TSTP Solution File: NUN017_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN017_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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:40:11 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 337
% Syntax : Number of formulae : 975 ( 307 unt; 33 typ; 0 def)
% Number of atoms : 2335 ( 473 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2346 ( 953 ~; 906 |; 110 &)
% ( 292 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 12 ( 8 >; 4 *; 0 +; 0 <<)
% Number of predicates : 205 ( 203 usr; 187 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 1151 (1131 !; 0 ?;1151 :)
% ( 20 !>; 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,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
n: nat ).
tff(func_def_10,type,
v: int ).
tff(func_def_11,type,
w: 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_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linorder:
!>[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,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_17,type,
pp: bool > $o ).
tff(f2023,plain,
$false,
inference(avatar_sat_refutation,[],[f648,f653,f658,f663,f668,f673,f678,f683,f688,f693,f698,f703,f708,f713,f718,f723,f728,f733,f738,f743,f748,f753,f758,f763,f768,f773,f778,f783,f788,f793,f798,f803,f808,f813,f818,f823,f828,f833,f838,f843,f848,f853,f858,f862,f866,f872,f877,f882,f887,f891,f895,f900,f906,f912,f916,f920,f924,f936,f941,f945,f949,f953,f957,f961,f965,f969,f973,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1027,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1164,f1168,f1172,f1176,f1180,f1212,f1237,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1274,f1279,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1386,f1489,f1493,f1497,f1501,f1505,f1509,f1513,f1517,f1575,f1579,f1583,f1587,f1591,f1598,f1613,f1619,f1623,f1627,f1631,f1643,f1661,f1665,f1669,f1673,f1687,f1757,f1761,f1765,f1788,f1796,f1800,f1810,f1815,f1820,f1824,f1839,f1843,f1847,f1851,f1860,f1864,f1875,f1879,f1883,f1895,f1899,f1903,f1907,f1938,f1942,f1947,f1952,f1956,f1960,f1965,f2021,f2022]) ).
tff(f2022,plain,
( ~ spl0_11
| spl0_46
| ~ spl0_42
| ~ spl0_162
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1891,f1877,f1807,f850,f869,f695]) ).
tff(f695,plain,
( spl0_11
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f869,plain,
( spl0_46
<=> ( v = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f850,plain,
( spl0_42
<=> ( zero_zero(int) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f1807,plain,
( spl0_162
<=> ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
tff(f1877,plain,
( spl0_173
<=> ! [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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
tff(f1891,plain,
( ( v = pls )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_173 ),
inference(forward_demodulation,[],[f1890,f852]) ).
tff(f852,plain,
( ( zero_zero(int) = pls )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f850]) ).
tff(f1890,plain,
( ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_173 ),
inference(trivial_inequality_removal,[],[f1889]) ).
tff(f1889,plain,
( ( pls != pls )
| ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_173 ),
inference(forward_demodulation,[],[f1888,f852]) ).
tff(f1888,plain,
( ( zero_zero(int) != pls )
| ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl0_162
| ~ spl0_173 ),
inference(superposition,[],[f1878,f1809]) ).
tff(f1809,plain,
( ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1807]) ).
tff(f1878,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1877]) ).
tff(f2021,plain,
( ~ spl0_186
| spl0_46
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1969,f1935,f869,f2018]) ).
tff(f2018,plain,
( spl0_186
<=> ( v = w ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
tff(f1935,plain,
( spl0_179
<=> ( pls = w ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
tff(f1969,plain,
( ( v != w )
| spl0_46
| ~ spl0_179 ),
inference(superposition,[],[f871,f1937]) ).
tff(f1937,plain,
( ( pls = w )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1935]) ).
tff(f871,plain,
( ( v != pls )
| spl0_46 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f1965,plain,
( spl0_185
| ~ spl0_179
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1961,f1958,f1935,f1963]) ).
tff(f1963,plain,
( spl0_185
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))) != power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))) )
| ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
tff(f1958,plain,
( spl0_184
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) != power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
tff(f1961,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))) != power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))) )
| ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ~ linordered_semidom(X0) )
| ~ spl0_179
| ~ spl0_184 ),
inference(forward_demodulation,[],[f1959,f1937]) ).
tff(f1959,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) != power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ linordered_semidom(X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1958]) ).
tff(f1960,plain,
spl0_184,
inference(avatar_split_clause,[],[f559,f1958]) ).
tff(f559,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) != power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ linordered_semidom(X0) ),
inference(definition_unfolding,[],[f424,f389,f389]) ).
tff(f389,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,[],[f76]) ).
tff(f76,axiom,
! [X7: int] : ( bit0(X7) = plus_plus(int,X7,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Bit0__def) ).
tff(f424,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) != power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) )
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) != power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,zero_zero(X0),X2)
| ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) != power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: X0,X2: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) )
=> ( ord_less_eq(X0,zero_zero(X0),X2)
=> ( ord_less_eq(X0,zero_zero(X0),X1)
=> ( X1 = X2 ) ) ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X4: X0,X5: X0] :
( ( power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))) = power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))) )
=> ( ord_less_eq(X0,zero_zero(X0),X5)
=> ( ord_less_eq(X0,zero_zero(X0),X4)
=> ( X4 = X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_power2__eq__imp__eq) ).
tff(f1956,plain,
( spl0_183
| ~ spl0_179
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1948,f1945,f1935,f1954]) ).
tff(f1954,plain,
( spl0_183
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))))
| ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
tff(f1945,plain,
( spl0_181
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
tff(f1948,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))))
| ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ linordered_semidom(X0) )
| ~ spl0_179
| ~ spl0_181 ),
inference(forward_demodulation,[],[f1946,f1937]) ).
tff(f1946,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1945]) ).
tff(f1952,plain,
( spl0_182
| ~ spl0_179
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1943,f1940,f1935,f1950]) ).
tff(f1950,plain,
( spl0_182
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))))
| ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
tff(f1940,plain,
( spl0_180
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
tff(f1943,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(w),bit1(w)))))
| ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ linordered_semidom(X0) )
| ~ spl0_179
| ~ spl0_180 ),
inference(forward_demodulation,[],[f1941,f1937]) ).
tff(f1941,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1940]) ).
tff(f1947,plain,
spl0_181,
inference(avatar_split_clause,[],[f561,f1945]) ).
tff(f561,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) ),
inference(definition_unfolding,[],[f426,f389,f389]) ).
tff(f426,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
=> ( ord_less_eq(X0,zero_zero(X0),X1)
=> ord_less(X0,X2,X1) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X4: X0,X5: X0] :
( ord_less(X0,power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))))
=> ( ord_less_eq(X0,zero_zero(X0),X4)
=> ord_less(X0,X5,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_power2__less__imp__less) ).
tff(f1942,plain,
spl0_180,
inference(avatar_split_clause,[],[f560,f1940]) ).
tff(f560,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_semidom(X0) ),
inference(definition_unfolding,[],[f425,f389,f389]) ).
tff(f425,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(X0,X2,X1)
| ~ ord_less_eq(X0,zero_zero(X0),X1)
| ~ ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
=> ( ord_less_eq(X0,zero_zero(X0),X1)
=> ord_less_eq(X0,X2,X1) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X4: X0,X5: X0] :
( ord_less_eq(X0,power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))))
=> ( ord_less_eq(X0,zero_zero(X0),X4)
=> ord_less_eq(X0,X5,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_power2__le__imp__le) ).
tff(f1938,plain,
( ~ spl0_11
| spl0_179
| ~ spl0_42
| ~ spl0_162
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1887,f1873,f1807,f850,f1935,f695]) ).
tff(f1873,plain,
( spl0_172
<=> ! [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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
tff(f1887,plain,
( ( pls = w )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_172 ),
inference(forward_demodulation,[],[f1886,f852]) ).
tff(f1886,plain,
( ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_172 ),
inference(trivial_inequality_removal,[],[f1885]) ).
tff(f1885,plain,
( ( pls != pls )
| ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl0_42
| ~ spl0_162
| ~ spl0_172 ),
inference(forward_demodulation,[],[f1884,f852]) ).
tff(f1884,plain,
( ( zero_zero(int) != pls )
| ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl0_162
| ~ spl0_172 ),
inference(superposition,[],[f1874,f1809]) ).
tff(f1874,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1873]) ).
tff(f1907,plain,
spl0_178,
inference(avatar_split_clause,[],[f556,f1905]) ).
tff(f1905,plain,
( spl0_178
<=> ! [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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
tff(f556,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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f416,f389,f389]) ).
tff(f416,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,[],[f278]) ).
tff(f278,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,[],[f277]) ).
tff(f277,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,[],[f236]) ).
tff(f236,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,[],[f158]) ).
tff(f158,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,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X2: X0,X3: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X2 )
| ( zero_zero(X0) != X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
tff(f1903,plain,
spl0_177,
inference(avatar_split_clause,[],[f555,f1901]) ).
tff(f1901,plain,
( spl0_177
<=> ! [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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
tff(f555,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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f417,f389,f389]) ).
tff(f417,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,[],[f278]) ).
