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__096ks_A_061_A1_A_D_Aks_H_096) ).
tff(f641,plain,
spl2_31,
inference(avatar_split_clause,[],[f450,f639]) ).
tff(f450,plain,
! [X2: list(int),X3: int,X0: list(int),X1: int,X4: int] : ( c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: list(int),X1: int,X2: list(int),X3: int,X4: int] : ( c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X52: list(int),X53: int,X49: list(int),X50: int,X51: int] : ( c_PresArith_Oatom_OLe(X53,X52) != nDvd(X51,X50,X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_atom_Osimps_I7_J) ).
tff(f637,plain,
spl2_30,
inference(avatar_split_clause,[],[f440,f635]) ).
tff(f635,plain,
( spl2_30
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
tff(f440,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X5: atom,X21: list(int),X22: int] : ( divisor(asubst(X22,X21,X5)) = divisor(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_divisor__asubst) ).
tff(f632,plain,
spl2_29,
inference(avatar_split_clause,[],[f493,f630]) ).
tff(f493,plain,
! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(forward_demodulation,[],[f435,f352]) ).
tff(f435,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X21: list(int),X22: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X22,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_divisor_Osimps_I1_J) ).
tff(f628,plain,
spl2_28,
inference(avatar_split_clause,[],[f439,f626]) ).
tff(f439,plain,
! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: list(int),X1: int,X2: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X21: list(int),X22: int,X23: int] : ( divisor(nDvd(X23,X22,X21)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_divisor_Osimps_I3_J) ).
tff(f624,plain,
spl2_27,
inference(avatar_split_clause,[],[f437,f622]) ).
tff(f437,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $tType,X11: list(X0),X31: X0] : ( cons(X0,X31,X11) != X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_not__Cons__self2) ).
tff(f620,plain,
spl2_26,
inference(avatar_split_clause,[],[f431,f618]) ).
tff(f618,plain,
( spl2_26
<=> ! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
tff(f431,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f296]) ).
tff(f296,plain,
! [X0: $tType] :
( cl_Groups_Ominus(list(X0))
| ~ cl_Groups_Ominus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType] :
( ( cl_Groups_Ominus(X0)
& zero(X0) )
=> cl_Groups_Ominus(list(X0)) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X61: $tType] :
( ( cl_Groups_Ominus(X61)
& zero(X61) )
=> cl_Groups_Ominus(list(X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
tff(f616,plain,
spl2_25,
inference(avatar_split_clause,[],[f430,f614]) ).
tff(f614,plain,
( spl2_25
<=> ! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
tff(f430,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f294]) ).
tff(f294,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType] :
( ( cl_Groups_Oplus(X0)
& zero(X0) )
=> cl_Groups_Oplus(list(X0)) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X61: $tType] :
( ( cl_Groups_Oplus(X61)
& zero(X61) )
=> cl_Groups_Oplus(list(X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
tff(f612,plain,
spl2_24,
inference(avatar_split_clause,[],[f436,f610]) ).
tff(f610,plain,
( spl2_24
<=> ! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
tff(f436,plain,
! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X1)
=> cl_Groups_Ominus(fun(X0,X1)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X61: $tType,X62: $tType] :
( cl_Groups_Ominus(X62)
=> cl_Groups_Ominus(fun(X61,X62)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
tff(f608,plain,
spl2_23,
inference(avatar_split_clause,[],[f353,f605]) ).
tff(f353,plain,
a = nDvd(d,l,ks1),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
a = nDvd(d,l,ks1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_NDvd) ).
tff(f603,plain,
spl2_22,
inference(avatar_split_clause,[],[f352,f600]) ).
tff(f598,plain,
spl2_21,
inference(avatar_split_clause,[],[f351,f595]) ).
tff(f351,plain,
cl_Groups_Ominus(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
cl_Groups_Ominus(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
tff(f593,plain,
spl2_20,
inference(avatar_split_clause,[],[f350,f590]) ).
tff(f350,plain,
cl_Groups_Ominus(bool),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
cl_Groups_Ominus(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
tff(f588,plain,
spl2_19,
inference(avatar_split_clause,[],[f349,f585]) ).
