TSTP Solution File: COM045_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM045_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:14 EDT 2024
% Result : Theorem 0.18s 0.61s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 355
% Syntax : Number of formulae : 1025 ( 219 unt; 55 typ; 0 def)
% Number of atoms : 2324 ( 849 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2378 (1024 ~; 992 |; 34 &)
% ( 209 <=>; 119 =>; 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 : 46 ( 22 >; 24 *; 0 +; 0 <<)
% Number of predicates : 219 ( 217 usr; 199 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 11 con; 0-5 aty)
% Number of variables : 2736 (2693 !; 4 ?;2736 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
atom: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
div_mod:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_4,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_5,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_8,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_9,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_10,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_11,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_12,type,
c_PresArith_Oatom_OLe: ( int * list(int) ) > atom ).
tff(func_def_13,type,
nDvd: ( int * int * list(int) ) > atom ).
tff(func_def_14,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_15,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_16,type,
divisor: atom > int ).
tff(func_def_17,type,
hd_coeff: atom > int ).
tff(func_def_18,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_19,type,
fFalse: bool ).
tff(func_def_20,type,
fTrue: bool ).
tff(func_def_21,type,
a: atom ).
tff(func_def_22,type,
d: int ).
tff(func_def_23,type,
e: list(int) ).
tff(func_def_24,type,
i: int ).
tff(func_def_25,type,
j: int ).
tff(func_def_26,type,
ks: list(int) ).
tff(func_def_27,type,
ks1: list(int) ).
tff(func_def_28,type,
l: int ).
tff(func_def_29,type,
sK0: list(int) ).
tff(func_def_30,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f3893,plain,
$false,
inference(avatar_sat_refutation,[],[f460,f465,f470,f475,f480,f485,f490,f495,f500,f505,f510,f515,f520,f525,f530,f535,f540,f545,f550,f555,f559,f563,f567,f571,f576,f580,f585,f590,f598,f603,f607,f613,f618,f623,f627,f631,f636,f640,f644,f648,f652,f656,f671,f683,f687,f699,f703,f714,f721,f725,f730,f735,f739,f743,f747,f751,f766,f781,f785,f800,f804,f808,f812,f818,f825,f830,f834,f840,f844,f848,f852,f856,f860,f864,f873,f880,f884,f888,f895,f899,f903,f931,f936,f942,f946,f950,f970,f976,f981,f985,f994,f998,f1013,f1018,f1022,f1040,f1044,f1048,f1052,f1059,f1063,f1067,f1071,f1075,f1084,f1088,f1102,f1120,f1124,f1133,f1138,f1143,f1148,f1169,f1195,f1199,f1203,f1220,f1224,f1240,f1249,f1256,f1288,f1292,f1302,f1336,f1340,f1344,f1386,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1492,f1496,f1528,f1533,f1537,f1541,f1576,f1624,f1662,f1666,f1670,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f2218,f2222,f2288,f2292,f2296,f2300,f2304,f2360,f2375,f2379,f2472,f2533,f2537,f2685,f2689,f2727,f2737,f2834,f2838,f3048,f3052,f3132,f3261,f3376,f3413,f3417,f3421,f3471,f3501,f3505,f3509,f3630,f3636,f3656,f3660,f3666,f3687,f3691,f3695,f3699,f3874,f3892]) ).
tff(f3892,plain,
( ~ spl2_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(avatar_contradiction_clause,[],[f3891]) ).
tff(f3891,plain,
( $false
| ~ spl2_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(trivial_inequality_removal,[],[f3890]) ).
tff(f3890,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3889,f584]) ).
tff(f584,plain,
( ( ks1 = cons(int,hd_coeff(a),ks) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f582]) ).
tff(f582,plain,
( spl2_27
<=> ( ks1 = cons(int,hd_coeff(a),ks) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
tff(f3889,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3888,f2380]) ).
tff(f2380,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_104
| ~ spl2_167 ),
inference(superposition,[],[f2374,f1074]) ).
tff(f1074,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_104 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f1073,plain,
( spl2_104
<=> ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_104])]) ).
tff(f2374,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_167 ),
inference(avatar_component_clause,[],[f2373]) ).
tff(f2373,plain,
( spl2_167
<=> ! [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_167])]) ).
tff(f3888,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3887,f2380]) ).
tff(f3887,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3886,f3694]) ).
tff(f3694,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_197 ),
inference(avatar_component_clause,[],[f3693]) ).
tff(f3693,plain,
( spl2_197
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_197])]) ).
tff(f3886,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3885,f584]) ).
tff(f3885,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_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3884,f2380]) ).
tff(f3884,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_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3883,f2380]) ).
tff(f3883,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_30
| spl2_49
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3838,f2636]) ).
tff(f2636,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),X0),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),X0),d) )
| ~ spl2_30
| ~ spl2_171 ),
inference(forward_demodulation,[],[f2599,f2536]) ).
tff(f2536,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_171 ),
inference(avatar_component_clause,[],[f2535]) ).
tff(f2535,plain,
( spl2_171
<=> ! [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_171])]) ).
tff(f2599,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),X0),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),X0),d) )
| ~ spl2_30
| ~ spl2_171 ),
inference(superposition,[],[f2536,f602]) ).
tff(f602,plain,
( ( div_mod(int,j,d) = div_mod(int,i,d) )
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f600,plain,
( spl2_30
<=> ( div_mod(int,j,d) = div_mod(int,i,d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
tff(f3838,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),j),aa(int,int,aa(int,fun(int,int),plus_plus(int),l),iprod(int,ks,e))),d) )
| spl2_49
| ~ spl2_197 ),
inference(superposition,[],[f720,f3694]) ).
tff(f720,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),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e))),d) )
| spl2_49 ),
inference(avatar_component_clause,[],[f718]) ).
tff(f718,plain,
( spl2_49
<=> ( 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),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e))),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
tff(f3874,plain,
( ~ spl2_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(avatar_contradiction_clause,[],[f3873]) ).
tff(f3873,plain,
( $false
| ~ spl2_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(trivial_inequality_removal,[],[f3872]) ).
tff(f3872,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3871,f584]) ).
tff(f3871,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3870,f2380]) ).
tff(f3870,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3869,f2380]) ).
tff(f3869,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3868,f3694]) ).
tff(f3868,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_27
| ~ spl2_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3867,f584]) ).
tff(f3867,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_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3866,f2380]) ).
tff(f3866,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_30
| spl2_49
| ~ spl2_104
| ~ spl2_167
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3865,f2380]) ).
tff(f3865,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_30
| spl2_49
| ~ spl2_171
| ~ spl2_197 ),
inference(forward_demodulation,[],[f3820,f2636]) ).
tff(f3820,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),j),aa(int,int,aa(int,fun(int,int),plus_plus(int),l),iprod(int,ks,e))),d) )
| spl2_49
| ~ spl2_197 ),
inference(superposition,[],[f720,f3694]) ).
tff(f3699,plain,
( spl2_198
| ~ spl2_6
| ~ spl2_17
| ~ spl2_100
| ~ spl2_103 ),
inference(avatar_split_clause,[],[f1080,f1069,f1057,f537,f482,f3697]) ).
tff(f3697,plain,
( spl2_198
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_198])]) ).
tff(f482,plain,
( spl2_6
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f537,plain,
( spl2_17
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f1057,plain,
( spl2_100
<=> ! [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_100])]) ).
tff(f1069,plain,
( spl2_103
<=> ! [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_103])]) ).
tff(f1080,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)) )
| ~ spl2_6
| ~ spl2_17
| ~ spl2_100
| ~ spl2_103 ),
inference(forward_demodulation,[],[f1079,f1076]) ).
tff(f1076,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) = 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)) )
| ~ spl2_6
| ~ spl2_100 ),
inference(resolution,[],[f1058,f484]) ).
tff(f484,plain,
( ab_semigroup_add(int)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f482]) ).
tff(f1058,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ab_semigroup_add(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)) ) )
| ~ spl2_100 ),
inference(avatar_component_clause,[],[f1057]) ).
tff(f1079,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2)),X1) )
| ~ spl2_17
| ~ spl2_103 ),
inference(resolution,[],[f1070,f539]) ).
tff(f539,plain,
( comm_semiring_1(int)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f537]) ).
tff(f1070,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(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) ) )
| ~ spl2_103 ),
inference(avatar_component_clause,[],[f1069]) ).
tff(f3695,plain,
( spl2_197
| ~ spl2_17
| ~ spl2_101 ),
inference(avatar_split_clause,[],[f1077,f1061,f537,f3693]) ).
tff(f1061,plain,
( spl2_101
<=> ! [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_101])]) ).
tff(f1077,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_17
| ~ spl2_101 ),
inference(resolution,[],[f1062,f539]) ).
tff(f1062,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_101 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f3691,plain,
( spl2_196
| ~ spl2_6
| ~ spl2_100 ),
inference(avatar_split_clause,[],[f1076,f1057,f482,f3689]) ).
tff(f3689,plain,
( spl2_196
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1)),X2) = 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_196])]) ).
tff(f3687,plain,
( spl2_195
| ~ spl2_57
| ~ spl2_86 ),
inference(avatar_split_clause,[],[f964,f948,f764,f3685]) ).
tff(f3685,plain,
( spl2_195
<=> ! [X0: $tType,X5: list(list(X0)),X4: list(list(X0)),X3: list(X0),X2: X0,X1: fun(X0,fun(list(X0),fun(list(list(X0)),list(list(X0)))))] : ( list_case(list(list(X0)),list(X0),X5,aa(X0,fun(list(X0),fun(list(list(X0)),list(list(X0)))),X1,X2),cons(list(X0),X3,list_rec(list(list(X0)),X0,X4,X1,X3))) = list_rec(list(list(X0)),X0,X4,X1,cons(X0,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_195])]) ).
tff(f764,plain,
( spl2_57
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
tff(f948,plain,
( spl2_86
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0,X2: list(X1)] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
tff(f964,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: fun(X0,fun(list(X0),fun(list(list(X0)),list(list(X0))))),X4: list(list(X0)),X5: list(list(X0))] : ( list_case(list(list(X0)),list(X0),X5,aa(X0,fun(list(X0),fun(list(list(X0)),list(list(X0)))),X1,X2),cons(list(X0),X3,list_rec(list(list(X0)),X0,X4,X1,X3))) = list_rec(list(list(X0)),X0,X4,X1,cons(X0,X2,X3)) )
| ~ spl2_57
| ~ spl2_86 ),
inference(superposition,[],[f949,f765]) ).
tff(f765,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) )
| ~ spl2_57 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f949,plain,
( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) )
| ~ spl2_86 ),
inference(avatar_component_clause,[],[f948]) ).
tff(f3666,plain,
( spl2_194
| ~ spl2_54
| ~ spl2_104
| ~ spl2_167
| ~ spl2_193 ),
inference(avatar_split_clause,[],[f3662,f3658,f2373,f1073,f741,f3664]) ).
tff(f3664,plain,
( spl2_194
<=> ! [X5: atom,X4: list(int),X0: int,X3: list(int),X2: int,X1: list(int)] :
( ~ i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),splice(int,cons(int,X0,X3),cons(int,X2,X4))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_194])]) ).
tff(f741,plain,
( spl2_54
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
tff(f3658,plain,
( spl2_193
<=> ! [X5: atom,X4: list(int),X0: int,X3: list(int),X2: int,X1: list(int)] :
( ~ i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_193])]) ).
tff(f3662,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( ~ i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),splice(int,cons(int,X0,X3),cons(int,X2,X4))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_54
| ~ spl2_104
| ~ spl2_167
| ~ spl2_193 ),
inference(forward_demodulation,[],[f3661,f742]) ).
tff(f742,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f741]) ).
tff(f3661,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( ~ i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),cons(int,X0,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_104
| ~ spl2_167
| ~ spl2_193 ),
inference(forward_demodulation,[],[f3659,f2380]) ).
tff(f3659,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( ~ i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_193 ),
inference(avatar_component_clause,[],[f3658]) ).
tff(f3660,plain,
( spl2_193
| ~ spl2_54
| ~ spl2_63 ),
inference(avatar_split_clause,[],[f821,f810,f741,f3658]) ).
tff(f810,plain,
( spl2_63
<=> ! [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_63])]) ).
tff(f821,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( ~ i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_54
| ~ spl2_63 ),
inference(superposition,[],[f811,f742]) ).
tff(f811,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) )
| ~ spl2_63 ),
inference(avatar_component_clause,[],[f810]) ).
tff(f3656,plain,
( spl2_192
| ~ spl2_20
| ~ spl2_136 ),
inference(avatar_split_clause,[],[f1477,f1413,f552,f3654]) ).
tff(f3654,plain,
( spl2_192
<=> ! [X0: $tType,X2: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0))),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X1,X2,X3,a) = atom_case(X0,X4,X5,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_192])]) ).
tff(f552,plain,
( spl2_20
<=> ( a = nDvd(d,l,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
tff(f1413,plain,
( spl2_136
<=> ! [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_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_136])]) ).
tff(f1477,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)),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X1,X2,X3,a) = atom_case(X0,X4,X5,X3,a) )
| ~ spl2_20
| ~ spl2_136 ),
inference(superposition,[],[f1414,f554]) ).
tff(f554,plain,
( ( a = nDvd(d,l,ks1) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f1414,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_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_136 ),
inference(avatar_component_clause,[],[f1413]) ).
tff(f3636,plain,
( spl2_191
| ~ spl2_54
| ~ spl2_104
| ~ spl2_167
| ~ spl2_190 ),
inference(avatar_split_clause,[],[f3632,f3628,f2373,f1073,f741,f3634]) ).
tff(f3634,plain,
( spl2_191
<=> ! [X5: atom,X4: list(int),X0: int,X3: list(int),X2: int,X1: list(int)] :
( i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),splice(int,cons(int,X0,X3),cons(int,X2,X4))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_191])]) ).
