TSTP Solution File: SWW498_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW498_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:35:24 EDT 2024
% Result : Theorem 0.20s 0.40s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 315
% Syntax : Number of formulae : 835 ( 265 unt; 31 typ; 0 def)
% Number of atoms : 1744 ( 423 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1546 ( 606 ~; 596 |; 48 &)
% ( 223 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 185 ( 183 usr; 173 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 821 ( 806 !; 0 ?; 821 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
int: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
real: $tType ).
tff(func_def_0,type,
fundam1563812824_csqrt: complex > complex ).
tff(func_def_1,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_2,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
min: int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_10,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
x: real ).
tff(func_def_14,type,
y: real ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(pred_def_11,type,
sP0: ( int * int ) > $o ).
tff(f1543,plain,
$false,
inference(avatar_sat_refutation,[],[f463,f468,f473,f478,f483,f488,f493,f498,f503,f508,f513,f518,f523,f528,f533,f538,f543,f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f647,f651,f658,f664,f668,f673,f678,f683,f688,f693,f697,f701,f706,f712,f716,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f766,f770,f774,f778,f782,f786,f790,f794,f801,f832,f847,f851,f855,f859,f863,f867,f871,f875,f879,f895,f910,f914,f918,f922,f926,f931,f955,f961,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1011,f1016,f1020,f1043,f1048,f1054,f1060,f1065,f1070,f1076,f1081,f1085,f1089,f1094,f1099,f1112,f1116,f1120,f1124,f1128,f1132,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1206,f1224,f1228,f1232,f1236,f1240,f1251,f1271,f1275,f1286,f1295,f1301,f1306,f1310,f1314,f1322,f1326,f1341,f1345,f1353,f1357,f1371,f1379,f1384,f1391,f1396,f1400,f1404,f1422,f1446,f1450,f1454,f1458,f1469,f1473,f1477,f1481,f1485,f1536,f1541,f1542]) ).
tff(f1542,plain,
( ~ spl1_157
| spl1_41
| ~ spl1_170 ),
inference(avatar_split_clause,[],[f1528,f1483,f661,f1393]) ).
tff(f1393,plain,
( spl1_157
<=> ord_less_eq(real,power_power(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
tff(f661,plain,
( spl1_41
<=> ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),number_number_of(nat,bit0(bit1(pls)))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
tff(f1483,plain,
( spl1_170
<=> ! [X0: real,X1: real] : ( times_times(real,X0,X1) = times_times(real,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_170])]) ).
tff(f1528,plain,
( ~ ord_less_eq(real,power_power(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| spl1_41
| ~ spl1_170 ),
inference(superposition,[],[f663,f1484]) ).
tff(f1484,plain,
( ! [X0: real,X1: real] : ( times_times(real,X0,X1) = times_times(real,X1,X0) )
| ~ spl1_170 ),
inference(avatar_component_clause,[],[f1483]) ).
tff(f663,plain,
( ~ ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| spl1_41 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f1541,plain,
( ~ spl1_10
| spl1_172
| ~ spl1_4
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1022,f968,f475,f1538,f505]) ).
tff(f505,plain,
( spl1_10
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f1538,plain,
( spl1_172
<=> ( one_one(int) = abs_abs(int,number_number_of(int,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_172])]) ).
tff(f475,plain,
( spl1_4
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f968,plain,
( spl1_92
<=> ! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
tff(f1022,plain,
( ( one_one(int) = abs_abs(int,number_number_of(int,min)) )
| ~ number_ring(int)
| ~ spl1_4
| ~ spl1_92 ),
inference(resolution,[],[f969,f477]) ).
tff(f477,plain,
( linordered_idom(int)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f475]) ).
tff(f969,plain,
( ! [X0: $tType] :
( ~ linordered_idom(X0)
| ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) )
| ~ number_ring(X0) )
| ~ spl1_92 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f1536,plain,
( ~ spl1_9
| spl1_171
| ~ spl1_3
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1021,f968,f470,f1533,f500]) ).
tff(f500,plain,
( spl1_9
<=> number_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f1533,plain,
( spl1_171
<=> ( one_one(real) = abs_abs(real,number_number_of(real,min)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_171])]) ).
tff(f470,plain,
( spl1_3
<=> linordered_idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f1021,plain,
( ( one_one(real) = abs_abs(real,number_number_of(real,min)) )
| ~ number_ring(real)
| ~ spl1_3
| ~ spl1_92 ),
inference(resolution,[],[f969,f472]) ).
tff(f472,plain,
( linordered_idom(real)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f470]) ).
tff(f1485,plain,
( spl1_170
| ~ spl1_29
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f947,f920,f600,f1483]) ).
tff(f600,plain,
( spl1_29
<=> comm_semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f920,plain,
( spl1_86
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
tff(f947,plain,
( ! [X0: real,X1: real] : ( times_times(real,X0,X1) = times_times(real,X1,X0) )
| ~ spl1_29
| ~ spl1_86 ),
inference(resolution,[],[f921,f602]) ).
tff(f602,plain,
( comm_semiring_1(real)
| ~ spl1_29 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f921,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) )
| ~ spl1_86 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f1481,plain,
( spl1_169
| ~ spl1_28
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f946,f920,f595,f1479]) ).
tff(f1479,plain,
( spl1_169
<=> ! [X0: nat,X1: nat] : ( times_times(nat,X1,X0) = times_times(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_169])]) ).
tff(f595,plain,
( spl1_28
<=> comm_semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f946,plain,
( ! [X0: nat,X1: nat] : ( times_times(nat,X1,X0) = times_times(nat,X0,X1) )
| ~ spl1_28
| ~ spl1_86 ),
inference(resolution,[],[f921,f597]) ).
tff(f597,plain,
( comm_semiring_1(nat)
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f1477,plain,
( spl1_168
| ~ spl1_80
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f1439,f1161,f873,f1475]) ).
tff(f1475,plain,
( spl1_168
<=> ! [X0: int] :
( ( one_one(int) != X0 )
| sP0(one_one(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_168])]) ).
tff(f873,plain,
( spl1_80
<=> ! [X0: int,X1: int] :
( sP0(X0,X1)
| ( one_one(int) != times_times(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
tff(f1161,plain,
( spl1_126
<=> ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
tff(f1439,plain,
( ! [X0: int] :
( ( one_one(int) != X0 )
| sP0(one_one(int),X0) )
| ~ spl1_80
| ~ spl1_126 ),
inference(superposition,[],[f874,f1162]) ).
tff(f1162,plain,
( ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 )
| ~ spl1_126 ),
inference(avatar_component_clause,[],[f1161]) ).
tff(f874,plain,
( ! [X0: int,X1: int] :
( ( one_one(int) != times_times(int,X1,X0) )
| sP0(X0,X1) )
| ~ spl1_80 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f1473,plain,
( spl1_167
| ~ spl1_30
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f945,f920,f605,f1471]) ).
tff(f1471,plain,
( spl1_167
<=> ! [X0: int,X1: int] : ( times_times(int,X1,X0) = times_times(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_167])]) ).
tff(f605,plain,
( spl1_30
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f945,plain,
( ! [X0: int,X1: int] : ( times_times(int,X1,X0) = times_times(int,X0,X1) )
| ~ spl1_30
| ~ spl1_86 ),
inference(resolution,[],[f921,f607]) ).
tff(f607,plain,
( comm_semiring_1(int)
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f1469,plain,
( spl1_166
| ~ spl1_27
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f944,f920,f590,f1467]) ).
tff(f1467,plain,
( spl1_166
<=> ! [X0: complex,X1: complex] : ( times_times(complex,X0,X1) = times_times(complex,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
tff(f590,plain,
( spl1_27
<=> comm_semiring_1(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f944,plain,
( ! [X0: complex,X1: complex] : ( times_times(complex,X0,X1) = times_times(complex,X1,X0) )
| ~ spl1_27
| ~ spl1_86 ),
inference(resolution,[],[f921,f592]) ).
tff(f592,plain,
( comm_semiring_1(complex)
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f590]) ).
tff(f1458,plain,
( spl1_165
| ~ spl1_25
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f883,f845,f580,f1456]) ).
tff(f1456,plain,
( spl1_165
<=> ! [X0: nat] : ( one_one(real) = power_power(real,one_one(real),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
tff(f580,plain,
( spl1_25
<=> monoid_mult(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f845,plain,
( spl1_73
<=> ! [X0: $tType,X1: nat] :
( ( one_one(X0) = power_power(X0,one_one(X0),X1) )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
tff(f883,plain,
( ! [X0: nat] : ( one_one(real) = power_power(real,one_one(real),X0) )
| ~ spl1_25
| ~ spl1_73 ),
inference(resolution,[],[f846,f582]) ).
tff(f582,plain,
( monoid_mult(real)
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f580]) ).
tff(f846,plain,
( ! [X0: $tType,X1: nat] :
( ~ monoid_mult(X0)
| ( one_one(X0) = power_power(X0,one_one(X0),X1) ) )
| ~ spl1_73 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f1454,plain,
( spl1_164
| ~ spl1_24
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f882,f845,f575,f1452]) ).
tff(f1452,plain,
( spl1_164
<=> ! [X0: nat] : ( one_one(nat) = power_power(nat,one_one(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_164])]) ).
tff(f575,plain,
( spl1_24
<=> monoid_mult(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f882,plain,
( ! [X0: nat] : ( one_one(nat) = power_power(nat,one_one(nat),X0) )
| ~ spl1_24
| ~ spl1_73 ),
inference(resolution,[],[f846,f577]) ).
tff(f577,plain,
( monoid_mult(nat)
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f575]) ).
tff(f1450,plain,
( spl1_163
| ~ spl1_26
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f881,f845,f585,f1448]) ).
