TSTP Solution File: NUM925_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925_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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:43:28 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 322
% Syntax : Number of formulae : 958 ( 312 unt; 34 typ; 0 def)
% Number of atoms : 2142 ( 634 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2086 ( 868 ~; 822 |; 82 &)
% ( 243 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 188 ( 186 usr; 171 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 990 ( 969 !; 0 ?; 990 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_8,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m1: int ).
tff(func_def_12,type,
n: nat ).
tff(func_def_13,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f2319,plain,
$false,
inference(avatar_sat_refutation,[],[f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f760,f765,f770,f775,f780,f785,f790,f795,f800,f805,f810,f815,f820,f825,f830,f835,f840,f845,f850,f855,f860,f865,f869,f873,f878,f882,f888,f894,f899,f906,f910,f914,f918,f930,f934,f938,f942,f946,f964,f969,f973,f977,f981,f985,f989,f994,f1016,f1020,f1024,f1028,f1032,f1036,f1044,f1061,f1065,f1069,f1073,f1089,f1093,f1098,f1105,f1111,f1120,f1128,f1132,f1136,f1140,f1144,f1172,f1182,f1186,f1190,f1194,f1198,f1202,f1206,f1210,f1214,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1267,f1357,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1445,f1449,f1453,f1457,f1461,f1465,f1480,f1485,f1489,f1493,f1524,f1528,f1550,f1555,f1559,f1563,f1567,f1590,f1594,f1598,f1699,f1703,f1726,f1730,f1737,f1764,f1769,f1778,f1796,f1802,f1806,f1810,f1820,f1827,f1831,f1835,f1839,f1927,f2091,f2095,f2131,f2141,f2145,f2213,f2264,f2268,f2284,f2288,f2292,f2296,f2318]) ).
tff(f2318,plain,
( spl0_40
| ~ spl0_69
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2214,f2138,f991,f837]) ).
tff(f837,plain,
( spl0_40
<=> ord_less(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f991,plain,
( spl0_69
<=> ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
tff(f2138,plain,
( spl0_162
<=> ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
tff(f2214,plain,
( ord_less(int,pls,pls)
| ~ spl0_69
| ~ spl0_162 ),
inference(superposition,[],[f993,f2140]) ).
tff(f2140,plain,
( ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f2138]) ).
tff(f993,plain,
( ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f991]) ).
tff(f2296,plain,
( spl0_170
| ~ spl0_47
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1075,f1059,f871,f2294]) ).
tff(f2294,plain,
( spl0_170
<=> ! [X0: int] :
( ord_less(int,X0,one_one(int))
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
tff(f871,plain,
( spl0_47
<=> ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f1059,plain,
( spl0_77
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
tff(f1075,plain,
( ! [X0: int] :
( ord_less(int,X0,one_one(int))
| ~ ord_less(int,X0,pls) )
| ~ spl0_47
| ~ spl0_77 ),
inference(superposition,[],[f1060,f872]) ).
tff(f872,plain,
( ! [X0: int] : ( plus_plus(int,pls,X0) = X0 )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f1060,plain,
( ! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1059]) ).
tff(f2292,plain,
( spl0_169
| ~ spl0_38
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1039,f1014,f827,f2290]) ).
tff(f2290,plain,
( spl0_169
<=> ! [X0: nat] : ( semiring_1_of_nat(int,X0) = number_number_of(int,semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
tff(f827,plain,
( spl0_38
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f1014,plain,
( spl0_70
<=> ! [X0: $tType,X1: nat] :
( ( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
tff(f1039,plain,
( ! [X0: nat] : ( semiring_1_of_nat(int,X0) = number_number_of(int,semiring_1_of_nat(int,X0)) )
| ~ spl0_38
| ~ spl0_70 ),
inference(resolution,[],[f1015,f829]) ).
tff(f829,plain,
( number_semiring(int)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f1015,plain,
( ! [X0: $tType,X1: nat] :
( ~ number_semiring(X0)
| ( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) ) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1014]) ).
tff(f2288,plain,
( spl0_168
| ~ spl0_37
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1038,f1014,f822,f2286]) ).
tff(f2286,plain,
( spl0_168
<=> ! [X0: nat] : ( semiring_1_of_nat(nat,X0) = number_number_of(nat,semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
tff(f822,plain,
( spl0_37
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f1038,plain,
( ! [X0: nat] : ( semiring_1_of_nat(nat,X0) = number_number_of(nat,semiring_1_of_nat(int,X0)) )
| ~ spl0_37
| ~ spl0_70 ),
inference(resolution,[],[f1015,f824]) ).
tff(f824,plain,
( number_semiring(nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f822]) ).
tff(f2284,plain,
( spl0_167
| ~ spl0_35
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1037,f1014,f812,f2282]) ).
tff(f2282,plain,
( spl0_167
<=> ! [X0: nat] : ( semiring_1_of_nat(real,X0) = number_number_of(real,semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
tff(f812,plain,
( spl0_35
<=> number_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f1037,plain,
( ! [X0: nat] : ( semiring_1_of_nat(real,X0) = number_number_of(real,semiring_1_of_nat(int,X0)) )
| ~ spl0_35
| ~ spl0_70 ),
inference(resolution,[],[f1015,f814]) ).
tff(f814,plain,
( number_semiring(real)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f812]) ).
tff(f2268,plain,
( spl0_166
| ~ spl0_39
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1005,f979,f832,f2266]) ).
tff(f2266,plain,
( spl0_166
<=> ! [X0: int] : ( one_one(int) = power_power(int,X0,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
tff(f832,plain,
( spl0_39
<=> power(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f979,plain,
( spl0_66
<=> ! [X0: $tType,X1: X0] :
( ( one_one(X0) = power_power(X0,X1,zero_zero(nat)) )
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
tff(f1005,plain,
( ! [X0: int] : ( one_one(int) = power_power(int,X0,zero_zero(nat)) )
| ~ spl0_39
| ~ spl0_66 ),
inference(resolution,[],[f980,f834]) ).
tff(f834,plain,
( power(int)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f832]) ).
tff(f980,plain,
( ! [X0: $tType,X1: X0] :
( ~ power(X0)
| ( one_one(X0) = power_power(X0,X1,zero_zero(nat)) ) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f979]) ).
tff(f2264,plain,
( spl0_165
| ~ spl0_36
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1004,f979,f817,f2262]) ).
tff(f2262,plain,
( spl0_165
<=> ! [X0: nat] : ( one_one(nat) = power_power(nat,X0,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
tff(f817,plain,
( spl0_36
<=> power(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f1004,plain,
( ! [X0: nat] : ( one_one(nat) = power_power(nat,X0,zero_zero(nat)) )
| ~ spl0_36
| ~ spl0_66 ),
inference(resolution,[],[f980,f819]) ).
tff(f819,plain,
( power(nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f817]) ).
tff(f2213,plain,
( spl0_164
| ~ spl0_34
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1003,f979,f807,f2211]) ).
tff(f2211,plain,
( spl0_164
<=> ! [X0: real] : ( one_one(real) = power_power(real,X0,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
tff(f807,plain,
( spl0_34
<=> power(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f1003,plain,
( ! [X0: real] : ( one_one(real) = power_power(real,X0,zero_zero(nat)) )
| ~ spl0_34
| ~ spl0_66 ),
inference(resolution,[],[f980,f809]) ).
tff(f809,plain,
( power(real)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f807]) ).
tff(f2145,plain,
( spl0_163
| ~ spl0_46
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f1123,f1109,f867,f2143]) ).
tff(f2143,plain,
( spl0_163
<=> ! [X0: int] : ( one_one(int) != plus_plus(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
tff(f867,plain,
( spl0_46
<=> ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f1109,plain,
( spl0_85
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
tff(f1123,plain,
( ! [X0: int] : ( one_one(int) != plus_plus(int,X0,X0) )
| ~ spl0_46
| ~ spl0_85 ),
inference(forward_demodulation,[],[f1121,f868]) ).
tff(f868,plain,
( ! [X0: int] : ( plus_plus(int,X0,pls) = X0 )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f867]) ).
tff(f1121,plain,
( ! [X0: int] : ( plus_plus(int,X0,X0) != plus_plus(int,one_one(int),pls) )
| ~ spl0_46
| ~ spl0_85 ),
inference(superposition,[],[f1110,f868]) ).
tff(f1110,plain,
( ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1109]) ).
tff(f2141,plain,
( spl0_162
| ~ spl0_53
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2134,f2129,f903,f2138]) ).
tff(f903,plain,
( spl0_53
<=> ( pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f2129,plain,
( spl0_161
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
tff(f2134,plain,
( ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls )
| ~ spl0_53
| ~ spl0_161 ),
inference(trivial_inequality_removal,[],[f2132]) ).
tff(f2132,plain,
( ( pls != pls )
| ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls )
| ~ spl0_53
| ~ spl0_161 ),
inference(superposition,[],[f2130,f905]) ).
tff(f905,plain,
( ( pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f903]) ).
tff(f2130,plain,
( ! [X0: int] :
( ( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( pls = X0 ) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2129]) ).