tff(f3628,plain,
( spl2_190
<=> ! [X5: atom,X4: list(int),X0: int,X3: list(int),X2: int,X1: list(int)] :
( i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_190])]) ).
tff(f3632,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),splice(int,cons(int,X0,X3),cons(int,X2,X4))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_54
| ~ spl2_104
| ~ spl2_167
| ~ spl2_190 ),
inference(forward_demodulation,[],[f3631,f742]) ).
tff(f3631,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( i_Z(X5,splice(int,cons(int,iprod(int,cons(int,hd_coeff(a),X1),cons(int,X0,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_104
| ~ spl2_167
| ~ spl2_190 ),
inference(forward_demodulation,[],[f3629,f2380]) ).
tff(f3629,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_190 ),
inference(avatar_component_clause,[],[f3628]) ).
tff(f3630,plain,
( spl2_190
| ~ spl2_54
| ~ spl2_62 ),
inference(avatar_split_clause,[],[f819,f806,f741,f3628]) ).
tff(f806,plain,
( spl2_62
<=> ! [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_62])]) ).
tff(f819,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int),X4: list(int),X5: atom] :
( i_Z(X5,splice(int,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),iprod(int,X1,cons(int,X2,splice(int,X3,X4)))),X3),cons(int,X2,X4)))
| ~ i_Z(asubst(X0,X1,X5),cons(int,X2,splice(int,X3,X4))) )
| ~ spl2_54
| ~ spl2_62 ),
inference(superposition,[],[f807,f742]) ).
tff(f807,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) )
| ~ spl2_62 ),
inference(avatar_component_clause,[],[f806]) ).
tff(f3509,plain,
( spl2_189
| ~ spl2_45
| ~ spl2_107 ),
inference(avatar_split_clause,[],[f1111,f1100,f685,f3507]) ).
tff(f3507,plain,
( spl2_189
<=> ! [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) )
| ( aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X2),X4)),X5) = X8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_189])]) ).
tff(f685,plain,
( spl2_45
<=> ! [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_45])]) ).
tff(f1100,plain,
( spl2_107
<=> ! [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_107])]) ).
tff(f1111,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) )
| ( aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X2),X4)),X5) = X8 ) )
| ~ spl2_45
| ~ spl2_107 ),
inference(superposition,[],[f686,f1101]) ).
tff(f1101,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_107 ),
inference(avatar_component_clause,[],[f1100]) ).
tff(f686,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_45 ),
inference(avatar_component_clause,[],[f685]) ).
tff(f3505,plain,
( spl2_188
| ~ spl2_105 ),
inference(avatar_split_clause,[],[f1095,f1082,f3503]) ).
tff(f3503,plain,
( spl2_188
<=> ! [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,aa(X0,fun(X0,X0),plus_plus(X0),X4),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_188])]) ).
tff(f1082,plain,
( spl2_105
<=> ! [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_105])]) ).
tff(f1095,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,aa(X0,fun(X0,X0),plus_plus(X0),X4),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X3),X2) )
| ~ semiring_div(X0) )
| ~ spl2_105 ),
inference(equality_resolution,[],[f1083]) ).
tff(f1083,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,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) )
| ~ semiring_div(X0) )
| ~ spl2_105 ),
inference(avatar_component_clause,[],[f1082]) ).
tff(f3501,plain,
( spl2_187
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f772,f764,f3499]) ).
tff(f3499,plain,
( spl2_187
<=> ! [X0: $tType,X1: $tType,X5: fun(list(list(X0)),X1),X4: list(X0),X6: X1,X3: X0,X2: fun(X0,fun(list(X0),fun(list(list(X0)),X1))),X7: list(list(X0))] : ( list_case(X1,list(X0),X6,aa(X0,fun(list(X0),fun(list(list(X0)),X1)),X2,X3),cons(list(X0),X4,X7)) = aa(list(list(X0)),X1,list_case(fun(list(list(X0)),X1),X0,X5,X2,cons(X0,X3,X4)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_187])]) ).
tff(f772,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(list(list(X0)),X1))),X3: X0,X6: X1,X7: list(list(X0)),X4: list(X0),X5: fun(list(list(X0)),X1)] : ( list_case(X1,list(X0),X6,aa(X0,fun(list(X0),fun(list(list(X0)),X1)),X2,X3),cons(list(X0),X4,X7)) = aa(list(list(X0)),X1,list_case(fun(list(list(X0)),X1),X0,X5,X2,cons(X0,X3,X4)),X7) )
| ~ spl2_57 ),
inference(superposition,[],[f765,f765]) ).
tff(f3471,plain,
( spl2_186
| ~ spl2_20
| ~ spl2_135 ),
inference(avatar_split_clause,[],[f1466,f1409,f552,f3469]) ).
tff(f3469,plain,
( spl2_186
<=> ! [X0: $tType,X2: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0))),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(list(int),X0))] : ( atom_case(X0,X1,X2,X3,a) = atom_case(X0,X4,X5,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_186])]) ).
tff(f1409,plain,
( spl2_135
<=> ! [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_135])]) ).
tff(f1466,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)),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X2,X3,a) = atom_case(X0,X4,X5,X3,a) )
| ~ spl2_20
| ~ spl2_135 ),
inference(superposition,[],[f1410,f554]) ).
tff(f1410,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_135 ),
inference(avatar_component_clause,[],[f1409]) ).
tff(f3421,plain,
( ~ spl2_16
| spl2_185
| ~ spl2_30
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f999,f992,f600,f3419,f532]) ).
tff(f532,plain,
( spl2_16
<=> semiring_div(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f3419,plain,
( spl2_185
<=> ! [X2: int,X0: int,X1: int] :
( ( div_mod(int,i,d) != div_mod(int,X0,d) )
| ( div_mod(int,aa(int,int,times_times(int,j),X1),d) = div_mod(int,aa(int,int,times_times(int,X0),X2),d) )
| ( div_mod(int,X1,d) != div_mod(int,X2,d) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_185])]) ).
tff(f992,plain,
( spl2_91
<=> ! [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_91])]) ).
tff(f999,plain,
( ! [X2: int,X0: int,X1: int] :
( ( div_mod(int,i,d) != div_mod(int,X0,d) )
| ( div_mod(int,X1,d) != div_mod(int,X2,d) )
| ( div_mod(int,aa(int,int,times_times(int,j),X1),d) = div_mod(int,aa(int,int,times_times(int,X0),X2),d) )
| ~ semiring_div(int) )
| ~ spl2_30
| ~ spl2_91 ),
inference(superposition,[],[f993,f602]) ).
tff(f993,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_91 ),
inference(avatar_component_clause,[],[f992]) ).
tff(f3417,plain,
( spl2_184
| ~ spl2_55
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f771,f764,f745,f3415]) ).
tff(f3415,plain,
( spl2_184
<=> ! [X0: $tType,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X7: list(list(int)),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X2: int,X1: fun(int,fun(list(int),fun(list(list(int)),X0)))] : ( list_case(X0,list(int),X6,aa(int,fun(list(int),fun(list(list(int)),X0)),X1,X2),cons(list(int),X3,X7)) = aa(list(list(int)),X0,atom_rec(fun(list(list(int)),X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_184])]) ).
tff(f745,plain,
( spl2_55
<=> ! [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_rec(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_55])]) ).
tff(f771,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(list(list(int)),X0))),X6: X0,X7: list(list(int)),X4: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X5: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0))))] : ( list_case(X0,list(int),X6,aa(int,fun(list(int),fun(list(list(int)),X0)),X1,X2),cons(list(int),X3,X7)) = aa(list(list(int)),X0,atom_rec(fun(list(list(int)),X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),X7) )
| ~ spl2_55
| ~ spl2_57 ),
inference(superposition,[],[f765,f746]) ).
tff(f746,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_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f745]) ).
tff(f3413,plain,
( spl2_183
| ~ spl2_56
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f770,f764,f749,f3411]) ).
tff(f3411,plain,
( spl2_183
<=> ! [X0: $tType,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X7: list(list(int)),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X2: int,X1: fun(int,fun(list(int),fun(list(list(int)),X0)))] : ( list_case(X0,list(int),X6,aa(int,fun(list(int),fun(list(list(int)),X0)),X1,X2),cons(list(int),X3,X7)) = aa(list(list(int)),X0,atom_case(fun(list(list(int)),X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_183])]) ).
tff(f749,plain,
( spl2_56
<=> ! [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_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
tff(f770,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(list(list(int)),X0))),X6: X0,X7: list(list(int)),X4: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0)))),X5: fun(int,fun(int,fun(list(int),fun(list(list(int)),X0))))] : ( list_case(X0,list(int),X6,aa(int,fun(list(int),fun(list(list(int)),X0)),X1,X2),cons(list(int),X3,X7)) = aa(list(list(int)),X0,atom_case(fun(list(list(int)),X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),X7) )
| ~ spl2_56
| ~ spl2_57 ),
inference(superposition,[],[f765,f750]) ).
tff(f750,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_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f749]) ).
tff(f3376,plain,
( spl2_182
| ~ spl2_10
| ~ spl2_93 ),
inference(avatar_split_clause,[],[f1014,f1011,f502,f3374]) ).
tff(f3374,plain,
( spl2_182
<=> ! [X2: list(int),X0: list(int),X1: list(int)] : ( iprod(int,aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),X0),X1),X2) = aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,X0,X2)),iprod(int,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_182])]) ).
tff(f502,plain,
( spl2_10
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f1011,plain,
( spl2_93
<=> ! [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_93])]) ).
tff(f1014,plain,
( ! [X2: list(int),X0: list(int),X1: list(int)] : ( iprod(int,aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),X0),X1),X2) = aa(int,int,aa(int,fun(int,int),plus_plus(int),iprod(int,X0,X2)),iprod(int,X1,X2)) )
| ~ spl2_10
| ~ spl2_93 ),
inference(resolution,[],[f1012,f504]) ).
tff(f504,plain,
( ring(int)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f502]) ).
tff(f1012,plain,
( ! [X0: $tType,X2: list(X0),X3: list(X0),X1: list(X0)] :
( ~ ring(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)) ) )
| ~ spl2_93 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f3261,plain,
( spl2_181
| ~ spl2_5
| ~ spl2_17
| ~ spl2_68
| ~ spl2_92 ),
inference(avatar_split_clause,[],[f1009,f996,f838,f537,f477,f3259]) ).
tff(f3259,plain,
( spl2_181
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),aa(int,int,times_times(int,X2),X3)) = aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X2),aa(int,int,times_times(int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_181])]) ).
tff(f477,plain,
( spl2_5
<=> ab_semigroup_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f838,plain,
( spl2_68
<=> ! [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_68])]) ).
tff(f996,plain,
( spl2_92
<=> ! [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_92])]) ).
tff(f1009,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),aa(int,int,times_times(int,X2),X3)) = aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X2),aa(int,int,times_times(int,X1),X3))) )
| ~ spl2_5
| ~ spl2_17
| ~ spl2_68
| ~ spl2_92 ),
inference(forward_demodulation,[],[f1008,f865]) ).
tff(f865,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_5
| ~ spl2_68 ),
inference(resolution,[],[f839,f479]) ).
tff(f479,plain,
( ab_semigroup_mult(int)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f477]) ).
tff(f839,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_68 ),
inference(avatar_component_clause,[],[f838]) ).
tff(f1008,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),aa(int,int,times_times(int,X2),X3)) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X2)),aa(int,int,times_times(int,X1),X3)) )
| ~ spl2_17
| ~ spl2_92 ),
inference(resolution,[],[f997,f539]) ).
tff(f997,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ~ comm_semiring_1(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)) ) )
| ~ spl2_92 ),
inference(avatar_component_clause,[],[f996]) ).
tff(f3132,plain,
( spl2_180
| ~ spl2_20
| ~ spl2_134 ),
inference(avatar_split_clause,[],[f1456,f1405,f552,f3130]) ).
tff(f3130,plain,
( spl2_180
<=> ! [X0: $tType,X2: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0))),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X1,X2,X3,a) = atom_rec(X0,X4,X5,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_180])]) ).
tff(f1405,plain,
( spl2_134
<=> ! [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_134])]) ).
tff(f1456,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)),X4: fun(int,fun(list(int),X0)),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X1,X2,X3,a) = atom_rec(X0,X4,X5,X3,a) )
| ~ spl2_20
| ~ spl2_134 ),
inference(superposition,[],[f1406,f554]) ).
tff(f1406,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_134 ),
inference(avatar_component_clause,[],[f1405]) ).
tff(f3052,plain,
( spl2_179
| ~ spl2_17
| ~ spl2_19
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f989,f983,f547,f537,f3050]) ).
tff(f3050,plain,
( spl2_179
<=> ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X1)),X1) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),hd_coeff(a))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_179])]) ).
tff(f547,plain,
( spl2_19
<=> ( one_one(int) = hd_coeff(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f983,plain,
( spl2_90
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
tff(f989,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X1)),X1) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),hd_coeff(a))),X1) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_90 ),
inference(forward_demodulation,[],[f988,f549]) ).
tff(f549,plain,
( ( one_one(int) = hd_coeff(a) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f547]) ).
tff(f988,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),one_one(int))),X1) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X0),X1)),X1) )
| ~ spl2_17
| ~ spl2_90 ),
inference(resolution,[],[f984,f539]) ).
tff(f984,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) ) )
| ~ spl2_90 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f3048,plain,
( spl2_178
| ~ spl2_17
| ~ spl2_19
| ~ spl2_89 ),
inference(avatar_split_clause,[],[f987,f979,f547,f537,f3046]) ).
tff(f3046,plain,
( spl2_178
<=> ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X0)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),hd_coeff(a))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_178])]) ).