tff(f1448,plain,
( spl1_163
<=> ! [X0: nat] : ( one_one(int) = power_power(int,one_one(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
tff(f585,plain,
( spl1_26
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f881,plain,
( ! [X0: nat] : ( one_one(int) = power_power(int,one_one(int),X0) )
| ~ spl1_26
| ~ spl1_73 ),
inference(resolution,[],[f846,f587]) ).
tff(f587,plain,
( monoid_mult(int)
| ~ spl1_26 ),
inference(avatar_component_clause,[],[f585]) ).
tff(f1446,plain,
( spl1_162
| ~ spl1_23
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f880,f845,f570,f1444]) ).
tff(f1444,plain,
( spl1_162
<=> ! [X0: nat] : ( one_one(complex) = power_power(complex,one_one(complex),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
tff(f570,plain,
( spl1_23
<=> monoid_mult(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f880,plain,
( ! [X0: nat] : ( one_one(complex) = power_power(complex,one_one(complex),X0) )
| ~ spl1_23
| ~ spl1_73 ),
inference(resolution,[],[f846,f572]) ).
tff(f572,plain,
( monoid_mult(complex)
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f570]) ).
tff(f1422,plain,
( spl1_160
| ~ spl1_161
| ~ spl1_44
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f904,f873,f676,f1419,f1416]) ).
tff(f1416,plain,
( spl1_160
<=> ! [X0: int] : sP0(X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
tff(f1419,plain,
( spl1_161
<=> ( pls = one_one(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_161])]) ).
tff(f676,plain,
( spl1_44
<=> ! [X0: int] : ( pls = times_times(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f904,plain,
( ! [X0: int] :
( ( pls != one_one(int) )
| sP0(X0,pls) )
| ~ spl1_44
| ~ spl1_80 ),
inference(superposition,[],[f874,f677]) ).
tff(f677,plain,
( ! [X0: int] : ( pls = times_times(int,pls,X0) )
| ~ spl1_44 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f1404,plain,
( spl1_159
| ~ spl1_29
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f820,f744,f600,f1402]) ).
tff(f1402,plain,
( spl1_159
<=> ! [X0: real] : ( times_times(real,one_one(real),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_159])]) ).
tff(f744,plain,
( spl1_58
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,one_one(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
tff(f820,plain,
( ! [X0: real] : ( times_times(real,one_one(real),X0) = X0 )
| ~ spl1_29
| ~ spl1_58 ),
inference(resolution,[],[f745,f602]) ).
tff(f745,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,one_one(X0),X1) = X1 ) )
| ~ spl1_58 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f1400,plain,
spl1_158,
inference(avatar_split_clause,[],[f344,f1398]) ).
tff(f1398,plain,
( spl1_158
<=> ! [X0: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
tff(f344,plain,
! [X0: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X0),number_number_of(nat,bit0(bit1(pls)))) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X0),number_number_of(nat,bit0(bit1(pls)))) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X5: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X5,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X5),number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_four__x__squared) ).
tff(f1396,plain,
( spl1_157
| ~ spl1_3
| ~ spl1_25
| ~ spl1_29
| ~ spl1_73
| ~ spl1_86
| ~ spl1_146
| ~ spl1_155 ),
inference(avatar_split_clause,[],[f1387,f1381,f1312,f920,f845,f600,f580,f470,f1393]) ).
tff(f1312,plain,
( spl1_146
<=> ! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
tff(f1381,plain,
( spl1_155
<=> ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
tff(f1387,plain,
( ord_less_eq(real,power_power(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_3
| ~ spl1_25
| ~ spl1_29
| ~ spl1_73
| ~ spl1_86
| ~ spl1_146
| ~ spl1_155 ),
inference(forward_demodulation,[],[f1386,f947]) ).
tff(f1386,plain,
( ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_3
| ~ spl1_25
| ~ spl1_73
| ~ spl1_146
| ~ spl1_155 ),
inference(forward_demodulation,[],[f1385,f1317]) ).
tff(f1317,plain,
( ! [X0: real] : ( power_power(real,X0,number_number_of(nat,bit0(bit1(pls)))) = power_power(real,abs_abs(real,X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ spl1_3
| ~ spl1_146 ),
inference(resolution,[],[f1313,f472]) ).
tff(f1313,plain,
( ! [X0: $tType,X1: X0] :
( ~ linordered_idom(X0)
| ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ spl1_146 ),
inference(avatar_component_clause,[],[f1312]) ).
tff(f1385,plain,
( ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_25
| ~ spl1_73
| ~ spl1_155 ),
inference(forward_demodulation,[],[f1383,f883]) ).
tff(f1383,plain,
( ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls)))))
| ~ spl1_155 ),
inference(avatar_component_clause,[],[f1381]) ).
tff(f1391,plain,
( spl1_156
| ~ spl1_28
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f819,f744,f595,f1389]) ).
tff(f1389,plain,
( spl1_156
<=> ! [X0: nat] : ( times_times(nat,one_one(nat),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
tff(f819,plain,
( ! [X0: nat] : ( times_times(nat,one_one(nat),X0) = X0 )
| ~ spl1_28
| ~ spl1_58 ),
inference(resolution,[],[f745,f597]) ).
tff(f1384,plain,
spl1_155,
inference(avatar_split_clause,[],[f336,f1381]) ).
tff(f336,plain,
ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096abs_A_I2_A_K_Ax_J_A_094_A2_A_060_061_A1_A_094_A2_096) ).
tff(f1379,plain,
( spl1_154
| ~ spl1_3
| ~ spl1_25
| ~ spl1_29
| ~ spl1_73
| ~ spl1_86
| ~ spl1_146
| ~ spl1_153 ),
inference(avatar_split_clause,[],[f1374,f1368,f1312,f920,f845,f600,f580,f470,f1376]) ).
tff(f1376,plain,
( spl1_154
<=> ord_less_eq(real,power_power(real,times_times(real,y,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
tff(f1368,plain,
( spl1_153
<=> ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
tff(f1374,plain,
( ord_less_eq(real,power_power(real,times_times(real,y,number_number_of(real,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_3
| ~ spl1_25
| ~ spl1_29
| ~ spl1_73
| ~ spl1_86
| ~ spl1_146
| ~ spl1_153 ),
inference(forward_demodulation,[],[f1373,f947]) ).
tff(f1373,plain,
( ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_3
| ~ spl1_25
| ~ spl1_73
| ~ spl1_146
| ~ spl1_153 ),
inference(forward_demodulation,[],[f1372,f1317]) ).
tff(f1372,plain,
( ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| ~ spl1_25
| ~ spl1_73
| ~ spl1_153 ),
inference(forward_demodulation,[],[f1370,f883]) ).
tff(f1370,plain,
( ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls)))))
| ~ spl1_153 ),
inference(avatar_component_clause,[],[f1368]) ).
tff(f1371,plain,
spl1_153,
inference(avatar_split_clause,[],[f335,f1368]) ).
tff(f335,plain,
ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less_eq(real,power_power(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),number_number_of(nat,bit0(bit1(pls)))),power_power(real,one_one(real),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096abs_A_I2_A_K_Ay_J_A_094_A2_A_060_061_A1_A_094_A2_096) ).
tff(f1357,plain,
spl1_152,
inference(avatar_split_clause,[],[f365,f1355]) ).
tff(f1355,plain,
( spl1_152
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = power_power(X0,power_power(X0,X2,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_152])]) ).
tff(f365,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = power_power(X0,power_power(X0,X2,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] : ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = power_power(X0,power_power(X0,X2,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: nat,X2: X0] : ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = power_power(X0,power_power(X0,X2,X1),number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X6: nat,X7: X0] : ( power_power(X0,X7,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X6)) = power_power(X0,power_power(X0,X7,X6),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_power__even__eq) ).
tff(f1353,plain,
spl1_151,
inference(avatar_split_clause,[],[f359,f1351]) ).
tff(f1351,plain,
( spl1_151
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
tff(f359,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(flattening,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: int,X2: int] :
( ord_less_eq(int,pls,X2)
=> ( ord_less_eq(int,pls,X1)
=> ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X24: int,X13: int] :
( ord_less_eq(int,pls,X13)
=> ( ord_less_eq(int,pls,X24)
=> ( times_times(X0,number_number_of(X0,X13),number_number_of(X0,X24)) = number_number_of(X0,times_times(int,X13,X24)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_semiring__mult__number__of) ).
tff(f1345,plain,
spl1_150,
inference(avatar_split_clause,[],[f371,f1343]) ).
tff(f1343,plain,
( spl1_150
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = times_times(X0,power_power(X0,X2,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
tff(f371,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = times_times(X0,power_power(X0,X2,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] : ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = times_times(X0,power_power(X0,X2,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: nat,X2: X0] : ( power_power(X0,X2,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) = times_times(X0,power_power(X0,X2,X1),power_power(X0,X2,X1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X6: nat,X5: X0] : ( power_power(X0,X5,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X6)) = times_times(X0,power_power(X0,X5,X6),power_power(X0,X5,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
tff(f1341,plain,
( spl1_149
| ~ spl1_30
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f818,f744,f605,f1339]) ).
tff(f1339,plain,
( spl1_149
<=> ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
tff(f818,plain,
( ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 )
| ~ spl1_30
| ~ spl1_58 ),
inference(resolution,[],[f745,f607]) ).
tff(f1326,plain,
spl1_148,
inference(avatar_split_clause,[],[f380,f1324]) ).