tff(f2131,plain,
( ~ spl0_10
| spl0_161
| ~ spl0_41
| ~ spl0_47
| ~ spl0_53
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2064,f1833,f903,f871,f842,f2129,f687]) ).
tff(f687,plain,
( spl0_10
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f842,plain,
( spl0_41
<=> ( zero_zero(int) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f1833,plain,
( spl0_156
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
tff(f2064,plain,
( ! [X0: int] :
( ( pls = X0 )
| ( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ linordered_idom(int) )
| ~ spl0_41
| ~ spl0_47
| ~ spl0_53
| ~ spl0_156 ),
inference(forward_demodulation,[],[f2063,f844]) ).
tff(f844,plain,
( ( zero_zero(int) = pls )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f842]) ).
tff(f2063,plain,
( ! [X0: int] :
( ( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( zero_zero(int) = X0 )
| ~ linordered_idom(int) )
| ~ spl0_41
| ~ spl0_47
| ~ spl0_53
| ~ spl0_156 ),
inference(forward_demodulation,[],[f2062,f844]) ).
tff(f2062,plain,
( ! [X0: int] :
( ( zero_zero(int) != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( zero_zero(int) = X0 )
| ~ linordered_idom(int) )
| ~ spl0_47
| ~ spl0_53
| ~ spl0_156 ),
inference(forward_demodulation,[],[f2058,f872]) ).
tff(f2058,plain,
( ! [X0: int] :
( ( zero_zero(int) != plus_plus(int,pls,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(int) = X0 )
| ~ linordered_idom(int) )
| ~ spl0_53
| ~ spl0_156 ),
inference(superposition,[],[f1834,f905]) ).
tff(f1834,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1833]) ).
tff(f2095,plain,
spl0_160,
inference(avatar_split_clause,[],[f596,f2093]) ).
tff(f2093,plain,
( spl0_160
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
tff(f596,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f503,f490]) ).
tff(f490,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
inference(definition_unfolding,[],[f357,f363,f365]) ).
tff(f365,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X5: int] : ( bit1(X5) = plus_plus(int,plus_plus(int,one_one(int),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Bit1__def) ).
tff(f363,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X5: int] : ( bit0(X5) = plus_plus(int,X5,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Bit0__def) ).
tff(f357,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nat__1__add__1) ).
tff(f503,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f380,f363,f365,f363,f365]) ).
tff(f380,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
& ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
& ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0,X8: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X7,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X7 )
| ( zero_zero(X0) != X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_sum__power2__gt__zero__iff) ).
tff(f2091,plain,
spl0_159,
inference(avatar_split_clause,[],[f595,f2089]) ).
tff(f2089,plain,
( spl0_159
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
tff(f595,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f502,f490]) ).
tff(f502,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f381,f363,f365,f363,f365]) ).
tff(f381,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f1927,plain,
( spl0_158
| ~ spl0_67
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1601,f1552,f983,f1925]) ).
tff(f1925,plain,
( spl0_158
<=> ! [X0: nat] :
( ( pls != semiring_1_of_nat(int,X0) )
| ( plus_plus(nat,one_one(nat),n) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
tff(f983,plain,
( spl0_67
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
tff(f1552,plain,
( spl0_134
<=> ( pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
tff(f1601,plain,
( ! [X0: nat] :
( ( pls != semiring_1_of_nat(int,X0) )
| ( plus_plus(nat,one_one(nat),n) = X0 ) )
| ~ spl0_67
| ~ spl0_134 ),
inference(superposition,[],[f984,f1554]) ).
tff(f1554,plain,
( ( pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1552]) ).
tff(f984,plain,
( ! [X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) )
| ( X0 = X1 ) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f1839,plain,
spl0_157,
inference(avatar_split_clause,[],[f594,f1837]) ).
tff(f1837,plain,
( spl0_157
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
tff(f594,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f501,f490]) ).
tff(f501,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f376,f363,f365,f363,f365]) ).
tff(f376,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0,X8: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X7,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X7 )
& ( zero_zero(X0) = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__power2__eq__zero__iff) ).
tff(f1835,plain,
spl0_156,
inference(avatar_split_clause,[],[f593,f1833]) ).
tff(f593,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f500,f490]) ).
tff(f500,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f377,f363,f365,f363,f365]) ).
tff(f377,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f1831,plain,
spl0_155,
inference(avatar_split_clause,[],[f538,f1829]) ).
tff(f1829,plain,
( spl0_155
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X1,X0)),plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
tff(f538,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X1,X0)),plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ),
inference(definition_unfolding,[],[f450,f365,f363,f365]) ).
tff(f450,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X4: int,X5: int] : ( plus_plus(int,bit0(X5),bit1(X4)) = bit1(plus_plus(int,X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add__Bit0__Bit1) ).
tff(f1827,plain,
spl0_154,
inference(avatar_split_clause,[],[f536,f1825]) ).
tff(f1825,plain,
( spl0_154
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X1,X0)),plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
tff(f536,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X1,X0)),plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f448,f365,f365,f363]) ).
tff(f448,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X4: int,X5: int] : ( bit1(plus_plus(int,X5,X4)) = plus_plus(int,bit1(X5),bit0(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit1__Bit0) ).
tff(f1820,plain,
spl0_153,
inference(avatar_split_clause,[],[f597,f1818]) ).
tff(f1818,plain,
( spl0_153
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
tff(f597,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))))
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f564,f490]) ).
tff(f564,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f563]) ).
tff(f563,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f504]) ).
tff(f504,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f379,f363,f365,f363,f365]) ).
tff(f379,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f1810,plain,
spl0_152,
inference(avatar_split_clause,[],[f640,f1808]) ).
tff(f1808,plain,
( spl0_152
<=> ! [X0: real,X1: real] :
( ( zero_zero(real) != plus_plus(real,power_power(real,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,X0,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(real) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
tff(f640,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) != plus_plus(real,power_power(real,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,X0,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(real) = X1 ) ),
inference(forward_demodulation,[],[f557,f490]) ).
tff(f557,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = X1 )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) ) ),
inference(definition_unfolding,[],[f481,f363,f365,f363,f365]) ).
tff(f481,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = X1 )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: real,X1: real] :
( ( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(real) != X0 )
| ( zero_zero(real) != X1 ) )
& ( ( ( zero_zero(real) = X0 )
& ( zero_zero(real) = X1 ) )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ) ) ),
inference(flattening,[],[f299]) ).
tff(f299,plain,
! [X0: real,X1: real] :
( ( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(real) != X0 )
| ( zero_zero(real) != X1 ) )
& ( ( ( zero_zero(real) = X0 )
& ( zero_zero(real) = X1 ) )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ) ) ),
inference(nnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(real) = X0 )
& ( zero_zero(real) = X1 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X7: real,X8: real] :
( ( plus_plus(real,power_power(real,X8,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X7,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(real) )
<=> ( ( zero_zero(real) = X7 )
& ( zero_zero(real) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_realpow__two__sum__zero__iff) ).
tff(f1806,plain,
spl0_151,
inference(avatar_split_clause,[],[f639,f1804]) ).
tff(f1804,plain,
( spl0_151
<=> ! [X0: real,X1: real] :
( ( zero_zero(real) != plus_plus(real,power_power(real,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,X0,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(real) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
tff(f639,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) != plus_plus(real,power_power(real,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,X0,plus_plus(nat,one_one(nat),one_one(nat)))) )
| ( zero_zero(real) = X0 ) ),
inference(forward_demodulation,[],[f556,f490]) ).
tff(f556,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = X0 )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) ) ),
inference(definition_unfolding,[],[f482,f363,f365,f363,f365]) ).
tff(f482,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = X0 )
| ( zero_zero(real) != plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f1802,plain,
spl0_150,
inference(avatar_split_clause,[],[f592,f1800]) ).
tff(f1800,plain,
( spl0_150
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
tff(f592,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))) )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f562,f490]) ).
tff(f562,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f561]) ).
tff(f561,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f499]) ).
tff(f499,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f378,f363,f365,f363,f365]) ).
tff(f378,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f1796,plain,
spl0_149,
inference(avatar_split_clause,[],[f490,f1793]) ).
tff(f1793,plain,
( spl0_149
<=> ( plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
tff(f1778,plain,
spl0_148,
inference(avatar_split_clause,[],[f591,f1776]) ).
tff(f1776,plain,
( spl0_148
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
tff(f591,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f498,f490]) ).
tff(f498,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f375,f363,f365,f363,f365]) ).
tff(f375,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X21: X0,X22: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X22,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X21,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_not__sum__power2__lt__zero) ).
tff(f1769,plain,
spl0_147,
inference(avatar_split_clause,[],[f638,f1766]) ).
tff(f1766,plain,
( spl0_147
<=> ( zero_zero(real) = plus_plus(real,power_power(real,zero_zero(real),plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,zero_zero(real),plus_plus(nat,one_one(nat),one_one(nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
tff(f638,plain,
zero_zero(real) = plus_plus(real,power_power(real,zero_zero(real),plus_plus(nat,one_one(nat),one_one(nat))),power_power(real,zero_zero(real),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f579,f490]) ).