tff(f979,plain,
( spl2_89
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
tff(f987,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X0)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),hd_coeff(a))),X0) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_89 ),
inference(forward_demodulation,[],[f986,f549]) ).
tff(f986,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X0)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),one_one(int))),X0) )
| ~ spl2_17
| ~ spl2_89 ),
inference(resolution,[],[f980,f539]) ).
tff(f980,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) ) )
| ~ spl2_89 ),
inference(avatar_component_clause,[],[f979]) ).
tff(f2838,plain,
( spl2_177
| ~ spl2_94
| ~ spl2_95 ),
inference(avatar_split_clause,[],[f1029,f1020,f1016,f2836]) ).
tff(f2836,plain,
( spl2_177
<=> ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X1)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_177])]) ).
tff(f1016,plain,
( spl2_94
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).
tff(f1020,plain,
( spl2_95
<=> ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).
tff(f1029,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X1)) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0)),X1) )
| ~ spl2_94
| ~ spl2_95 ),
inference(superposition,[],[f1021,f1017]) ).
tff(f1017,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) )
| ~ spl2_94 ),
inference(avatar_component_clause,[],[f1016]) ).
tff(f1021,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) )
| ~ spl2_95 ),
inference(avatar_component_clause,[],[f1020]) ).
tff(f2834,plain,
( spl2_176
| ~ spl2_16
| ~ spl2_88 ),
inference(avatar_split_clause,[],[f977,f974,f532,f2832]) ).
tff(f2832,plain,
( spl2_176
<=> ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_176])]) ).
tff(f974,plain,
( spl2_88
<=> ! [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_88])]) ).
tff(f977,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_88 ),
inference(resolution,[],[f975,f534]) ).
tff(f534,plain,
( semiring_div(int)
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f532]) ).
tff(f975,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) )
| ~ spl2_88 ),
inference(avatar_component_clause,[],[f974]) ).
tff(f2737,plain,
( spl2_175
| ~ spl2_58 ),
inference(avatar_split_clause,[],[f789,f779,f2735]) ).
tff(f2735,plain,
( spl2_175
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_175])]) ).
tff(f779,plain,
( spl2_58
<=> ! [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_58])]) ).
tff(f789,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),X1)),X2) )
| ~ spl2_58 ),
inference(forward_demodulation,[],[f787,f780]) ).
tff(f780,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_58 ),
inference(avatar_component_clause,[],[f779]) ).
tff(f787,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X3),aa(int,int,times_times(int,X0),div_mod(int,X1,X2))),X2) = div_mod(int,aa(int,int,times_times(int,X3),div_mod(int,aa(int,int,times_times(int,X0),X1),X2)),X2) )
| ~ spl2_58 ),
inference(superposition,[],[f780,f780]) ).
tff(f2727,plain,
( spl2_174
| ~ spl2_27
| ~ spl2_133 ),
inference(avatar_split_clause,[],[f1439,f1401,f582,f2725]) ).
tff(f2725,plain,
( spl2_174
<=> ! [X0: $tType,X3: X0,X2: fun(int,fun(list(int),X0)),X1: X0] : ( list_case(X0,int,X1,X2,ks1) = list_case(X0,int,X3,X2,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_174])]) ).
tff(f1401,plain,
( spl2_133
<=> ! [X1: $tType,X0: $tType,X5: X1,X6: X1,X4: list(X0),X3: X0,X2: fun(X0,fun(list(X0),X1))] : ( list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_133])]) ).
tff(f1439,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X3: X0,X1: X0] : ( list_case(X0,int,X1,X2,ks1) = list_case(X0,int,X3,X2,ks1) )
| ~ spl2_27
| ~ spl2_133 ),
inference(superposition,[],[f1402,f584]) ).
tff(f1402,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4)) )
| ~ spl2_133 ),
inference(avatar_component_clause,[],[f1401]) ).
tff(f2689,plain,
( spl2_173
| ~ spl2_42
| ~ spl2_107 ),
inference(avatar_split_clause,[],[f1109,f1100,f654,f2687]) ).
tff(f2687,plain,
( spl2_173
<=> ! [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) )
| ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),aa(int,int,times_times(int,X2),X3)) = X7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_173])]) ).
tff(f654,plain,
( spl2_42
<=> ! [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_42])]) ).
tff(f1109,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) )
| ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),aa(int,int,times_times(int,X2),X3)) = X7 ) )
| ~ spl2_42
| ~ spl2_107 ),
inference(superposition,[],[f655,f1101]) ).
tff(f655,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_42 ),
inference(avatar_component_clause,[],[f654]) ).
tff(f2685,plain,
( spl2_172
| ~ spl2_54
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f769,f764,f741,f2683]) ).
tff(f2683,plain,
( spl2_172
<=> ! [X0: $tType,X5: $tType,X6: X5,X4: list(X0),X7: fun(X0,fun(list(X0),X5)),X3: list(X0),X2: X0,X1: X0] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,X1),cons(X0,X2,splice(X0,X3,X4))) = list_case(X5,X0,X6,X7,splice(X0,cons(X0,X1,X3),cons(X0,X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_172])]) ).
tff(f769,plain,
( ! [X5: $tType,X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: X5,X7: fun(X0,fun(list(X0),X5)),X4: list(X0)] : ( aa(list(X0),X5,aa(X0,fun(list(X0),X5),X7,X1),cons(X0,X2,splice(X0,X3,X4))) = list_case(X5,X0,X6,X7,splice(X0,cons(X0,X1,X3),cons(X0,X2,X4))) )
| ~ spl2_54
| ~ spl2_57 ),
inference(superposition,[],[f765,f742]) ).
tff(f2537,plain,
( spl2_171
| ~ spl2_16
| ~ spl2_85 ),
inference(avatar_split_clause,[],[f953,f944,f532,f2535]) ).
tff(f944,plain,
( spl2_85
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
tff(f953,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X2)),X1),X2) )
| ~ spl2_16
| ~ spl2_85 ),
inference(resolution,[],[f945,f534]) ).
tff(f945,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) ) )
| ~ spl2_85 ),
inference(avatar_component_clause,[],[f944]) ).
tff(f2533,plain,
( spl2_170
| ~ spl2_16
| ~ spl2_84 ),
inference(avatar_split_clause,[],[f951,f940,f532,f2531]) ).
tff(f2531,plain,
( spl2_170
<=> ! [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_170])]) ).
tff(f940,plain,
( spl2_84
<=> ! [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_84])]) ).
tff(f951,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_84 ),
inference(resolution,[],[f941,f534]) ).
tff(f941,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_84 ),
inference(avatar_component_clause,[],[f940]) ).
tff(f2472,plain,
( spl2_169
| ~ spl2_17
| ~ spl2_19
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f938,f934,f547,f537,f2470]) ).
tff(f2470,plain,
( spl2_169
<=> ! [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_169])]) ).
tff(f934,plain,
( spl2_83
<=> ! [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_83])]) ).
tff(f938,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),hd_coeff(a)),hd_coeff(a))),X0) )
| ~ spl2_17
| ~ spl2_19
| ~ spl2_83 ),
inference(forward_demodulation,[],[f937,f549]) ).
tff(f937,plain,
( ! [X0: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X0) = aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),X0) )
| ~ spl2_17
| ~ spl2_83 ),
inference(resolution,[],[f935,f539]) ).
tff(f935,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_83 ),
inference(avatar_component_clause,[],[f934]) ).
tff(f2379,plain,
( spl2_168
| ~ spl2_91 ),
inference(avatar_split_clause,[],[f1005,f992,f2377]) ).
tff(f2377,plain,
( spl2_168
<=> ! [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_168])]) ).
tff(f1005,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_91 ),
inference(equality_resolution,[],[f993]) ).
tff(f2375,plain,
( spl2_167
| ~ spl2_10
| ~ spl2_82 ),
inference(avatar_split_clause,[],[f932,f929,f502,f2373]) ).
tff(f929,plain,
( spl2_82
<=> ! [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_82])]) ).
tff(f932,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_10
| ~ spl2_82 ),
inference(resolution,[],[f930,f504]) ).
tff(f930,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_82 ),
inference(avatar_component_clause,[],[f929]) ).
tff(f2360,plain,
( spl2_166
| ~ spl2_57
| ~ spl2_86 ),
inference(avatar_split_clause,[],[f963,f948,f764,f2358]) ).
tff(f2358,plain,
( spl2_166
<=> ! [X1: $tType,X0: $tType,X5: fun(X1,X1),X3: X0,X4: list(X0),X6: X1,X2: fun(X0,fun(list(X0),fun(X1,X1)))] : ( list_rec(X1,X0,X6,X2,cons(X0,X3,X4)) = aa(X1,X1,list_case(fun(X1,X1),X0,X5,X2,cons(X0,X3,X4)),list_rec(X1,X0,X6,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_166])]) ).
tff(f963,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X0,X6: X1,X4: list(X0),X5: fun(X1,X1)] : ( list_rec(X1,X0,X6,X2,cons(X0,X3,X4)) = aa(X1,X1,list_case(fun(X1,X1),X0,X5,X2,cons(X0,X3,X4)),list_rec(X1,X0,X6,X2,X4)) )
| ~ spl2_57
| ~ spl2_86 ),
inference(superposition,[],[f949,f765]) ).
tff(f2304,plain,
( spl2_165
| ~ spl2_55
| ~ spl2_86 ),
inference(avatar_split_clause,[],[f960,f948,f745,f2302]) ).
tff(f2302,plain,
( spl2_165
<=> ! [X0: $tType,X2: int,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X1: fun(int,fun(list(int),fun(X0,X0)))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_rec(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_165])]) ).
tff(f960,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(X0,X0))),X6: X0,X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X5: fun(int,fun(int,fun(list(int),fun(X0,X0))))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_rec(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) )
| ~ spl2_55
| ~ spl2_86 ),
inference(superposition,[],[f949,f746]) ).
tff(f2300,plain,
( spl2_164
| ~ spl2_20
| ~ spl2_155 ),
inference(avatar_split_clause,[],[f2140,f1757,f552,f2298]) ).
tff(f2298,plain,
( spl2_164
<=> ! [X2: int,X0: int,X1: list(int),X3: list(int)] : ( c_PresArith_Oatom_OLe(X0,X1) != asubst(X2,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_164])]) ).
tff(f1757,plain,
( spl2_155
<=> ! [X5: list(int),X4: int,X0: int,X3: int,X2: int,X1: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,nDvd(X2,X3,ks1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_155])]) ).
tff(f2140,plain,
( ! [X2: int,X3: list(int),X0: int,X1: list(int)] : ( c_PresArith_Oatom_OLe(X0,X1) != asubst(X2,X3,a) )
| ~ spl2_20
| ~ spl2_155 ),
inference(superposition,[],[f1758,f554]) ).
tff(f1758,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int),X4: int,X5: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,nDvd(X2,X3,ks1)) )
| ~ spl2_155 ),
inference(avatar_component_clause,[],[f1757]) ).
tff(f2296,plain,
( spl2_163
| ~ spl2_56
| ~ spl2_86 ),
inference(avatar_split_clause,[],[f959,f948,f749,f2294]) ).
tff(f2294,plain,
( spl2_163
<=> ! [X0: $tType,X2: int,X3: list(int),X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X6: X0,X5: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X1: fun(int,fun(list(int),fun(X0,X0)))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_case(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_163])]) ).
tff(f959,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),fun(X0,X0))),X6: X0,X4: fun(int,fun(int,fun(list(int),fun(X0,X0)))),X5: fun(int,fun(int,fun(list(int),fun(X0,X0))))] : ( list_rec(X0,int,X6,X1,cons(int,X2,X3)) = aa(X0,X0,atom_case(fun(X0,X0),X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)),list_rec(X0,int,X6,X1,X3)) )
| ~ spl2_56
| ~ spl2_86 ),
inference(superposition,[],[f949,f750]) ).
tff(f2292,plain,
( spl2_162
| ~ spl2_20
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f920,f897,f552,f2290]) ).
tff(f2290,plain,
( spl2_162
<=> ! [X0: $tType,X3: fun(int,fun(int,fun(list(int),X0))),X2: fun(int,fun(list(int),X0)),X1: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X1,d),l),ks1) = atom_case(X0,X2,X3,X1,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_162])]) ).
tff(f897,plain,
( spl2_80
<=> ! [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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).
tff(f920,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X3: fun(int,fun(int,fun(list(int),X0))),X1: fun(int,fun(int,fun(list(int),X0)))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X1,d),l),ks1) = atom_case(X0,X2,X3,X1,a) )
| ~ spl2_20
| ~ spl2_80 ),
inference(superposition,[],[f898,f554]) ).
tff(f898,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) )
| ~ spl2_80 ),
inference(avatar_component_clause,[],[f897]) ).
tff(f2288,plain,
( spl2_161
| ~ spl2_20
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f904,f893,f552,f2286]) ).
tff(f2286,plain,
( spl2_161
<=> ! [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_rec(X0,X1,X2,X3,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_161])]) ).
tff(f893,plain,
( spl2_79
<=> ! [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_rec(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_79])]) ).
tff(f904,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_rec(X0,X1,X2,X3,a) )
| ~ spl2_20
| ~ spl2_79 ),
inference(superposition,[],[f894,f554]) ).
tff(f894,plain,
( ! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X6,X5,X4,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_79 ),
inference(avatar_component_clause,[],[f893]) ).
tff(f2222,plain,
( spl2_160
| ~ spl2_57
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f919,f897,f764,f2220]) ).
tff(f2220,plain,
( spl2_160
<=> ! [X0: $tType,X5: X0,X6: fun(int,fun(list(int),X0)),X4: list(int),X7: fun(int,fun(int,fun(list(int),X0))),X3: int,X2: int,X1: fun(int,fun(int,fun(list(int),X0)))] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_case(X0,X6,X7,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_160])]) ).