tff(f1324,plain,
( spl1_148
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
tff(f380,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( times_times(X0,times_times(X0,X4,X3),times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X4,X2),times_times(X0,X3,X1)) ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X25: X0,X26: X0,X27: X0,X28: X0] : ( times_times(X0,times_times(X0,X28,X27),times_times(X0,X26,X25)) = times_times(X0,times_times(X0,X28,X26),times_times(X0,X27,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
tff(f1322,plain,
spl1_147,
inference(avatar_split_clause,[],[f356,f1320]) ).
tff(f1320,plain,
( spl1_147
<=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
tff(f356,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X12: X0,X2: int,X13: int] : ( times_times(X0,number_number_of(X0,X13),times_times(X0,number_number_of(X0,X2),X12)) = times_times(X0,number_number_of(X0,times_times(int,X13,X2)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_mult__number__of__left) ).
tff(f1314,plain,
spl1_146,
inference(avatar_split_clause,[],[f348,f1312]) ).
tff(f348,plain,
! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X1),number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0] : ( power_power(X0,X7,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,abs_abs(X0,X7),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_power2__abs) ).
tff(f1310,plain,
spl1_145,
inference(avatar_split_clause,[],[f347,f1308]) ).
tff(f1308,plain,
( spl1_145
<=> ! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = abs_abs(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
tff(f347,plain,
! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = abs_abs(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = abs_abs(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = abs_abs(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0] : ( power_power(X0,X7,number_number_of(nat,bit0(bit1(pls)))) = abs_abs(X0,power_power(X0,X7,number_number_of(nat,bit0(bit1(pls))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_abs__power2) ).
tff(f1306,plain,
( spl1_144
| ~ spl1_25
| ~ spl1_118
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1297,f1292,f1114,f580,f1303]) ).
tff(f1303,plain,
( spl1_144
<=> ( one_one(real) = plus_plus(real,times_times(real,x,x),times_times(real,y,y)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_144])]) ).
tff(f1114,plain,
( spl1_118
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
tff(f1292,plain,
( spl1_142
<=> ( one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_142])]) ).
tff(f1297,plain,
( ( one_one(real) = plus_plus(real,times_times(real,x,x),times_times(real,y,y)) )
| ~ spl1_25
| ~ spl1_118
| ~ spl1_142 ),
inference(forward_demodulation,[],[f1296,f1138]) ).
tff(f1138,plain,
( ! [X0: real] : ( power_power(real,X0,number_number_of(nat,bit0(bit1(pls)))) = times_times(real,X0,X0) )
| ~ spl1_25
| ~ spl1_118 ),
inference(resolution,[],[f1115,f582]) ).
tff(f1115,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ spl1_118 ),
inference(avatar_component_clause,[],[f1114]) ).
tff(f1296,plain,
( ( one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),times_times(real,y,y)) )
| ~ spl1_25
| ~ spl1_118
| ~ spl1_142 ),
inference(forward_demodulation,[],[f1294,f1138]) ).
tff(f1294,plain,
( ( one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))) )
| ~ spl1_142 ),
inference(avatar_component_clause,[],[f1292]) ).
tff(f1301,plain,
( spl1_143
| ~ spl1_27
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f817,f744,f590,f1299]) ).
tff(f1299,plain,
( spl1_143
<=> ! [X0: complex] : ( times_times(complex,one_one(complex),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_143])]) ).
tff(f817,plain,
( ! [X0: complex] : ( times_times(complex,one_one(complex),X0) = X0 )
| ~ spl1_27
| ~ spl1_58 ),
inference(resolution,[],[f745,f592]) ).
tff(f1295,plain,
spl1_142,
inference(avatar_split_clause,[],[f334,f1292]) ).
tff(f334,plain,
one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f93]) ).
tff(f93,axiom,
one_one(real) = plus_plus(real,power_power(real,x,number_number_of(nat,bit0(bit1(pls)))),power_power(real,y,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_xy) ).
tff(f1286,plain,
spl1_141,
inference(avatar_split_clause,[],[f377,f1284]) ).
tff(f1284,plain,
( spl1_141
<=> ! [X0: $tType,X3: X0,X2: X0,X1: nat] :
( ( power_power(X0,times_times(X0,X3,X2),X1) = times_times(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
tff(f377,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( power_power(X0,times_times(X0,X3,X2),X1) = times_times(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0,X3: X0] : ( power_power(X0,times_times(X0,X3,X2),X1) = times_times(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: nat,X2: X0,X3: X0] : ( power_power(X0,times_times(X0,X3,X2),X1) = times_times(X0,power_power(X0,X3,X1),power_power(X0,X2,X1)) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X20: nat,X18: X0,X5: X0] : ( power_power(X0,times_times(X0,X5,X18),X20) = times_times(X0,power_power(X0,X5,X20),power_power(X0,X18,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
tff(f1275,plain,
spl1_140,
inference(avatar_split_clause,[],[f364,f1273]) ).
tff(f1273,plain,
( spl1_140
<=> ! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit1(bit1(pls)))) = times_times(X0,times_times(X0,X1,X1),X1) )
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
tff(f364,plain,
! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit1(bit1(pls)))) = times_times(X0,times_times(X0,X1,X1),X1) )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit1(bit1(pls)))) = times_times(X0,times_times(X0,X1,X1),X1) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( power_power(X0,X1,number_number_of(nat,bit1(bit1(pls)))) = times_times(X0,times_times(X0,X1,X1),X1) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X7: X0] : ( power_power(X0,X7,number_number_of(nat,bit1(bit1(pls)))) = times_times(X0,times_times(X0,X7,X7),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_power3__eq__cube) ).
tff(f1271,plain,
spl1_139,
inference(avatar_split_clause,[],[f353,f1269]) ).
tff(f1269,plain,
( spl1_139
<=> ! [X0: $tType,X1: nat] :
( ( one_one(X0) = power_power(X0,number_number_of(X0,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
tff(f353,plain,
! [X0: $tType,X1: nat] :
( ( one_one(X0) = power_power(X0,number_number_of(X0,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType] :
( ! [X1: nat] : ( one_one(X0) = power_power(X0,number_number_of(X0,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: nat] : ( one_one(X0) = power_power(X0,number_number_of(X0,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1)) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X6: nat] : ( one_one(X0) = power_power(X0,number_number_of(X0,min),times_times(nat,number_number_of(nat,bit0(bit1(pls))),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_power__m1__even) ).
tff(f1251,plain,
( spl1_138
| ~ spl1_29
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f816,f740,f600,f1249]) ).
tff(f1249,plain,
( spl1_138
<=> ! [X0: real] : ( times_times(real,X0,one_one(real)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
tff(f740,plain,
( spl1_57
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f816,plain,
( ! [X0: real] : ( times_times(real,X0,one_one(real)) = X0 )
| ~ spl1_29
| ~ spl1_57 ),
inference(resolution,[],[f741,f602]) ).
tff(f741,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X1,one_one(X0)) = X1 ) )
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f1240,plain,
spl1_137,
inference(avatar_split_clause,[],[f376,f1238]) ).
tff(f1238,plain,
( spl1_137
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,times_times(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
tff(f376,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,times_times(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,times_times(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,times_times(X0,X3,X2),X1) = times_times(X0,times_times(X0,X3,X1),X2) ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X26: X0,X27: X0,X28: X0] : ( times_times(X0,times_times(X0,X28,X27),X26) = times_times(X0,times_times(X0,X28,X26),X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
tff(f1236,plain,
spl1_136,
inference(avatar_split_clause,[],[f374,f1234]) ).
tff(f1234,plain,
( spl1_136
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
tff(f374,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X25: X0,X26: X0,X28: X0] : ( times_times(X0,X28,times_times(X0,X26,X25)) = times_times(X0,times_times(X0,X28,X26),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f1232,plain,
spl1_135,
inference(avatar_split_clause,[],[f373,f1230]) ).
tff(f1230,plain,
( spl1_135
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
tff(f373,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X25: X0,X26: X0,X28: X0] : ( times_times(X0,X28,times_times(X0,X26,X25)) = times_times(X0,X26,times_times(X0,X28,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f1228,plain,
spl1_134,
inference(avatar_split_clause,[],[f372,f1226]) ).
tff(f1226,plain,
( spl1_134
<=> ! [X0: $tType,X3: X0,X2: nat,X1: nat] :
( ( power_power(X0,power_power(X0,X3,X2),X1) = power_power(X0,X3,times_times(nat,X2,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
tff(f372,plain,
! [X0: $tType,X2: nat,X3: X0,X1: nat] :
( ( power_power(X0,power_power(X0,X3,X2),X1) = power_power(X0,X3,times_times(nat,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat,X3: X0] : ( power_power(X0,power_power(X0,X3,X2),X1) = power_power(X0,X3,times_times(nat,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: nat,X2: nat,X3: X0] : ( power_power(X0,power_power(X0,X3,X2),X1) = power_power(X0,X3,times_times(nat,X2,X1)) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X20: nat,X21: nat,X5: X0] : ( power_power(X0,power_power(X0,X5,X21),X20) = power_power(X0,X5,times_times(nat,X21,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
tff(f1224,plain,
spl1_133,
inference(avatar_split_clause,[],[f354,f1222]) ).
tff(f1222,plain,
( spl1_133
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
tff(f354,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int,X13: int] : ( number_number_of(X0,times_times(int,X13,X2)) = times_times(X0,number_number_of(X0,X13),number_number_of(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_number__of__mult) ).
tff(f1206,plain,
( spl1_132
| ~ spl1_28
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f815,f740,f595,f1204]) ).
tff(f1204,plain,
( spl1_132
<=> ! [X0: nat] : ( times_times(nat,X0,one_one(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
tff(f815,plain,
( ! [X0: nat] : ( times_times(nat,X0,one_one(nat)) = X0 )
| ~ spl1_28
| ~ spl1_57 ),
inference(resolution,[],[f741,f597]) ).