tff(f579,plain,
zero_zero(real) = plus_plus(real,power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(equality_resolution,[],[f578]) ).
tff(f578,plain,
! [X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ( zero_zero(real) != X1 ) ),
inference(equality_resolution,[],[f555]) ).
tff(f555,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))) )
| ( zero_zero(real) != X0 )
| ( zero_zero(real) != X1 ) ),
inference(definition_unfolding,[],[f483,f363,f365,f363,f365]) ).
tff(f483,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(real) != X0 )
| ( zero_zero(real) != X1 ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f1764,plain,
spl0_146,
inference(avatar_split_clause,[],[f511,f1762]) ).
tff(f1762,plain,
( spl0_146
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),X1),X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
tff(f511,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),X1),X1)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f392,f365]) ).
tff(f392,plain,
! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ! [X1: int] : ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int] : ( number_number_of(X0,bit1(X2)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X2)),number_number_of(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_number__of__Bit1) ).
tff(f1737,plain,
( spl0_145
| ~ spl0_61
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1608,f1552,f944,f1734]) ).
tff(f1734,plain,
( spl0_145
<=> ( zero_zero(nat) = plus_plus(nat,one_one(nat),n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
tff(f944,plain,
( spl0_61
<=> ! [X0: nat] :
( ( pls != semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
tff(f1608,plain,
( ( zero_zero(nat) = plus_plus(nat,one_one(nat),n) )
| ~ spl0_61
| ~ spl0_134 ),
inference(trivial_inequality_removal,[],[f1600]) ).
tff(f1600,plain,
( ( pls != pls )
| ( zero_zero(nat) = plus_plus(nat,one_one(nat),n) )
| ~ spl0_61
| ~ spl0_134 ),
inference(superposition,[],[f945,f1554]) ).
tff(f945,plain,
( ! [X0: nat] :
( ( pls != semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) = X0 ) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f944]) ).
tff(f1730,plain,
spl0_144,
inference(avatar_split_clause,[],[f457,f1728]) ).
tff(f1728,plain,
( spl0_144
<=> ! [X0: int,X1: int] :
( ( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0)) )
| ord_less(int,X0,pls)
| ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
tff(f457,plain,
! [X0: int,X1: int] :
( ( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0)) )
| ord_less(int,X0,pls)
| ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: int,X1: int] :
( ( ( ( ( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0)) )
| ord_less(int,X0,pls) )
& ( ( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X0,pls) ) )
| ord_less(int,X1,pls) )
& ( ( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X1,pls) ) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: int,X1: int] :
( ( ~ ord_less(int,X1,pls)
=> ( ( ~ ord_less(int,X0,pls)
=> ( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0)) ) )
& ( ord_less(int,X0,pls)
=> ( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ) ) )
& ( ord_less(int,X1,pls)
=> ( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X12: int,X3: int] :
( ( ~ ord_less(int,X3,pls)
=> ( ( ~ ord_less(int,X12,pls)
=> ( plus_plus(nat,number_number_of(nat,X3),number_number_of(nat,X12)) = number_number_of(nat,plus_plus(int,X3,X12)) ) )
& ( ord_less(int,X12,pls)
=> ( number_number_of(nat,X3) = plus_plus(nat,number_number_of(nat,X3),number_number_of(nat,X12)) ) ) ) )
& ( ord_less(int,X3,pls)
=> ( number_number_of(nat,X12) = plus_plus(nat,number_number_of(nat,X3),number_number_of(nat,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__nat__number__of) ).
tff(f1726,plain,
spl0_143,
inference(avatar_split_clause,[],[f395,f1724]) ).
tff(f1724,plain,
( spl0_143
<=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
tff(f395,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X6: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X6)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__number__of__left) ).
tff(f1703,plain,
spl0_142,
inference(avatar_split_clause,[],[f552,f1701]) ).
tff(f1701,plain,
( spl0_142
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
tff(f552,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0)) ),
inference(definition_unfolding,[],[f470,f365,f365]) ).
tff(f470,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X16: int,X17: int] :
( ord_less(int,bit1(X17),bit1(X16))
<=> ord_less(int,X17,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__int__code_I16_J) ).
tff(f1699,plain,
spl0_141,
inference(avatar_split_clause,[],[f551,f1697]) ).
tff(f1697,plain,
( spl0_141
<=> ! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
tff(f551,plain,
! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,plus_plus(int,one_one(int),X0),X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f471,f365,f365]) ).
tff(f471,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f1598,plain,
spl0_140,
inference(avatar_split_clause,[],[f537,f1596]) ).
tff(f1596,plain,
( spl0_140
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
tff(f537,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f449,f363,f363,f363]) ).
tff(f449,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X4: int,X5: int] : ( plus_plus(int,bit0(X5),bit0(X4)) = bit0(plus_plus(int,X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__Bit0__Bit0) ).
tff(f1594,plain,
spl0_139,
inference(avatar_split_clause,[],[f510,f1592]) ).
tff(f1592,plain,
( spl0_139
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
tff(f510,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f391,f363]) ).
tff(f391,plain,
! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int] : ( number_number_of(X0,bit0(X2)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X2)),number_number_of(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_number__of__Bit0) ).
tff(f1590,plain,
spl0_138,
inference(avatar_split_clause,[],[f484,f1588]) ).
tff(f1588,plain,
( spl0_138
<=> ! [X2: nat,X0: int,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
tff(f484,plain,
! [X2: nat,X0: int,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: int,X1: nat,X2: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X6: int,X13: nat,X14: nat] : ( plus_plus(int,semiring_1_of_nat(int,X14),plus_plus(int,semiring_1_of_nat(int,X13),X6)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X14,X13)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__int__left) ).
tff(f1567,plain,
spl0_137,
inference(avatar_split_clause,[],[f568,f1565]) ).
tff(f1565,plain,
( spl0_137
<=> ! [X0: $tType,X1: nat] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
| ( zero_zero(nat) = X1 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
tff(f568,plain,
! [X0: $tType,X1: nat] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
| ( zero_zero(nat) = X1 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(equality_resolution,[],[f424]) ).
tff(f424,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X15: nat,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,X15) )
<=> ( ( zero_zero(nat) != X15 )
& ( zero_zero(X0) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_power__eq__0__iff) ).
tff(f1563,plain,
spl0_136,
inference(avatar_split_clause,[],[f542,f1561]) ).
tff(f1561,plain,
( spl0_136
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,plus_plus(int,one_one(int),X1),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
tff(f542,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,plus_plus(int,one_one(int),X1),X1) ) ),
inference(definition_unfolding,[],[f460,f365,f365]) ).
tff(f460,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: int,X1: int] :
( ( ( bit1(X0) = bit1(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int] :
( ( bit1(X0) = bit1(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X9: int,X10: int] :
( ( bit1(X10) = bit1(X9) )
<=> ( X9 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).
tff(f1559,plain,
spl0_135,
inference(avatar_split_clause,[],[f456,f1557]) ).
tff(f1557,plain,
( spl0_135
<=> ! [X0: int,X1: int] :
( ( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X0,pls)
| ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
tff(f456,plain,
! [X0: int,X1: int] :
( ( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X0,pls)
| ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f257]) ).
tff(f1555,plain,
( ~ spl0_7
| spl0_134
| ~ spl0_41
| ~ spl0_50
| ~ spl0_53
| ~ spl0_99
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1518,f1491,f1204,f903,f885,f842,f1552,f672]) ).
tff(f672,plain,
( spl0_7
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f885,plain,
( spl0_50
<=> ( one_one(int) = semiring_1_of_nat(int,one_one(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f1204,plain,
( spl0_99
<=> ! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
tff(f1491,plain,
( spl0_130
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( zero_zero(X0) = X1 )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
tff(f1518,plain,
( ( pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)) )
| ~ ring_11004092258visors(int)
| ~ spl0_41
| ~ spl0_50
| ~ spl0_53
| ~ spl0_99
| ~ spl0_130 ),
inference(forward_demodulation,[],[f1517,f844]) ).
tff(f1517,plain,
( ( zero_zero(int) = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)) )
| ~ ring_11004092258visors(int)
| ~ spl0_41
| ~ spl0_50
| ~ spl0_53
| ~ spl0_99
| ~ spl0_130 ),
inference(forward_demodulation,[],[f1516,f1280]) ).
tff(f1280,plain,
( ! [X0: nat] : ( semiring_1_of_nat(int,plus_plus(nat,one_one(nat),X0)) = plus_plus(int,one_one(int),semiring_1_of_nat(int,X0)) )
| ~ spl0_50
| ~ spl0_99 ),
inference(superposition,[],[f1205,f887]) ).
tff(f887,plain,
( ( one_one(int) = semiring_1_of_nat(int,one_one(nat)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f885]) ).
tff(f1205,plain,
( ! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1204]) ).
tff(f1516,plain,
( ( zero_zero(int) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) )
| ~ ring_11004092258visors(int)
| ~ spl0_41
| ~ spl0_53
| ~ spl0_130 ),
inference(trivial_inequality_removal,[],[f1515]) ).