tff(f919,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X7: fun(int,fun(int,fun(list(int),X0))),X4: list(int),X5: X0] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_case(X0,X6,X7,X1,nDvd(X2,X3,X4)) )
| ~ spl2_57
| ~ spl2_80 ),
inference(superposition,[],[f898,f765]) ).
tff(f2218,plain,
( spl2_159
| ~ spl2_57
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f908,f893,f764,f2216]) ).
tff(f2216,plain,
( spl2_159
<=> ! [X0: $tType,X5: X0,X6: fun(int,fun(list(int),X0)),X4: list(int),X7: fun(int,fun(int,fun(list(int),X0))),X3: int,X2: int,X1: fun(int,fun(int,fun(list(int),X0)))] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_rec(X0,X6,X7,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_159])]) ).
tff(f908,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0)),X7: fun(int,fun(int,fun(list(int),X0))),X4: list(int),X5: X0] : ( list_case(X0,int,X5,aa(int,fun(int,fun(list(int),X0)),X1,X2),cons(int,X3,X4)) = atom_rec(X0,X6,X7,X1,nDvd(X2,X3,X4)) )
| ~ spl2_57
| ~ spl2_79 ),
inference(superposition,[],[f894,f765]) ).
tff(f1771,plain,
( spl2_158
| ~ spl2_55
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f918,f897,f745,f1769]) ).
tff(f1769,plain,
( spl2_158
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_158])]) ).
tff(f918,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_55
| ~ spl2_80 ),
inference(superposition,[],[f898,f746]) ).
tff(f1767,plain,
( spl2_157
| ~ spl2_56
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f917,f897,f749,f1765]) ).
tff(f1765,plain,
( spl2_157
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_157])]) ).
tff(f917,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,aa(int,fun(int,fun(list(int),X0)),X1,X2),X5,X6,c_PresArith_Oatom_OLe(X3,X4)) = atom_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_56
| ~ spl2_80 ),
inference(superposition,[],[f898,f750]) ).
tff(f1763,plain,
( spl2_156
| ~ spl2_55
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f907,f893,f745,f1761]) ).
tff(f1761,plain,
( spl2_156
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,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_156])]) ).
tff(f907,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,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_55
| ~ spl2_79 ),
inference(superposition,[],[f894,f746]) ).
tff(f1759,plain,
( spl2_155
| ~ spl2_27
| ~ spl2_121 ),
inference(avatar_split_clause,[],[f1250,f1247,f582,f1757]) ).
tff(f1247,plain,
( spl2_121
<=> ! [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_121])]) ).
tff(f1250,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int),X4: int,X5: list(int)] : ( c_PresArith_Oatom_OLe(X4,X5) != asubst(X0,X1,nDvd(X2,X3,ks1)) )
| ~ spl2_27
| ~ spl2_121 ),
inference(superposition,[],[f1248,f584]) ).
tff(f1248,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_121 ),
inference(avatar_component_clause,[],[f1247]) ).
tff(f1755,plain,
( spl2_154
| ~ spl2_56
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f906,f893,f749,f1753]) ).
tff(f1753,plain,
( spl2_154
<=> ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,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_154])]) ).
tff(f906,plain,
( ! [X0: $tType,X2: int,X3: int,X1: fun(int,fun(int,fun(list(int),X0))),X8: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(list(int),X0)),X4: list(int),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X7,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_56
| ~ spl2_79 ),
inference(superposition,[],[f894,f750]) ).
tff(f1751,plain,
( spl2_153
| ~ spl2_5
| ~ spl2_17
| ~ spl2_68
| ~ spl2_74 ),
inference(avatar_split_clause,[],[f876,f862,f838,f537,f477,f1749]) ).
tff(f1749,plain,
( spl2_153
<=> ! [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_153])]) ).
tff(f862,plain,
( spl2_74
<=> ! [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_74])]) ).
tff(f876,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_5
| ~ spl2_17
| ~ spl2_68
| ~ spl2_74 ),
inference(forward_demodulation,[],[f875,f865]) ).
tff(f875,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X1)),X2) = aa(int,int,times_times(int,aa(int,int,times_times(int,X0),X2)),X1) )
| ~ spl2_17
| ~ spl2_74 ),
inference(resolution,[],[f863,f539]) ).
tff(f863,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_74 ),
inference(avatar_component_clause,[],[f862]) ).
tff(f1747,plain,
( spl2_152
| ~ spl2_17
| ~ spl2_72 ),
inference(avatar_split_clause,[],[f869,f854,f537,f1745]) ).
tff(f1745,plain,
( spl2_152
<=> ! [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_152])]) ).
tff(f854,plain,
( spl2_72
<=> ! [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_72])]) ).
tff(f869,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),aa(int,int,times_times(int,X1),X2)) = aa(int,int,times_times(int,X1),aa(int,int,times_times(int,X0),X2)) )
| ~ spl2_17
| ~ spl2_72 ),
inference(resolution,[],[f855,f539]) ).
tff(f855,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_72 ),
inference(avatar_component_clause,[],[f854]) ).
tff(f1743,plain,
( spl2_151
| ~ spl2_16
| ~ spl2_71 ),
inference(avatar_split_clause,[],[f868,f850,f532,f1741]) ).
tff(f1741,plain,
( spl2_151
<=> ! [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_151])]) ).
tff(f850,plain,
( spl2_71
<=> ! [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_71])]) ).
tff(f868,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,div_mod(int,X0,X1)),X2) = div_mod(int,aa(int,int,times_times(int,X0),X2),aa(int,int,times_times(int,X1),X2)) )
| ~ spl2_16
| ~ spl2_71 ),
inference(resolution,[],[f851,f534]) ).
tff(f851,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_71 ),
inference(avatar_component_clause,[],[f850]) ).
tff(f1739,plain,
( spl2_150
| ~ spl2_16
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f867,f846,f532,f1737]) ).
tff(f1737,plain,
( spl2_150
<=> ! [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_150])]) ).
tff(f846,plain,
( spl2_70
<=> ! [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_70])]) ).
tff(f867,plain,
( ! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X0),div_mod(int,X1,X2)) = div_mod(int,aa(int,int,times_times(int,X0),X1),aa(int,int,times_times(int,X0),X2)) )
| ~ spl2_16
| ~ spl2_70 ),
inference(resolution,[],[f847,f534]) ).
tff(f847,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_70 ),
inference(avatar_component_clause,[],[f846]) ).
tff(f1735,plain,
( spl2_149
| ~ spl2_16
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f866,f842,f532,f1733]) ).
tff(f1733,plain,
( spl2_149
<=> ! [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_149])]) ).
tff(f842,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,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).
tff(f866,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),div_mod(int,X1,X2)),X2) )
| ~ spl2_16
| ~ spl2_69 ),
inference(resolution,[],[f843,f534]) ).
tff(f843,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_69 ),
inference(avatar_component_clause,[],[f842]) ).
tff(f1731,plain,
( spl2_148
| ~ spl2_5
| ~ spl2_68 ),
inference(avatar_split_clause,[],[f865,f838,f477,f1729]) ).
tff(f1729,plain,
( spl2_148
<=> ! [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_148])]) ).
tff(f1670,plain,
( spl2_147
| ~ spl2_16
| ~ spl2_67 ),
inference(avatar_split_clause,[],[f836,f832,f532,f1668]) ).
tff(f1668,plain,
( spl2_147
<=> ! [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_147])]) ).
tff(f832,plain,
( spl2_67
<=> ! [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_67])]) ).
tff(f836,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X2),X1)),X1) )
| ~ spl2_16
| ~ spl2_67 ),
inference(resolution,[],[f833,f534]) ).
tff(f833,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_67 ),
inference(avatar_component_clause,[],[f832]) ).
tff(f1666,plain,
( spl2_146
| ~ spl2_16
| ~ spl2_66 ),
inference(avatar_split_clause,[],[f835,f828,f532,f1664]) ).
tff(f1664,plain,
( spl2_146
<=> ! [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_146])]) ).
tff(f828,plain,
( spl2_66
<=> ! [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_66])]) ).
tff(f835,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),aa(int,int,times_times(int,X1),X2)),X1) )
| ~ spl2_16
| ~ spl2_66 ),
inference(resolution,[],[f829,f534]) ).
tff(f829,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_66 ),
inference(avatar_component_clause,[],[f828]) ).
tff(f1662,plain,
( spl2_145
| ~ spl2_47
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f754,f741,f701,f1660]) ).
tff(f1660,plain,
( spl2_145
<=> ! [X0: $tType,X5: X0,X3: list(X0),X4: list(X0),X6: list(X0),X2: X0,X1: X0] :
( ( splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) != cons(X0,X5,X6) )
| ( cons(X0,X2,splice(X0,X3,X4)) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_145])]) ).
tff(f701,plain,
( spl2_47
<=> ! [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_47])]) ).
tff(f754,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: list(X0),X4: list(X0),X5: X0] :
( ( splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) != cons(X0,X5,X6) )
| ( cons(X0,X2,splice(X0,X3,X4)) = X6 ) )
| ~ spl2_47
| ~ spl2_54 ),
inference(superposition,[],[f702,f742]) ).
tff(f702,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X1 = X3 ) )
| ~ spl2_47 ),
inference(avatar_component_clause,[],[f701]) ).
tff(f1624,plain,
( spl2_144
| ~ spl2_17
| ~ spl2_65 ),
inference(avatar_split_clause,[],[f826,f823,f537,f1622]) ).
tff(f1622,plain,
( spl2_144
<=> ! [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_144])]) ).
tff(f823,plain,
( spl2_65
<=> ! [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_65])]) ).
tff(f826,plain,
( ! [X0: int,X1: int] : ( aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1) )
| ~ spl2_17
| ~ spl2_65 ),
inference(resolution,[],[f824,f539]) ).
tff(f824,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_65 ),
inference(avatar_component_clause,[],[f823]) ).
tff(f1576,plain,
( spl2_143
| ~ spl2_16
| ~ spl2_61 ),
inference(avatar_split_clause,[],[f814,f802,f532,f1574]) ).
tff(f1574,plain,
( spl2_143
<=> ! [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_143])]) ).
tff(f802,plain,
( spl2_61
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).
tff(f814,plain,
( ! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,times_times(int,X0),X1),X2) = div_mod(int,aa(int,int,times_times(int,div_mod(int,X0,X2)),X1),X2) )
| ~ spl2_16
| ~ spl2_61 ),
inference(resolution,[],[f803,f534]) ).
tff(f803,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) ) )
| ~ spl2_61 ),
inference(avatar_component_clause,[],[f802]) ).
tff(f1541,plain,
( spl2_142
| ~ spl2_30
| ~ spl2_58 ),
inference(avatar_split_clause,[],[f788,f779,f600,f1539]) ).
tff(f1539,plain,
( spl2_142
<=> ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),j),d) = div_mod(int,aa(int,int,times_times(int,X0),i),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_142])]) ).
tff(f788,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),j),d) = div_mod(int,aa(int,int,times_times(int,X0),i),d) )
| ~ spl2_30
| ~ spl2_58 ),
inference(forward_demodulation,[],[f786,f780]) ).
tff(f786,plain,
( ! [X0: int] : ( div_mod(int,aa(int,int,times_times(int,X0),j),d) = div_mod(int,aa(int,int,times_times(int,X0),div_mod(int,i,d)),d) )
| ~ spl2_30
| ~ spl2_58 ),
inference(superposition,[],[f780,f602]) ).
tff(f1537,plain,
( spl2_141
| ~ spl2_20
| ~ spl2_129 ),
inference(avatar_split_clause,[],[f1431,f1384,f552,f1535]) ).
tff(f1535,plain,
( spl2_141
<=> ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_141])]) ).
tff(f1384,plain,
( spl2_129
<=> ! [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_129])]) ).
tff(f1431,plain,
( ! [X0: int,X1: list(int)] : ( d = divisor(asubst(X0,X1,a)) )
| ~ spl2_20
| ~ spl2_129 ),
inference(superposition,[],[f1385,f554]) ).
tff(f1385,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,nDvd(X2,X3,ks1))) = X2 )
| ~ spl2_129 ),
inference(avatar_component_clause,[],[f1384]) ).
tff(f1533,plain,
( spl2_140
| ~ spl2_28
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f768,f764,f587,f1531]) ).
tff(f1531,plain,
( spl2_140
<=> ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( list_case(X0,int,X1,X2,ks1) = aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_140])]) ).
tff(f587,plain,
( spl2_28
<=> ( ks1 = cons(int,hd_coeff(a),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
tff(f768,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( list_case(X0,int,X1,X2,ks1) = aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),sK0) )
| ~ spl2_28
| ~ spl2_57 ),
inference(superposition,[],[f765,f589]) ).
tff(f589,plain,
( ( ks1 = cons(int,hd_coeff(a),sK0) )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f1528,plain,
( spl2_139
| ~ spl2_27
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f767,f764,f582,f1526]) ).
tff(f1526,plain,
( spl2_139
<=> ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),ks) = list_case(X0,int,X1,X2,ks1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_139])]) ).
tff(f767,plain,
( ! [X0: $tType,X2: fun(int,fun(list(int),X0)),X1: X0] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X2,hd_coeff(a)),ks) = list_case(X0,int,X1,X2,ks1) )
| ~ spl2_27
| ~ spl2_57 ),
inference(superposition,[],[f765,f584]) ).
tff(f1496,plain,
( spl2_138
| ~ spl2_16
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f753,f737,f532,f1494]) ).
tff(f1494,plain,
( spl2_138
<=> ! [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_138])]) ).
tff(f737,plain,
( spl2_53
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
tff(f753,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X1) )
| ~ spl2_16
| ~ spl2_53 ),
inference(resolution,[],[f738,f534]) ).