tff(f1899,plain,
spl0_176,
inference(avatar_split_clause,[],[f554,f1897]) ).
tff(f1897,plain,
( spl0_176
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ~ ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
tff(f554,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ~ ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f412,f389,f389]) ).
tff(f412,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ~ ord_less_eq(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,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(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))
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ~ ord_less_eq(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(flattening,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less_eq(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))
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ~ ord_less_eq(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(nnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less_eq(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))
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ord_less_eq(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))
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X2: X0,X3: X0] :
( ord_less_eq(X0,plus_plus(X0,power_power(X0,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
<=> ( ( zero_zero(X0) = X2 )
& ( zero_zero(X0) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_sum__power2__le__zero__iff) ).
tff(f1895,plain,
spl0_175,
inference(avatar_split_clause,[],[f553,f1893]) ).
tff(f1893,plain,
( spl0_175
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
tff(f553,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f413,f389,f389]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ ord_less_eq(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,[],[f276]) ).
tff(f1883,plain,
( spl0_174
| ~ spl0_48
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1195,f1138,f879,f1881]) ).
tff(f1881,plain,
( spl0_174
<=> ! [X0: int] :
( ord_less(int,number_number_of(int,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
tff(f879,plain,
( spl0_48
<=> ( pls = number_number_of(int,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f1138,plain,
( spl0_94
<=> ! [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_94])]) ).
tff(f1195,plain,
( ! [X0: int] :
( ord_less(int,number_number_of(int,X0),pls)
| ~ ord_less(int,X0,pls) )
| ~ spl0_48
| ~ spl0_94 ),
inference(superposition,[],[f1139,f881]) ).
tff(f881,plain,
( ( pls = number_number_of(int,pls) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f879]) ).
tff(f1139,plain,
( ! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1138]) ).
tff(f1879,plain,
spl0_173,
inference(avatar_split_clause,[],[f551,f1877]) ).
tff(f551,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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f409,f389,f389]) ).
tff(f409,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,[],[f274]) ).
tff(f274,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,[],[f273]) ).
tff(f273,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,[],[f234]) ).
tff(f234,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,[],[f156]) ).
tff(f156,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,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X2: X0,X3: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X2 )
& ( zero_zero(X0) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sum__power2__eq__zero__iff) ).
tff(f1875,plain,
spl0_172,
inference(avatar_split_clause,[],[f550,f1873]) ).
tff(f550,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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f410,f389,f389]) ).
tff(f410,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,[],[f274]) ).
tff(f1864,plain,
spl0_171,
inference(avatar_split_clause,[],[f618,f1862]) ).
tff(f1862,plain,
( spl0_171
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
tff(f618,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,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f617]) ).
tff(f617,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,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f557]) ).
tff(f557,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,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f415,f389,f389]) ).
tff(f415,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,[],[f278]) ).
tff(f1860,plain,
spl0_170,
inference(avatar_split_clause,[],[f616,f1858]) ).
tff(f1858,plain,
( spl0_170
<=> ! [X0: $tType] :
( ord_less_eq(X0,plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
tff(f616,plain,
! [X0: $tType] :
( ord_less_eq(X0,plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f615]) ).
tff(f615,plain,
! [X0: $tType,X2: X0] :
( ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f552]) ).
tff(f552,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f414,f389,f389]) ).
tff(f414,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(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))
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f1851,plain,
spl0_169,
inference(avatar_split_clause,[],[f614,f1849]) ).
tff(f1849,plain,
( spl0_169
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
tff(f614,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f613]) ).
tff(f613,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f549]) ).
tff(f549,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f411,f389,f389]) ).
tff(f411,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,[],[f274]) ).
tff(f1847,plain,
( spl0_168
| ~ spl0_48
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1194,f1138,f879,f1845]) ).
tff(f1845,plain,
( spl0_168
<=> ! [X0: int] :
( ord_less(int,pls,number_number_of(int,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
tff(f1194,plain,
( ! [X0: int] :
( ord_less(int,pls,number_number_of(int,X0))
| ~ ord_less(int,pls,X0) )
| ~ spl0_48
| ~ spl0_94 ),
inference(superposition,[],[f1139,f881]) ).
tff(f1843,plain,
spl0_167,
inference(avatar_split_clause,[],[f609,f1841]) ).
tff(f1841,plain,
( spl0_167
<=> ! [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,bit1(pls),bit1(pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
tff(f609,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,bit1(pls),bit1(pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
inference(definition_unfolding,[],[f532,f389,f389]) ).
tff(f532,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,[],[f330]) ).
tff(f330,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,[],[f329]) ).
tff(f329,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,[],[f218]) ).
tff(f218,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,[],[f97]) ).
tff(f97,axiom,
! [X2: real,X3: real] :
( ( plus_plus(real,power_power(real,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(real,X2,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(real) )
<=> ( ( zero_zero(real) = X2 )
& ( zero_zero(real) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_realpow__two__sum__zero__iff) ).
tff(f1839,plain,
spl0_166,
inference(avatar_split_clause,[],[f608,f1837]) ).
tff(f1837,plain,
( spl0_166
<=> ! [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,bit1(pls),bit1(pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
tff(f608,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,bit1(pls),bit1(pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
inference(definition_unfolding,[],[f533,f389,f389]) ).
tff(f533,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,[],[f330]) ).
tff(f1824,plain,
spl0_165,
inference(avatar_split_clause,[],[f548,f1822]) ).
tff(f1822,plain,
( spl0_165
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
tff(f548,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f408,f389,f389]) ).
tff(f408,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less_eq(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,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ord_less_eq(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(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] : ord_less_eq(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)))))) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X4: X0,X5: X0] : ord_less_eq(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_sum__power2__ge__zero) ).
tff(f1820,plain,
spl0_164,
inference(avatar_split_clause,[],[f547,f1818]) ).
tff(f1818,plain,
( spl0_164
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
tff(f547,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f407,f389,f389]) ).
tff(f407,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,[],[f232]) ).
tff(f232,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,[],[f154]) ).
tff(f154,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,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X4: X0,X5: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_not__sum__power2__lt__zero) ).
tff(f1815,plain,
spl0_163,
inference(avatar_split_clause,[],[f629,f1812]) ).
tff(f1812,plain,
( spl0_163
<=> ( zero_zero(real) = plus_plus(real,power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
tff(f629,plain,
zero_zero(real) = plus_plus(real,power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(equality_resolution,[],[f628]) ).
tff(f628,plain,
! [X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,zero_zero(real),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(real) != X1 ) ),
inference(equality_resolution,[],[f607]) ).
tff(f607,plain,
! [X0: real,X1: real] :
( ( zero_zero(real) = plus_plus(real,power_power(real,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(real,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(real) != X0 )
| ( zero_zero(real) != X1 ) ),
inference(definition_unfolding,[],[f534,f389,f389]) ).
tff(f534,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,[],[f330]) ).
tff(f1810,plain,
spl0_162,
inference(avatar_split_clause,[],[f634,f1807]) ).
tff(f634,plain,
pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f539,f375]) ).
tff(f375,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f71]) ).
tff(f71,axiom,
zero_zero(int) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Pls__def) ).
tff(f539,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f384,f389,f389]) ).
tff(f384,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096v_A_094_A2_A_L_Aw_A_094_A2_A_061_A0_096) ).
tff(f1800,plain,
( spl0_161
| ~ spl0_48
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1190,f1134,f879,f1798]) ).
tff(f1798,plain,
( spl0_161
<=> ! [X0: int] :
( ~ ord_less(int,number_number_of(int,X0),pls)
| ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
tff(f1134,plain,
( spl0_93
<=> ! [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_93])]) ).
tff(f1190,plain,
( ! [X0: int] :
( ~ ord_less(int,number_number_of(int,X0),pls)
| ord_less(int,X0,pls) )
| ~ spl0_48
| ~ spl0_93 ),
inference(superposition,[],[f1135,f881]) ).
tff(f1135,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ord_less(int,X1,X0) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1134]) ).
tff(f1796,plain,
spl0_160,
inference(avatar_split_clause,[],[f421,f1794]) ).
tff(f1794,plain,
( spl0_160
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
tff(f421,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(flattening,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: int,X2: int] :
( ord_less_eq(int,pls,X2)
=> ( ord_less_eq(int,pls,X1)
=> ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ) ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X15: int,X12: int] :
( ord_less_eq(int,pls,X12)
=> ( ord_less_eq(int,pls,X15)
=> ( plus_plus(X0,number_number_of(X0,X12),number_number_of(X0,X15)) = number_number_of(X0,plus_plus(int,X12,X15)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_semiring__add__number__of) ).
tff(f1788,plain,
spl0_159,
inference(avatar_split_clause,[],[f622,f1786]) ).
tff(f1786,plain,
( spl0_159
<=> ! [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) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
tff(f622,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) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(equality_resolution,[],[f443]) ).
tff(f443,plain,
! [X0: $tType,X2: X0,X1: int] :
( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) )
| ( zero_zero(X0) != X2 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != number_number_of(nat,X1) )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,number_number_of(nat,X1)) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f287]) ).