tff(f1515,plain,
( ( pls != pls )
| ( zero_zero(int) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) )
| ~ ring_11004092258visors(int)
| ~ spl0_41
| ~ spl0_53
| ~ spl0_130 ),
inference(forward_demodulation,[],[f1513,f844]) ).
tff(f1513,plain,
( ( zero_zero(int) != pls )
| ( zero_zero(int) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) )
| ~ ring_11004092258visors(int)
| ~ spl0_53
| ~ spl0_130 ),
inference(superposition,[],[f1492,f905]) ).
tff(f1492,plain,
( ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( zero_zero(X0) = X1 )
| ~ ring_11004092258visors(X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1491]) ).
tff(f1550,plain,
spl0_133,
inference(avatar_split_clause,[],[f421,f1548]) ).
tff(f1548,plain,
( spl0_133
<=> ! [X0: $tType,X1: int] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) )
| ~ semiring_0(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
tff(f421,plain,
! [X0: $tType,X1: int] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) )
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) ) )
& ( ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) != number_number_of(nat,X1) ) ) )
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) ) )
& ( ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
| ( zero_zero(nat) != number_number_of(nat,X1) ) ) )
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( ( semiring_0(X0)
& power(X0) )
=> ! [X1: int] :
( ( ( zero_zero(nat) != number_number_of(nat,X1) )
=> ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) ) )
& ( ( zero_zero(nat) = number_number_of(nat,X1) )
=> ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( ( semiring_0(X0)
& power(X0) )
=> ! [X2: int] :
( ( ( number_number_of(nat,X2) != zero_zero(nat) )
=> ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X2)) ) )
& ( ( number_number_of(nat,X2) = zero_zero(nat) )
=> ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_power__0__left__number__of) ).
tff(f1528,plain,
spl0_132,
inference(avatar_split_clause,[],[f589,f1526]) ).
tff(f1526,plain,
( spl0_132
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
tff(f589,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f496,f490]) ).
tff(f496,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f374,f363,f365]) ).
tff(f374,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 ) )
& ( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) != X1 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zero__less__power2) ).
tff(f1524,plain,
spl0_131,
inference(avatar_split_clause,[],[f422,f1522]) ).
tff(f1522,plain,
( spl0_131
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
tff(f422,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1493,plain,
spl0_130,
inference(avatar_split_clause,[],[f587,f1491]) ).
tff(f587,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))) )
| ( zero_zero(X0) = X1 )
| ~ ring_11004092258visors(X0) ),
inference(forward_demodulation,[],[f494,f490]) ).
tff(f494,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f368,f363,f365]) ).
tff(f368,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ) )
| ~ ring_11004092258visors(X0) ),
inference(nnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
<=> ( zero_zero(X0) = X1 ) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
<=> ( zero_zero(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__eq__power2) ).
tff(f1489,plain,
spl0_129,
inference(avatar_split_clause,[],[f548,f1487]) ).
tff(f1487,plain,
( spl0_129
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
tff(f548,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f466,f365,f363]) ).
tff(f466,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X16: int,X17: int] :
( ord_less(int,bit1(X17),bit0(X16))
<=> ord_less(int,X17,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__int__code_I15_J) ).
tff(f1485,plain,
( ~ spl0_128
| ~ spl0_46
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f1011,f987,f867,f1482]) ).
tff(f1482,plain,
( spl0_128
<=> ( pls = plus_plus(int,one_one(int),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
tff(f987,plain,
( spl0_68
<=> ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
tff(f1011,plain,
( ( pls != plus_plus(int,one_one(int),pls) )
| ~ spl0_46
| ~ spl0_68 ),
inference(superposition,[],[f988,f868]) ).
tff(f988,plain,
( ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f987]) ).
tff(f1480,plain,
spl0_127,
inference(avatar_split_clause,[],[f547,f1478]) ).
tff(f1478,plain,
( spl0_127
<=> ! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
tff(f547,plain,
! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X1),X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f467,f365,f363]) ).
tff(f467,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f291]) ).
tff(f1465,plain,
spl0_126,
inference(avatar_split_clause,[],[f613,f1463]) ).
tff(f1463,plain,
( spl0_126
<=> ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
tff(f613,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f612,f360]) ).
tff(f360,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X5: int] : ( plus_plus(int,X5,pls) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__Pls__right) ).
tff(f612,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))) )
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f515,f360]) ).
tff(f515,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))) )
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f405,f363,f365]) ).
tff(f405,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_semiring__one__add__one__is__two) ).
tff(f1461,plain,
spl0_125,
inference(avatar_split_clause,[],[f607,f1459]) ).
tff(f1459,plain,
( spl0_125
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,one_one(int))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
tff(f607,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,one_one(int))) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f606,f360]) ).
tff(f606,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,plus_plus(int,one_one(int),pls))) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f509,f360]) ).
tff(f509,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f390,f365]) ).
tff(f390,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X3: int] : ( plus_plus(X0,number_number_of(X0,X3),one_one(X0)) = number_number_of(X0,plus_plus(int,X3,bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I3_J) ).
tff(f1457,plain,
spl0_124,
inference(avatar_split_clause,[],[f605,f1455]) ).
tff(f1455,plain,
( spl0_124
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,one_one(int),X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
tff(f605,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,one_one(int),X1)) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f604,f360]) ).
tff(f604,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),X1)) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f508,f360]) ).
tff(f508,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f389,f365]) ).
tff(f389,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: int] : ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int] : ( plus_plus(X0,one_one(X0),number_number_of(X0,X2)) = number_number_of(X0,plus_plus(int,bit1(pls),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__special_I2_J) ).
tff(f1453,plain,
spl0_123,
inference(avatar_split_clause,[],[f603,f1451]) ).
tff(f1451,plain,
( spl0_123
<=> ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
tff(f603,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f602,f360]) ).
tff(f602,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f507,f360]) ).
tff(f507,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f386,f363,f365]) ).
tff(f386,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_one__add__one__is__two) ).
tff(f1449,plain,
( spl0_122
| ~ spl0_11
| ~ spl0_54
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1001,f975,f908,f692,f1447]) ).
tff(f1447,plain,
( spl0_122
<=> ! [X0: real] : ( plus_plus(real,zero_zero(real),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
tff(f692,plain,
( spl0_11
<=> number_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f908,plain,
( spl0_54
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
tff(f975,plain,
( spl0_65
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
tff(f1001,plain,
( ! [X0: real] : ( plus_plus(real,zero_zero(real),X0) = X0 )
| ~ spl0_11
| ~ spl0_54
| ~ spl0_65 ),
inference(forward_demodulation,[],[f999,f919]) ).
tff(f919,plain,
( ( zero_zero(real) = number_number_of(real,pls) )
| ~ spl0_11
| ~ spl0_54 ),
inference(resolution,[],[f909,f694]) ).
tff(f694,plain,
( number_ring(real)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f692]) ).
tff(f909,plain,
( ! [X0: $tType] :
( ~ number_ring(X0)
| ( zero_zero(X0) = number_number_of(X0,pls) ) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f908]) ).
tff(f999,plain,
( ! [X0: real] : ( plus_plus(real,number_number_of(real,pls),X0) = X0 )
| ~ spl0_11
| ~ spl0_65 ),
inference(resolution,[],[f976,f694]) ).
tff(f976,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f975]) ).
tff(f1445,plain,
spl0_121,
inference(avatar_split_clause,[],[f393,f1443]) ).
tff(f1443,plain,
( spl0_121
<=> ! [X0: $tType,X2: int,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
tff(f393,plain,
! [X0: $tType,X2: int,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),number_number_of(X0,X2)) = number_number_of(X0,plus_plus(int,X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_number__of__add) ).
tff(f1401,plain,
( spl0_120
| ~ spl0_11
| ~ spl0_54
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f997,f971,f908,f692,f1399]) ).
tff(f1399,plain,
( spl0_120
<=> ! [X0: real] : ( plus_plus(real,X0,zero_zero(real)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
tff(f971,plain,
( spl0_64
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
tff(f997,plain,
( ! [X0: real] : ( plus_plus(real,X0,zero_zero(real)) = X0 )
| ~ spl0_11
| ~ spl0_54
| ~ spl0_64 ),
inference(forward_demodulation,[],[f995,f919]) ).
tff(f995,plain,
( ! [X0: real] : ( plus_plus(real,X0,number_number_of(real,pls)) = X0 )
| ~ spl0_11
| ~ spl0_64 ),
inference(resolution,[],[f972,f694]) ).
tff(f972,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f971]) ).
tff(f1397,plain,
spl0_119,
inference(avatar_split_clause,[],[f621,f1395]) ).
tff(f1395,plain,
( spl0_119
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,one_one(int))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
tff(f621,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,one_one(int))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f620,f360]) ).
tff(f620,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,plus_plus(int,one_one(int),pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f519,f360]) ).
tff(f519,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f414,f365]) ).
tff(f414,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls)) )
& ( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X8: int] :
( ord_less(X0,number_number_of(X0,X8),one_one(X0))
<=> ord_less(int,X8,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_less__special_I4_J) ).
