TSTP Solution File: SWW613_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:35:39 EDT 2024
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 519
% Syntax : Number of formulae : 1448 ( 360 unt; 59 typ; 0 def)
% Number of atoms : 4509 ( 671 equ)
% Maximal formula atoms : 130 ( 3 avg)
% Number of connectives : 4857 (1747 ~;1497 |; 951 &)
% ( 333 <=>; 329 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number arithmetic : 4366 (1245 atm; 608 fun;1046 num;1467 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 57 ( 35 >; 22 *; 0 +; 0 <<)
% Number of predicates : 320 ( 315 usr; 307 prp; 0-2 aty)
% Number of functors : 56 ( 45 usr; 24 con; 0-5 aty)
% Number of variables : 1755 (1596 !; 159 ?;1755 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(type_def_9,type,
list_int: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
abs: $int > $int ).
tff(func_def_14,type,
div: ( $int * $int ) > $int ).
tff(func_def_15,type,
mod: ( $int * $int ) > $int ).
tff(func_def_23,type,
gcd: ( $int * $int ) > $int ).
tff(func_def_24,type,
ref: ty > ty ).
tff(func_def_25,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_26,type,
contents: ( ty * uni ) > uni ).
tff(func_def_27,type,
list: ty > ty ).
tff(func_def_28,type,
nil: ty > uni ).
tff(func_def_29,type,
cons: ( ty * uni * uni ) > uni ).
tff(func_def_30,type,
match_list: ( ty * ty * uni * uni * uni ) > uni ).
tff(func_def_31,type,
cons_proj_1: ( ty * uni ) > uni ).
tff(func_def_32,type,
cons_proj_2: ( ty * uni ) > uni ).
tff(func_def_33,type,
t2tb: list_int > uni ).
tff(func_def_34,type,
tb2t: uni > list_int ).
tff(func_def_35,type,
t2tb1: $int > uni ).
tff(func_def_36,type,
tb2t1: uni > $int ).
tff(func_def_38,type,
sK3: $int ).
tff(func_def_39,type,
sK4: $int ).
tff(func_def_40,type,
sK5: list_int ).
tff(func_def_41,type,
sK6: $int ).
tff(func_def_42,type,
sK7: $int ).
tff(func_def_43,type,
sK8: list_int ).
tff(func_def_44,type,
sK9: $int ).
tff(func_def_45,type,
sK10: $int ).
tff(func_def_46,type,
sK11: list_int ).
tff(func_def_47,type,
sK12: $int ).
tff(func_def_48,type,
sK13: $int ).
tff(func_def_49,type,
sK14: $int > $int ).
tff(func_def_50,type,
sK15: $int > $int ).
tff(func_def_51,type,
sK16: $int > $int ).
tff(func_def_52,type,
sK17: $int > $int ).
tff(func_def_53,type,
sK18: $int > $int ).
tff(func_def_54,type,
sK19: ( $int * $int ) > $int ).
tff(func_def_55,type,
sK20: ( $int * $int * $int ) > $int ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(pred_def_4,type,
divides: ( $int * $int ) > $o ).
tff(pred_def_5,type,
even: $int > $o ).
tff(pred_def_6,type,
odd: $int > $o ).
tff(pred_def_7,type,
prime: $int > $o ).
tff(pred_def_8,type,
coprime: ( $int * $int ) > $o ).
tff(pred_def_9,type,
sP0: $int > $o ).
tff(pred_def_10,type,
sP1: $int > $o ).
tff(pred_def_11,type,
sP2: $int > $o ).
tff(f3761,plain,
$false,
inference(avatar_sat_refutation,[],[f625,f630,f635,f640,f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f760,f765,f770,f775,f779,f784,f788,f792,f797,f801,f818,f822,f835,f839,f844,f848,f852,f856,f860,f877,f881,f885,f889,f893,f897,f901,f910,f914,f918,f922,f926,f941,f945,f949,f953,f957,f961,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1056,f1068,f1108,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1158,f1162,f1166,f1170,f1174,f1193,f1197,f1201,f1205,f1209,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1250,f1255,f1340,f1344,f1348,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1394,f1398,f1449,f1453,f1457,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1634,f1638,f1642,f1646,f1650,f1655,f1659,f1663,f1667,f1671,f1675,f1716,f1780,f1784,f1788,f1792,f1796,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1924,f2138,f2163,f2169,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2287,f2291,f2295,f2299,f2303,f2415,f2419,f2428,f2432,f2436,f2440,f2480,f2484,f2519,f2556,f2560,f2564,f2568,f2629,f2651,f2660,f2673,f2686,f2699,f2720,f2737,f2744,f2751,f2758,f2765,f2779,f2783,f2787,f2791,f2795,f2804,f2820,f2836,f2858,f2860,f2865,f2891,f2922,f2945,f2946,f2969,f2999,f3015,f3026,f3029,f3040,f3108,f3118,f3125,f3160,f3222,f3256,f3264,f3269,f3270,f3277,f3282,f3312,f3316,f3321,f3326,f3332,f3415,f3419,f3423,f3463,f3469,f3475,f3481,f3487,f3493,f3499,f3506,f3511,f3516,f3521,f3526,f3632,f3643,f3651,f3657,f3661,f3667,f3673,f3679,f3685,f3692,f3701,f3707,f3720,f3736,f3739,f3743,f3748,f3757,f3760]) ).