tff(f287,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
| ( zero_zero(nat) = number_number_of(nat,X1) )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != number_number_of(nat,X1) )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,number_number_of(nat,X1)) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(nnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
<=> ( ( zero_zero(nat) != number_number_of(nat,X1) )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
<=> ( ( zero_zero(nat) != number_number_of(nat,X1) )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X1: int,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,X1)) )
<=> ( ( zero_zero(nat) != number_number_of(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) )
=> ! [X18: int,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X18)) )
<=> ( ( zero_zero(nat) != number_number_of(nat,X18) )
& ( zero_zero(X0) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_power__eq__0__iff__number__of) ).
tff(f1765,plain,
spl0_158,
inference(avatar_split_clause,[],[f484,f1763]) ).
tff(f1763,plain,
( spl0_158
<=> ! [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_158])]) ).
tff(f484,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,[],[f267]) ).
tff(f267,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,[],[f195]) ).
tff(f195,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,[],[f55]) ).
tff(f55,axiom,
! [X15: int,X12: int] :
( ( ~ ord_less(int,X12,pls)
=> ( ( ~ ord_less(int,X15,pls)
=> ( plus_plus(nat,number_number_of(nat,X12),number_number_of(nat,X15)) = number_number_of(nat,plus_plus(int,X12,X15)) ) )
& ( ord_less(int,X15,pls)
=> ( number_number_of(nat,X12) = plus_plus(nat,number_number_of(nat,X12),number_number_of(nat,X15)) ) ) ) )
& ( ord_less(int,X12,pls)
=> ( number_number_of(nat,X15) = plus_plus(nat,number_number_of(nat,X12),number_number_of(nat,X15)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__nat__number__of) ).
tff(f1761,plain,
spl0_157,
inference(avatar_split_clause,[],[f418,f1759]) ).
tff(f1759,plain,
( spl0_157
<=> ! [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_157])]) ).
tff(f418,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,[],[f237]) ).
tff(f237,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,[],[f159]) ).
tff(f159,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,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X10: X0,X11: int,X12: int] : ( plus_plus(X0,number_number_of(X0,X12),plus_plus(X0,number_number_of(X0,X11),X10)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X12,X11)),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__number__of__left) ).
tff(f1757,plain,
( spl0_155
| spl0_156 ),
inference(avatar_split_clause,[],[f635,f1755,f1752]) ).
tff(f1752,plain,
( spl0_155
<=> ! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
tff(f1755,plain,
( spl0_156
<=> ! [X1: int] : ( zero_zero(nat) != number_number_of(nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
tff(f635,plain,
! [X0: $tType,X2: X0,X1: int] :
( ( zero_zero(nat) != number_number_of(nat,X1) )
| ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(inner_rewriting,[],[f442]) ).
tff(f442,plain,
! [X0: $tType,X2: X0,X1: int] :
( ( zero_zero(nat) != number_number_of(nat,X1) )
| ( zero_zero(X0) != power_power(X0,X2,number_number_of(nat,X1)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f1687,plain,
( spl0_154
| ~ spl0_48
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1189,f1134,f879,f1685]) ).
tff(f1685,plain,
( spl0_154
<=> ! [X0: int] :
( ~ ord_less(int,pls,number_number_of(int,X0))
| ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
tff(f1189,plain,
( ! [X0: int] :
( ~ ord_less(int,pls,number_number_of(int,X0))
| ord_less(int,pls,X0) )
| ~ spl0_48
| ~ spl0_93 ),
inference(superposition,[],[f1135,f881]) ).
tff(f1673,plain,
spl0_153,
inference(avatar_split_clause,[],[f580,f1671]) ).
tff(f1671,plain,
( spl0_153
<=> ! [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_153])]) ).
tff(f580,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,[],[f480,f389,f389,f389]) ).
tff(f480,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X6: int,X7: int] : ( plus_plus(int,bit0(X7),bit0(X6)) = bit0(plus_plus(int,X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_add__Bit0__Bit0) ).
tff(f1669,plain,
spl0_152,
inference(avatar_split_clause,[],[f545,f1667]) ).
tff(f1667,plain,
( spl0_152
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
tff(f545,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f404,f389]) ).
tff(f404,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,[],[f272]) ).
tff(f272,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,[],[f229]) ).
tff(f229,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,[],[f5]) ).
tff(f5,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/sandbox/benchmark/theBenchmark.p',fact_4_zero__less__power2) ).
tff(f1665,plain,
spl0_151,
inference(avatar_split_clause,[],[f544,f1663]) ).
tff(f1663,plain,
( spl0_151
<=> ! [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_151])]) ).
tff(f544,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,[],[f400,f389]) ).
tff(f400,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,[],[f227]) ).
tff(f227,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,[],[f151]) ).
tff(f151,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,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X11: int] : ( number_number_of(X0,bit0(X11)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X11)),number_number_of(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_number__of__Bit0) ).
tff(f1661,plain,
spl0_150,
inference(avatar_split_clause,[],[f441,f1659]) ).
tff(f1659,plain,
( spl0_150
<=> ! [X0: $tType,X2: X0,X1: int] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,number_number_of(nat,X1)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
tff(f441,plain,
! [X0: $tType,X2: X0,X1: int] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,number_number_of(nat,X1)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f1643,plain,
( spl0_149
| ~ spl0_48
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1186,f1126,f879,f1641]) ).
tff(f1641,plain,
( spl0_149
<=> ! [X0: int] :
( ord_less_eq(int,number_number_of(int,X0),pls)
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
tff(f1126,plain,
( spl0_91
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
tff(f1186,plain,
( ! [X0: int] :
( ord_less_eq(int,number_number_of(int,X0),pls)
| ~ ord_less_eq(int,X0,pls) )
| ~ spl0_48
| ~ spl0_91 ),
inference(superposition,[],[f1127,f881]) ).
tff(f1127,plain,
( ! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1126]) ).
tff(f1631,plain,
spl0_148,
inference(avatar_split_clause,[],[f541,f1629]) ).
tff(f1629,plain,
( spl0_148
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
tff(f541,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f392,f389]) ).
tff(f392,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,[],[f270]) ).
tff(f270,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,[],[f220]) ).
tff(f220,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,[],[f7]) ).
tff(f7,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/sandbox/benchmark/theBenchmark.p',fact_6_zero__eq__power2) ).
tff(f1627,plain,
spl0_147,
inference(avatar_split_clause,[],[f483,f1625]) ).
tff(f1625,plain,
( spl0_147
<=> ! [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_147])]) ).
tff(f483,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,[],[f267]) ).
tff(f1623,plain,
spl0_146,
inference(avatar_split_clause,[],[f445,f1621]) ).
tff(f1621,plain,
( spl0_146
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
tff(f445,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
& ( ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(nnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(flattening,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( ( linorder(X0)
& number(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( ( linorder(X0)
& number(X0) )
=> ! [X18: int,X13: int] :
( ord_less_eq(X0,number_number_of(X0,X13),number_number_of(X0,X18))
<=> ~ ord_less(X0,number_number_of(X0,X18),number_number_of(X0,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__number__of__eq__not__less) ).
tff(f1619,plain,
spl0_145,
inference(avatar_split_clause,[],[f444,f1617]) ).
tff(f1617,plain,
( spl0_145
<=> ! [X0: $tType,X2: int,X1: int] :
( ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linorder(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
tff(f444,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linorder(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1613,plain,
spl0_144,
inference(avatar_split_clause,[],[f612,f1611]) ).
tff(f1611,plain,
( spl0_144
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
tff(f612,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f546]) ).
tff(f546,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,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f403,f389]) ).
tff(f403,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,[],[f272]) ).
tff(f1598,plain,
( spl0_143
| ~ spl0_48
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1185,f1126,f879,f1596]) ).
tff(f1596,plain,
( spl0_143
<=> ! [X0: int] :
( ord_less_eq(int,pls,number_number_of(int,X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
tff(f1185,plain,
( ! [X0: int] :
( ord_less_eq(int,pls,number_number_of(int,X0))
| ~ ord_less_eq(int,pls,X0) )
| ~ spl0_48
| ~ spl0_91 ),
inference(superposition,[],[f1127,f881]) ).
tff(f1591,plain,
spl0_142,
inference(avatar_split_clause,[],[f611,f1589]) ).
tff(f1589,plain,
( spl0_142
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
tff(f611,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(equality_resolution,[],[f540]) ).
tff(f540,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ( zero_zero(X0) != X1 )
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f393,f389]) ).
tff(f393,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,[],[f270]) ).
tff(f1587,plain,
spl0_141,
inference(avatar_split_clause,[],[f558,f1585]) ).
tff(f1585,plain,
( spl0_141
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
tff(f558,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f419,f389]) ).
tff(f419,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,[],[f238]) ).
tff(f238,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,[],[f6]) ).
tff(f6,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/sandbox/benchmark/theBenchmark.p',fact_5_zero__power2) ).
tff(f1583,plain,
spl0_140,
inference(avatar_split_clause,[],[f543,f1581]) ).
tff(f1581,plain,
( spl0_140
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
tff(f543,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f399,f389]) ).