tff(f1183,plain,
spl1_131,
inference(avatar_split_clause,[],[f440,f1181]) ).
tff(f1181,plain,
( spl1_131
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,pls)
| ord_less_eq(int,X1,X0)
| ~ ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
tff(f440,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,pls)
| ord_less_eq(int,X1,X0)
| ~ ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ( ~ ord_less_eq(int,X1,pls)
& ~ ord_less_eq(int,X1,X0) ) )
& ( ord_less_eq(int,X1,pls)
| ord_less_eq(int,X1,X0)
| ~ ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(flattening,[],[f282]) ).
tff(f282,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ( ~ ord_less_eq(int,X1,pls)
& ~ ord_less_eq(int,X1,X0) ) )
& ( ord_less_eq(int,X1,pls)
| ord_less_eq(int,X1,X0)
| ~ ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(nnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ord_less_eq(int,X1,pls)
| ord_less_eq(int,X1,X0) ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ~ ord_less_eq(int,X1,X0)
=> ord_less_eq(int,X1,pls) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X14: int,X15: int] :
( ord_less_eq(nat,number_number_of(nat,X15),number_number_of(nat,X14))
<=> ( ~ ord_less_eq(int,X15,X14)
=> ord_less_eq(int,X15,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__nat__number__of) ).
tff(f1179,plain,
spl1_130,
inference(avatar_split_clause,[],[f415,f1177]) ).
tff(f1177,plain,
( spl1_130
<=> ! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
tff(f415,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: int,X1: int] :
( ( one_one(int) = times_times(int,X1,X0) )
=> ( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 ) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X6: int,X19: int] :
( ( one_one(int) = times_times(int,X19,X6) )
=> ( ( number_number_of(int,min) = X19 )
| ( one_one(int) = X19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_pos__zmult__eq__1__iff__lemma) ).
tff(f1175,plain,
spl1_129,
inference(avatar_split_clause,[],[f388,f1173]) ).
tff(f1173,plain,
( spl1_129
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
tff(f388,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1) )
& ( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int,X4: int] :
( ord_less_eq(X0,number_number_of(X0,X4),number_number_of(X0,X3))
<=> ord_less_eq(int,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_le__number__of) ).
tff(f1171,plain,
spl1_128,
inference(avatar_split_clause,[],[f387,f1169]) ).
tff(f1169,plain,
( spl1_128
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
tff(f387,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f1167,plain,
spl1_127,
inference(avatar_split_clause,[],[f386,f1165]) ).
tff(f1165,plain,
( spl1_127
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
tff(f386,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls)) )
& ( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4: int] :
( ord_less_eq(X0,number_number_of(X0,X4),one_one(X0))
<=> ord_less_eq(int,X4,bit1(pls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_le__special_I4_J) ).
tff(f1163,plain,
( spl1_126
| ~ spl1_30
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f814,f740,f605,f1161]) ).
tff(f814,plain,
( ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 )
| ~ spl1_30
| ~ spl1_57 ),
inference(resolution,[],[f741,f607]) ).
tff(f1159,plain,
spl1_125,
inference(avatar_split_clause,[],[f385,f1157]) ).
tff(f1157,plain,
( spl1_125
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
tff(f385,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f1155,plain,
spl1_124,
inference(avatar_split_clause,[],[f384,f1153]) ).
tff(f1153,plain,
( spl1_124
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
tff(f384,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1) )
& ( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X3))
<=> ord_less_eq(int,bit1(pls),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_le__special_I2_J) ).
tff(f1151,plain,
spl1_123,
inference(avatar_split_clause,[],[f383,f1149]) ).
tff(f1149,plain,
( spl1_123
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
tff(f383,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f257]) ).
tff(f1132,plain,
spl1_122,
inference(avatar_split_clause,[],[f445,f1130]) ).
tff(f1130,plain,
( spl1_122
<=> ! [X2: int,X0: nat,X1: nat] : ( power_power(int,power_power(int,X2,X1),X0) = power_power(int,X2,times_times(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
tff(f445,plain,
! [X2: int,X0: nat,X1: nat] : ( power_power(int,power_power(int,X2,X1),X0) = power_power(int,X2,times_times(nat,X1,X0)) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: nat,X1: nat,X2: int] : ( power_power(int,power_power(int,X2,X1),X0) = power_power(int,X2,times_times(nat,X1,X0)) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X12: nat,X18: nat,X5: int] : ( power_power(int,power_power(int,X5,X18),X12) = power_power(int,X5,times_times(nat,X18,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_zpower__zpower) ).
tff(f1128,plain,
spl1_121,
inference(avatar_split_clause,[],[f382,f1126]) ).
tff(f1126,plain,
( spl1_121
<=> ! [X0: $tType,X1: nat] :
( ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X1)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).
tff(f382,plain,
! [X0: $tType,X1: nat] :
( ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X1)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: nat] : ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X1)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: nat] : ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X1)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: nat] : ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X1)) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X6: nat] : ( one_one(X0) = abs_abs(X0,power_power(X0,number_number_of(X0,min),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_abs__power__minus__one) ).
tff(f1124,plain,
( spl1_120
| ~ spl1_27
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f813,f740,f590,f1122]) ).
tff(f1122,plain,
( spl1_120
<=> ! [X0: complex] : ( times_times(complex,X0,one_one(complex)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
tff(f813,plain,
( ! [X0: complex] : ( times_times(complex,X0,one_one(complex)) = X0 )
| ~ spl1_27
| ~ spl1_57 ),
inference(resolution,[],[f741,f592]) ).
tff(f1120,plain,
spl1_119,
inference(avatar_split_clause,[],[f369,f1118]) ).
tff(f1118,plain,
( spl1_119
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
tff(f369,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( times_times(X0,X5,X5) = power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(f1116,plain,
spl1_118,
inference(avatar_split_clause,[],[f363,f1114]) ).
tff(f363,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( times_times(X0,X1,X1) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X7: X0] : ( power_power(X0,X7,number_number_of(nat,bit0(bit1(pls)))) = times_times(X0,X7,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square) ).
tff(f1112,plain,
spl1_117,
inference(avatar_split_clause,[],[f346,f1110]) ).
tff(f1110,plain,
( spl1_117
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
tff(f346,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1)) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0] : ( times_times(X0,X7,X7) = times_times(X0,abs_abs(X0,X7),abs_abs(X0,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_abs__mult__self) ).
tff(f1099,plain,
( spl1_116
| ~ spl1_29
| ~ spl1_86
| ~ spl1_111 ),
inference(avatar_split_clause,[],[f1077,f1073,f920,f600,f1096]) ).
tff(f1096,plain,
( spl1_116
<=> ord_less_eq(real,abs_abs(real,times_times(real,x,number_number_of(real,bit0(bit1(pls))))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
tff(f1073,plain,
( spl1_111
<=> ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
tff(f1077,plain,
( ord_less_eq(real,abs_abs(real,times_times(real,x,number_number_of(real,bit0(bit1(pls))))),one_one(real))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_111 ),
inference(forward_demodulation,[],[f1075,f947]) ).
tff(f1075,plain,
( ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),one_one(real))
| ~ spl1_111 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f1094,plain,
( spl1_115
| ~ spl1_29
| ~ spl1_86
| ~ spl1_110 ),
inference(avatar_split_clause,[],[f1071,f1067,f920,f600,f1091]) ).
tff(f1091,plain,
( spl1_115
<=> ord_less_eq(real,abs_abs(real,times_times(real,y,number_number_of(real,bit0(bit1(pls))))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
tff(f1067,plain,
( spl1_110
<=> ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
tff(f1071,plain,
( ord_less_eq(real,abs_abs(real,times_times(real,y,number_number_of(real,bit0(bit1(pls))))),one_one(real))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_110 ),
inference(forward_demodulation,[],[f1069,f947]) ).
tff(f1069,plain,
( ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),one_one(real))
| ~ spl1_110 ),
inference(avatar_component_clause,[],[f1067]) ).
tff(f1089,plain,
spl1_114,
inference(avatar_split_clause,[],[f389,f1087]) ).
tff(f1087,plain,
( spl1_114
<=> ! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( number_number_of(X0,X2) != number_number_of(X0,X1) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
tff(f389,plain,
! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( number_number_of(X0,X2) != number_number_of(X0,X1) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( number_number_of(X0,X2) != number_number_of(X0,X1) ) ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X1 = X2 ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X1 = X2 ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X1) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X3: int,X4: int] :
( ( number_number_of(X0,X3) = number_number_of(X0,X4) )
<=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_eq__number__of) ).
tff(f1085,plain,
( spl1_113
| ~ spl1_29
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f812,f736,f600,f1083]) ).
tff(f1083,plain,
( spl1_113
<=> ! [X0: real] : ( power_power(real,X0,one_one(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
tff(f736,plain,
( spl1_56
<=> ! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,one_one(nat)) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f812,plain,
( ! [X0: real] : ( power_power(real,X0,one_one(nat)) = X0 )
| ~ spl1_29
| ~ spl1_56 ),
inference(resolution,[],[f737,f602]) ).
tff(f737,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_semiring_1(X0)
| ( power_power(X0,X1,one_one(nat)) = X1 ) )
| ~ spl1_56 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f1081,plain,
spl1_112,
inference(avatar_split_clause,[],[f357,f1079]) ).
tff(f1079,plain,
( spl1_112
<=> ! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
tff(f357,plain,
! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_one__power2) ).
tff(f1076,plain,
spl1_111,
inference(avatar_split_clause,[],[f333,f1073]) ).
tff(f333,plain,
ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),one_one(real)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x)),one_one(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
tff(f1070,plain,
spl1_110,
inference(avatar_split_clause,[],[f332,f1067]) ).