tff(f3760,plain,
( ~ spl21_98
| spl21_21
| spl21_19
| ~ spl21_20
| ~ spl21_165 ),
inference(avatar_split_clause,[],[f1962,f1790,f717,f712,f722,f1155]) ).
tff(f1155,plain,
( spl21_98
<=> sP2(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_98])]) ).
tff(f722,plain,
( spl21_21
<=> $less(sK10,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_21])]) ).
tff(f712,plain,
( spl21_19
<=> coprime(sK10,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
tff(f717,plain,
( spl21_20
<=> $less(sK10,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).
tff(f1790,plain,
( spl21_165
<=> ! [X2: $int,X0: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_165])]) ).
tff(f1962,plain,
( coprime(sK10,sK13)
| $less(sK10,1)
| ~ sP2(sK13)
| ~ spl21_20
| ~ spl21_165 ),
inference(resolution,[],[f1791,f719]) ).
tff(f719,plain,
( $less(sK10,sK13)
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f717]) ).
tff(f1791,plain,
( ! [X2: $int,X0: $int] :
( ~ $less(X2,X0)
| coprime(X2,X0)
| $less(X2,1)
| ~ sP2(X0) )
| ~ spl21_165 ),
inference(avatar_component_clause,[],[f1790]) ).
tff(f3757,plain,
( ~ spl21_98
| spl21_305
| spl21_306
| ~ spl21_17
| ~ spl21_165 ),
inference(avatar_split_clause,[],[f1961,f1790,f702,f3754,f3750,f1155]) ).
tff(f3750,plain,
( spl21_305
<=> $less(sK7,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_305])]) ).
tff(f3754,plain,
( spl21_306
<=> coprime(sK7,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_306])]) ).
tff(f702,plain,
( spl21_17
<=> $less(sK7,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
tff(f1961,plain,
( coprime(sK7,sK13)
| $less(sK7,1)
| ~ sP2(sK13)
| ~ spl21_17
| ~ spl21_165 ),
inference(resolution,[],[f1791,f704]) ).
tff(f704,plain,
( $less(sK7,sK13)
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f702]) ).
tff(f3748,plain,
( ~ spl21_304
| spl21_137
| ~ spl21_251 ),
inference(avatar_split_clause,[],[f3061,f3008,f1459,f3745]) ).
tff(f3745,plain,
( spl21_304
<=> divides(2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_304])]) ).
tff(f1459,plain,
( spl21_137
<=> divides(2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_137])]) ).
tff(f3008,plain,
( spl21_251
<=> ( sK3 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_251])]) ).
tff(f3061,plain,
( ~ divides(2,sK4)
| spl21_137
| ~ spl21_251 ),
inference(superposition,[],[f1460,f3010]) ).
tff(f3010,plain,
( ( sK3 = sK4 )
| ~ spl21_251 ),
inference(avatar_component_clause,[],[f3008]) ).
tff(f1460,plain,
( ~ divides(2,sK3)
| spl21_137 ),
inference(avatar_component_clause,[],[f1459]) ).
tff(f3743,plain,
( ~ spl21_301
| ~ spl21_242
| ~ spl21_262
| ~ spl21_22
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1949,f1786,f727,f3253,f2833,f3725]) ).
tff(f3725,plain,
( spl21_301
<=> sP1(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_301])]) ).
tff(f2833,plain,
( spl21_242
<=> $less(1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_242])]) ).
tff(f3253,plain,
( spl21_262
<=> $less(sK10,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_262])]) ).
tff(f727,plain,
( spl21_22
<=> divides(sK10,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).