tff(f349,plain,
cl_Groups_Oplus(int),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
cl_Groups_Oplus(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
tff(f583,plain,
spl2_18,
inference(avatar_split_clause,[],[f348,f580]) ).
tff(f348,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f578,plain,
spl2_17,
inference(avatar_split_clause,[],[f347,f575]) ).
tff(f347,plain,
semiring_div(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
semiring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f573,plain,
spl2_16,
inference(avatar_split_clause,[],[f346,f570]) ).
tff(f346,plain,
zero(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f568,plain,
spl2_15,
inference(avatar_split_clause,[],[f345,f565]) ).
tff(f345,plain,
ring(int),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f563,plain,
spl2_14,
inference(avatar_split_clause,[],[f344,f560]) ).
tff(f560,plain,
( spl2_14
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f344,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f558,plain,
spl2_13,
inference(avatar_split_clause,[],[f343,f555]) ).
tff(f343,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f553,plain,
spl2_12,
inference(avatar_split_clause,[],[f342,f550]) ).
tff(f342,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
tff(f548,plain,
spl2_11,
inference(avatar_split_clause,[],[f341,f545]) ).
tff(f545,plain,
( spl2_11
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f341,plain,
semiri456707255roduct(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f543,plain,
spl2_10,
inference(avatar_split_clause,[],[f340,f540]) ).
tff(f540,plain,
( spl2_10
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f340,plain,
pp(fTrue),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f538,plain,
spl2_9,
inference(avatar_split_clause,[],[f339,f535]) ).
tff(f535,plain,
( spl2_9
<=> comm_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f339,plain,
comm_semiring(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
comm_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
tff(f533,plain,
spl2_8,
inference(avatar_split_clause,[],[f338,f530]) ).
tff(f530,plain,
( spl2_8
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f338,plain,
semiring(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
tff(f528,plain,
spl2_7,
inference(avatar_split_clause,[],[f337,f525]) ).
tff(f525,plain,
( spl2_7
<=> comm_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f337,plain,
comm_ring(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
comm_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
tff(f523,plain,
spl2_6,
inference(avatar_split_clause,[],[f336,f520]) ).
tff(f520,plain,
( spl2_6
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f336,plain,
monoid_add(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
monoid_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f518,plain,
spl2_5,
inference(avatar_split_clause,[],[f335,f515]) ).
tff(f515,plain,
( spl2_5
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f335,plain,
one(int),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f513,plain,
spl2_4,
inference(avatar_split_clause,[],[f334,f510]) ).
tff(f510,plain,
( spl2_4
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f334,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f508,plain,
spl2_3,
inference(avatar_split_clause,[],[f333,f505]) ).
tff(f333,plain,
ab_semigroup_mult(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
tff(f503,plain,
spl2_2,
inference(avatar_split_clause,[],[f332,f500]) ).
tff(f500,plain,
( spl2_2
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f332,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f498,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f331,f495]) ).
tff(f495,plain,
( spl2_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f331,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM041_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 04:39:49 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (25888)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (25891)WARNING: value z3 for option sas not known
% 0.15/0.38 % (25891)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 % (25895)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 % (25889)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (25890)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 % (25892)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (25894)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 % (25893)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)
% 0.15/0.40 % (25895)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level% Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % (25896)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.43 % (25897)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)
% 0.22/0.43 % (25898)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)
% 0.22/0.44 % (25896)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.44 % (25897)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.44 % Exception at run slice level
% 0.22/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.46 % (25899)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)
% 0.22/0.52 % (25893)First to succeed.
% 0.22/0.53 % (25893)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Theorem for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (25893)------------------------------
% 0.22/0.54 % (25893)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.54 % (25893)Termination reason: Refutation
% 0.22/0.54
% 0.22/0.54 % (25893)Memory used [KB]: 2290
% 0.22/0.54 % (25893)Time elapsed: 0.140 s
% 0.22/0.54 % (25893)Instructions burned: 262 (million)
% 0.22/0.54 % (25893)------------------------------
% 0.22/0.54 % (25893)------------------------------
% 0.22/0.54 % (25888)Success in time 0.18 s
%------------------------------------------------------------------------------