tff(f332,plain,
ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),one_one(real)),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
ord_less_eq(real,abs_abs(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y)),one_one(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096) ).
tff(f1065,plain,
( spl1_109
| ~ spl1_29
| ~ spl1_86
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f1055,f1051,f920,f600,f1062]) ).
tff(f1062,plain,
( spl1_109
<=> ord_less_eq(real,number_number_of(real,min),times_times(real,x,number_number_of(real,bit0(bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
tff(f1051,plain,
( spl1_107
<=> ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
tff(f1055,plain,
( ord_less_eq(real,number_number_of(real,min),times_times(real,x,number_number_of(real,bit0(bit1(pls)))))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_107 ),
inference(forward_demodulation,[],[f1053,f947]) ).
tff(f1053,plain,
( ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),x))
| ~ spl1_107 ),
inference(avatar_component_clause,[],[f1051]) ).
tff(f1060,plain,
( spl1_108
| ~ spl1_29
| ~ spl1_86
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f1049,f1045,f920,f600,f1057]) ).
tff(f1057,plain,
( spl1_108
<=> ord_less_eq(real,number_number_of(real,min),times_times(real,y,number_number_of(real,bit0(bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
tff(f1045,plain,
( spl1_106
<=> ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
tff(f1049,plain,
( ord_less_eq(real,number_number_of(real,min),times_times(real,y,number_number_of(real,bit0(bit1(pls)))))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_106 ),
inference(forward_demodulation,[],[f1047,f947]) ).
tff(f1047,plain,
( ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),y))
| ~ spl1_106 ),
inference(avatar_component_clause,[],[f1045]) ).
tff(f1054,plain,
spl1_107,
inference(avatar_split_clause,[],[f331,f1051]) ).
tff(f331,plain,
ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),x)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_N1_A_060_061_A2_A_K_Ax_096) ).
tff(f1048,plain,
spl1_106,
inference(avatar_split_clause,[],[f330,f1045]) ).
tff(f330,plain,
ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),y)),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
ord_less_eq(real,number_number_of(real,min),times_times(real,number_number_of(real,bit0(bit1(pls))),y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42__096_N1_A_060_061_A2_A_K_Ay_096) ).
tff(f1043,plain,
( spl1_105
| ~ spl1_28
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f811,f736,f595,f1041]) ).
tff(f1041,plain,
( spl1_105
<=> ! [X0: nat] : ( power_power(nat,X0,one_one(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
tff(f811,plain,
( ! [X0: nat] : ( power_power(nat,X0,one_one(nat)) = X0 )
| ~ spl1_28
| ~ spl1_56 ),
inference(resolution,[],[f737,f597]) ).
tff(f1020,plain,
( spl1_104
| ~ spl1_30
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f810,f736,f605,f1018]) ).
tff(f1018,plain,
( spl1_104
<=> ! [X0: int] : ( power_power(int,X0,one_one(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
tff(f810,plain,
( ! [X0: int] : ( power_power(int,X0,one_one(nat)) = X0 )
| ~ spl1_30
| ~ spl1_56 ),
inference(resolution,[],[f737,f607]) ).
tff(f1016,plain,
( spl1_103
| ~ spl1_29
| ~ spl1_86
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f962,f958,f920,f600,f1013]) ).
tff(f1013,plain,
( spl1_103
<=> ord_less_eq(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
tff(f958,plain,
( spl1_90
<=> ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
tff(f962,plain,
( ord_less_eq(real,times_times(real,x,number_number_of(real,bit0(bit1(pls)))),one_one(real))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_90 ),
inference(forward_demodulation,[],[f960,f947]) ).
tff(f960,plain,
( ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),one_one(real))
| ~ spl1_90 ),
inference(avatar_component_clause,[],[f958]) ).
tff(f1011,plain,
( spl1_102
| ~ spl1_29
| ~ spl1_86
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f956,f952,f920,f600,f1008]) ).
tff(f1008,plain,
( spl1_102
<=> ord_less_eq(real,times_times(real,y,number_number_of(real,bit0(bit1(pls)))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).
tff(f952,plain,
( spl1_89
<=> ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
tff(f956,plain,
( ord_less_eq(real,times_times(real,y,number_number_of(real,bit0(bit1(pls)))),one_one(real))
| ~ spl1_29
| ~ spl1_86
| ~ spl1_89 ),
inference(forward_demodulation,[],[f954,f947]) ).
tff(f954,plain,
( ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y),one_one(real))
| ~ spl1_89 ),
inference(avatar_component_clause,[],[f952]) ).
tff(f1006,plain,
spl1_101,
inference(avatar_split_clause,[],[f444,f1004]) ).
tff(f1004,plain,
( spl1_101
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
tff(f444,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X8: int,X9: int] :
( ord_less_eq(int,number_number_of(int,X9),number_number_of(int,X8))
<=> ord_less_eq(int,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_less__eq__number__of__int__code) ).
tff(f1002,plain,
spl1_100,
inference(avatar_split_clause,[],[f443,f1000]) ).
tff(f1000,plain,
( spl1_100
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
tff(f443,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(cnf_transformation,[],[f284]) ).
tff(f998,plain,
spl1_99,
inference(avatar_split_clause,[],[f442,f996]) ).
tff(f996,plain,
( spl1_99
<=> ! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less_eq(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
tff(f442,plain,
! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less_eq(int,X1,pls) ),
inference(cnf_transformation,[],[f283]) ).
tff(f994,plain,
spl1_98,
inference(avatar_split_clause,[],[f441,f992]) ).
tff(f992,plain,
( spl1_98
<=> ! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
tff(f441,plain,
! [X0: int,X1: int] :
( ord_less_eq(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f990,plain,
spl1_97,
inference(avatar_split_clause,[],[f435,f988]) ).
tff(f988,plain,
( spl1_97
<=> ! [X0: int,X1: int] :
( ( number_number_of(int,min) = X0 )
| ( one_one(int) = X0 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
tff(f435,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X0 )
| ( one_one(int) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: int,X1: int] :
( ( sP0(X0,X1)
| ( ( ( number_number_of(int,min) != X0 )
| ( number_number_of(int,min) != X1 ) )
& ( ( one_one(int) != X0 )
| ( one_one(int) != X1 ) ) ) )
& ( ( ( number_number_of(int,min) = X0 )
& ( number_number_of(int,min) = X1 ) )
| ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f279]) ).
tff(f279,plain,
! [X0: int,X1: int] :
( ( sP0(X0,X1)
| ( ( ( number_number_of(int,min) != X0 )
| ( number_number_of(int,min) != X1 ) )
& ( ( one_one(int) != X0 )
| ( one_one(int) != X1 ) ) ) )
& ( ( ( number_number_of(int,min) = X0 )
& ( number_number_of(int,min) = X1 ) )
| ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: int,X1: int] :
( sP0(X0,X1)
<=> ( ( ( number_number_of(int,min) = X0 )
& ( number_number_of(int,min) = X1 ) )
| ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f986,plain,
spl1_96,
inference(avatar_split_clause,[],[f434,f984]) ).
tff(f984,plain,
( spl1_96
<=> ! [X0: int,X1: int] :
( ( number_number_of(int,min) = X0 )
| ( one_one(int) = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
tff(f434,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X0 )
| ( one_one(int) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tff(f982,plain,
spl1_95,
inference(avatar_split_clause,[],[f433,f980]) ).
tff(f980,plain,
( spl1_95
<=> ! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X0 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
tff(f433,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tff(f978,plain,
( spl1_94
| ~ spl1_27
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f809,f736,f590,f976]) ).
tff(f976,plain,
( spl1_94
<=> ! [X0: complex] : ( power_power(complex,X0,one_one(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
tff(f809,plain,
( ! [X0: complex] : ( power_power(complex,X0,one_one(nat)) = X0 )
| ~ spl1_27
| ~ spl1_56 ),
inference(resolution,[],[f737,f592]) ).
tff(f974,plain,
spl1_93,
inference(avatar_split_clause,[],[f432,f972]) ).
tff(f972,plain,
( spl1_93
<=> ! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).
tff(f432,plain,
! [X0: int,X1: int] :
( ( number_number_of(int,min) = X1 )
| ( one_one(int) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tff(f970,plain,
spl1_92,
inference(avatar_split_clause,[],[f381,f968]) ).
tff(f381,plain,
! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f237]) ).
tff(f237,plain,
! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ( one_one(X0) = abs_abs(X0,number_number_of(X0,min)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_abs__minus__one) ).
tff(f966,plain,
spl1_91,
inference(avatar_split_clause,[],[f343,f964]) ).
tff(f964,plain,
( spl1_91
<=> ! [X0: nat] : ord_less_eq(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
tff(f343,plain,
! [X0: nat] : ord_less_eq(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),X0)),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat] : ord_less_eq(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),X0)),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X6: nat] : ord_less_eq(real,one_one(real),power_power(real,number_number_of(real,bit0(bit1(pls))),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_two__realpow__ge__one) ).
tff(f961,plain,
spl1_90,
inference(avatar_split_clause,[],[f329,f958]) ).
tff(f329,plain,
ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),one_one(real)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),one_one(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0962_A_K_Ax_A_060_061_A1_096) ).
tff(f955,plain,
spl1_89,
inference(avatar_split_clause,[],[f328,f952]) ).
tff(f328,plain,
ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y),one_one(real)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit1(pls))),y),one_one(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__0962_A_K_Ay_A_060_061_A1_096) ).
tff(f931,plain,
( spl1_88
| ~ spl1_9
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f803,f728,f500,f928]) ).