tff(f1393,plain,
spl0_118,
inference(avatar_split_clause,[],[f619,f1391]) ).
tff(f1391,plain,
( spl0_118
<=> ! [X0: $tType,X1: int] :
( ~ ord_less(int,X1,one_one(int))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
tff(f619,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(int,X1,one_one(int))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f618,f360]) ).
tff(f618,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(int,X1,plus_plus(int,one_one(int),pls))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f518,f360]) ).
tff(f518,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f415,f365]) ).
tff(f415,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f1389,plain,
spl0_117,
inference(avatar_split_clause,[],[f617,f1387]) ).
tff(f1387,plain,
( spl0_117
<=> ! [X0: $tType,X1: int] :
( ord_less(int,one_one(int),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
tff(f617,plain,
! [X0: $tType,X1: int] :
( ord_less(int,one_one(int),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f616,f360]) ).
tff(f616,plain,
! [X0: $tType,X1: int] :
( ord_less(int,plus_plus(int,one_one(int),pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f517,f360]) ).
tff(f517,plain,
! [X0: $tType,X1: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f410,f365]) ).
tff(f410,plain,
! [X0: $tType,X1: int] :
( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1) )
& ( ord_less(int,bit1(pls),X1)
| ~ ord_less(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(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X7: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X7))
<=> ord_less(int,bit1(pls),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_less__special_I2_J) ).
tff(f1385,plain,
spl0_116,
inference(avatar_split_clause,[],[f615,f1383]) ).
tff(f1383,plain,
( spl0_116
<=> ! [X0: $tType,X1: int] :
( ~ ord_less(int,one_one(int),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
tff(f615,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(int,one_one(int),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f614,f360]) ).
tff(f614,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(int,plus_plus(int,one_one(int),pls),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f516,f360]) ).
tff(f516,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f411,f365]) ).
tff(f411,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f1381,plain,
spl0_115,
inference(avatar_split_clause,[],[f590,f1379]) ).
tff(f1379,plain,
( spl0_115
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
tff(f590,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))))
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f560,f490]) ).
tff(f560,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f497]) ).
tff(f497,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f373,f363,f365]) ).
tff(f373,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f1377,plain,
spl0_114,
inference(avatar_split_clause,[],[f569,f1375]) ).
tff(f1375,plain,
( spl0_114
<=> ! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
tff(f569,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(equality_resolution,[],[f423]) ).
tff(f423,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(nat) != X1 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1373,plain,
spl0_113,
inference(avatar_split_clause,[],[f455,f1371]) ).
tff(f1371,plain,
( spl0_113
<=> ! [X0: int,X1: int] :
( ( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
tff(f455,plain,
! [X0: int,X1: int] :
( ( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) )
| ~ ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f257]) ).
tff(f1369,plain,
spl0_112,
inference(avatar_split_clause,[],[f419,f1367]) ).
tff(f1367,plain,
( spl0_112
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
tff(f419,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1) )
& ( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X7: int,X8: int] :
( ord_less(X0,number_number_of(X0,X8),number_number_of(X0,X7))
<=> ord_less(int,X8,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__number__of) ).
tff(f1365,plain,
spl0_111,
inference(avatar_split_clause,[],[f418,f1363]) ).
tff(f1363,plain,
( spl0_111
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
tff(f418,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f1357,plain,
( spl0_110
| ~ spl0_37
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f956,f940,f822,f1354]) ).
tff(f1354,plain,
( spl0_110
<=> ( one_one(nat) = number_number_of(nat,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
tff(f940,plain,
( spl0_60
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
tff(f956,plain,
( ( one_one(nat) = number_number_of(nat,one_one(int)) )
| ~ spl0_37
| ~ spl0_60 ),
inference(resolution,[],[f941,f824]) ).
tff(f941,plain,
( ! [X0: $tType] :
( ~ number_semiring(X0)
| ( one_one(X0) = number_number_of(X0,one_one(int)) ) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f940]) ).
tff(f1267,plain,
( spl0_109
| ~ spl0_12
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f954,f936,f697,f1264]) ).
tff(f1264,plain,
( spl0_109
<=> ( one_one(int) = number_number_of(int,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
tff(f697,plain,
( spl0_12
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f936,plain,
( spl0_59
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
tff(f954,plain,
( ( one_one(int) = number_number_of(int,one_one(int)) )
| ~ spl0_12
| ~ spl0_59 ),
inference(resolution,[],[f937,f699]) ).
tff(f699,plain,
( number_ring(int)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f697]) ).
tff(f937,plain,
( ! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,one_one(int)) ) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f936]) ).
tff(f1243,plain,
spl0_108,
inference(avatar_split_clause,[],[f609,f1241]) ).
tff(f1241,plain,
( spl0_108
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
tff(f609,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f513,f490]) ).
tff(f513,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f402,f363,f365]) ).
tff(f402,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_zero__power2) ).
tff(f1239,plain,
spl0_107,
inference(avatar_split_clause,[],[f608,f1237]) ).
tff(f1237,plain,
( spl0_107
<=> ! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
tff(f608,plain,
! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f512,f490]) ).
tff(f512,plain,
! [X0: $tType] :
( ( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f401,f363,f365]) ).
tff(f401,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,[],[f232]) ).
tff(f232,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,[],[f3]) ).
tff(f3,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/sandbox2/benchmark/theBenchmark.p',fact_2_one__power2) ).
tff(f1235,plain,
spl0_106,
inference(avatar_split_clause,[],[f588,f1233]) ).
tff(f1233,plain,
( spl0_106
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
tff(f588,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f495,f490]) ).
tff(f495,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f370,f363,f365]) ).
tff(f370,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X20: X0] : ~ ord_less(X0,power_power(X0,X20,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_power2__less__0) ).
tff(f1231,plain,
spl0_105,
inference(avatar_split_clause,[],[f586,f1229]) ).
tff(f1229,plain,
( spl0_105
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
tff(f586,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ ring_11004092258visors(X0) ),
inference(forward_demodulation,[],[f559,f490]) ).
tff(f559,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(equality_resolution,[],[f493]) ).
tff(f493,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ( zero_zero(X0) != X1 )
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f369,f363,f365]) ).
tff(f369,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ( zero_zero(X0) != X1 )
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f1227,plain,
spl0_104,
inference(avatar_split_clause,[],[f529,f1225]) ).
tff(f1225,plain,
( spl0_104
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
tff(f529,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ),
inference(definition_unfolding,[],[f436,f365]) ).
tff(f436,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: int] :
( ( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) )
& ( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X10: int] :
( ord_less(int,bit1(X10),pls)
<=> ord_less(int,X10,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I12_J) ).
tff(f1223,plain,
spl0_103,
inference(avatar_split_clause,[],[f528,f1221]) ).
tff(f1221,plain,
( spl0_103
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
tff(f528,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f437,f365]) ).
tff(f437,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f282]) ).
tff(f1219,plain,
( spl0_102
| ~ spl0_11
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f953,f936,f692,f1216]) ).
tff(f1216,plain,
( spl0_102
<=> ( one_one(real) = number_number_of(real,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
tff(f953,plain,
( ( one_one(real) = number_number_of(real,one_one(int)) )
| ~ spl0_11
| ~ spl0_59 ),
inference(resolution,[],[f937,f694]) ).
tff(f1214,plain,
spl0_101,
inference(avatar_split_clause,[],[f476,f1212]) ).
tff(f1212,plain,
( spl0_101
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
tff(f476,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(flattening,[],[f296]) ).
tff(f296,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(nnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ( X0 = X1 )
| ord_less(int,X1,X0) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X19: int,X11: int] :
( ord_less(int,X11,plus_plus(int,X19,one_one(int)))
<=> ( ( X11 = X19 )
| ord_less(int,X11,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zless__add1__eq) ).
tff(f1210,plain,
spl0_100,
inference(avatar_split_clause,[],[f454,f1208]) ).
tff(f1208,plain,
( spl0_100
<=> ! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
tff(f454,plain,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X1),number_number_of(int,X0)) = number_number_of(int,plus_plus(int,X1,X0)) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X2: int,X3: int] : ( plus_plus(int,number_number_of(int,X3),number_number_of(int,X2)) = number_number_of(int,plus_plus(int,X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_plus__numeral__code_I9_J) ).
tff(f1206,plain,
spl0_99,
inference(avatar_split_clause,[],[f453,f1204]) ).
tff(f453,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X13: nat,X14: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X14,X13)) = plus_plus(int,semiring_1_of_nat(int,X14),semiring_1_of_nat(int,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__int) ).
tff(f1202,plain,
spl0_98,
inference(avatar_split_clause,[],[f417,f1200]) ).
tff(f1200,plain,
( spl0_98
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
tff(f417,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls) )
& ( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) )
| ~ 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(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X8: int] :
( ord_less(X0,number_number_of(X0,X8),zero_zero(X0))
<=> ord_less(int,X8,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_less__special_I3_J) ).
tff(f1198,plain,
spl0_97,
inference(avatar_split_clause,[],[f416,f1196]) ).