tff(f399,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X20: X0] : ord_less_eq(X0,zero_zero(X0),power_power(X0,X20,number_number_of(nat,bit0(bit1(pls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zero__le__power2) ).
tff(f1579,plain,
spl0_139,
inference(avatar_split_clause,[],[f542,f1577]) ).
tff(f1577,plain,
( spl0_139
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
tff(f542,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f398,f389]) ).
tff(f398,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,[],[f225]) ).
tff(f225,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,[],[f95]) ).
tff(f95,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/sandbox/benchmark/theBenchmark.p',fact_94_power2__less__0) ).
tff(f1575,plain,
spl0_138,
inference(avatar_split_clause,[],[f405,f1573]) ).
tff(f1573,plain,
( spl0_138
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
tff(f405,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X11: int,X12: int] : ( number_number_of(X0,plus_plus(int,X12,X11)) = plus_plus(X0,number_number_of(X0,X12),number_number_of(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__number__of__eq) ).
tff(f1517,plain,
spl0_137,
inference(avatar_split_clause,[],[f529,f1515]) ).
tff(f1515,plain,
( spl0_137
<=> ! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
tff(f529,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: int,X1: int] :
( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ( ~ ord_less(int,pls,X0)
& ord_less(int,X1,X0) ) )
& ( ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) )
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(flattening,[],[f326]) ).
tff(f326,plain,
! [X0: int,X1: int] :
( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ( ~ ord_less(int,pls,X0)
& ord_less(int,X1,X0) ) )
& ( ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) )
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(nnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) ) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ord_less(int,X1,X0)
& ( ord_less(int,X1,X0)
=> ord_less(int,pls,X0) ) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X14: int,X13: int] :
( ord_less(nat,number_number_of(nat,X13),number_number_of(nat,X14))
<=> ( ord_less(int,X13,X14)
& ( ord_less(int,X13,X14)
=> ord_less(int,pls,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_less__nat__number__of) ).
tff(f1513,plain,
spl0_136,
inference(avatar_split_clause,[],[f526,f1511]) ).
tff(f1511,plain,
( spl0_136
<=> ! [X0: int,X1: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
tff(f526,plain,
! [X0: int,X1: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f327]) ).
tff(f1509,plain,
spl0_135,
inference(avatar_split_clause,[],[f482,f1507]) ).
tff(f1507,plain,
( spl0_135
<=> ! [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_135])]) ).
tff(f482,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,[],[f267]) ).
tff(f1505,plain,
spl0_134,
inference(avatar_split_clause,[],[f440,f1503]) ).
tff(f1503,plain,
( spl0_134
<=> ! [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_134])]) ).
tff(f440,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,[],[f286]) ).
tff(f286,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,[],[f262]) ).
tff(f262,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,[],[f261]) ).
tff(f261,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,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X2: int,X3: int] :
( ord_less(X0,number_number_of(X0,X3),number_number_of(X0,X2))
<=> ord_less(int,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__number__of) ).
tff(f1501,plain,
spl0_133,
inference(avatar_split_clause,[],[f439,f1499]) ).
tff(f1499,plain,
( spl0_133
<=> ! [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_133])]) ).
tff(f439,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,[],[f286]) ).
tff(f1497,plain,
spl0_132,
inference(avatar_split_clause,[],[f438,f1495]) ).
tff(f1495,plain,
( spl0_132
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
tff(f438,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1) )
& ( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X2: int,X3: int] :
( ord_less_eq(X0,number_number_of(X0,X3),number_number_of(X0,X2))
<=> ord_less_eq(int,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_le__number__of) ).
tff(f1493,plain,
( spl0_131
| ~ spl0_53
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1445,f1365,f904,f1491]) ).
tff(f1491,plain,
( spl0_131
<=> ! [X0: int,X1: int] : ( bit1(X1) != number_number_of(int,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
tff(f904,plain,
( spl0_53
<=> ! [X0: int,X1: int] : ( plus_plus(int,X0,X0) != bit1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f1365,plain,
( spl0_128
<=> ! [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_128])]) ).
tff(f1445,plain,
( ! [X0: int,X1: int] : ( bit1(X1) != number_number_of(int,plus_plus(int,X0,X0)) )
| ~ spl0_53
| ~ spl0_128 ),
inference(superposition,[],[f905,f1366]) ).
tff(f1366,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)) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1365]) ).
tff(f905,plain,
( ! [X0: int,X1: int] : ( plus_plus(int,X0,X0) != bit1(X1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f904]) ).
tff(f1489,plain,
spl0_130,
inference(avatar_split_clause,[],[f437,f1487]) ).
tff(f1487,plain,
( spl0_130
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
tff(f437,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f1386,plain,
( spl0_129
| ~ spl0_48
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1182,f1122,f879,f1384]) ).
tff(f1384,plain,
( spl0_129
<=> ! [X0: int] :
( ~ ord_less_eq(int,number_number_of(int,X0),pls)
| ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
tff(f1122,plain,
( spl0_90
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
tff(f1182,plain,
( ! [X0: int] :
( ~ ord_less_eq(int,number_number_of(int,X0),pls)
| ord_less_eq(int,X0,pls) )
| ~ spl0_48
| ~ spl0_90 ),
inference(superposition,[],[f1123,f881]) ).
tff(f1123,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ord_less_eq(int,X1,X0) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1122]) ).
tff(f1367,plain,
spl0_128,
inference(avatar_split_clause,[],[f481,f1365]) ).
tff(f481,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,[],[f194]) ).
tff(f194,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,[],[f60]) ).
tff(f60,axiom,
! [X11: int,X12: int] : ( plus_plus(int,number_number_of(int,X12),number_number_of(int,X11)) = number_number_of(int,plus_plus(int,X12,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_J) ).
tff(f1363,plain,
spl0_127,
inference(avatar_split_clause,[],[f436,f1361]) ).
tff(f1361,plain,
( spl0_127
<=> ! [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_127])]) ).
tff(f436,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,[],[f284]) ).
tff(f284,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,[],[f258]) ).
tff(f258,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,[],[f257]) ).
tff(f257,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,[],[f169]) ).
tff(f169,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,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less(X0,number_number_of(X0,X3),zero_zero(X0))
<=> ord_less(int,X3,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_less__special_I3_J) ).
tff(f1359,plain,
spl0_126,
inference(avatar_split_clause,[],[f435,f1357]) ).
tff(f1357,plain,
( spl0_126
<=> ! [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_126])]) ).
tff(f435,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,[],[f284]) ).
tff(f1355,plain,
spl0_125,
inference(avatar_split_clause,[],[f434,f1353]) ).
tff(f1353,plain,
( spl0_125
<=> ! [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_125])]) ).
tff(f434,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,[],[f283]) ).
tff(f283,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,[],[f256]) ).
tff(f256,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,[],[f255]) ).
tff(f255,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,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X2: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X2))
<=> ord_less(int,pls,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__special_I1_J) ).
tff(f1351,plain,
spl0_124,
inference(avatar_split_clause,[],[f433,f1349]) ).
tff(f1349,plain,
( spl0_124
<=> ! [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_124])]) ).
tff(f433,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,[],[f283]) ).
tff(f1347,plain,
spl0_123,
inference(avatar_split_clause,[],[f432,f1345]) ).
tff(f1345,plain,
( spl0_123
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
tff(f432,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls) )
& ( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ 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_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less_eq(X0,number_number_of(X0,X3),zero_zero(X0))
<=> ord_less_eq(int,X3,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_le__special_I3_J) ).
tff(f1343,plain,
spl0_122,
inference(avatar_split_clause,[],[f431,f1341]) ).
tff(f1341,plain,
( spl0_122
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
tff(f431,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f1339,plain,
spl0_121,
inference(avatar_split_clause,[],[f430,f1337]) ).
tff(f1337,plain,
( spl0_121
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
tff(f430,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1) )
& ( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X2: int] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X2))
<=> ord_less_eq(int,pls,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le__special_I1_J) ).
tff(f1335,plain,
( spl0_120
| ~ spl0_48
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1181,f1122,f879,f1333]) ).
tff(f1333,plain,
( spl0_120
<=> ! [X0: int] :
( ~ ord_less_eq(int,pls,number_number_of(int,X0))
| ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
tff(f1181,plain,
( ! [X0: int] :
( ~ ord_less_eq(int,pls,number_number_of(int,X0))
| ord_less_eq(int,pls,X0) )
| ~ spl0_48
| ~ spl0_90 ),
inference(superposition,[],[f1123,f881]) ).
tff(f1331,plain,
spl0_119,
inference(avatar_split_clause,[],[f429,f1329]) ).
tff(f1329,plain,
( spl0_119
<=> ! [X0: $tType,X1: int] :
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
tff(f429,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1327,plain,
spl0_118,
inference(avatar_split_clause,[],[f402,f1325]) ).
tff(f1325,plain,
( spl0_118
<=> ! [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_118])]) ).
tff(f402,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,[],[f271]) ).
tff(f271,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,[],[f228]) ).
tff(f228,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,[],[f78]) ).
tff(f78,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/sandbox/benchmark/theBenchmark.p',fact_77_even__less__0__iff) ).