tff(f738,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X2,X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X1) ) )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f1492,plain,
( spl2_137
| ~ spl2_16
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f752,f733,f532,f1490]) ).
tff(f1490,plain,
( spl2_137
<=> ! [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_137])]) ).
tff(f733,plain,
( spl2_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) )
| ~ semiring_div(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
tff(f752,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0),X1) )
| ~ spl2_16
| ~ spl2_52 ),
inference(resolution,[],[f734,f534]) ).
tff(f734,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,X1,X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1),X2) ) )
| ~ spl2_52 ),
inference(avatar_component_clause,[],[f733]) ).
tff(f1415,plain,
( spl2_136
| ~ spl2_79
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f916,f897,f893,f1413]) ).
tff(f916,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_case(X0,X7,X8,X1,nDvd(X2,X3,X4)) )
| ~ spl2_79
| ~ spl2_80 ),
inference(superposition,[],[f898,f894]) ).
tff(f1411,plain,
( spl2_135
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f915,f897,f1409]) ).
tff(f915,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_80 ),
inference(superposition,[],[f898,f898]) ).
tff(f1407,plain,
( spl2_134
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f905,f893,f1405]) ).
tff(f905,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_79 ),
inference(superposition,[],[f894,f894]) ).
tff(f1403,plain,
( spl2_133
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f775,f764,f1401]) ).
tff(f775,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X0,X6: X1,X4: list(X0),X5: X1] : ( list_case(X1,X0,X5,X2,cons(X0,X3,X4)) = list_case(X1,X0,X6,X2,cons(X0,X3,X4)) )
| ~ spl2_57 ),
inference(superposition,[],[f765,f765]) ).
tff(f1399,plain,
( spl2_132
| ~ spl2_22
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f758,f741,f561,f1397]) ).
tff(f1397,plain,
( spl2_132
<=> ! [X0: $tType,X4: list(X0),X3: list(X0),X2: X0,X1: X0] : ( cons(X0,X2,splice(X0,X3,X4)) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_132])]) ).
tff(f561,plain,
( spl2_22
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
tff(f758,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X4: list(X0)] : ( cons(X0,X2,splice(X0,X3,X4)) != splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) )
| ~ spl2_22
| ~ spl2_54 ),
inference(superposition,[],[f562,f742]) ).
tff(f562,plain,
( ! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f561]) ).
tff(f1395,plain,
( spl2_131
| ~ spl2_44
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f756,f741,f681,f1393]) ).
tff(f1393,plain,
( spl2_131
<=> ! [X0: $tType,X5: X0,X3: list(X0),X4: list(X0),X6: list(X0),X2: X0,X1: X0] :
( ( splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) != cons(X0,X5,X6) )
| ( X1 = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_131])]) ).
tff(f681,plain,
( spl2_44
<=> ! [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_44])]) ).
tff(f756,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: X0,X6: list(X0),X4: list(X0),X5: X0] :
( ( splice(X0,cons(X0,X1,X3),cons(X0,X2,X4)) != cons(X0,X5,X6) )
| ( X1 = X5 ) )
| ~ spl2_44
| ~ spl2_54 ),
inference(superposition,[],[f682,f742]) ).
tff(f682,plain,
( ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( cons(X0,X4,X3) != cons(X0,X2,X1) )
| ( X2 = X4 ) )
| ~ spl2_44 ),
inference(avatar_component_clause,[],[f681]) ).
tff(f1391,plain,
( ~ spl2_18
| spl2_130
| ~ spl2_15
| ~ spl2_51 ),
inference(avatar_split_clause,[],[f731,f728,f527,f1388,f542]) ).
tff(f542,plain,
( spl2_18
<=> cl_Groups_Oplus(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f1388,plain,
( spl2_130
<=> ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_130])]) ).
tff(f527,plain,
( spl2_15
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f728,plain,
( spl2_51
<=> ! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
tff(f731,plain,
( ( plus_plus(list(int)) = zipwith0(int,int,int,plus_plus(int)) )
| ~ cl_Groups_Oplus(int)
| ~ spl2_15
| ~ spl2_51 ),
inference(resolution,[],[f729,f529]) ).
tff(f529,plain,
( zero(int)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f527]) ).
tff(f729,plain,
( ! [X0: $tType] :
( ~ zero(X0)
| ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ cl_Groups_Oplus(X0) )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f1386,plain,
( spl2_129
| ~ spl2_27
| ~ spl2_120 ),
inference(avatar_split_clause,[],[f1241,f1238,f582,f1384]) ).
tff(f1238,plain,
( spl2_120
<=> ! [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_120])]) ).
tff(f1241,plain,
( ! [X2: int,X3: int,X0: int,X1: list(int)] : ( divisor(asubst(X0,X1,nDvd(X2,X3,ks1))) = X2 )
| ~ spl2_27
| ~ spl2_120 ),
inference(superposition,[],[f1239,f584]) ).
tff(f1239,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_120 ),
inference(avatar_component_clause,[],[f1238]) ).
tff(f1344,plain,
( spl2_128
| ~ spl2_41
| ~ spl2_107 ),
inference(avatar_split_clause,[],[f1107,f1100,f650,f1342]) ).
tff(f1342,plain,
( spl2_128
<=> ! [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_128])]) ).
tff(f650,plain,
( spl2_41
<=> ! [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_41])]) ).
tff(f1107,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_41
| ~ spl2_107 ),
inference(superposition,[],[f651,f1101]) ).
tff(f651,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_41 ),
inference(avatar_component_clause,[],[f650]) ).
tff(f1340,plain,
( spl2_127
| ~ spl2_55
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f774,f764,f745,f1338]) ).
tff(f1338,plain,
( spl2_127
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X6: X0,X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_127])]) ).
tff(f774,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: X0,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) )
| ~ spl2_55
| ~ spl2_57 ),
inference(superposition,[],[f765,f746]) ).
tff(f1336,plain,
( spl2_126
| ~ spl2_56
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f773,f764,f749,f1334]) ).
tff(f1334,plain,
( spl2_126
<=> ! [X0: $tType,X5: fun(int,fun(int,fun(list(int),X0))),X3: list(int),X4: fun(int,fun(int,fun(list(int),X0))),X6: X0,X2: int,X1: fun(int,fun(list(int),X0))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_126])]) ).
tff(f773,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: X0,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = list_case(X0,int,X6,X1,cons(int,X2,X3)) )
| ~ spl2_56
| ~ spl2_57 ),
inference(superposition,[],[f765,f750]) ).
tff(f1302,plain,
( spl2_125
| ~ spl2_55
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f761,f749,f745,f1300]) ).
tff(f1300,plain,
( spl2_125
<=> ! [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_case(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_125])]) ).
tff(f761,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_case(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) )
| ~ spl2_55
| ~ spl2_56 ),
inference(superposition,[],[f750,f746]) ).
tff(f1292,plain,
( spl2_124
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f760,f749,f1290]) ).
tff(f1290,plain,
( spl2_124
<=> ! [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_124])]) ).
tff(f760,plain,
( ! [X0: $tType,X2: int,X3: list(int),X1: fun(int,fun(list(int),X0)),X6: fun(int,fun(int,fun(list(int),X0))),X7: fun(int,fun(int,fun(list(int),X0))),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_case(X0,X1,X4,X5,c_PresArith_Oatom_OLe(X2,X3)) = atom_case(X0,X1,X6,X7,c_PresArith_Oatom_OLe(X2,X3)) )
| ~ spl2_56 ),
inference(superposition,[],[f750,f750]) ).
tff(f1288,plain,
( spl2_123
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f759,f745,f1286]) ).
tff(f1286,plain,
( spl2_123
<=> ! [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_123])]) ).
tff(f759,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_55 ),
inference(superposition,[],[f746,f746]) ).
tff(f1256,plain,
( spl2_122
| ~ spl2_17
| ~ spl2_50 ),
inference(avatar_split_clause,[],[f726,f723,f537,f1254]) ).
tff(f1254,plain,
( spl2_122
<=> ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X1),X0) = aa(int,int,times_times(int,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_122])]) ).
tff(f723,plain,
( spl2_50
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
tff(f726,plain,
( ! [X0: int,X1: int] : ( aa(int,int,times_times(int,X1),X0) = aa(int,int,times_times(int,X0),X1) )
| ~ spl2_17
| ~ spl2_50 ),
inference(resolution,[],[f724,f539]) ).
tff(f724,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( aa(X0,X0,times_times(X0,X2),X1) = aa(X0,X0,times_times(X0,X1),X2) ) )
| ~ spl2_50 ),
inference(avatar_component_clause,[],[f723]) ).
tff(f1249,plain,
( spl2_121
| ~ spl2_26
| ~ spl2_107 ),
inference(avatar_split_clause,[],[f1106,f1100,f578,f1247]) ).
tff(f578,plain,
( spl2_26
<=> ! [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_26])]) ).
tff(f1106,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_26
| ~ spl2_107 ),
inference(superposition,[],[f579,f1101]) ).
tff(f579,plain,
( ! [X2: list(int),X3: int,X0: list(int),X1: int,X4: int] : ( c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f578]) ).
tff(f1240,plain,
( spl2_120
| ~ spl2_23
| ~ spl2_107 ),
inference(avatar_split_clause,[],[f1105,f1100,f565,f1238]) ).
tff(f565,plain,
( spl2_23
<=> ! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
tff(f1105,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_23
| ~ spl2_107 ),
inference(superposition,[],[f566,f1101]) ).
tff(f566,plain,
( ! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f565]) ).
tff(f1224,plain,
( spl2_119
| ~ spl2_16
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f704,f697,f532,f1222]) ).
tff(f1222,plain,
( spl2_119
<=> ! [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_119])]) ).
tff(f697,plain,
( spl2_46
<=> ! [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_46])]) ).
tff(f704,plain,
( ! [X0: int,X1: int] : ( div_mod(int,X0,X1) = div_mod(int,div_mod(int,X0,X1),X1) )
| ~ spl2_16
| ~ spl2_46 ),
inference(resolution,[],[f698,f534]) ).
tff(f698,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_46 ),
inference(avatar_component_clause,[],[f697]) ).
tff(f1220,plain,
( spl2_118
| ~ spl2_28
| ~ spl2_116 ),
inference(avatar_split_clause,[],[f1210,f1197,f587,f1217]) ).
tff(f1217,plain,
( spl2_118
<=> ( ks = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_118])]) ).
tff(f1197,plain,
( spl2_116
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_116])]) ).
tff(f1210,plain,
( ( ks = sK0 )
| ~ spl2_28
| ~ spl2_116 ),
inference(trivial_inequality_removal,[],[f1208]) ).
tff(f1208,plain,
( ( ks1 != ks1 )
| ( ks = sK0 )
| ~ spl2_28
| ~ spl2_116 ),
inference(superposition,[],[f1198,f589]) ).
tff(f1198,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_116 ),
inference(avatar_component_clause,[],[f1197]) ).
tff(f1203,plain,
( spl2_117
| ~ spl2_28
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f706,f701,f587,f1201]) ).
tff(f1201,plain,
( spl2_117
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_117])]) ).
tff(f706,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( sK0 = X1 ) )
| ~ spl2_28
| ~ spl2_47 ),
inference(superposition,[],[f702,f589]) ).
tff(f1199,plain,
( spl2_116
| ~ spl2_27
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f705,f701,f582,f1197]) ).
tff(f705,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( ks = X1 ) )
| ~ spl2_27
| ~ spl2_47 ),
inference(superposition,[],[f702,f584]) ).
tff(f1195,plain,
( spl2_115
| ~ spl2_27
| ~ spl2_44 ),
inference(avatar_split_clause,[],[f688,f681,f582,f1193]) ).
tff(f1193,plain,
( spl2_115
<=> ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_115])]) ).
tff(f688,plain,
( ! [X0: int,X1: list(int)] :
( ( ks1 != cons(int,X0,X1) )
| ( hd_coeff(a) = X0 ) )
| ~ spl2_27
| ~ spl2_44 ),
inference(superposition,[],[f682,f584]) ).
tff(f1169,plain,
spl2_114,
inference(avatar_split_clause,[],[f338,f1167]) ).
tff(f1167,plain,
( spl2_114
<=> ! [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_114])]) ).
tff(f338,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,[],[f220]) ).
tff(f220,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,[],[f130]) ).
tff(f130,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2)),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X2),X1)) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X9: list(X0),X10: list(X0),X11: list(X0)] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10)),X9) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_list__add__assoc) ).
tff(f1148,plain,
spl2_113,
inference(avatar_split_clause,[],[f398,f1146]) ).
tff(f1146,plain,
( spl2_113
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,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_113])]) ).
tff(f398,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,[],[f276]) ).
tff(f276,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,[],[f184]) ).
tff(f184,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,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
tff(f1143,plain,
spl2_112,
inference(avatar_split_clause,[],[f340,f1141]) ).
tff(f1141,plain,
( spl2_112
<=> ! [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_112])]) ).
tff(f340,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,[],[f222]) ).
tff(f222,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,[],[f132]) ).
tff(f132,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,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( semiring(X0)
=> ! [X12: X0,X4: X0,X44: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X44)),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X44)),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)),X44)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_combine__common__factor) ).
tff(f1138,plain,
spl2_111,
inference(avatar_split_clause,[],[f411,f1136]) ).
tff(f1136,plain,
( spl2_111
<=> ! [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_111])]) ).
tff(f411,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,[],[f284]) ).
tff(f284,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,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: list(X2),X4: X2,X5: list(X0),X6: X0,X7: fun(X0,fun(X2,X1))] : ( aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),cons(X0,X6,X5)),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),aa(list(X2),list(X1),aa(list(X0),fun(list(X2),list(X1)),zipwith0(X0,X2,X1,X7),X5),X3)) )
| ~ zero(X0)
| ~ zero(X2) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,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,[],[f39]) ).