tff(f1786,plain,
( spl21_164
<=> ! [X2: $int,X0: $int] :
( ~ divides(X2,X0)
| ~ $less(X2,X0)
| ~ $less(1,X2)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_164])]) ).
tff(f1949,plain,
( ~ $less(sK10,sK6)
| ~ $less(1,sK10)
| ~ sP1(sK6)
| ~ spl21_22
| ~ spl21_164 ),
inference(resolution,[],[f1787,f729]) ).
tff(f729,plain,
( divides(sK10,sK6)
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f727]) ).
tff(f1787,plain,
( ! [X2: $int,X0: $int] :
( ~ divides(X2,X0)
| ~ $less(X2,X0)
| ~ $less(1,X2)
| ~ sP1(X0) )
| ~ spl21_164 ),
inference(avatar_component_clause,[],[f1786]) ).
tff(f3739,plain,
( ~ spl21_66
| ~ spl21_256
| spl21_301 ),
inference(avatar_split_clause,[],[f3738,f3725,f3111,f963]) ).
tff(f963,plain,
( spl21_66
<=> sP1(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).
tff(f3111,plain,
( spl21_256
<=> ( sK6 = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_256])]) ).
tff(f3738,plain,
( ~ sP1(sK7)
| ~ spl21_256
| spl21_301 ),
inference(forward_demodulation,[],[f3727,f3113]) ).
tff(f3113,plain,
( ( sK6 = sK7 )
| ~ spl21_256 ),
inference(avatar_component_clause,[],[f3111]) ).
tff(f3727,plain,
( ~ sP1(sK6)
| spl21_301 ),
inference(avatar_component_clause,[],[f3725]) ).
tff(f3736,plain,
( ~ spl21_301
| ~ spl21_302
| ~ spl21_303
| ~ spl21_15
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1947,f1786,f692,f3733,f3729,f3725]) ).
tff(f3729,plain,
( spl21_302
<=> $less(1,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_302])]) ).
tff(f3733,plain,
( spl21_303
<=> $less(sK12,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_303])]) ).
tff(f692,plain,
( spl21_15
<=> divides(sK12,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
tff(f1947,plain,
( ~ $less(sK12,sK6)
| ~ $less(1,sK12)
| ~ sP1(sK6)
| ~ spl21_15
| ~ spl21_164 ),
inference(resolution,[],[f1787,f694]) ).
tff(f694,plain,
( divides(sK12,sK6)
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f692]) ).
tff(f3720,plain,
( ~ spl21_296
| ~ spl21_299
| ~ spl21_300
| ~ spl21_16
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1946,f1786,f697,f3717,f3713,f3694]) ).
tff(f3694,plain,
( spl21_296
<=> sP1(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_296])]) ).
tff(f3713,plain,
( spl21_299
<=> $less(1,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_299])]) ).
tff(f3717,plain,
( spl21_300
<=> $less(sK13,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_300])]) ).
tff(f697,plain,
( spl21_16
<=> divides(sK13,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
tff(f1946,plain,
( ~ $less(sK13,sK3)
| ~ $less(1,sK13)
| ~ sP1(sK3)
| ~ spl21_16
| ~ spl21_164 ),
inference(resolution,[],[f1787,f699]) ).
tff(f699,plain,
( divides(sK13,sK3)
| ~ spl21_16 ),
inference(avatar_component_clause,[],[f697]) ).
tff(f3707,plain,
( ~ spl21_298
| ~ spl21_251
| spl21_296 ),
inference(avatar_split_clause,[],[f3702,f3694,f3008,f3704]) ).
tff(f3704,plain,
( spl21_298
<=> sP1(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_298])]) ).
tff(f3702,plain,
( ~ sP1(sK4)
| ~ spl21_251
| spl21_296 ),
inference(forward_demodulation,[],[f3696,f3010]) ).
tff(f3696,plain,
( ~ sP1(sK3)
| spl21_296 ),
inference(avatar_component_clause,[],[f3694]) ).
tff(f3701,plain,
( ~ spl21_296
| ~ spl21_297
| ~ spl21_254
| ~ spl21_11
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1945,f1786,f672,f3023,f3698,f3694]) ).
tff(f3698,plain,
( spl21_297
<=> $less(1,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_297])]) ).
tff(f3023,plain,
( spl21_254
<=> $less(sK7,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_254])]) ).
tff(f672,plain,
( spl21_11
<=> divides(sK7,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
tff(f1945,plain,
( ~ $less(sK7,sK3)
| ~ $less(1,sK7)
| ~ sP1(sK3)
| ~ spl21_11
| ~ spl21_164 ),
inference(resolution,[],[f1787,f674]) ).