tff(f1323,plain,
spl0_117,
inference(avatar_split_clause,[],[f401,f1321]) ).
tff(f1321,plain,
( spl0_117
<=> ! [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_117])]) ).
tff(f401,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,[],[f271]) ).
tff(f1279,plain,
spl0_116,
inference(avatar_split_clause,[],[f633,f1276]) ).
tff(f1276,plain,
( spl0_116
<=> ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
tff(f633,plain,
ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f538,f375]) ).
tff(f538,plain,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f383,f389]) ).
tff(f383,plain,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__0960_A_060_Av_A_094_A2_096) ).
tff(f1274,plain,
spl0_115,
inference(avatar_split_clause,[],[f632,f1271]) ).
tff(f1271,plain,
( spl0_115
<=> ord_less_eq(int,pls,power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
tff(f632,plain,
ord_less_eq(int,pls,power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f537,f375]) ).
tff(f537,plain,
ord_less_eq(int,zero_zero(int),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f382,f389]) ).
tff(f382,plain,
ord_less_eq(int,zero_zero(int),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less_eq(int,zero_zero(int),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0960_A_060_061_Aw_A_094_A2_096) ).
tff(f1269,plain,
spl0_114,
inference(avatar_split_clause,[],[f604,f1267]) ).
tff(f1267,plain,
( spl0_114
<=> ! [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_114])]) ).
tff(f604,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,[],[f520,f389,f389]) ).
tff(f520,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,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,[],[f213]) ).
tff(f213,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X9: int,X8: int] :
( ord_less(int,bit0(X8),bit0(X9))
<=> ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I14_J) ).
tff(f1265,plain,
spl0_113,
inference(avatar_split_clause,[],[f603,f1263]) ).
tff(f1263,plain,
( spl0_113
<=> ! [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_113])]) ).
tff(f603,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,[],[f521,f389,f389]) ).
tff(f521,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f323]) ).
tff(f1261,plain,
spl0_112,
inference(avatar_split_clause,[],[f592,f1259]) ).
tff(f1259,plain,
( spl0_112
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
tff(f592,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f504,f389,f389]) ).
tff(f504,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X16: int,X17: int] :
( ord_less_eq(int,bit0(X17),bit0(X16))
<=> ord_less_eq(int,X17,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__eq__int__code_I13_J) ).
tff(f1257,plain,
spl0_111,
inference(avatar_split_clause,[],[f591,f1255]) ).
tff(f1255,plain,
( spl0_111
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
tff(f591,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(definition_unfolding,[],[f505,f389,f389]) ).
tff(f505,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit0(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f315]) ).
tff(f1253,plain,
spl0_110,
inference(avatar_split_clause,[],[f579,f1251]) ).
tff(f1251,plain,
( spl0_110
<=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
tff(f579,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ),
inference(definition_unfolding,[],[f479,f389]) ).
tff(f479,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X6: int,X7: int] : ( plus_plus(int,bit0(X7),bit1(X6)) = bit1(plus_plus(int,X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
tff(f1249,plain,
spl0_109,
inference(avatar_split_clause,[],[f578,f1247]) ).
tff(f1247,plain,
( spl0_109
<=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
tff(f578,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f478,f389]) ).
tff(f478,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X6: int,X7: int] : ( bit1(plus_plus(int,X7,X6)) = plus_plus(int,bit1(X7),bit0(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__Bit1__Bit0) ).
tff(f1245,plain,
spl0_108,
inference(avatar_split_clause,[],[f427,f1243]) ).
tff(f1243,plain,
( spl0_108
<=> ! [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_108])]) ).
tff(f427,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,[],[f280]) ).
tff(f280,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,[],[f250]) ).
tff(f250,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,[],[f249]) ).
tff(f249,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,[],[f165]) ).
tff(f165,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,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X2: int,X3: int] :
( ( number_number_of(X0,X2) = number_number_of(X0,X3) )
<=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_eq__number__of) ).
tff(f1237,plain,
spl0_107,
inference(avatar_split_clause,[],[f390,f1235]) ).
tff(f1235,plain,
( spl0_107
<=> ! [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_107])]) ).
tff(f390,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,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,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_double__eq__0__iff) ).
tff(f1212,plain,
( spl0_105
| ~ spl0_106
| ~ spl0_49
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1086,f1035,f884,f1209,f1205]) ).
tff(f1205,plain,
( spl0_105
<=> ord_less(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
tff(f1209,plain,
( spl0_106
<=> ord_less(nat,zero_zero(nat),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
tff(f884,plain,
( spl0_49
<=> ( zero_zero(nat) = number_number_of(nat,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f1035,plain,
( spl0_77
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
tff(f1086,plain,
( ~ ord_less(nat,zero_zero(nat),zero_zero(nat))
| ord_less(int,pls,pls)
| ~ spl0_49
| ~ spl0_77 ),
inference(superposition,[],[f1036,f886]) ).
tff(f886,plain,
( ( zero_zero(nat) = number_number_of(nat,pls) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f884]) ).
tff(f1036,plain,
( ! [X0: int] :
( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ord_less(int,pls,X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1035]) ).
tff(f1180,plain,
spl0_104,
inference(avatar_split_clause,[],[f600,f1178]) ).
tff(f1178,plain,
( spl0_104
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
tff(f600,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),bit1(X0)) ),
inference(definition_unfolding,[],[f516,f389]) ).
tff(f516,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X9: int,X8: int] :
( ord_less(int,bit0(X8),bit1(X9))
<=> ord_less_eq(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I15_J) ).
tff(f1176,plain,
spl0_103,
inference(avatar_split_clause,[],[f599,f1174]) ).
tff(f1174,plain,
( spl0_103
<=> ! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
tff(f599,plain,
! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(definition_unfolding,[],[f517,f389]) ).
tff(f517,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f321]) ).
tff(f1172,plain,
spl0_102,
inference(avatar_split_clause,[],[f596,f1170]) ).
tff(f1170,plain,
( spl0_102
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
tff(f596,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f512,f389]) ).
tff(f512,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,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,[],[f209]) ).
tff(f209,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X9: int,X8: int] :
( ord_less(int,bit1(X8),bit0(X9))
<=> ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rel__simps_I16_J) ).
tff(f1168,plain,
( spl0_101
| ~ spl0_56
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1033,f1011,f918,f1166]) ).
tff(f1166,plain,
( spl0_101
<=> ! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,bit1(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
tff(f918,plain,
( spl0_56
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
tff(f1011,plain,
( spl0_75
<=> ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
tff(f1033,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,bit1(X0),bit1(X1)) )
| ~ spl0_56
| ~ spl0_75 ),
inference(resolution,[],[f1012,f919]) ).
tff(f919,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(int,X1,X0)
| ord_less_eq(int,X1,X0) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f918]) ).
tff(f1012,plain,
( ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f1164,plain,
spl0_100,
inference(avatar_split_clause,[],[f595,f1162]) ).
tff(f1162,plain,
( spl0_100
<=> ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
tff(f595,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f513,f389]) ).
tff(f513,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f319]) ).
tff(f1160,plain,
spl0_99,
inference(avatar_split_clause,[],[f588,f1158]) ).
tff(f1158,plain,
( spl0_99
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
tff(f588,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,X1),bit1(X0)) ),
inference(definition_unfolding,[],[f500,f389]) ).
tff(f500,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit0(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X9: int,X8: int] :
( ord_less_eq(int,bit0(X8),bit1(X9))
<=> ord_less_eq(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_rel__simps_I32_J) ).
tff(f1156,plain,
spl0_98,
inference(avatar_split_clause,[],[f587,f1154]) ).
tff(f1154,plain,
( spl0_98
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
tff(f587,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(definition_unfolding,[],[f501,f389]) ).
tff(f501,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1152,plain,
spl0_97,
inference(avatar_split_clause,[],[f584,f1150]) ).
tff(f1150,plain,
( spl0_97
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
tff(f584,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f496,f389]) ).
tff(f496,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X9: int,X8: int] :
( ord_less_eq(int,bit1(X8),bit0(X9))
<=> ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I33_J) ).
tff(f1148,plain,
spl0_96,
inference(avatar_split_clause,[],[f583,f1146]) ).
tff(f1146,plain,
( spl0_96
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
tff(f583,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f497,f389]) ).
tff(f497,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f311]) ).
tff(f1144,plain,
spl0_95,
inference(avatar_split_clause,[],[f582,f1142]) ).
tff(f1142,plain,
( spl0_95
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
tff(f582,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
inference(definition_unfolding,[],[f490,f389,f389]) ).
tff(f490,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: int,X1: int] :
( ( ( bit0(X0) = bit0(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: int,X1: int] :
( ( bit0(X0) = bit0(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X9: int,X8: int] :
( ( bit0(X8) = bit0(X9) )
<=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I48_J) ).
tff(f1140,plain,
spl0_94,
inference(avatar_split_clause,[],[f531,f1138]) ).
tff(f531,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,[],[f328]) ).
tff(f328,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,[],[f217]) ).
tff(f217,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,[],[f59]) ).