tff(f39,axiom,
! [X1: $tType,X0: $tType,X2: $tType] :
( ( zero(X1)
& zero(X2) )
=> ! [X27: list(X2),X28: X2,X29: list(X1),X30: X1,X31: fun(X1,fun(X2,X0))] : ( aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X31),cons(X1,X30,X29)),cons(X2,X28,X27)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X31,X30),X28),aa(list(X2),list(X0),aa(list(X1),fun(list(X2),list(X0)),zipwith0(X1,X2,X0,X31),X29),X27)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I2_J) ).
tff(f1133,plain,
spl2_110,
inference(avatar_split_clause,[],[f401,f1131]) ).
tff(f1131,plain,
( spl2_110
<=> ! [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_110])]) ).
tff(f401,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,[],[f282]) ).
tff(f282,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,[],[f281]) ).
tff(f281,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,[],[f186]) ).
tff(f186,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,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ! [X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),cons(X0,X25,X11)),cons(X0,X24,X10)) = cons(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X25),X24),aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_list__add__Cons) ).
tff(f1124,plain,
spl2_109,
inference(avatar_split_clause,[],[f347,f1122]) ).
tff(f1122,plain,
( spl2_109
<=> ! [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_109])]) ).
tff(f347,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,[],[f290]) ).
tff(f290,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,[],[f289]) ).
tff(f289,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
| ( ( X1 != X3 )
& ( X2 != X4 ) ) )
& ( ( X1 = X3 )
| ( X2 = X4 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) ) ) )
| ~ semiri456707255roduct(X0) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X3)),aa(X0,X0,times_times(X0,X2),X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X1)),aa(X0,X0,times_times(X0,X2),X3)) )
<=> ( ( X1 = X3 )
| ( X2 = X4 ) ) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,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,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X39: X0,X30: X0,X28: X0,X40: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X40),X28)),aa(X0,X0,times_times(X0,X30),X39)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X40),X39)),aa(X0,X0,times_times(X0,X30),X28)) )
<=> ( ( X28 = X39 )
| ( X30 = X40 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_crossproduct__eq) ).
tff(f1120,plain,
( spl2_108
| ~ spl2_20
| ~ spl2_45 ),
inference(avatar_split_clause,[],[f693,f685,f552,f1118]) ).
tff(f1118,plain,
( spl2_108
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( ks1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_108])]) ).
tff(f693,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( ks1 = X2 ) )
| ~ spl2_20
| ~ spl2_45 ),
inference(superposition,[],[f686,f554]) ).
tff(f1102,plain,
spl2_107,
inference(avatar_split_clause,[],[f428,f1100]) ).
tff(f428,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,[],[f208]) ).
tff(f208,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,[],[f98]) ).
tff(f98,axiom,
! [X58: list(int),X59: int,X60: int,X38: int,X61: list(int),X62: int] : ( asubst(X62,X61,nDvd(X38,X60,cons(int,X59,X58))) = nDvd(X38,aa(int,int,aa(int,fun(int,int),plus_plus(int),X60),aa(int,int,times_times(int,X59),X62)),aa(list(int),list(int),aa(list(int),fun(list(int),list(int)),plus_plus(list(int)),map(int,int,times_times(int,X59),X61)),X58)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_asubst_Osimps_I3_J) ).
tff(f1088,plain,
spl2_106,
inference(avatar_split_clause,[],[f438,f1086]) ).
tff(f1086,plain,
( spl2_106
<=> ! [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_106])]) ).
tff(f438,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,[],[f348]) ).
tff(f348,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,[],[f290]) ).
tff(f1084,plain,
spl2_105,
inference(avatar_split_clause,[],[f376,f1082]) ).
tff(f376,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,[],[f254]) ).
tff(f254,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,[],[f253]) ).
tff(f253,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,[],[f162]) ).
tff(f162,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,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X13: X0,X4: X0,X14: X0,X12: X0,X5: X0] :
( ( div_mod(X0,X5,X12) = div_mod(X0,X14,X12) )
=> ( ( div_mod(X0,X4,X12) = div_mod(X0,X13,X12) )
=> ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X14),X13),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_mod__add__cong) ).
tff(f1075,plain,
( spl2_104
| ~ spl2_13
| ~ spl2_19
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f662,f629,f547,f517,f1073]) ).
tff(f517,plain,
( spl2_13
<=> comm_monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f629,plain,
( spl2_36
<=> ! [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_36])]) ).
tff(f662,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,hd_coeff(a)),X0) = X0 )
| ~ spl2_13
| ~ spl2_19
| ~ spl2_36 ),
inference(forward_demodulation,[],[f661,f549]) ).
tff(f661,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,one_one(int)),X0) = X0 )
| ~ spl2_13
| ~ spl2_36 ),
inference(resolution,[],[f630,f519]) ).
tff(f519,plain,
( comm_monoid_mult(int)
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f517]) ).
tff(f630,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) )
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f629]) ).
tff(f1071,plain,
spl2_103,
inference(avatar_split_clause,[],[f394,f1069]) ).
tff(f394,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,[],[f272]) ).
tff(f272,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,[],[f180]) ).
tff(f180,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),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,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
tff(f1067,plain,
spl2_102,
inference(avatar_split_clause,[],[f392,f1065]) ).
tff(f1065,plain,
( spl2_102
<=> ! [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_102])]) ).
tff(f392,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,[],[f270]) ).
tff(f270,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,[],[f178]) ).
tff(f178,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,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12)),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f1063,plain,
spl2_101,
inference(avatar_split_clause,[],[f391,f1061]) ).
tff(f391,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,[],[f269]) ).
tff(f269,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,[],[f177]) ).
tff(f177,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,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X15: X0,X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X15)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f1059,plain,
spl2_100,
inference(avatar_split_clause,[],[f337,f1057]) ).
tff(f337,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,[],[f219]) ).
tff(f219,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,[],[f129]) ).
tff(f129,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2)),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),X1)) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1052,plain,
spl2_99,
inference(avatar_split_clause,[],[f389,f1050]) ).
tff(f1050,plain,
( spl2_99
<=> ! [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_99])]) ).
tff(f389,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,[],[f267]) ).
tff(f267,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,[],[f175]) ).
tff(f175,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,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X12)),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
tff(f1048,plain,
spl2_98,
inference(avatar_split_clause,[],[f388,f1046]) ).
tff(f1046,plain,
( spl2_98
<=> ! [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_98])]) ).
tff(f388,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,[],[f266]) ).
tff(f266,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,[],[f174]) ).
tff(f174,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,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X37: X0,X24: X0,X25: X0] : ( aa(X0,X0,times_times(X0,X25),aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X24),X37)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X25),X24)),aa(X0,X0,times_times(X0,X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
tff(f1044,plain,
spl2_97,
inference(avatar_split_clause,[],[f336,f1042]) ).
tff(f1042,plain,
( spl2_97
<=> ! [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_97])]) ).
tff(f336,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,[],[f218]) ).
tff(f218,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,[],[f128]) ).
tff(f128,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,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( comm_semiring(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4)),X12) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X12)),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__class_Odistrib) ).
tff(f1040,plain,
( spl2_96
| ~ spl2_11
| ~ spl2_19
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f658,f621,f547,f507,f1038]) ).
tff(f1038,plain,
( spl2_96
<=> ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
tff(f507,plain,
( spl2_11
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f621,plain,
( spl2_34
<=> ! [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_34])]) ).
tff(f658,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),hd_coeff(a)) = X0 )
| ~ spl2_11
| ~ spl2_19
| ~ spl2_34 ),
inference(forward_demodulation,[],[f657,f549]) ).
tff(f657,plain,
( ! [X0: int] : ( aa(int,int,times_times(int,X0),one_one(int)) = X0 )
| ~ spl2_11
| ~ spl2_34 ),
inference(resolution,[],[f622,f509]) ).
tff(f509,plain,
( monoid_mult(int)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f507]) ).
tff(f622,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) )
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f1022,plain,
spl2_95,
inference(avatar_split_clause,[],[f410,f1020]) ).
tff(f410,plain,
! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int,X2: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X2),X1)),X0) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X0)),aa(int,int,times_times(int,X1),X0)) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X48: int,X49: int,X50: int] : ( aa(int,int,times_times(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X50),X49)),X48) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X50),X48)),aa(int,int,times_times(int,X49),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_int__distrib_I1_J) ).
tff(f1018,plain,
spl2_94,
inference(avatar_split_clause,[],[f409,f1016]) ).
tff(f409,plain,
! [X2: int,X0: int,X1: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: int,X1: int,X2: int] : ( aa(int,int,times_times(int,X2),aa(int,int,aa(int,fun(int,int),plus_plus(int),X1),X0)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X2),X1)),aa(int,int,times_times(int,X2),X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X49: int,X50: int,X48: int] : ( aa(int,int,times_times(int,X48),aa(int,int,aa(int,fun(int,int),plus_plus(int),X50),X49)) = aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,times_times(int,X48),X50)),aa(int,int,times_times(int,X48),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_int__distrib_I2_J) ).
tff(f1013,plain,
spl2_93,
inference(avatar_split_clause,[],[f345,f1011]) ).
tff(f345,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,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0),X3: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X3),X2),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X3,X1)),iprod(X0,X2,X1)) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X9: list(X0),X10: list(X0),X11: list(X0)] : ( iprod(X0,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),plus_plus(list(X0)),X11),X10),X9) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),iprod(X0,X11,X9)),iprod(X0,X10,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_iprod__left__add__distrib) ).
tff(f998,plain,
spl2_92,
inference(avatar_split_clause,[],[f397,f996]) ).
tff(f397,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,[],[f275]) ).
tff(f275,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,[],[f183]) ).
tff(f183,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,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X35: X0,X36: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X35)),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),aa(X0,X0,times_times(X0,X35),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
tff(f994,plain,
spl2_91,
inference(avatar_split_clause,[],[f375,f992]) ).
tff(f375,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,[],[f252]) ).
tff(f252,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,[],[f251]) ).
tff(f251,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,[],[f161]) ).
tff(f161,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/sandbox/benchmark/theBenchmark.p',fact_65_mod__mult__cong) ).
tff(f985,plain,
spl2_90,
inference(avatar_split_clause,[],[f383,f983]) ).
tff(f383,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),one_one(X0))),X1) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X2),X1)),X1) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X32: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X32) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X5),X32)),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
tff(f981,plain,
spl2_89,
inference(avatar_split_clause,[],[f382,f979]) ).
tff(f382,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X2),aa(X0,X0,times_times(X0,X1),X2)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))),X2) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0,X32: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),aa(X0,X0,times_times(X0,X5),X32)) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),one_one(X0))),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
tff(f976,plain,
spl2_88,
inference(avatar_split_clause,[],[f374,f974]) ).
tff(f374,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,[],[f250]) ).
tff(f250,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,[],[f160]) ).
tff(f160,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,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X5,X12)),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mod__add__eq) ).
tff(f970,plain,
spl2_87,
inference(avatar_split_clause,[],[f452,f967]) ).
tff(f967,plain,
( spl2_87
<=> ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
tff(f452,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d),
inference(forward_demodulation,[],[f451,f328]) ).
tff(f328,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_A_061_Ii_Amod_Ad_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_Amod_Ad_J_Amod_Ad_096) ).
tff(f451,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(forward_demodulation,[],[f329,f326]) ).
tff(f326,plain,
div_mod(int,j,d) = div_mod(int,i,d),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
div_mod(int,j,d) = div_mod(int,i,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096i_Amod_Ad_A_061_Aj_Amod_Ad_096) ).
tff(f329,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,j,d)),div_mod(int,iprod(int,ks,e),d)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,j,d)),div_mod(int,iprod(int,ks,e),d)),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e)),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096_Ij_Amod_Ad_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_Amod_Ad_J_Amod_Ad_A_061_Ij_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_096) ).
tff(f950,plain,
spl2_86,
inference(avatar_split_clause,[],[f427,f948]) ).
tff(f427,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),fun(X0,X0))),X5: X0] : ( list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2)) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType,X1: $tType,X19: list(X1),X8: X1,X46: fun(X1,fun(list(X1),fun(X0,X0))),X47: X0] : ( list_rec(X0,X1,X47,X46,cons(X1,X8,X19)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X46,X8),X19),list_rec(X0,X1,X47,X46,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list_Orecs_I2_J) ).
tff(f946,plain,
spl2_85,
inference(avatar_split_clause,[],[f372,f944]) ).
tff(f372,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X5,X12)),X4),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zmod__simps_I1_J) ).
tff(f942,plain,
spl2_84,
inference(avatar_split_clause,[],[f370,f940]) ).
tff(f370,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,[],[f246]) ).
tff(f246,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,[],[f156]) ).
tff(f156,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,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X12) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),div_mod(X0,X4,X12)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_mod__add__right__eq) ).
tff(f936,plain,
spl2_83,
inference(avatar_split_clause,[],[f379,f934]) ).
tff(f379,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,[],[f257]) ).
tff(f257,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,[],[f165]) ).
tff(f165,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,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X32: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X32),X32) = aa(X0,X0,times_times(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),one_one(X0)),one_one(X0))),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
tff(f931,plain,
spl2_82,
inference(avatar_split_clause,[],[f346,f929]) ).
tff(f346,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,[],[f228]) ).
tff(f228,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,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( iprod(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X4),X2)),iprod(X0,X3,X1)) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( iprod(X0,cons(X0,X25,X11),cons(X0,X24,X10)) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),aa(X0,X0,times_times(X0,X25),X24)),iprod(X0,X11,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iprod__Cons) ).
tff(f903,plain,
( spl2_81
| ~ spl2_20
| ~ spl2_42 ),
inference(avatar_split_clause,[],[f677,f654,f552,f901]) ).
tff(f901,plain,
( spl2_81
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( l = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
tff(f677,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( l = X1 ) )
| ~ spl2_20
| ~ spl2_42 ),
inference(superposition,[],[f655,f554]) ).