tff(f1196,plain,
( spl0_97
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
tff(f416,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f1194,plain,
spl0_96,
inference(avatar_split_clause,[],[f413,f1192]) ).
tff(f1192,plain,
( spl0_96
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
tff(f413,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1) )
& ( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X7: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X7))
<=> ord_less(int,pls,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_less__special_I1_J) ).
tff(f1190,plain,
spl0_95,
inference(avatar_split_clause,[],[f412,f1188]) ).
tff(f1188,plain,
( spl0_95
<=> ! [X0: $tType,X1: int] :
( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
tff(f412,plain,
! [X0: $tType,X1: int] :
( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f1186,plain,
spl0_94,
inference(avatar_split_clause,[],[f372,f1184]) ).
tff(f1184,plain,
( spl0_94
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
tff(f372,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0)) )
& ( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_even__less__0__iff) ).
tff(f1182,plain,
spl0_93,
inference(avatar_split_clause,[],[f371,f1180]) ).
tff(f1180,plain,
( spl0_93
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
tff(f371,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f1172,plain,
( spl0_92
| ~ spl0_32
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f948,f928,f797,f1169]) ).
tff(f1169,plain,
( spl0_92
<=> ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
tff(f797,plain,
( spl0_32
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f928,plain,
( spl0_57
<=> ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
tff(f948,plain,
( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
| ~ spl0_32
| ~ spl0_57 ),
inference(resolution,[],[f929,f799]) ).
tff(f799,plain,
( semiring_1(nat)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f797]) ).
tff(f929,plain,
( ! [X0: $tType] :
( ~ semiring_1(X0)
| ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) ) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f928]) ).
tff(f1144,plain,
spl0_91,
inference(avatar_split_clause,[],[f544,f1142]) ).
tff(f1142,plain,
( spl0_91
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
tff(f544,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f462,f363,f363]) ).
tff(f462,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X9: int,X10: int] :
( ord_less(int,bit0(X10),bit0(X9))
<=> ord_less(int,X10,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I14_J) ).
tff(f1140,plain,
spl0_90,
inference(avatar_split_clause,[],[f543,f1138]) ).
tff(f1138,plain,
( spl0_90
<=> ! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
tff(f543,plain,
! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f463,f363,f363]) ).
tff(f463,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1136,plain,
spl0_89,
inference(avatar_split_clause,[],[f408,f1134]) ).
tff(f1134,plain,
( spl0_89
<=> ! [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,[spl0_89])]) ).
tff(f408,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,[],[f268]) ).
tff(f268,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,[],[f240]) ).
tff(f240,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,[],[f239]) ).
tff(f239,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,[],[f166]) ).
tff(f166,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,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X7: int,X8: int] :
( ( number_number_of(X0,X8) = number_number_of(X0,X7) )
<=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_eq__number__of) ).
tff(f1132,plain,
spl0_88,
inference(avatar_split_clause,[],[f397,f1130]) ).
tff(f1130,plain,
( spl0_88
<=> ! [X0: $tType,X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
tff(f397,plain,
! [X0: $tType,X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1) )
& ( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ) )
| ~ linordered_semidom(X0) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X15: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X15))
<=> ord_less(nat,zero_zero(nat),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_of__nat__0__less__iff) ).
tff(f1128,plain,
spl0_87,
inference(avatar_split_clause,[],[f396,f1126]) ).
tff(f1126,plain,
( spl0_87
<=> ! [X0: $tType,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
tff(f396,plain,
! [X0: $tType,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f1120,plain,
( spl0_86
| ~ spl0_31
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f947,f928,f792,f1117]) ).
tff(f1117,plain,
( spl0_86
<=> ( zero_zero(real) = semiring_1_of_nat(real,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
tff(f792,plain,
( spl0_31
<=> semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f947,plain,
( ( zero_zero(real) = semiring_1_of_nat(real,zero_zero(nat)) )
| ~ spl0_31
| ~ spl0_57 ),
inference(resolution,[],[f929,f794]) ).
tff(f794,plain,
( semiring_1(real)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f792]) ).
tff(f1111,plain,
spl0_85,
inference(avatar_split_clause,[],[f534,f1109]) ).
tff(f534,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1) ),
inference(definition_unfolding,[],[f446,f365,f363]) ).
tff(f446,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X4: int,X5: int] : ( bit0(X5) != bit1(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
tff(f1105,plain,
spl0_84,
inference(avatar_split_clause,[],[f488,f1102]) ).
tff(f1102,plain,
( spl0_84
<=> ( one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
tff(f488,plain,
one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f353,f365]) ).
tff(f353,plain,
number_number_of(nat,bit1(pls)) = one_one(nat),
inference(cnf_transformation,[],[f61]) ).
tff(f61,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Numeral1__eq1__nat) ).
tff(f1098,plain,
spl0_83,
inference(avatar_split_clause,[],[f487,f1095]) ).
tff(f1095,plain,
( spl0_83
<=> ( one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
tff(f487,plain,
one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f351,f365]) ).
tff(f351,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f60]) ).
tff(f60,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_one__is__num__one) ).
tff(f1093,plain,
spl0_82,
inference(avatar_split_clause,[],[f451,f1091]) ).
tff(f1091,plain,
( spl0_82
<=> ! [X0: nat,X1: nat] : ( power_power(int,semiring_1_of_nat(int,X1),X0) = semiring_1_of_nat(int,power_power(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
tff(f451,plain,
! [X0: nat,X1: nat] : ( power_power(int,semiring_1_of_nat(int,X1),X0) = semiring_1_of_nat(int,power_power(nat,X1,X0)) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: nat,X1: nat] : ( power_power(int,semiring_1_of_nat(int,X1),X0) = semiring_1_of_nat(int,power_power(nat,X1,X0)) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X13: nat,X14: nat] : ( power_power(int,semiring_1_of_nat(int,X14),X13) = semiring_1_of_nat(int,power_power(nat,X14,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_int__power) ).
tff(f1089,plain,
spl0_81,
inference(avatar_split_clause,[],[f366,f1087]) ).
tff(f1087,plain,
( spl0_81
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
tff(f366,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_double__eq__0__iff) ).
tff(f1073,plain,
spl0_80,
inference(avatar_split_clause,[],[f540,f1071]) ).
tff(f1071,plain,
( spl0_80
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
tff(f540,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
inference(definition_unfolding,[],[f458,f363,f363]) ).
tff(f458,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: int,X1: int] :
( ( ( bit0(X0) = bit0(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: int,X1: int] :
( ( bit0(X0) = bit0(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X9: int,X10: int] :
( ( bit0(X10) = bit0(X9) )
<=> ( X9 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).
tff(f1069,plain,
spl0_79,
inference(avatar_split_clause,[],[f480,f1067]) ).
tff(f1067,plain,
( spl0_79
<=> ! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
tff(f480,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: int,X1: int] :
( ( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
inference(nnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X9: int,X10: int] :
( ord_less(int,number_number_of(int,X10),number_number_of(int,X9))
<=> ord_less(int,X10,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__number__of__int__code) ).
tff(f1065,plain,
spl0_78,
inference(avatar_split_clause,[],[f479,f1063]) ).
tff(f1063,plain,
( spl0_78
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
tff(f479,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1061,plain,
spl0_77,
inference(avatar_split_clause,[],[f477,f1059]) ).
tff(f477,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1044,plain,
( spl0_76
| ~ spl0_11
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f919,f908,f692,f1041]) ).
tff(f1041,plain,
( spl0_76
<=> ( zero_zero(real) = number_number_of(real,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
tff(f1036,plain,
spl0_75,
inference(avatar_split_clause,[],[f558,f1034]) ).
tff(f1034,plain,
( spl0_75
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
tff(f558,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f367]) ).
tff(f367,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f1032,plain,
spl0_74,
inference(avatar_split_clause,[],[f527,f1030]) ).
tff(f1030,plain,
( spl0_74
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
tff(f527,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f434,f363]) ).
tff(f434,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: int] :
( ( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) )
& ( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X10: int] :
( ord_less(int,bit0(X10),pls)
<=> ord_less(int,X10,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I10_J) ).
tff(f1028,plain,
spl0_73,
inference(avatar_split_clause,[],[f526,f1026]) ).
tff(f1026,plain,
( spl0_73
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
tff(f526,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f435,f363]) ).
tff(f435,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1024,plain,
spl0_72,
inference(avatar_split_clause,[],[f525,f1022]) ).
tff(f1022,plain,
( spl0_72
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
tff(f525,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f432,f363]) ).
tff(f432,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: int] :
( ( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) )
& ( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X10: int] :
( ord_less(int,pls,bit0(X10))
<=> ord_less(int,pls,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_rel__simps_I4_J) ).
tff(f1020,plain,
spl0_71,
inference(avatar_split_clause,[],[f524,f1018]) ).
tff(f1018,plain,
( spl0_71
<=> ! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
tff(f524,plain,
! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f433,f363]) ).
tff(f433,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f1016,plain,
spl0_70,
inference(avatar_split_clause,[],[f407,f1014]) ).