tff(f59,axiom,
! [X9: int,X8: int] :
( ord_less(int,number_number_of(int,X8),number_number_of(int,X9))
<=> ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_less__number__of__int__code) ).
tff(f1136,plain,
spl0_93,
inference(avatar_split_clause,[],[f530,f1134]) ).
tff(f530,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,[],[f328]) ).
tff(f1132,plain,
spl0_92,
inference(avatar_split_clause,[],[f527,f1130]) ).
tff(f1130,plain,
( spl0_92
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
tff(f527,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f327]) ).
tff(f1128,plain,
spl0_91,
inference(avatar_split_clause,[],[f525,f1126]) ).
tff(f525,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
inference(nnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X9: int,X8: int] :
( ord_less_eq(int,number_number_of(int,X8),number_number_of(int,X9))
<=> ord_less_eq(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__eq__number__of__int__code) ).
tff(f1124,plain,
spl0_90,
inference(avatar_split_clause,[],[f524,f1122]) ).
tff(f524,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,number_number_of(int,X1),number_number_of(int,X0)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1085,plain,
spl0_89,
inference(avatar_split_clause,[],[f610,f1083]) ).
tff(f1083,plain,
( spl0_89
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
tff(f610,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f391]) ).
tff(f391,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f1081,plain,
spl0_88,
inference(avatar_split_clause,[],[f573,f1079]) ).
tff(f1079,plain,
( spl0_88
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
tff(f573,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f464,f389]) ).
tff(f464,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,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,[],[f183]) ).
tff(f183,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X8: int] :
( ord_less(int,bit0(X8),pls)
<=> ord_less(int,X8,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_rel__simps_I10_J) ).
tff(f1077,plain,
spl0_87,
inference(avatar_split_clause,[],[f572,f1075]) ).
tff(f1075,plain,
( spl0_87
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
tff(f572,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f465,f389]) ).
tff(f465,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f299]) ).
tff(f1073,plain,
spl0_86,
inference(avatar_split_clause,[],[f571,f1071]) ).
tff(f1071,plain,
( spl0_86
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
tff(f571,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f460,f389]) ).
tff(f460,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,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,[],[f181]) ).
tff(f181,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X8: int] :
( ord_less(int,pls,bit0(X8))
<=> ord_less(int,pls,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I4_J) ).
tff(f1069,plain,
spl0_85,
inference(avatar_split_clause,[],[f570,f1067]) ).
tff(f1067,plain,
( spl0_85
<=> ! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
tff(f570,plain,
! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f461,f389]) ).
tff(f461,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1065,plain,
spl0_84,
inference(avatar_split_clause,[],[f569,f1063]) ).
tff(f1063,plain,
( spl0_84
<=> ! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
tff(f569,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f456,f389]) ).
tff(f456,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X8: int] :
( ord_less_eq(int,bit0(X8),pls)
<=> ord_less_eq(int,X8,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rel__simps_I27_J) ).
tff(f1061,plain,
spl0_83,
inference(avatar_split_clause,[],[f568,f1059]) ).
tff(f1059,plain,
( spl0_83
<=> ! [X0: int] :
( ord_less_eq(int,plus_plus(int,X0,X0),pls)
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
tff(f568,plain,
! [X0: int] :
( ord_less_eq(int,plus_plus(int,X0,X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(definition_unfolding,[],[f457,f389]) ).
tff(f457,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1057,plain,
( spl0_82
| ~ spl0_10
| ~ spl0_58
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1020,f987,f933,f690,f1055]) ).
tff(f1055,plain,
( spl0_82
<=> ! [X0: real] : ( plus_plus(real,zero_zero(real),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
tff(f690,plain,
( spl0_10
<=> number_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f933,plain,
( spl0_58
<=> ( zero_zero(real) = number_number_of(real,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
tff(f987,plain,
( spl0_69
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
tff(f1020,plain,
( ! [X0: real] : ( plus_plus(real,zero_zero(real),X0) = X0 )
| ~ spl0_10
| ~ spl0_58
| ~ spl0_69 ),
inference(forward_demodulation,[],[f1018,f935]) ).
tff(f935,plain,
( ( zero_zero(real) = number_number_of(real,pls) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f1018,plain,
( ! [X0: real] : ( plus_plus(real,number_number_of(real,pls),X0) = X0 )
| ~ spl0_10
| ~ spl0_69 ),
inference(resolution,[],[f988,f692]) ).
tff(f692,plain,
( number_ring(real)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f690]) ).
tff(f988,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f987]) ).
tff(f1053,plain,
spl0_81,
inference(avatar_split_clause,[],[f567,f1051]) ).
tff(f1051,plain,
( spl0_81
<=> ! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
tff(f567,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f452,f389]) ).
tff(f452,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: int] :
( ( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X8: int] :
( ord_less_eq(int,pls,bit0(X8))
<=> ord_less_eq(int,pls,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rel__simps_I21_J) ).
tff(f1049,plain,
spl0_80,
inference(avatar_split_clause,[],[f566,f1047]) ).
tff(f1047,plain,
( spl0_80
<=> ! [X0: int] :
( ord_less_eq(int,pls,plus_plus(int,X0,X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
tff(f566,plain,
! [X0: int] :
( ord_less_eq(int,pls,plus_plus(int,X0,X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(definition_unfolding,[],[f453,f389]) ).
tff(f453,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f1045,plain,
spl0_79,
inference(avatar_split_clause,[],[f487,f1043]) ).
tff(f1043,plain,
( spl0_79
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
tff(f487,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) )
& ( ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) )
| ~ ord_less(int,X1,X0) ) ),
inference(flattening,[],[f305]) ).
tff(f305,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) )
& ( ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) )
| ~ ord_less(int,X1,X0) ) ),
inference(nnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X18: int,X19: int] :
( ord_less(int,X19,X18)
<=> ( ( X18 != X19 )
& ord_less_eq(int,X19,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__int__def) ).
tff(f1041,plain,
spl0_78,
inference(avatar_split_clause,[],[f475,f1039]) ).
tff(f1039,plain,
( spl0_78
<=> ! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
tff(f475,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: int] :
( ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) )
& ( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
inference(nnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X13: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X13))
<=> ord_less(int,pls,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__0__number__of) ).
tff(f1037,plain,
spl0_77,
inference(avatar_split_clause,[],[f474,f1035]) ).
tff(f474,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f304]) ).
tff(f1027,plain,
( spl0_76
| ~ spl0_10
| ~ spl0_58
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f1016,f983,f933,f690,f1025]) ).
tff(f1025,plain,
( spl0_76
<=> ! [X0: real] : ( plus_plus(real,X0,zero_zero(real)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
tff(f983,plain,
( spl0_68
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
tff(f1016,plain,
( ! [X0: real] : ( plus_plus(real,X0,zero_zero(real)) = X0 )
| ~ spl0_10
| ~ spl0_58
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1014,f935]) ).
tff(f1014,plain,
( ! [X0: real] : ( plus_plus(real,X0,number_number_of(real,pls)) = X0 )
| ~ spl0_10
| ~ spl0_68 ),
inference(resolution,[],[f984,f692]) ).
tff(f984,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f983]) ).
tff(f1013,plain,
spl0_75,
inference(avatar_split_clause,[],[f509,f1011]) ).
tff(f509,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,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,[],[f207]) ).
tff(f207,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X9: int,X8: int] :
( ord_less(int,bit1(X8),bit1(X9))
<=> ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I17_J) ).
tff(f1009,plain,
spl0_74,
inference(avatar_split_clause,[],[f508,f1007]) ).
tff(f1007,plain,
( spl0_74
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
tff(f508,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1005,plain,
spl0_73,
inference(avatar_split_clause,[],[f493,f1003]) ).
tff(f1003,plain,
( spl0_73
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
tff(f493,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X16: int,X17: int] :
( ord_less_eq(int,bit1(X17),bit1(X16))
<=> ord_less_eq(int,X17,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__eq__int__code_I16_J) ).
tff(f1001,plain,
spl0_72,
inference(avatar_split_clause,[],[f492,f999]) ).
tff(f999,plain,
( spl0_72
<=> ! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
tff(f492,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f997,plain,
spl0_71,
inference(avatar_split_clause,[],[f467,f995]) ).
tff(f995,plain,
( spl0_71
<=> ! [X0: int] :
( ( zero_zero(nat) = number_number_of(nat,X0) )
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
tff(f467,plain,
! [X0: int] :
( ( zero_zero(nat) = number_number_of(nat,X0) )
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: int] :
( ( ( zero_zero(nat) = number_number_of(nat,X0) )
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ( zero_zero(nat) != number_number_of(nat,X0) ) ) ),
inference(nnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int] :
( ( zero_zero(nat) = number_number_of(nat,X0) )
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X13: int] :
( ( zero_zero(nat) = number_number_of(nat,X13) )
<=> ord_less_eq(int,X13,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_eq__number__of__0) ).
tff(f993,plain,
spl0_70,
inference(avatar_split_clause,[],[f466,f991]) ).