tff(f899,plain,
spl2_80,
inference(avatar_split_clause,[],[f434,f897]) ).
tff(f434,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,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_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType,X19: list(int),X20: int,X21: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X45,X21),X20),X19) = atom_case(X0,X47,X46,X45,nDvd(X21,X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_atom_Osimps_I12_J) ).
tff(f895,plain,
spl2_79,
inference(avatar_split_clause,[],[f433,f893]) ).
tff(f433,plain,
! [X0: $tType,X2: int,X3: int,X1: list(int),X6: fun(int,fun(list(int),X0)),X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0)))] : ( atom_rec(X0,X6,X5,X4,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,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: list(int),X2: int,X3: int,X4: fun(int,fun(int,fun(list(int),X0))),X5: fun(int,fun(int,fun(list(int),X0))),X6: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X6,X5,X4,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,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType,X19: list(int),X20: int,X21: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X47,X46,X45,nDvd(X21,X20,X19)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X45,X21),X20),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_atom_Orecs_I3_J) ).
tff(f888,plain,
spl2_78,
inference(avatar_split_clause,[],[f354,f886]) ).
tff(f886,plain,
( spl2_78
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) != aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_78])]) ).
tff(f354,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,[],[f232]) ).
tff(f232,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,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__left__imp__eq) ).
tff(f884,plain,
spl2_77,
inference(avatar_split_clause,[],[f353,f882]) ).
tff(f882,plain,
( spl2_77
<=> ! [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_77])]) ).
tff(f353,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,[],[f231]) ).
tff(f231,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,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X1),X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X12: X0,X5: X0,X4: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X5) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X5) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__right__imp__eq) ).
tff(f880,plain,
spl2_76,
inference(avatar_split_clause,[],[f339,f878]) ).
tff(f878,plain,
( spl2_76
<=> ! [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_76])]) ).
tff(f339,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,[],[f221]) ).
tff(f221,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,[],[f131]) ).
tff(f131,plain,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X12: X0,X4: X0,X5: X0] :
( ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) )
=> ( X4 = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__imp__eq) ).
tff(f873,plain,
( spl2_75
| ~ spl2_20
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f674,f650,f552,f871]) ).
tff(f871,plain,
( spl2_75
<=> ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( d = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
tff(f674,plain,
( ! [X2: list(int),X0: int,X1: int] :
( ( a != nDvd(X0,X1,X2) )
| ( d = X0 ) )
| ~ spl2_20
| ~ spl2_41 ),
inference(superposition,[],[f651,f554]) ).
tff(f864,plain,
spl2_74,
inference(avatar_split_clause,[],[f387,f862]) ).
tff(f387,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,[],[f265]) ).
tff(f265,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,[],[f173]) ).
tff(f173,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,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X34: X0,X35: X0,X36: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X35)),X34) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
tff(f860,plain,
spl2_73,
inference(avatar_split_clause,[],[f385,f858]) ).
tff(f858,plain,
( spl2_73
<=> ! [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_73])]) ).
tff(f385,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,[],[f263]) ).
tff(f263,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,[],[f171]) ).
tff(f171,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,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X36: X0] : ( aa(X0,X0,times_times(X0,X36),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X36),X34)),X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f856,plain,
spl2_72,
inference(avatar_split_clause,[],[f384,f854]) ).
tff(f384,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,[],[f262]) ).
tff(f262,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,[],[f170]) ).
tff(f170,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,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X33: X0,X34: X0,X36: X0] : ( aa(X0,X0,times_times(X0,X36),aa(X0,X0,times_times(X0,X34),X33)) = aa(X0,X0,times_times(X0,X34),aa(X0,X0,times_times(X0,X36),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f852,plain,
spl2_71,
inference(avatar_split_clause,[],[f369,f850]) ).
tff(f369,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,[],[f245]) ).
tff(f245,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,[],[f155]) ).
tff(f155,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/sandbox/benchmark/theBenchmark.p',fact_67_mod__mult__mult2) ).
tff(f848,plain,
spl2_70,
inference(avatar_split_clause,[],[f368,f846]) ).
tff(f368,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,[],[f244]) ).
tff(f244,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,[],[f154]) ).
tff(f154,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/sandbox/benchmark/theBenchmark.p',fact_68_mod__mult__mult1) ).
tff(f844,plain,
spl2_69,
inference(avatar_split_clause,[],[f367,f842]) ).
tff(f367,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X2),X1) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,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,[],[f153]) ).
tff(f153,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/sandbox/benchmark/theBenchmark.p',fact_69_mod__mult__eq) ).
tff(f840,plain,
spl2_68,
inference(avatar_split_clause,[],[f335,f838]) ).
tff(f335,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,[],[f217]) ).
tff(f217,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,[],[f127]) ).
tff(f127,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,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( ab_semigroup_mult(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,aa(X0,X0,times_times(X0,X5),X4)),X12) = aa(X0,X0,times_times(X0,X5),aa(X0,X0,times_times(X0,X4),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ab__semigroup__mult__class_Omult__ac_I1_J) ).
tff(f834,plain,
spl2_67,
inference(avatar_split_clause,[],[f366,f832]) ).
tff(f366,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,[],[f242]) ).
tff(f242,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,[],[f152]) ).
tff(f152,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,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,times_times(X0,X12),X4)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_mod__mult__self1) ).
tff(f830,plain,
spl2_66,
inference(avatar_split_clause,[],[f365,f828]) ).
tff(f365,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,[],[f241]) ).
tff(f241,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,[],[f151]) ).
tff(f151,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,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X12: X0,X4: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),aa(X0,X0,times_times(X0,X4),X12)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_mod__mult__self2) ).
tff(f825,plain,
spl2_65,
inference(avatar_split_clause,[],[f381,f823]) ).
tff(f381,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,[],[f259]) ).
tff(f259,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,[],[f167]) ).
tff(f167,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,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X12: X0,X5: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X12),X5) = aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f818,plain,
( spl2_64
| ~ spl2_20
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f591,f578,f552,f816]) ).
tff(f816,plain,
( spl2_64
<=> ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
tff(f591,plain,
( ! [X0: int,X1: list(int)] : ( a != c_PresArith_Oatom_OLe(X0,X1) )
| ~ spl2_20
| ~ spl2_26 ),
inference(superposition,[],[f579,f554]) ).
tff(f812,plain,
spl2_63,
inference(avatar_split_clause,[],[f414,f810]) ).
tff(f414,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,[],[f297]) ).
tff(f297,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,[],[f198]) ).
tff(f198,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,[],[f99]) ).
tff(f99,axiom,
! [X29: list(int),X8: atom,X58: list(int),X60: int] :
( i_Z(asubst(X60,X58,X8),X29)
<=> i_Z(X8,cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X60),iprod(int,X58,X29)),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_IZ__asubst) ).
tff(f808,plain,
spl2_62,
inference(avatar_split_clause,[],[f413,f806]) ).
tff(f413,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,[],[f297]) ).
tff(f804,plain,
spl2_61,
inference(avatar_split_clause,[],[f363,f802]) ).
tff(f363,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X3),X1),X2) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X3,X2)),X1),X2) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X12: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,times_times(X0,X5),X4),X12) = div_mod(X0,aa(X0,X0,times_times(X0,div_mod(X0,X5,X12)),X4),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zmod__simps_I4_J) ).
tff(f800,plain,
spl2_60,
inference(avatar_split_clause,[],[f362,f798]) ).
tff(f798,plain,
( spl2_60
<=> ! [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_60])]) ).
tff(f362,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,[],[f238]) ).
tff(f238,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,[],[f148]) ).
tff(f148,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/sandbox/benchmark/theBenchmark.p',fact_71_mod__mult__right__eq) ).
tff(f785,plain,
spl2_59,
inference(avatar_split_clause,[],[f412,f783]) ).
tff(f783,plain,
( spl2_59
<=> ! [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_59])]) ).
tff(f412,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,[],[f296]) ).
tff(f296,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])],[f285,f295]) ).
tff(f295,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(f285,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,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X41: fun(X0,X1),X31: fun(X0,X1)] :
( ! [X42: X0] : ( aa(X0,X1,X31,X42) = aa(X0,X1,X41,X42) )
=> ( X31 = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
tff(f781,plain,
spl2_58,
inference(avatar_split_clause,[],[f407,f779]) ).
tff(f407,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,[],[f192]) ).
tff(f192,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,[],[f73]) ).
tff(f73,axiom,
! [X12: int,X4: int,X5: int] : ( div_mod(int,aa(int,int,times_times(int,X5),div_mod(int,X4,X12)),X12) = div_mod(int,aa(int,int,times_times(int,X5),X4),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zmod__simps_I3_J) ).
tff(f766,plain,
spl2_57,
inference(avatar_split_clause,[],[f426,f764]) ).
tff(f426,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X1: $tType,X19: list(X1),X8: X1,X46: fun(X1,fun(list(X1),X0)),X47: X0] : ( list_case(X0,X1,X47,X46,cons(X1,X8,X19)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X46,X8),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list_Osimps_I5_J) ).
tff(f751,plain,
spl2_56,
inference(avatar_split_clause,[],[f425,f749]) ).
tff(f425,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_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,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_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X19: list(int),X52: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( aa(list(int),X0,aa(int,fun(list(int),X0),X47,X52),X19) = atom_case(X0,X47,X46,X45,c_PresArith_Oatom_OLe(X52,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_atom_Osimps_I10_J) ).
tff(f747,plain,
spl2_55,
inference(avatar_split_clause,[],[f424,f745]) ).
tff(f424,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_rec(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,[],[f204]) ).
tff(f204,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_rec(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,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType,X19: list(int),X52: int,X45: fun(int,fun(int,fun(list(int),X0))),X46: fun(int,fun(int,fun(list(int),X0))),X47: fun(int,fun(list(int),X0))] : ( atom_rec(X0,X47,X46,X45,c_PresArith_Oatom_OLe(X52,X19)) = aa(list(int),X0,aa(int,fun(list(int),X0),X47,X52),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_atom_Orecs_I1_J) ).
tff(f743,plain,
spl2_54,
inference(avatar_split_clause,[],[f420,f741]) ).
tff(f420,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] : ( splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1))) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X10: list(X0),X24: X0,X11: list(X0),X25: X0] : ( splice(X0,cons(X0,X25,X11),cons(X0,X24,X10)) = cons(X0,X25,cons(X0,X24,splice(X0,X11,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_splice_Osimps_I3_J) ).
tff(f739,plain,
spl2_53,
inference(avatar_split_clause,[],[f361,f737]) ).
tff(f361,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,[],[f237]) ).
tff(f237,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,[],[f147]) ).
tff(f147,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,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X5: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X5),X4),X4) = div_mod(X0,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_mod__add__self2) ).
tff(f735,plain,
spl2_52,
inference(avatar_split_clause,[],[f360,f733]) ).
tff(f360,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,[],[f236]) ).
tff(f236,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,[],[f146]) ).
tff(f146,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,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X5: X0,X4: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X4),X5),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_mod__add__self1) ).
tff(f730,plain,
spl2_51,
inference(avatar_split_clause,[],[f400,f728]) ).
tff(f400,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(flattening,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) )
| ~ zero(X0)
| ~ cl_Groups_Oplus(X0) ),
inference(ennf_transformation,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType] :
( ( zero(X0)
& cl_Groups_Oplus(X0) )
=> ( plus_plus(list(X0)) = zipwith0(X0,X0,X0,plus_plus(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_list__add__def) ).
tff(f725,plain,
spl2_50,
inference(avatar_split_clause,[],[f380,f723]) ).
tff(f380,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,[],[f258]) ).
tff(f258,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,[],[f166]) ).
tff(f166,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,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X4: X0,X5: X0] : ( aa(X0,X0,times_times(X0,X5),X4) = aa(X0,X0,times_times(X0,X4),X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f721,plain,
( ~ spl2_49
| spl2_48 ),
inference(avatar_split_clause,[],[f716,f711,f718]) ).
tff(f711,plain,
( spl2_48
<=> ( 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),j),iprod(int,ks,e)),d)),d) = 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),j),iprod(int,ks,e))),d) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
tff(f716,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),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),j),iprod(int,ks,e))),d) )
| spl2_48 ),
inference(forward_demodulation,[],[f715,f330]) ).