tff(f674,plain,
( divides(sK7,sK3)
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f672]) ).
tff(f3692,plain,
( spl21_295
| ~ spl21_16
| ~ spl21_251 ),
inference(avatar_split_clause,[],[f3054,f3008,f697,f3689]) ).
tff(f3689,plain,
( spl21_295
<=> divides(sK13,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_295])]) ).
tff(f3054,plain,
( divides(sK13,sK4)
| ~ spl21_16
| ~ spl21_251 ),
inference(superposition,[],[f699,f3010]) ).
tff(f3685,plain,
( spl21_294
| ~ spl21_26
| ~ spl21_158 ),
inference(avatar_split_clause,[],[f1740,f1665,f747,f3683]) ).
tff(f3683,plain,
( spl21_294
<=> ! [X0: $int] :
( divides($product(sK12,X0),sK6)
| ~ divides(X0,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_294])]) ).
tff(f747,plain,
( spl21_26
<=> ( sK6 = $product(sK12,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_26])]) ).
tff(f1665,plain,
( spl21_158
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides($product(X2,X0),$product(X2,X1))
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_158])]) ).
tff(f1740,plain,
( ! [X0: $int] :
( divides($product(sK12,X0),sK6)
| ~ divides(X0,sK10) )
| ~ spl21_26
| ~ spl21_158 ),
inference(superposition,[],[f1666,f749]) ).
tff(f749,plain,
( ( sK6 = $product(sK12,sK10) )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f747]) ).
tff(f1666,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( divides($product(X2,X0),$product(X2,X1))
| ~ divides(X0,X1) )
| ~ spl21_158 ),
inference(avatar_component_clause,[],[f1665]) ).
tff(f3679,plain,
( spl21_293
| ~ spl21_26
| ~ spl21_158 ),
inference(avatar_split_clause,[],[f1735,f1665,f747,f3677]) ).
tff(f3677,plain,
( spl21_293
<=> ! [X0: $int] :
( divides(sK6,$product(sK12,X0))
| ~ divides(sK10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_293])]) ).
tff(f1735,plain,
( ! [X0: $int] :
( divides(sK6,$product(sK12,X0))
| ~ divides(sK10,X0) )
| ~ spl21_26
| ~ spl21_158 ),
inference(superposition,[],[f1666,f749]) ).
tff(f3673,plain,
( spl21_292
| ~ spl21_26
| ~ spl21_157 ),
inference(avatar_split_clause,[],[f1729,f1661,f747,f3671]) ).
tff(f3671,plain,
( spl21_292
<=> ! [X0: $int] :
( divides($product(X0,sK10),sK6)
| ~ divides(X0,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_292])]) ).
tff(f1661,plain,
( spl21_157
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides($product(X0,X2),$product(X1,X2))
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_157])]) ).
tff(f1729,plain,
( ! [X0: $int] :
( divides($product(X0,sK10),sK6)
| ~ divides(X0,sK12) )
| ~ spl21_26
| ~ spl21_157 ),
inference(superposition,[],[f1662,f749]) ).
tff(f1662,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( divides($product(X0,X2),$product(X1,X2))
| ~ divides(X0,X1) )
| ~ spl21_157 ),
inference(avatar_component_clause,[],[f1661]) ).
tff(f3667,plain,
( spl21_291
| ~ spl21_26
| ~ spl21_157 ),
inference(avatar_split_clause,[],[f1724,f1661,f747,f3665]) ).
tff(f3665,plain,
( spl21_291
<=> ! [X0: $int] :
( divides(sK6,$product(X0,sK10))
| ~ divides(sK12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_291])]) ).
tff(f1724,plain,
( ! [X0: $int] :
( divides(sK6,$product(X0,sK10))
| ~ divides(sK12,X0) )
| ~ spl21_26
| ~ spl21_157 ),
inference(superposition,[],[f1662,f749]) ).
tff(f3661,plain,
( spl21_290
| ~ spl21_28
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1434,f1387,f757,f3659]) ).
tff(f3659,plain,
( spl21_290
<=> ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,div(sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_290])]) ).
tff(f757,plain,
( spl21_28
<=> ( sK3 = $product(div(sK3,sK4),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_28])]) ).
tff(f1387,plain,
( spl21_131
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X1,X2))
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_131])]) ).
tff(f1434,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,div(sK3,sK4)) )
| ~ spl21_28
| ~ spl21_131 ),
inference(superposition,[],[f1388,f759]) ).