tff(f928,plain,
( spl1_88
<=> ( one_one(real) = number_number_of(real,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
tff(f728,plain,
( spl1_54
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f803,plain,
( ( one_one(real) = number_number_of(real,bit1(pls)) )
| ~ spl1_9
| ~ spl1_54 ),
inference(resolution,[],[f729,f502]) ).
tff(f502,plain,
( number_ring(real)
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f500]) ).
tff(f729,plain,
( ! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f926,plain,
spl1_87,
inference(avatar_split_clause,[],[f414,f924]) ).
tff(f924,plain,
( spl1_87
<=> ! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
tff(f414,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X10: int,X11: int] : ( times_times(int,bit0(X11),X10) = bit0(times_times(int,X11,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mult__Bit0) ).
tff(f922,plain,
spl1_86,
inference(avatar_split_clause,[],[f370,f920]) ).
tff(f370,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X29: X0,X7: X0] : ( times_times(X0,X7,X29) = times_times(X0,X29,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(f918,plain,
spl1_85,
inference(avatar_split_clause,[],[f352,f916]) ).
tff(f916,plain,
( spl1_85
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
tff(f352,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X7: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X7) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mult__numeral__1) ).
tff(f914,plain,
spl1_84,
inference(avatar_split_clause,[],[f351,f912]) ).
tff(f912,plain,
( spl1_84
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).
tff(f351,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X7: X0] : ( times_times(X0,X7,number_number_of(X0,bit1(pls))) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult__numeral__1__right) ).
tff(f910,plain,
spl1_83,
inference(avatar_split_clause,[],[f342,f908]) ).
tff(f908,plain,
( spl1_83
<=> ! [X0: complex] : ( power_power(complex,fundam1563812824_csqrt(X0),number_number_of(nat,bit0(bit1(pls)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).
tff(f342,plain,
! [X0: complex] : ( power_power(complex,fundam1563812824_csqrt(X0),number_number_of(nat,bit0(bit1(pls)))) = X0 ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: complex] : ( power_power(complex,fundam1563812824_csqrt(X0),number_number_of(nat,bit0(bit1(pls)))) = X0 ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X12: complex] : ( power_power(complex,fundam1563812824_csqrt(X12),number_number_of(nat,bit0(bit1(pls)))) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_csqrt) ).
tff(f895,plain,
( spl1_82
| ~ spl1_8
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f802,f728,f495,f892]) ).
tff(f892,plain,
( spl1_82
<=> ( one_one(complex) = number_number_of(complex,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
tff(f495,plain,
( spl1_8
<=> number_ring(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f802,plain,
( ( one_one(complex) = number_number_of(complex,bit1(pls)) )
| ~ spl1_8
| ~ spl1_54 ),
inference(resolution,[],[f729,f497]) ).
tff(f497,plain,
( number_ring(complex)
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f495]) ).
tff(f879,plain,
spl1_81,
inference(avatar_split_clause,[],[f439,f877]) ).
tff(f877,plain,
( spl1_81
<=> ! [X0: int,X1: int] :
( ( one_one(int) = times_times(int,X1,X0) )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
tff(f439,plain,
! [X0: int,X1: int] :
( ( one_one(int) = times_times(int,X1,X0) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: int,X1: int] :
( ( ( one_one(int) = times_times(int,X1,X0) )
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ( one_one(int) != times_times(int,X1,X0) ) ) ),
inference(nnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: int,X1: int] :
( ( one_one(int) = times_times(int,X1,X0) )
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f197,f254]) ).
tff(f197,plain,
! [X0: int,X1: int] :
( ( one_one(int) = times_times(int,X1,X0) )
<=> ( ( ( number_number_of(int,min) = X0 )
& ( number_number_of(int,min) = X1 ) )
| ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) ) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X16: int,X17: int] :
( ( times_times(int,X17,X16) = one_one(int) )
<=> ( ( ( number_number_of(int,min) = X16 )
& ( number_number_of(int,min) = X17 ) )
| ( ( one_one(int) = X16 )
& ( one_one(int) = X17 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_zmult__eq__1__iff) ).
tff(f875,plain,
spl1_80,
inference(avatar_split_clause,[],[f438,f873]) ).
tff(f438,plain,
! [X0: int,X1: int] :
( sP0(X0,X1)
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(cnf_transformation,[],[f281]) ).
tff(f871,plain,
spl1_79,
inference(avatar_split_clause,[],[f429,f869]) ).
tff(f869,plain,
( spl1_79
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
tff(f429,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X22: int,X23: int] :
( ord_less_eq(int,bit1(X23),bit1(X22))
<=> ord_less_eq(int,X23,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
tff(f867,plain,
spl1_78,
inference(avatar_split_clause,[],[f428,f865]) ).
tff(f865,plain,
( spl1_78
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
tff(f428,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f277]) ).
tff(f863,plain,
spl1_77,
inference(avatar_split_clause,[],[f425,f861]) ).
tff(f861,plain,
( spl1_77
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
tff(f425,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X22: int,X23: int] :
( ord_less_eq(int,bit0(X23),bit1(X22))
<=> ord_less_eq(int,X23,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__eq__int__code_I14_J) ).
tff(f859,plain,
spl1_76,
inference(avatar_split_clause,[],[f424,f857]) ).
tff(f857,plain,
( spl1_76
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_76])]) ).
tff(f424,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f855,plain,
spl1_75,
inference(avatar_split_clause,[],[f421,f853]) ).
tff(f853,plain,
( spl1_75
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
tff(f421,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X8: int,X9: int] :
( ord_less_eq(int,bit0(X9),bit0(X8))
<=> ord_less_eq(int,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I31_J) ).
tff(f851,plain,
spl1_74,
inference(avatar_split_clause,[],[f420,f849]) ).
tff(f849,plain,
( spl1_74
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
tff(f420,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f847,plain,
spl1_73,
inference(avatar_split_clause,[],[f362,f845]) ).
tff(f362,plain,
! [X0: $tType,X1: nat] :
( ( one_one(X0) = power_power(X0,one_one(X0),X1) )
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( ! [X1: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X1) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X1) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X6: nat] : ( one_one(X0) = power_power(X0,one_one(X0),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_power__one) ).
tff(f832,plain,
( spl1_72
| ~ spl1_4
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f796,f724,f475,f829]) ).
tff(f829,plain,
( spl1_72
<=> ( one_one(int) = abs_abs(int,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
tff(f724,plain,
( spl1_53
<=> ! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,one_one(X0)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f796,plain,
( ( one_one(int) = abs_abs(int,one_one(int)) )
| ~ spl1_4
| ~ spl1_53 ),
inference(resolution,[],[f725,f477]) ).
tff(f725,plain,
( ! [X0: $tType] :
( ~ linordered_idom(X0)
| ( one_one(X0) = abs_abs(X0,one_one(X0)) ) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f724]) ).
tff(f801,plain,
( spl1_71
| ~ spl1_3
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f795,f724,f470,f798]) ).
tff(f798,plain,
( spl1_71
<=> ( one_one(real) = abs_abs(real,one_one(real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
tff(f795,plain,
( ( one_one(real) = abs_abs(real,one_one(real)) )
| ~ spl1_3
| ~ spl1_53 ),
inference(resolution,[],[f725,f472]) ).
tff(f794,plain,
spl1_70,
inference(avatar_split_clause,[],[f411,f792]) ).
tff(f792,plain,
( spl1_70
<=> ! [X0: int] :
( ord_less_eq(int,bit1(X0),min)
| ~ ord_less_eq(int,X0,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
tff(f411,plain,
! [X0: int] :
( ord_less_eq(int,bit1(X0),min)
| ~ ord_less_eq(int,X0,min) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: int] :
( ( ord_less_eq(int,bit1(X0),min)
| ~ ord_less_eq(int,X0,min) )
& ( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit1(X0),min) ) ),
inference(nnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int] :
( ord_less_eq(int,bit1(X0),min)
<=> ord_less_eq(int,X0,min) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X9: int] :
( ord_less_eq(int,bit1(X9),min)
<=> ord_less_eq(int,X9,min) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I30_J) ).
tff(f790,plain,
spl1_69,
inference(avatar_split_clause,[],[f410,f788]) ).
tff(f788,plain,
( spl1_69
<=> ! [X0: int] :
( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit1(X0),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
tff(f410,plain,
! [X0: int] :
( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit1(X0),min) ),
inference(cnf_transformation,[],[f270]) ).
tff(f786,plain,
spl1_68,
inference(avatar_split_clause,[],[f409,f784]) ).
tff(f784,plain,
( spl1_68
<=> ! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
tff(f409,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X9: int] :
( ord_less_eq(int,bit0(X9),pls)
<=> ord_less_eq(int,X9,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I27_J) ).
tff(f782,plain,
spl1_67,
inference(avatar_split_clause,[],[f408,f780]) ).
tff(f780,plain,
( spl1_67
<=> ! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
tff(f408,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f269]) ).
tff(f778,plain,
spl1_66,
inference(avatar_split_clause,[],[f407,f776]) ).
tff(f776,plain,
( spl1_66
<=> ! [X0: int] :
( ord_less_eq(int,bit0(X0),min)
| ~ ord_less_eq(int,X0,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
tff(f407,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),min)
| ~ ord_less_eq(int,X0,min) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),min)
| ~ ord_less_eq(int,X0,min) )
& ( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit0(X0),min) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),min)
<=> ord_less_eq(int,X0,min) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X9: int] :
( ord_less_eq(int,bit0(X9),min)
<=> ord_less_eq(int,X9,min) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I28_J) ).
tff(f774,plain,
spl1_65,
inference(avatar_split_clause,[],[f406,f772]) ).
tff(f772,plain,
( spl1_65
<=> ! [X0: int] :
( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit0(X0),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
tff(f406,plain,
! [X0: int] :
( ord_less_eq(int,X0,min)
| ~ ord_less_eq(int,bit0(X0),min) ),
inference(cnf_transformation,[],[f268]) ).