tff(f991,plain,
( spl0_70
<=> ! [X0: int] :
( ord_less_eq(int,X0,pls)
| ( zero_zero(nat) != number_number_of(nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
tff(f466,plain,
! [X0: int] :
( ord_less_eq(int,X0,pls)
| ( zero_zero(nat) != number_number_of(nat,X0) ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f989,plain,
spl0_69,
inference(avatar_split_clause,[],[f397,f987]) ).
tff(f397,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X20: X0] : ( plus_plus(X0,number_number_of(X0,pls),X20) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__numeral__0) ).
tff(f985,plain,
spl0_68,
inference(avatar_split_clause,[],[f396,f983]) ).
tff(f396,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X20: X0] : ( plus_plus(X0,X20,number_number_of(X0,pls)) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__numeral__0__right) ).
tff(f973,plain,
spl0_67,
inference(avatar_split_clause,[],[f563,f971]) ).
tff(f971,plain,
( spl0_67
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
tff(f563,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ),
inference(definition_unfolding,[],[f446,f389]) ).
tff(f446,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X8: int] :
( ( pls = bit0(X8) )
<=> ( pls = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I44_J) ).
tff(f969,plain,
spl0_66,
inference(avatar_split_clause,[],[f463,f967]) ).
tff(f967,plain,
( spl0_66
<=> ! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
tff(f463,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,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,[],[f182]) ).
tff(f182,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X8: int] :
( ord_less(int,bit1(X8),pls)
<=> ord_less(int,X8,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rel__simps_I12_J) ).
tff(f965,plain,
spl0_65,
inference(avatar_split_clause,[],[f462,f963]) ).
tff(f963,plain,
( spl0_65
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
tff(f462,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f298]) ).
tff(f961,plain,
spl0_64,
inference(avatar_split_clause,[],[f459,f959]) ).
tff(f959,plain,
( spl0_64
<=> ! [X0: int] :
( ord_less(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
tff(f459,plain,
! [X0: int] :
( ord_less(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: int] :
( ( ord_less(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less(int,pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: int] :
( ord_less(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X8: int] :
( ord_less(int,pls,bit1(X8))
<=> ord_less_eq(int,pls,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I5_J) ).
tff(f957,plain,
spl0_63,
inference(avatar_split_clause,[],[f458,f955]) ).
tff(f955,plain,
( spl0_63
<=> ! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less(int,pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
tff(f458,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f953,plain,
spl0_62,
inference(avatar_split_clause,[],[f455,f951]) ).
tff(f951,plain,
( spl0_62
<=> ! [X0: int] :
( ord_less_eq(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
tff(f455,plain,
! [X0: int] :
( ord_less_eq(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: int] :
( ( ord_less_eq(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) )
& ( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: int] :
( ord_less_eq(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X8: int] :
( ord_less_eq(int,bit1(X8),pls)
<=> ord_less(int,X8,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_rel__simps_I29_J) ).
tff(f949,plain,
spl0_61,
inference(avatar_split_clause,[],[f454,f947]) ).
tff(f947,plain,
( spl0_61
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
tff(f454,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f294]) ).
tff(f945,plain,
spl0_60,
inference(avatar_split_clause,[],[f451,f943]) ).
tff(f943,plain,
( spl0_60
<=> ! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
tff(f451,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: int] :
( ( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) )
& ( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: int] :
( ord_less_eq(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X8: int] :
( ord_less_eq(int,pls,bit1(X8))
<=> ord_less_eq(int,pls,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_rel__simps_I22_J) ).
tff(f941,plain,
spl0_59,
inference(avatar_split_clause,[],[f450,f939]) ).
tff(f939,plain,
( spl0_59
<=> ! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
tff(f450,plain,
! [X0: int] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f292]) ).
tff(f936,plain,
( spl0_58
| ~ spl0_10
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f925,f910,f690,f933]) ).
tff(f910,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(f925,plain,
( ( zero_zero(real) = number_number_of(real,pls) )
| ~ spl0_10
| ~ spl0_54 ),
inference(resolution,[],[f911,f692]) ).
tff(f911,plain,
( ! [X0: $tType] :
( ~ number_ring(X0)
| ( zero_zero(X0) = number_number_of(X0,pls) ) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f910]) ).
tff(f924,plain,
spl0_57,
inference(avatar_split_clause,[],[f488,f922]) ).
tff(f922,plain,
( spl0_57
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
tff(f488,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: int,X1: int] :
( ( ( bit1(X0) = bit1(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: int,X1: int] :
( ( bit1(X0) = bit1(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X9: int,X8: int] :
( ( bit1(X8) = bit1(X9) )
<=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I51_J) ).
tff(f920,plain,
spl0_56,
inference(avatar_split_clause,[],[f485,f918]) ).
tff(f485,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f916,plain,
spl0_55,
inference(avatar_split_clause,[],[f420,f914]) ).
tff(f914,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(f420,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_semiring__numeral__0__eq__0) ).
tff(f912,plain,
spl0_54,
inference(avatar_split_clause,[],[f394,f910]) ).
tff(f394,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_number__of__Pls) ).
tff(f906,plain,
spl0_53,
inference(avatar_split_clause,[],[f576,f904]) ).
tff(f576,plain,
! [X0: int,X1: int] : ( plus_plus(int,X0,X0) != bit1(X1) ),
inference(definition_unfolding,[],[f476,f389]) ).
tff(f476,plain,
! [X0: int,X1: int] : ( bit0(X0) != bit1(X1) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: int,X1: int] : ( bit0(X0) != bit1(X1) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X6: int,X7: int] : ( bit1(X7) != bit0(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I50_J) ).
tff(f900,plain,
~ spl0_52,
inference(avatar_split_clause,[],[f535,f897]) ).
tff(f897,plain,
( spl0_52
<=> ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f535,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(definition_unfolding,[],[f331,f389,f389]) ).
tff(f331,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(flattening,[],[f140]) ).
tff(f140,negated_conjecture,
~ ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(negated_conjecture,[],[f139]) ).
tff(f139,conjecture,
ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f895,plain,
spl0_51,
inference(avatar_split_clause,[],[f388,f893]) ).
tff(f893,plain,
( spl0_51
<=> ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f388,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X7: int] : ( plus_plus(int,pls,X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__Pls) ).
tff(f891,plain,
spl0_50,
inference(avatar_split_clause,[],[f387,f889]) ).
tff(f889,plain,
( spl0_50
<=> ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f387,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X7: int] : ( plus_plus(int,X7,pls) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add__Pls__right) ).
tff(f887,plain,
spl0_49,
inference(avatar_split_clause,[],[f379,f884]) ).
tff(f379,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(cnf_transformation,[],[f33]) ).
tff(f33,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nat__number__of__Pls) ).
tff(f882,plain,
spl0_48,
inference(avatar_split_clause,[],[f631,f879]) ).
tff(f631,plain,
pls = number_number_of(int,pls),
inference(forward_demodulation,[],[f381,f375]) ).
tff(f381,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f61]) ).
tff(f61,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_zero__is__num__zero) ).
tff(f877,plain,
spl0_47,
inference(avatar_split_clause,[],[f378,f874]) ).
tff(f874,plain,
( spl0_47
<=> ord_less(nat,zero_zero(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f378,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_n0) ).
tff(f872,plain,
( ~ spl0_46
| spl0_41
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f867,f850,f845,f869]) ).
tff(f845,plain,
( spl0_41
<=> ( v = zero_zero(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f867,plain,
( ( v != pls )
| spl0_41
| ~ spl0_42 ),
inference(superposition,[],[f847,f852]) ).
tff(f847,plain,
( ( v != zero_zero(int) )
| spl0_41 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f866,plain,
spl0_45,
inference(avatar_split_clause,[],[f625,f864]) ).
tff(f864,plain,
( spl0_45
<=> ! [X1: int] : ~ ord_less(int,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f625,plain,
! [X1: int] : ~ ord_less(int,X1,X1),
inference(equality_resolution,[],[f486]) ).
tff(f486,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f862,plain,
spl0_44,
inference(avatar_split_clause,[],[f385,f860]) ).
tff(f860,plain,
( spl0_44
<=> ! [X0: int] : ( pls != bit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f385,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X7: int] : ( pls != bit1(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I46_J) ).
tff(f858,plain,
spl0_43,
inference(avatar_split_clause,[],[f376,f855]) ).
tff(f855,plain,
( spl0_43
<=> ord_less_eq(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f376,plain,
ord_less_eq(int,pls,pls),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
ord_less_eq(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I19_J) ).
tff(f853,plain,
spl0_42,
inference(avatar_split_clause,[],[f375,f850]) ).
tff(f848,plain,
~ spl0_41,
inference(avatar_split_clause,[],[f372,f845]) ).
tff(f372,plain,
v != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
v != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
tff(f843,plain,
spl0_40,
inference(avatar_split_clause,[],[f371,f840]) ).
tff(f840,plain,
( spl0_40
<=> linorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f371,plain,
linorder(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f838,plain,
spl0_39,
inference(avatar_split_clause,[],[f370,f835]) ).
tff(f835,plain,
( spl0_39
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f370,plain,
linorder(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
tff(f833,plain,
spl0_38,
inference(avatar_split_clause,[],[f369,f830]) ).