tff(f407,plain,
! [X0: $tType,X1: nat] :
( ( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ! [X1: nat] : ( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: nat] : ( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X13: nat] : ( number_number_of(X0,semiring_1_of_nat(int,X13)) = semiring_1_of_nat(X0,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__int) ).
tff(f994,plain,
spl0_69,
inference(avatar_split_clause,[],[f583,f991]) ).
tff(f583,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(forward_demodulation,[],[f356,f343]) ).
tff(f343,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f72]) ).
tff(f72,axiom,
zero_zero(int) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Pls__def) ).
tff(f356,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f989,plain,
spl0_68,
inference(avatar_split_clause,[],[f491,f987]) ).
tff(f491,plain,
! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(definition_unfolding,[],[f358,f365]) ).
tff(f358,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X5: int] : ( pls != bit1(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
tff(f985,plain,
spl0_67,
inference(avatar_split_clause,[],[f474,f983]) ).
tff(f474,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: nat,X1: nat] :
( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X15: nat,X18: nat] :
( ( semiring_1_of_nat(int,X15) = semiring_1_of_nat(int,X18) )
<=> ( X15 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_int__int__eq) ).
tff(f981,plain,
spl0_66,
inference(avatar_split_clause,[],[f406,f979]) ).
tff(f406,plain,
! [X0: $tType,X1: X0] :
( ( one_one(X0) = power_power(X0,X1,zero_zero(nat)) )
| ~ power(X0) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType] :
( ! [X1: X0] : ( one_one(X0) = power_power(X0,X1,zero_zero(nat)) )
| ~ power(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( power(X0)
=> ! [X1: X0] : ( one_one(X0) = power_power(X0,X1,zero_zero(nat)) ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType] :
( power(X0)
=> ! [X20: X0] : ( one_one(X0) = power_power(X0,X20,zero_zero(nat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power__0) ).
tff(f977,plain,
spl0_65,
inference(avatar_split_clause,[],[f388,f975]) ).
tff(f388,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X20: X0] : ( plus_plus(X0,number_number_of(X0,pls),X20) = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__numeral__0) ).
tff(f973,plain,
spl0_64,
inference(avatar_split_clause,[],[f387,f971]) ).
tff(f387,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X20: X0] : ( plus_plus(X0,X20,number_number_of(X0,pls)) = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__numeral__0__right) ).
tff(f969,plain,
( spl0_63
| ~ spl0_47
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f926,f916,f871,f966]) ).
tff(f966,plain,
( spl0_63
<=> ord_less(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
tff(f916,plain,
( spl0_56
<=> ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
tff(f926,plain,
( ord_less(int,pls,one_one(int))
| ~ spl0_47
| ~ spl0_56 ),
inference(superposition,[],[f917,f872]) ).
tff(f917,plain,
( ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int)))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f916]) ).
tff(f964,plain,
spl0_62,
inference(avatar_split_clause,[],[f355,f961]) ).
tff(f961,plain,
( spl0_62
<=> ord_less(int,m1,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
tff(f355,plain,
ord_less(int,m1,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f95]) ).
tff(f95,axiom,
ord_less(int,m1,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mn) ).
tff(f946,plain,
spl0_61,
inference(avatar_split_clause,[],[f625,f944]) ).
tff(f625,plain,
! [X0: nat] :
( ( pls != semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) = X0 ) ),
inference(forward_demodulation,[],[f438,f343]) ).
tff(f438,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: nat] :
( ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) != X0 ) )
& ( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
<=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X15: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X15) )
<=> ( zero_zero(nat) = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_int__eq__0__conv) ).
tff(f942,plain,
spl0_60,
inference(avatar_split_clause,[],[f611,f940]) ).
tff(f611,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f610,f360]) ).
tff(f610,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,plus_plus(int,one_one(int),pls)) )
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f514,f360]) ).
tff(f514,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) )
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f404,f365]) ).
tff(f404,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_semiring__numeral__1__eq__1) ).
tff(f938,plain,
spl0_59,
inference(avatar_split_clause,[],[f599,f936]) ).
tff(f599,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f598,f360]) ).
tff(f598,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,plus_plus(int,one_one(int),pls)) )
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f505,f360]) ).
tff(f505,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f384,f365]) ).
tff(f384,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_numeral__1__eq__1) ).
tff(f934,plain,
spl0_58,
inference(avatar_split_clause,[],[f521,f932]) ).
tff(f932,plain,
( spl0_58
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
tff(f521,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ),
inference(definition_unfolding,[],[f428,f363]) ).
tff(f428,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X9: int] :
( ( pls = bit0(X9) )
<=> ( pls = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I38_J) ).
tff(f930,plain,
spl0_57,
inference(avatar_split_clause,[],[f400,f928]) ).
tff(f400,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_of__nat__0) ).
tff(f918,plain,
spl0_56,
inference(avatar_split_clause,[],[f577,f916]) ).
tff(f577,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f478]) ).
tff(f478,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f297]) ).
tff(f914,plain,
spl0_55,
inference(avatar_split_clause,[],[f403,f912]) ).
tff(f912,plain,
( spl0_55
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
tff(f403,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_semiring__numeral__0__eq__0) ).
tff(f910,plain,
spl0_54,
inference(avatar_split_clause,[],[f382,f908]) ).
tff(f382,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_semiring__norm_I112_J) ).
tff(f906,plain,
( spl0_53
| ~ spl0_41
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f901,f896,f842,f903]) ).
tff(f896,plain,
( spl0_52
<=> ( zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f901,plain,
( ( pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ spl0_41
| ~ spl0_52 ),
inference(forward_demodulation,[],[f900,f844]) ).
tff(f900,plain,
( ( zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) )
| ~ spl0_52 ),
inference(forward_demodulation,[],[f898,f490]) ).
tff(f898,plain,
( ( zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f896]) ).
tff(f899,plain,
spl0_52,
inference(avatar_split_clause,[],[f485,f896]) ).
tff(f485,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
inference(definition_unfolding,[],[f301,f363,f365]) ).
tff(f301,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f139]) ).
tff(f139,negated_conjecture,
( ~ zero_zero(int) != power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f138]) ).
tff(f138,conjecture,
zero_zero(int) != power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f894,plain,
( ~ spl0_51
| ~ spl0_49
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f889,f885,f880,f891]) ).
tff(f891,plain,
( spl0_51
<=> ord_less(int,one_one(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f880,plain,
( spl0_49
<=> ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f889,plain,
( ~ ord_less(int,one_one(int),pls)
| ~ spl0_49
| ~ spl0_50 ),
inference(superposition,[],[f881,f887]) ).
tff(f881,plain,
( ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f888,plain,
spl0_50,
inference(avatar_split_clause,[],[f350,f885]) ).
tff(f350,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f54]) ).
tff(f54,axiom,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_int__1) ).
tff(f882,plain,
spl0_49,
inference(avatar_split_clause,[],[f584,f880]) ).
tff(f584,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls),
inference(forward_demodulation,[],[f362,f343]) ).
tff(f362,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X5: nat] : ~ ord_less(int,semiring_1_of_nat(int,X5),zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_int__less__0__conv) ).
tff(f878,plain,
spl0_48,
inference(avatar_split_clause,[],[f582,f875]) ).
tff(f875,plain,
( spl0_48
<=> ( pls = semiring_1_of_nat(int,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f582,plain,
pls = semiring_1_of_nat(int,zero_zero(nat)),
inference(forward_demodulation,[],[f352,f343]) ).
tff(f352,plain,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_int__0) ).
tff(f873,plain,
spl0_47,
inference(avatar_split_clause,[],[f361,f871]) ).
tff(f361,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X5: int] : ( plus_plus(int,pls,X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__Pls) ).
tff(f869,plain,
spl0_46,
inference(avatar_split_clause,[],[f360,f867]) ).
tff(f865,plain,
spl0_45,
inference(avatar_split_clause,[],[f347,f862]) ).
tff(f862,plain,
( spl0_45
<=> ( zero_zero(nat) = number_number_of(nat,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f347,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_semiring__norm_I113_J) ).
tff(f860,plain,
spl0_44,
inference(avatar_split_clause,[],[f581,f857]) ).
tff(f857,plain,
( spl0_44
<=> ( pls = number_number_of(int,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f581,plain,
pls = number_number_of(int,pls),
inference(forward_demodulation,[],[f349,f343]) ).
tff(f349,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__is__num__zero) ).
tff(f855,plain,
spl0_43,
inference(avatar_split_clause,[],[f346,f852]) ).
tff(f852,plain,
( spl0_43
<=> ord_less(int,one_one(int),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f346,plain,
ord_less(int,one_one(int),t),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
tff(f850,plain,
spl0_42,
inference(avatar_split_clause,[],[f345,f847]) ).
tff(f847,plain,
( spl0_42
<=> ord_less(nat,zero_zero(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f345,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n0) ).
tff(f845,plain,
spl0_41,
inference(avatar_split_clause,[],[f343,f842]) ).
tff(f840,plain,
~ spl0_40,
inference(avatar_split_clause,[],[f341,f837]) ).
tff(f341,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f27]) ).
tff(f27,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I2_J) ).