tff(f770,plain,
spl1_64,
inference(avatar_split_clause,[],[f405,f768]) ).
tff(f768,plain,
( spl1_64
<=> ! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
tff(f405,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: int] :
( ( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X9: int] :
( ord_less_eq(int,pls,bit1(X9))
<=> ord_less_eq(int,pls,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rel__simps_I22_J) ).
tff(f766,plain,
spl1_63,
inference(avatar_split_clause,[],[f404,f764]) ).
tff(f764,plain,
( spl1_63
<=> ! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f404,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f267]) ).
tff(f762,plain,
spl1_62,
inference(avatar_split_clause,[],[f403,f760]) ).
tff(f760,plain,
( spl1_62
<=> ! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
tff(f403,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: int] :
( ( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X9: int] :
( ord_less_eq(int,pls,bit0(X9))
<=> ord_less_eq(int,pls,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I21_J) ).
tff(f758,plain,
spl1_61,
inference(avatar_split_clause,[],[f402,f756]) ).
tff(f756,plain,
( spl1_61
<=> ! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
tff(f402,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f266]) ).
tff(f754,plain,
spl1_60,
inference(avatar_split_clause,[],[f401,f752]) ).
tff(f752,plain,
( spl1_60
<=> ! [X0: int] :
( ord_less_eq(int,min,bit1(X0))
| ~ ord_less_eq(int,min,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f401,plain,
! [X0: int] :
( ord_less_eq(int,min,bit1(X0))
| ~ ord_less_eq(int,min,X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: int] :
( ( ord_less_eq(int,min,bit1(X0))
| ~ ord_less_eq(int,min,X0) )
& ( ord_less_eq(int,min,X0)
| ~ ord_less_eq(int,min,bit1(X0)) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: int] :
( ord_less_eq(int,min,bit1(X0))
<=> ord_less_eq(int,min,X0) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X9: int] :
( ord_less_eq(int,min,bit1(X9))
<=> ord_less_eq(int,min,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_rel__simps_I26_J) ).
tff(f750,plain,
spl1_59,
inference(avatar_split_clause,[],[f400,f748]) ).
tff(f748,plain,
( spl1_59
<=> ! [X0: int] :
( ord_less_eq(int,min,X0)
| ~ ord_less_eq(int,min,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
tff(f400,plain,
! [X0: int] :
( ord_less_eq(int,min,X0)
| ~ ord_less_eq(int,min,bit1(X0)) ),
inference(cnf_transformation,[],[f265]) ).
tff(f746,plain,
spl1_58,
inference(avatar_split_clause,[],[f368,f744]) ).
tff(f368,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,one_one(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( times_times(X0,one_one(X0),X1) = X1 ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X7: X0] : ( times_times(X0,one_one(X0),X7) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
tff(f742,plain,
spl1_57,
inference(avatar_split_clause,[],[f367,f740]) ).
tff(f367,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,one_one(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( times_times(X0,X1,one_one(X0)) = X1 ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X7: X0] : ( times_times(X0,X7,one_one(X0)) = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
tff(f738,plain,
spl1_56,
inference(avatar_split_clause,[],[f366,f736]) ).
tff(f366,plain,
! [X0: $tType,X1: X0] :
( ( power_power(X0,X1,one_one(nat)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,one_one(nat)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( power_power(X0,X1,one_one(nat)) = X1 ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X5: X0] : ( power_power(X0,X5,one_one(nat)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
tff(f734,plain,
spl1_55,
inference(avatar_split_clause,[],[f358,f732]) ).
tff(f732,plain,
( spl1_55
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f358,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_semiring__numeral__1__eq__1) ).
tff(f730,plain,
spl1_54,
inference(avatar_split_clause,[],[f349,f728]) ).
tff(f349,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
tff(f726,plain,
spl1_53,
inference(avatar_split_clause,[],[f345,f724]) ).
tff(f345,plain,
! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,one_one(X0)) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType] :
( ( one_one(X0) = abs_abs(X0,one_one(X0)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ( one_one(X0) = abs_abs(X0,one_one(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_abs__one) ).
tff(f716,plain,
spl1_52,
inference(avatar_split_clause,[],[f418,f714]) ).
tff(f714,plain,
( spl1_52
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f418,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: int,X1: int] :
( ( ( bit1(X0) = bit1(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
inference(nnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: int,X1: int] :
( ( bit1(X0) = bit1(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X8: int,X9: int] :
( ( bit1(X9) = bit1(X8) )
<=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I51_J) ).
tff(f712,plain,
spl1_51,
inference(avatar_split_clause,[],[f416,f710]) ).
tff(f710,plain,
( spl1_51
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f416,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: int,X1: int] :
( ( ( bit0(X0) = bit0(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: int,X1: int] :
( ( bit0(X0) = bit0(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X8: int,X9: int] :
( ( bit0(X9) = bit0(X8) )
<=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I48_J) ).
tff(f706,plain,
spl1_50,
inference(avatar_split_clause,[],[f456,f703]) ).
tff(f703,plain,
( spl1_50
<=> sP0(number_number_of(int,min),number_number_of(int,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f456,plain,
sP0(number_number_of(int,min),number_number_of(int,min)),
inference(equality_resolution,[],[f455]) ).
tff(f455,plain,
! [X1: int] :
( sP0(number_number_of(int,min),X1)
| ( number_number_of(int,min) != X1 ) ),
inference(equality_resolution,[],[f437]) ).
tff(f437,plain,
! [X0: int,X1: int] :
( sP0(X0,X1)
| ( number_number_of(int,min) != X0 )
| ( number_number_of(int,min) != X1 ) ),
inference(cnf_transformation,[],[f280]) ).
tff(f701,plain,
spl1_49,
inference(avatar_split_clause,[],[f396,f699]) ).
tff(f699,plain,
( spl1_49
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f396,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X8: int] :
( ( pls = bit0(X8) )
<=> ( pls = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I38_J) ).
tff(f697,plain,
spl1_48,
inference(avatar_split_clause,[],[f392,f695]) ).
tff(f695,plain,
( spl1_48
<=> ! [X0: int] :
( ( min = X0 )
| ( min != bit1(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f392,plain,
! [X0: int] :
( ( min = X0 )
| ( min != bit1(X0) ) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: int] :
( ( ( min = bit1(X0) )
| ( min != X0 ) )
& ( ( min = X0 )
| ( min != bit1(X0) ) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: int] :
( ( min = bit1(X0) )
<=> ( min = X0 ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X8: int] :
( ( min = bit1(X8) )
<=> ( min = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rel__simps_I43_J) ).
tff(f693,plain,
spl1_47,
inference(avatar_split_clause,[],[f326,f690]) ).
tff(f690,plain,
( spl1_47
<=> ( number_number_of(nat,bit1(pls)) = one_one(nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
tff(f326,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(cnf_transformation,[],[f46]) ).
tff(f46,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__numeral__1__eq__1) ).
tff(f688,plain,
spl1_46,
inference(avatar_split_clause,[],[f325,f685]) ).
tff(f685,plain,
( spl1_46
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f325,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f69]) ).
tff(f69,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_one__is__num__one) ).
tff(f683,plain,
~ spl1_45,
inference(avatar_split_clause,[],[f324,f680]) ).
tff(f680,plain,
( spl1_45
<=> ( number_number_of(int,pls) = number_number_of(int,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f324,plain,
number_number_of(int,pls) != number_number_of(int,min),
inference(cnf_transformation,[],[f60]) ).
tff(f60,axiom,
number_number_of(int,pls) != number_number_of(int,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_eq__number__of__Pls__Min) ).
tff(f678,plain,
spl1_44,
inference(avatar_split_clause,[],[f341,f676]) ).
tff(f341,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X2: int] : ( pls = times_times(int,pls,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_mult__Pls) ).
tff(f673,plain,
spl1_43,
inference(avatar_split_clause,[],[f458,f670]) ).
tff(f670,plain,
( spl1_43
<=> sP0(one_one(int),one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f458,plain,
sP0(one_one(int),one_one(int)),
inference(equality_resolution,[],[f457]) ).
tff(f457,plain,
! [X1: int] :
( sP0(one_one(int),X1)
| ( one_one(int) != X1 ) ),
inference(equality_resolution,[],[f436]) ).
tff(f436,plain,
! [X0: int,X1: int] :
( sP0(X0,X1)
| ( one_one(int) != X0 )
| ( one_one(int) != X1 ) ),
inference(cnf_transformation,[],[f280]) ).
tff(f668,plain,
spl1_42,
inference(avatar_split_clause,[],[f412,f666]) ).
tff(f666,plain,
( spl1_42
<=> ! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
tff(f412,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X10: int,X11: int] : ( bit0(X11) != bit1(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I49_J) ).
tff(f664,plain,
( ~ spl1_41
| spl1_40 ),
inference(avatar_split_clause,[],[f659,f655,f661]) ).
tff(f655,plain,
( spl1_40
<=> ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
tff(f659,plain,
( ~ ord_less_eq(real,power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),x),number_number_of(nat,bit0(bit1(pls)))),one_one(real))
| spl1_40 ),
inference(forward_demodulation,[],[f657,f344]) ).
tff(f657,plain,
( ~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real))
| spl1_40 ),
inference(avatar_component_clause,[],[f655]) ).
tff(f658,plain,
~ spl1_40,
inference(avatar_split_clause,[],[f285,f655]) ).
tff(f285,plain,
~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
inference(flattening,[],[f129]) ).
tff(f129,negated_conjecture,
~ ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
inference(negated_conjecture,[],[f128]) ).