tff(f830,plain,
( spl0_38
<=> linorder(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f369,plain,
linorder(real),
inference(cnf_transformation,[],[f130]) ).
tff(f130,axiom,
linorder(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
tff(f828,plain,
spl0_37,
inference(avatar_split_clause,[],[f368,f825]) ).
tff(f825,plain,
( spl0_37
<=> linorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f368,plain,
linorder(bool),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
linorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
tff(f823,plain,
spl0_36,
inference(avatar_split_clause,[],[f367,f820]) ).
tff(f820,plain,
( spl0_36
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f367,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f818,plain,
spl0_35,
inference(avatar_split_clause,[],[f366,f815]) ).
tff(f815,plain,
( spl0_35
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f366,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f813,plain,
spl0_34,
inference(avatar_split_clause,[],[f365,f810]) ).
tff(f810,plain,
( spl0_34
<=> linordered_semidom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f365,plain,
linordered_semidom(real),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
linordered_semidom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
tff(f808,plain,
spl0_33,
inference(avatar_split_clause,[],[f364,f805]) ).
tff(f805,plain,
( spl0_33
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f364,plain,
number_semiring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f803,plain,
spl0_32,
inference(avatar_split_clause,[],[f363,f800]) ).
tff(f800,plain,
( spl0_32
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f363,plain,
number(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f798,plain,
spl0_31,
inference(avatar_split_clause,[],[f362,f795]) ).
tff(f795,plain,
( spl0_31
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f362,plain,
number(nat),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
number(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
tff(f793,plain,
spl0_30,
inference(avatar_split_clause,[],[f361,f790]) ).
tff(f790,plain,
( spl0_30
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f361,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
number_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
tff(f788,plain,
spl0_29,
inference(avatar_split_clause,[],[f360,f785]) ).
tff(f785,plain,
( spl0_29
<=> number(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f360,plain,
number(real),
inference(cnf_transformation,[],[f136]) ).
tff(f136,axiom,
number(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
tff(f783,plain,
spl0_28,
inference(avatar_split_clause,[],[f359,f780]) ).
tff(f780,plain,
( spl0_28
<=> number_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f359,plain,
number_semiring(real),
inference(cnf_transformation,[],[f128]) ).
tff(f128,axiom,
number_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
tff(f778,plain,
spl0_27,
inference(avatar_split_clause,[],[f358,f775]) ).
tff(f775,plain,
( spl0_27
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f358,plain,
semiring_1(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f773,plain,
spl0_26,
inference(avatar_split_clause,[],[f357,f770]) ).
tff(f770,plain,
( spl0_26
<=> power(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f357,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f768,plain,
spl0_25,
inference(avatar_split_clause,[],[f356,f765]) ).
tff(f765,plain,
( spl0_25
<=> mult_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f356,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f763,plain,
spl0_24,
inference(avatar_split_clause,[],[f355,f760]) ).
tff(f760,plain,
( spl0_24
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f355,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f758,plain,
spl0_23,
inference(avatar_split_clause,[],[f354,f755]) ).
tff(f755,plain,
( spl0_23
<=> no_zero_divisors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f354,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f753,plain,
spl0_22,
inference(avatar_split_clause,[],[f353,f750]) ).
tff(f750,plain,
( spl0_22
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f353,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
tff(f748,plain,
spl0_21,
inference(avatar_split_clause,[],[f352,f745]) ).
tff(f745,plain,
( spl0_21
<=> no_zero_divisors(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f352,plain,
no_zero_divisors(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
tff(f743,plain,
spl0_20,
inference(avatar_split_clause,[],[f351,f740]) ).
tff(f740,plain,
( spl0_20
<=> power(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f351,plain,
power(nat),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
power(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
tff(f738,plain,
spl0_19,
inference(avatar_split_clause,[],[f350,f735]) ).
tff(f735,plain,
( spl0_19
<=> mult_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f350,plain,
mult_zero(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
mult_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
tff(f733,plain,
spl0_18,
inference(avatar_split_clause,[],[f349,f730]) ).
tff(f730,plain,
( spl0_18
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f349,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f728,plain,
spl0_17,
inference(avatar_split_clause,[],[f348,f725]) ).
tff(f725,plain,
( spl0_17
<=> mult_zero(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f348,plain,
mult_zero(real),
inference(cnf_transformation,[],[f132]) ).
tff(f132,axiom,
mult_zero(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
tff(f723,plain,
spl0_16,
inference(avatar_split_clause,[],[f347,f720]) ).
tff(f720,plain,
( spl0_16
<=> no_zero_divisors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f347,plain,
no_zero_divisors(real),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
no_zero_divisors(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
tff(f718,plain,
spl0_15,
inference(avatar_split_clause,[],[f346,f715]) ).
tff(f715,plain,
( spl0_15
<=> power(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f346,plain,
power(real),
inference(cnf_transformation,[],[f135]) ).
tff(f135,axiom,
power(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
tff(f713,plain,
spl0_14,
inference(avatar_split_clause,[],[f345,f710]) ).
tff(f710,plain,
( spl0_14
<=> zero_neq_one(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f345,plain,
zero_neq_one(real),
inference(cnf_transformation,[],[f129]) ).
tff(f129,axiom,
zero_neq_one(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
tff(f708,plain,
spl0_13,
inference(avatar_split_clause,[],[f344,f705]) ).
tff(f705,plain,
( spl0_13
<=> semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f344,plain,
semiring_1(real),
inference(cnf_transformation,[],[f131]) ).
tff(f131,axiom,
semiring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
tff(f703,plain,
spl0_12,
inference(avatar_split_clause,[],[f343,f700]) ).
tff(f700,plain,
( spl0_12
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f343,plain,
number_ring(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f698,plain,
spl0_11,
inference(avatar_split_clause,[],[f342,f695]) ).
tff(f342,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f693,plain,
spl0_10,
inference(avatar_split_clause,[],[f341,f690]) ).
tff(f341,plain,
number_ring(real),
inference(cnf_transformation,[],[f134]) ).
tff(f134,axiom,
number_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
tff(f688,plain,
spl0_9,
inference(avatar_split_clause,[],[f340,f685]) ).
tff(f685,plain,
( spl0_9
<=> linordered_idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f340,plain,
linordered_idom(real),
inference(cnf_transformation,[],[f127]) ).
tff(f127,axiom,
linordered_idom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
tff(f683,plain,
spl0_8,
inference(avatar_split_clause,[],[f339,f680]) ).
tff(f680,plain,
( spl0_8
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f339,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f678,plain,
spl0_7,
inference(avatar_split_clause,[],[f338,f675]) ).
tff(f675,plain,
( spl0_7
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f338,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f673,plain,
spl0_6,
inference(avatar_split_clause,[],[f337,f670]) ).
tff(f670,plain,
( spl0_6
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f337,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f668,plain,
spl0_5,
inference(avatar_split_clause,[],[f336,f665]) ).
tff(f665,plain,
( spl0_5
<=> ring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f336,plain,
ring_char_0(real),
inference(cnf_transformation,[],[f133]) ).
tff(f133,axiom,
ring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
tff(f663,plain,
spl0_4,
inference(avatar_split_clause,[],[f335,f660]) ).
tff(f660,plain,
( spl0_4
<=> linord219039673up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f335,plain,
linord219039673up_add(real),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
linord219039673up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
tff(f658,plain,
spl0_3,
inference(avatar_split_clause,[],[f334,f655]) ).
tff(f655,plain,
( spl0_3
<=> ring_11004092258visors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f334,plain,
ring_11004092258visors(real),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
ring_11004092258visors(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
tff(f653,plain,
spl0_2,
inference(avatar_split_clause,[],[f333,f650]) ).
tff(f650,plain,
( spl0_2
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f333,plain,
pp(fTrue),
inference(cnf_transformation,[],[f138]) ).
tff(f138,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f648,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f332,f645]) ).
tff(f645,plain,
( spl0_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f332,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f137]) ).
tff(f137,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN017_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 02:18:17 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (7337)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (7340)WARNING: value z3 for option sas not known
% 0.14/0.39 % (7338)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (7340)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)
% 0.14/0.39 % (7339)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (7341)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (7342)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)
% 0.14/0.39 % (7343)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)
% 0.14/0.39 % (7344)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)
% 0.14/0.39 % (7344)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.41 % (7345)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.41 % (7346)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)
% 0.14/0.41 % (7347)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)
% 0.14/0.41 % (7345)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.41 % (7346)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.41 % Exception at run slice level
% 0.14/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42 % (7342)First to succeed.
% 0.21/0.43 % (7348)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)
% 0.21/0.44 % (7342)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (7342)------------------------------
% 0.21/0.45 % (7342)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.45 % (7342)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (7342)Memory used [KB]: 1630
% 0.21/0.45 % (7342)Time elapsed: 0.052 s
% 0.21/0.45 % (7342)Instructions burned: 88 (million)
% 0.21/0.45 % (7342)------------------------------
% 0.21/0.45 % (7342)------------------------------
% 0.21/0.45 % (7337)Success in time 0.077 s
%------------------------------------------------------------------------------