tff(f835,plain,
spl0_39,
inference(avatar_split_clause,[],[f340,f832]) ).
tff(f340,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f830,plain,
spl0_38,
inference(avatar_split_clause,[],[f339,f827]) ).
tff(f339,plain,
number_semiring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f825,plain,
spl0_37,
inference(avatar_split_clause,[],[f338,f822]) ).
tff(f338,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
number_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
tff(f820,plain,
spl0_36,
inference(avatar_split_clause,[],[f337,f817]) ).
tff(f337,plain,
power(nat),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
power(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
tff(f815,plain,
spl0_35,
inference(avatar_split_clause,[],[f336,f812]) ).
tff(f336,plain,
number_semiring(real),
inference(cnf_transformation,[],[f127]) ).
tff(f127,axiom,
number_semiring(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
tff(f810,plain,
spl0_34,
inference(avatar_split_clause,[],[f335,f807]) ).
tff(f335,plain,
power(real),
inference(cnf_transformation,[],[f134]) ).
tff(f134,axiom,
power(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
tff(f805,plain,
spl0_33,
inference(avatar_split_clause,[],[f334,f802]) ).
tff(f802,plain,
( spl0_33
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f334,plain,
semiring_1(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f800,plain,
spl0_32,
inference(avatar_split_clause,[],[f333,f797]) ).
tff(f333,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f795,plain,
spl0_31,
inference(avatar_split_clause,[],[f332,f792]) ).
tff(f332,plain,
semiring_1(real),
inference(cnf_transformation,[],[f129]) ).
tff(f129,axiom,
semiring_1(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
tff(f790,plain,
spl0_30,
inference(avatar_split_clause,[],[f331,f787]) ).
tff(f787,plain,
( spl0_30
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f331,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f785,plain,
spl0_29,
inference(avatar_split_clause,[],[f330,f782]) ).
tff(f782,plain,
( spl0_29
<=> no_zero_divisors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f330,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f780,plain,
spl0_28,
inference(avatar_split_clause,[],[f329,f777]) ).
tff(f777,plain,
( spl0_28
<=> mult_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f329,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f775,plain,
spl0_27,
inference(avatar_split_clause,[],[f328,f772]) ).
tff(f772,plain,
( spl0_27
<=> mult_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f328,plain,
mult_zero(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
mult_zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
tff(f770,plain,
spl0_26,
inference(avatar_split_clause,[],[f327,f767]) ).
tff(f767,plain,
( spl0_26
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f327,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
tff(f765,plain,
spl0_25,
inference(avatar_split_clause,[],[f326,f762]) ).
tff(f762,plain,
( spl0_25
<=> no_zero_divisors(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f326,plain,
no_zero_divisors(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
tff(f760,plain,
spl0_24,
inference(avatar_split_clause,[],[f325,f757]) ).
tff(f757,plain,
( spl0_24
<=> no_zero_divisors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f325,plain,
no_zero_divisors(real),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
no_zero_divisors(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
tff(f755,plain,
spl0_23,
inference(avatar_split_clause,[],[f324,f752]) ).
tff(f752,plain,
( spl0_23
<=> zero_neq_one(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f324,plain,
zero_neq_one(real),
inference(cnf_transformation,[],[f128]) ).
tff(f128,axiom,
zero_neq_one(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
tff(f750,plain,
spl0_22,
inference(avatar_split_clause,[],[f323,f747]) ).
tff(f747,plain,
( spl0_22
<=> mult_zero(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f323,plain,
mult_zero(real),
inference(cnf_transformation,[],[f131]) ).
tff(f131,axiom,
mult_zero(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
tff(f745,plain,
spl0_21,
inference(avatar_split_clause,[],[f322,f742]) ).
tff(f742,plain,
( spl0_21
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f322,plain,
number(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f740,plain,
spl0_20,
inference(avatar_split_clause,[],[f321,f737]) ).
tff(f737,plain,
( spl0_20
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f321,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f735,plain,
spl0_19,
inference(avatar_split_clause,[],[f320,f732]) ).
tff(f732,plain,
( spl0_19
<=> semiring_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f320,plain,
semiring_0(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
tff(f730,plain,
spl0_18,
inference(avatar_split_clause,[],[f319,f727]) ).
tff(f727,plain,
( spl0_18
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f319,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f725,plain,
spl0_17,
inference(avatar_split_clause,[],[f318,f722]) ).
tff(f722,plain,
( spl0_17
<=> semiring_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f318,plain,
semiring_0(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
semiring_0(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
tff(f720,plain,
spl0_16,
inference(avatar_split_clause,[],[f317,f717]) ).
tff(f717,plain,
( spl0_16
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f317,plain,
number(nat),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
number(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
tff(f715,plain,
spl0_15,
inference(avatar_split_clause,[],[f316,f712]) ).
tff(f712,plain,
( spl0_15
<=> linordered_semidom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f316,plain,
linordered_semidom(real),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
linordered_semidom(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
tff(f710,plain,
spl0_14,
inference(avatar_split_clause,[],[f315,f707]) ).
tff(f707,plain,
( spl0_14
<=> semiring_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f315,plain,
semiring_0(real),
inference(cnf_transformation,[],[f130]) ).
tff(f130,axiom,
semiring_0(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
tff(f705,plain,
spl0_13,
inference(avatar_split_clause,[],[f314,f702]) ).
tff(f702,plain,
( spl0_13
<=> number(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f314,plain,
number(real),
inference(cnf_transformation,[],[f135]) ).
tff(f135,axiom,
number(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
tff(f700,plain,
spl0_12,
inference(avatar_split_clause,[],[f313,f697]) ).
tff(f313,plain,
number_ring(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f695,plain,
spl0_11,
inference(avatar_split_clause,[],[f312,f692]) ).
tff(f312,plain,
number_ring(real),
inference(cnf_transformation,[],[f133]) ).
tff(f133,axiom,
number_ring(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
tff(f690,plain,
spl0_10,
inference(avatar_split_clause,[],[f311,f687]) ).
tff(f311,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f685,plain,
spl0_9,
inference(avatar_split_clause,[],[f310,f682]) ).
tff(f682,plain,
( spl0_9
<=> linordered_idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f310,plain,
linordered_idom(real),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
linordered_idom(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
tff(f680,plain,
spl0_8,
inference(avatar_split_clause,[],[f309,f677]) ).
tff(f677,plain,
( spl0_8
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f309,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
ring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f675,plain,
spl0_7,
inference(avatar_split_clause,[],[f308,f672]) ).
tff(f308,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f670,plain,
spl0_6,
inference(avatar_split_clause,[],[f307,f667]) ).
tff(f667,plain,
( spl0_6
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f307,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f665,plain,
spl0_5,
inference(avatar_split_clause,[],[f306,f662]) ).
tff(f662,plain,
( spl0_5
<=> linord219039673up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f306,plain,
linord219039673up_add(real),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
linord219039673up_add(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
tff(f660,plain,
spl0_4,
inference(avatar_split_clause,[],[f305,f657]) ).
tff(f657,plain,
( spl0_4
<=> ring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f305,plain,
ring_char_0(real),
inference(cnf_transformation,[],[f132]) ).
tff(f132,axiom,
ring_char_0(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
tff(f655,plain,
spl0_3,
inference(avatar_split_clause,[],[f304,f652]) ).
tff(f652,plain,
( spl0_3
<=> ring_11004092258visors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f304,plain,
ring_11004092258visors(real),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
ring_11004092258visors(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
tff(f650,plain,
spl0_2,
inference(avatar_split_clause,[],[f303,f647]) ).
tff(f647,plain,
( spl0_2
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f303,plain,
pp(fTrue),
inference(cnf_transformation,[],[f137]) ).
tff(f137,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f645,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f302,f642]) ).
tff(f642,plain,
( spl0_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f302,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f136]) ).
tff(f136,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM925_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 14:14:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (17092)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (17095)WARNING: value z3 for option sas not known
% 0.13/0.38 % (17099)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)
% 0.13/0.38 % (17097)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)
% 0.13/0.38 % (17094)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (17095)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)
% 0.13/0.38 % (17098)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)
% 0.13/0.38 % (17096)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (17093)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (17099)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.38 % Exception at run slice level
% 0.20/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.40 % (17100)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.40 % (17101)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)
% 0.20/0.40 % (17100)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.40 % Exception at run slice level
% 0.20/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.40 % (17101)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.40 % (17102)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.41 % (17103)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)
% 0.20/0.42 % (17097)First to succeed.
% 0.20/0.43 % (17102)Also succeeded, but the first one will report.
% 0.20/0.43 % (17098)Also succeeded, but the first one will report.
% 0.20/0.43 % (17097)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17092"
% 0.20/0.43 % (17097)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (17097)------------------------------
% 0.20/0.44 % (17097)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.44 % (17097)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (17097)Memory used [KB]: 1776
% 0.20/0.44 % (17097)Time elapsed: 0.057 s
% 0.20/0.44 % (17097)Instructions burned: 108 (million)
% 0.20/0.44 % (17092)Success in time 0.079 s
%------------------------------------------------------------------------------