tff(f128,conjecture,
ord_less_eq(real,times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,x,number_number_of(nat,bit0(bit1(pls))))),one_one(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f651,plain,
spl1_39,
inference(avatar_split_clause,[],[f339,f649]) ).
tff(f649,plain,
( spl1_39
<=> ! [X0: int] : ( pls != bit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
tff(f339,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X10: int] : ( pls != bit1(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I39_J) ).
tff(f647,plain,
spl1_38,
inference(avatar_split_clause,[],[f337,f645]) ).
tff(f645,plain,
( spl1_38
<=> ! [X0: int] : ( min != bit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
tff(f337,plain,
! [X0: int] : ( min != bit0(X0) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: int] : ( min != bit0(X0) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X11: int] : ( min != bit0(X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_rel__simps_I45_J) ).
tff(f643,plain,
spl1_37,
inference(avatar_split_clause,[],[f323,f640]) ).
tff(f640,plain,
( spl1_37
<=> ord_less_eq(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
tff(f323,plain,
ord_less_eq(int,pls,pls),
inference(cnf_transformation,[],[f33]) ).
tff(f33,axiom,
ord_less_eq(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I19_J) ).
tff(f638,plain,
spl1_36,
inference(avatar_split_clause,[],[f322,f635]) ).
tff(f635,plain,
( spl1_36
<=> ord_less_eq(int,min,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f322,plain,
ord_less_eq(int,min,pls),
inference(cnf_transformation,[],[f53]) ).
tff(f53,axiom,
ord_less_eq(int,min,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I23_J) ).
tff(f633,plain,
spl1_35,
inference(avatar_split_clause,[],[f321,f630]) ).
tff(f630,plain,
( spl1_35
<=> ord_less_eq(int,min,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f321,plain,
ord_less_eq(int,min,min),
inference(cnf_transformation,[],[f42]) ).
tff(f42,axiom,
ord_less_eq(int,min,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rel__simps_I24_J) ).
tff(f628,plain,
spl1_34,
inference(avatar_split_clause,[],[f320,f625]) ).
tff(f625,plain,
( spl1_34
<=> ( pls = bit0(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f320,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Bit0__Pls) ).
tff(f623,plain,
spl1_33,
inference(avatar_split_clause,[],[f319,f620]) ).
tff(f620,plain,
( spl1_33
<=> ( min = bit1(min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f319,plain,
min = bit1(min),
inference(cnf_transformation,[],[f37]) ).
tff(f37,axiom,
min = bit1(min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Bit1__Min) ).
tff(f618,plain,
~ spl1_32,
inference(avatar_split_clause,[],[f318,f615]) ).
tff(f615,plain,
( spl1_32
<=> ord_less_eq(int,pls,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f318,plain,
~ ord_less_eq(int,pls,min),
inference(cnf_transformation,[],[f54]) ).
tff(f54,axiom,
~ ord_less_eq(int,pls,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I20_J) ).
tff(f613,plain,
~ spl1_31,
inference(avatar_split_clause,[],[f316,f610]) ).
tff(f610,plain,
( spl1_31
<=> ( pls = min ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f316,plain,
pls != min,
inference(cnf_transformation,[],[f39]) ).
tff(f39,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rel__simps_I40_J) ).
tff(f608,plain,
spl1_30,
inference(avatar_split_clause,[],[f315,f605]) ).
tff(f315,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f603,plain,
spl1_29,
inference(avatar_split_clause,[],[f314,f600]) ).
tff(f314,plain,
comm_semiring_1(real),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
comm_semiring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
tff(f598,plain,
spl1_28,
inference(avatar_split_clause,[],[f313,f595]) ).
tff(f313,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
tff(f593,plain,
spl1_27,
inference(avatar_split_clause,[],[f312,f590]) ).
tff(f312,plain,
comm_semiring_1(complex),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
comm_semiring_1(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
tff(f588,plain,
spl1_26,
inference(avatar_split_clause,[],[f311,f585]) ).
tff(f311,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
tff(f583,plain,
spl1_25,
inference(avatar_split_clause,[],[f310,f580]) ).
tff(f310,plain,
monoid_mult(real),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
monoid_mult(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
tff(f578,plain,
spl1_24,
inference(avatar_split_clause,[],[f309,f575]) ).
tff(f309,plain,
monoid_mult(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
monoid_mult(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
tff(f573,plain,
spl1_23,
inference(avatar_split_clause,[],[f308,f570]) ).
tff(f308,plain,
monoid_mult(complex),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
monoid_mult(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
tff(f568,plain,
spl1_22,
inference(avatar_split_clause,[],[f307,f565]) ).
tff(f565,plain,
( spl1_22
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f307,plain,
number(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f563,plain,
spl1_21,
inference(avatar_split_clause,[],[f306,f560]) ).
tff(f560,plain,
( spl1_21
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f306,plain,
number_semiring(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f558,plain,
spl1_20,
inference(avatar_split_clause,[],[f305,f555]) ).
tff(f555,plain,
( spl1_20
<=> number_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f305,plain,
number_semiring(real),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
number_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
tff(f553,plain,
spl1_19,
inference(avatar_split_clause,[],[f304,f550]) ).
tff(f550,plain,
( spl1_19
<=> number(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f304,plain,
number(real),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
number(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
tff(f548,plain,
spl1_18,
inference(avatar_split_clause,[],[f303,f545]) ).
tff(f545,plain,
( spl1_18
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f303,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
number_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
tff(f543,plain,
spl1_17,
inference(avatar_split_clause,[],[f302,f540]) ).
tff(f540,plain,
( spl1_17
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f302,plain,
number(nat),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
number(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
tff(f538,plain,
spl1_16,
inference(avatar_split_clause,[],[f301,f535]) ).
tff(f535,plain,
( spl1_16
<=> number(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f301,plain,
number(complex),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
number(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
tff(f533,plain,
spl1_15,
inference(avatar_split_clause,[],[f300,f530]) ).
tff(f530,plain,
( spl1_15
<=> number_semiring(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f300,plain,
number_semiring(complex),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
number_semiring(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
tff(f528,plain,
spl1_14,
inference(avatar_split_clause,[],[f299,f525]) ).
tff(f525,plain,
( spl1_14
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f299,plain,
semiring_1(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f523,plain,
spl1_13,
inference(avatar_split_clause,[],[f298,f520]) ).
tff(f520,plain,
( spl1_13
<=> semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f298,plain,
semiring_1(real),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
semiring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
tff(f518,plain,
spl1_12,
inference(avatar_split_clause,[],[f297,f515]) ).
tff(f515,plain,
( spl1_12
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f297,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f513,plain,
spl1_11,
inference(avatar_split_clause,[],[f296,f510]) ).
tff(f510,plain,
( spl1_11
<=> semiring_1(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f296,plain,
semiring_1(complex),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
semiring_1(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
tff(f508,plain,
spl1_10,
inference(avatar_split_clause,[],[f295,f505]) ).
tff(f295,plain,
number_ring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f503,plain,
spl1_9,
inference(avatar_split_clause,[],[f294,f500]) ).
tff(f294,plain,
number_ring(real),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
number_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
tff(f498,plain,
spl1_8,
inference(avatar_split_clause,[],[f293,f495]) ).
tff(f293,plain,
number_ring(complex),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
number_ring(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
tff(f493,plain,
spl1_7,
inference(avatar_split_clause,[],[f292,f490]) ).
tff(f490,plain,
( spl1_7
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f292,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f488,plain,
spl1_6,
inference(avatar_split_clause,[],[f291,f485]) ).
tff(f485,plain,
( spl1_6
<=> ring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f291,plain,
ring_char_0(real),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
ring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
tff(f483,plain,
spl1_5,
inference(avatar_split_clause,[],[f290,f480]) ).
tff(f480,plain,
( spl1_5
<=> ring_char_0(complex) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f290,plain,
ring_char_0(complex),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
ring_char_0(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
tff(f478,plain,
spl1_4,
inference(avatar_split_clause,[],[f289,f475]) ).
tff(f289,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f473,plain,
spl1_3,
inference(avatar_split_clause,[],[f288,f470]) ).
tff(f288,plain,
linordered_idom(real),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
linordered_idom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
tff(f468,plain,
spl1_2,
inference(avatar_split_clause,[],[f287,f465]) ).
tff(f465,plain,
( spl1_2
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f287,plain,
pp(fTrue),
inference(cnf_transformation,[],[f127]) ).
tff(f127,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f463,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f286,f460]) ).
tff(f460,plain,
( spl1_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f286,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW498_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Apr 30 02:30:33 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % (4811)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.36 % (4818)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.36 % (4818)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.36 % (4814)WARNING: value z3 for option sas not known
% 0.20/0.37 % (4813)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (4812)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (4814)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37 % (4817)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.37 % (4816)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.37 % Exception at run slice level% Exception at run slice level
% 0.20/0.37
% 0.20/0.37 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37
% 0.20/0.37 % (4815)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % (4819)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.38 % (4820)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.39 % (4819)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % (4820)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (4821)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.39 % (4816)First to succeed.
% 0.20/0.40 % (4822)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.40 % (4816)Refutation found. Thanks to Tanya!
% 0.20/0.40 % SZS status Theorem for theBenchmark
% 0.20/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41 % (4816)------------------------------
% 0.20/0.41 % (4816)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.41 % (4816)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (4816)Memory used [KB]: 1430
% 0.20/0.41 % (4816)Time elapsed: 0.039 s
% 0.20/0.41 % (4816)Instructions burned: 64 (million)
% 0.20/0.41 % (4816)------------------------------
% 0.20/0.41 % (4816)------------------------------
% 0.20/0.41 % (4811)Success in time 0.062 s
%------------------------------------------------------------------------------