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,[],[f3]) ).
tff(f3,axiom,
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/sandbox/benchmark/theBenchmark.p',fact_2__096_Il_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_J_Amod_Ad_A_061_Il_Amod_Ad_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_J_Amod_Ad_096) ).
tff(f715,plain,
( ( 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) != 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),j),iprod(int,ks,e))),d) )
| spl2_48 ),
inference(forward_demodulation,[],[f713,f452]) ).
tff(f713,plain,
( ( 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),j),iprod(int,ks,e)),d)),d) != 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),j),iprod(int,ks,e))),d) )
| spl2_48 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f714,plain,
~ spl2_48,
inference(avatar_split_clause,[],[f304,f711]) ).
tff(f304,plain,
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),j),iprod(int,ks,e)),d)),d) != 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),j),iprod(int,ks,e))),d),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
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),j),iprod(int,ks,e)),d)),d) != 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),j),iprod(int,ks,e))),d),
inference(flattening,[],[f120]) ).
tff(f120,negated_conjecture,
( ~ 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),j),iprod(int,ks,e)),d)),d) = 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),j),iprod(int,ks,e))),d) ),
inference(negated_conjecture,[],[f119]) ).
tff(f119,conjecture,
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),j),iprod(int,ks,e)),d)),d) = 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),j),iprod(int,ks,e))),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f703,plain,
spl2_47,
inference(avatar_split_clause,[],[f422,f701]) ).
tff(f422,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,[],[f301]) ).
tff(f301,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,[],[f300]) ).
tff(f300,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,[],[f203]) ).
tff(f203,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,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X16: list(X0),X43: X0,X19: list(X0),X8: X0] :
( ( cons(X0,X8,X19) = cons(X0,X43,X16) )
<=> ( ( X16 = X19 )
& ( X8 = X43 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_list_Oinject) ).
tff(f699,plain,
spl2_46,
inference(avatar_split_clause,[],[f359,f697]) ).
tff(f359,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,[],[f235]) ).
tff(f235,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,[],[f145]) ).
tff(f145,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,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X4: X0,X5: X0] : ( div_mod(X0,X5,X4) = div_mod(X0,div_mod(X0,X5,X4),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_mod__mod__trivial) ).
tff(f687,plain,
spl2_45,
inference(avatar_split_clause,[],[f431,f685]) ).
tff(f431,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,[],[f303]) ).
tff(f303,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,[],[f302]) ).
tff(f302,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,[],[f209]) ).
tff(f209,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,[],[f32]) ).
tff(f32,axiom,
! [X16: list(int),X17: int,X18: int,X19: list(int),X20: int,X21: int] :
( ( nDvd(X21,X20,X19) = nDvd(X18,X17,X16) )
<=> ( ( X16 = X19 )
& ( X17 = X20 )
& ( X18 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_atom_Osimps_I3_J) ).
tff(f683,plain,
spl2_44,
inference(avatar_split_clause,[],[f421,f681]) ).
tff(f421,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,[],[f301]) ).
tff(f671,plain,
( ~ spl2_43
| ~ spl2_22
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f593,f587,f561,f668]) ).
tff(f668,plain,
( spl2_43
<=> ( ks1 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
tff(f593,plain,
( ( ks1 != sK0 )
| ~ spl2_22
| ~ spl2_28 ),
inference(superposition,[],[f562,f589]) ).
tff(f656,plain,
spl2_42,
inference(avatar_split_clause,[],[f430,f654]) ).
tff(f430,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,[],[f303]) ).
tff(f652,plain,
spl2_41,
inference(avatar_split_clause,[],[f429,f650]) ).
tff(f429,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,[],[f303]) ).
tff(f648,plain,
spl2_40,
inference(avatar_split_clause,[],[f378,f646]) ).
tff(f646,plain,
( spl2_40
<=> ! [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_40])]) ).
tff(f378,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
tff(f644,plain,
spl2_39,
inference(avatar_split_clause,[],[f377,f642]) ).
tff(f642,plain,
( spl2_39
<=> ! [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_39])]) ).
tff(f377,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f640,plain,
spl2_38,
inference(avatar_split_clause,[],[f344,f638]) ).
tff(f638,plain,
( spl2_38
<=> ! [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_38])]) ).
tff(f344,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mult__1__left) ).
tff(f636,plain,
( ~ spl2_37
| ~ spl2_22
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f592,f582,f561,f633]) ).
tff(f633,plain,
( spl2_37
<=> ( ks = ks1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
tff(f592,plain,
( ( ks != ks1 )
| ~ spl2_22
| ~ spl2_27 ),
inference(superposition,[],[f562,f584]) ).
tff(f631,plain,
spl2_36,
inference(avatar_split_clause,[],[f343,f629]) ).
tff(f343,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X1) = X1 ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,one_one(X0)),X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_mult__1) ).
tff(f627,plain,
spl2_35,
inference(avatar_split_clause,[],[f342,f625]) ).
tff(f625,plain,
( spl2_35
<=> ! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
tff(f342,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( comm_monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mult_Ocomm__neutral) ).
tff(f623,plain,
spl2_34,
inference(avatar_split_clause,[],[f341,f621]) ).
tff(f341,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( aa(X0,X0,times_times(X0,X1),one_one(X0)) = X1 ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X5: X0] : ( aa(X0,X0,times_times(X0,X5),one_one(X0)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_mult__1__right) ).
tff(f618,plain,
spl2_33,
inference(avatar_split_clause,[],[f416,f616]) ).
tff(f616,plain,
( spl2_33
<=> ! [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_33])]) ).
tff(f416,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,[],[f299]) ).
tff(f299,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,[],[f298]) ).
tff(f298,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,[],[f199]) ).
tff(f199,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,[],[f91]) ).
tff(f91,axiom,
! [X16: list(int),X51: int,X19: list(int),X52: int] :
( ( c_PresArith_Oatom_OLe(X52,X19) = c_PresArith_Oatom_OLe(X51,X16) )
<=> ( ( X16 = X19 )
& ( X51 = X52 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_atom_Osimps_I1_J) ).
tff(f613,plain,
spl2_32,
inference(avatar_split_clause,[],[f327,f610]) ).
tff(f610,plain,
( spl2_32
<=> ( div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
tff(f327,plain,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_assms_I3_J) ).
tff(f607,plain,
spl2_31,
inference(avatar_split_clause,[],[f415,f605]) ).
tff(f605,plain,
( spl2_31
<=> ! [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_31])]) ).
tff(f415,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,[],[f299]) ).
tff(f603,plain,
spl2_30,
inference(avatar_split_clause,[],[f326,f600]) ).
tff(f598,plain,
( spl2_29
| ~ spl2_20
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f572,f565,f552,f595]) ).
tff(f595,plain,
( spl2_29
<=> ( d = divisor(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
tff(f572,plain,
( ( d = divisor(a) )
| ~ spl2_20
| ~ spl2_23 ),
inference(superposition,[],[f566,f554]) ).
tff(f590,plain,
spl2_28,
inference(avatar_split_clause,[],[f454,f587]) ).
tff(f454,plain,
ks1 = cons(int,hd_coeff(a),sK0),
inference(forward_demodulation,[],[f332,f323]) ).
tff(f323,plain,
one_one(int) = hd_coeff(a),
inference(cnf_transformation,[],[f35]) ).
tff(f35,axiom,
one_one(int) = hd_coeff(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_assms_I2_J) ).
tff(f332,plain,
ks1 = cons(int,one_one(int),sK0),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
ks1 = cons(int,one_one(int),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f215,f286]) ).
tff(f286,plain,
( ? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) )
=> ( ks1 = cons(int,one_one(int),sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
? [X0: list(int)] : ( ks1 = cons(int,one_one(int),X0) ),
inference(ennf_transformation,[],[f122]) ).
tff(f122,plain,
~ ! [X0: list(int)] : ( ks1 != cons(int,one_one(int),X0) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
~ ! [X26: list(int)] : ( ks1 != cons(int,one_one(int),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__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(f585,plain,
spl2_27,
inference(avatar_split_clause,[],[f450,f582]) ).
tff(f450,plain,
ks1 = cons(int,hd_coeff(a),ks),
inference(forward_demodulation,[],[f325,f323]) ).
tff(f325,plain,
ks1 = cons(int,one_one(int),ks),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
ks1 = cons(int,one_one(int),ks),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__096ks_A_061_A1_A_D_Aks_H_096) ).
tff(f580,plain,
spl2_26,
inference(avatar_split_clause,[],[f418,f578]) ).
tff(f418,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,[],[f200]) ).
tff(f200,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,[],[f94]) ).
tff(f94,axiom,
! [X56: list(int),X57: int,X53: list(int),X54: int,X55: int] : ( c_PresArith_Oatom_OLe(X57,X56) != nDvd(X55,X54,X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_atom_Osimps_I7_J) ).
tff(f576,plain,
spl2_25,
inference(avatar_split_clause,[],[f406,f574]) ).
tff(f574,plain,
( spl2_25
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
tff(f406,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(asubst(X2,X1,X0)) = divisor(X0) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X5: atom,X22: list(int),X23: int] : ( divisor(asubst(X23,X22,X5)) = divisor(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_divisor__asubst) ).
tff(f571,plain,
spl2_24,
inference(avatar_split_clause,[],[f455,f569]) ).
tff(f569,plain,
( spl2_24
<=> ! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
tff(f455,plain,
! [X0: list(int),X1: int] : ( hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(forward_demodulation,[],[f402,f323]) ).
tff(f402,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: list(int),X1: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X22: list(int),X23: int] : ( one_one(int) = divisor(c_PresArith_Oatom_OLe(X23,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_divisor_Osimps_I1_J) ).
tff(f567,plain,
spl2_23,
inference(avatar_split_clause,[],[f405,f565]) ).
tff(f405,plain,
! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: list(int),X1: int,X2: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X22: list(int),X23: int,X15: int] : ( divisor(nDvd(X15,X23,X22)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_divisor_Osimps_I3_J) ).
tff(f563,plain,
spl2_22,
inference(avatar_split_clause,[],[f403,f561]) ).
tff(f403,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( cons(X0,X1,X2) != X2 ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( cons(X0,X1,X2) != X2 ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X25: X0,X11: list(X0)] : ( cons(X0,X25,X11) != X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_not__Cons__self) ).
tff(f559,plain,
spl2_21,
inference(avatar_split_clause,[],[f399,f557]) ).
tff(f557,plain,
( spl2_21
<=> ! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
tff(f399,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(flattening,[],[f277]) ).
tff(f277,plain,
! [X0: $tType] :
( cl_Groups_Oplus(list(X0))
| ~ cl_Groups_Oplus(X0)
| ~ zero(X0) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType] :
( ( cl_Groups_Oplus(X0)
& zero(X0) )
=> cl_Groups_Oplus(list(X0)) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X63: $tType] :
( ( cl_Groups_Oplus(X63)
& zero(X63) )
=> cl_Groups_Oplus(list(X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
tff(f555,plain,
spl2_20,
inference(avatar_split_clause,[],[f324,f552]) ).
tff(f324,plain,
a = nDvd(d,l,ks1),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
a = nDvd(d,l,ks1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_NDvd) ).
tff(f550,plain,
spl2_19,
inference(avatar_split_clause,[],[f323,f547]) ).
tff(f545,plain,
spl2_18,
inference(avatar_split_clause,[],[f322,f542]) ).
tff(f322,plain,
cl_Groups_Oplus(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
cl_Groups_Oplus(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
tff(f540,plain,
spl2_17,
inference(avatar_split_clause,[],[f321,f537]) ).
tff(f321,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f535,plain,
spl2_16,
inference(avatar_split_clause,[],[f320,f532]) ).
tff(f320,plain,
semiring_div(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_div(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f530,plain,
spl2_15,
inference(avatar_split_clause,[],[f319,f527]) ).
tff(f319,plain,
zero(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f525,plain,
spl2_14,
inference(avatar_split_clause,[],[f318,f522]) ).
tff(f522,plain,
( spl2_14
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f318,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f520,plain,
spl2_13,
inference(avatar_split_clause,[],[f317,f517]) ).
tff(f317,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
tff(f515,plain,
spl2_12,
inference(avatar_split_clause,[],[f316,f512]) ).
tff(f512,plain,
( spl2_12
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f316,plain,
semiri456707255roduct(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f510,plain,
spl2_11,
inference(avatar_split_clause,[],[f315,f507]) ).
tff(f315,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f505,plain,
spl2_10,
inference(avatar_split_clause,[],[f314,f502]) ).
tff(f314,plain,
ring(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f500,plain,
spl2_9,
inference(avatar_split_clause,[],[f313,f497]) ).
tff(f497,plain,
( spl2_9
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f313,plain,
pp(fTrue),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f495,plain,
spl2_8,
inference(avatar_split_clause,[],[f312,f492]) ).
tff(f492,plain,
( spl2_8
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f312,plain,
one(int),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f490,plain,
spl2_7,
inference(avatar_split_clause,[],[f311,f487]) ).
tff(f487,plain,
( spl2_7
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f311,plain,
semiring(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
tff(f485,plain,
spl2_6,
inference(avatar_split_clause,[],[f310,f482]) ).
tff(f310,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f480,plain,
spl2_5,
inference(avatar_split_clause,[],[f309,f477]) ).
tff(f309,plain,
ab_semigroup_mult(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
tff(f475,plain,
spl2_4,
inference(avatar_split_clause,[],[f308,f472]) ).
tff(f472,plain,
( spl2_4
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f308,plain,
monoid_add(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f470,plain,
spl2_3,
inference(avatar_split_clause,[],[f307,f467]) ).
tff(f467,plain,
( spl2_3
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f307,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f465,plain,
spl2_2,
inference(avatar_split_clause,[],[f306,f462]) ).
tff(f462,plain,
( spl2_2
<=> comm_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f306,plain,
comm_semiring(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
comm_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
tff(f460,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f305,f457]) ).
tff(f457,plain,
( spl2_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f305,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COM045_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri May 3 21:25:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (3514)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37 % (3517)WARNING: value z3 for option sas not known
% 0.12/0.37 % (3519)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.37 % (3518)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37 % (3520)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.37 % (3521)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.37 % (3516)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37 % (3517)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.37 % (3521)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % Exception at run slice level% Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % (3515)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.38 % Exception at run slice level
% 0.12/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.39 % (3522)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.39 % (3523)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.12/0.39 % (3522)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.39 % (3523)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.39 % Exception at run slice level
% 0.12/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.39 % (3524)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)
% 0.18/0.41 % (3525)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)
% 0.18/0.58 % (3519)First to succeed.
% 0.18/0.61 % (3519)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3514"
% 0.18/0.61 % (3519)Refutation found. Thanks to Tanya!
% 0.18/0.61 % SZS status Theorem for theBenchmark
% 0.18/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.89/0.62 % (3519)------------------------------
% 1.89/0.62 % (3519)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.89/0.62 % (3519)Termination reason: Refutation
% 1.89/0.62
% 1.89/0.62 % (3519)Memory used [KB]: 3451
% 1.89/0.62 % (3519)Time elapsed: 0.242 s
% 1.89/0.62 % (3519)Instructions burned: 502 (million)
% 1.89/0.62 % (3514)Success in time 0.271 s
%------------------------------------------------------------------------------