tff(f759,plain,
( ( sK3 = $product(div(sK3,sK4),sK4) )
| ~ spl21_28 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f1388,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X1,X2))
| ~ divides(X0,X1) )
| ~ spl21_131 ),
inference(avatar_component_clause,[],[f1387]) ).
tff(f3657,plain,
( ~ spl21_289
| ~ spl21_251
| ~ spl21_256
| spl21_287 ),
inference(avatar_split_clause,[],[f3645,f3640,f3111,f3008,f3654]) ).
tff(f3654,plain,
( spl21_289
<=> divides(sK4,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_289])]) ).
tff(f3640,plain,
( spl21_287
<=> divides(sK3,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_287])]) ).
tff(f3645,plain,
( ~ divides(sK4,sK7)
| ~ spl21_251
| ~ spl21_256
| spl21_287 ),
inference(forward_demodulation,[],[f3644,f3010]) ).
tff(f3644,plain,
( ~ divides(sK3,sK7)
| ~ spl21_256
| spl21_287 ),
inference(forward_demodulation,[],[f3641,f3113]) ).
tff(f3641,plain,
( ~ divides(sK3,sK6)
| spl21_287 ),
inference(avatar_component_clause,[],[f3640]) ).
tff(f3651,plain,
( ~ spl21_288
| ~ spl21_251
| spl21_286 ),
inference(avatar_split_clause,[],[f3646,f3636,f3008,f3648]) ).
tff(f3648,plain,
( spl21_288
<=> prime(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_288])]) ).
tff(f3636,plain,
( spl21_286
<=> prime(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_286])]) ).
tff(f3646,plain,
( ~ prime(sK4)
| ~ spl21_251
| spl21_286 ),
inference(forward_demodulation,[],[f3638,f3010]) ).
tff(f3638,plain,
( ~ prime(sK3)
| spl21_286 ),
inference(avatar_component_clause,[],[f3636]) ).
tff(f3643,plain,
( ~ spl21_286
| spl21_287
| ~ spl21_254
| ~ spl21_39
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f862,f850,f820,f3023,f3640,f3636]) ).
tff(f820,plain,
( spl21_39
<=> ! [X13: $int] :
( divides(X13,sK6)
| ~ $less(sK7,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_39])]) ).
tff(f850,plain,
( spl21_44
<=> ! [X0: $int] : divides(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_44])]) ).
tff(f862,plain,
( ~ $less(sK7,sK3)
| divides(sK3,sK6)
| ~ prime(sK3)
| ~ spl21_39
| ~ spl21_44 ),
inference(resolution,[],[f851,f821]) ).
tff(f821,plain,
( ! [X13: $int] :
( ~ divides(X13,sK3)
| ~ $less(sK7,X13)
| divides(X13,sK6)
| ~ prime(X13) )
| ~ spl21_39 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f851,plain,
( ! [X0: $int] : divides(X0,X0)
| ~ spl21_44 ),
inference(avatar_component_clause,[],[f850]) ).
tff(f3632,plain,
( ~ spl21_2
| spl21_284
| ~ spl21_285
| ~ spl21_16
| ~ spl21_38 ),
inference(avatar_split_clause,[],[f826,f816,f697,f3629,f3625,f627]) ).
tff(f627,plain,
( spl21_2
<=> prime(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
tff(f3625,plain,
( spl21_284
<=> coprime(sK4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_284])]) ).
tff(f3629,plain,
( spl21_285
<=> $less(sK4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_285])]) ).
tff(f816,plain,
( spl21_38
<=> ! [X15: $int] :
( coprime(sK4,X15)
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_38])]) ).
tff(f826,plain,
( ~ $less(sK4,sK13)
| coprime(sK4,sK13)
| ~ prime(sK13)
| ~ spl21_16
| ~ spl21_38 ),
inference(resolution,[],[f817,f699]) ).
tff(f817,plain,
( ! [X15: $int] :
( ~ divides(X15,sK3)
| ~ $less(sK4,X15)
| coprime(sK4,X15)
| ~ prime(X15) )
| ~ spl21_38 ),
inference(avatar_component_clause,[],[f816]) ).
tff(f3526,plain,
( spl21_283
| ~ spl21_256
| ~ spl21_277 ),
inference(avatar_split_clause,[],[f3494,f3490,f3111,f3523]) ).
tff(f3523,plain,
( spl21_283
<=> ( sK7 = $product(sK13,sK19(sK13,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_283])]) ).
tff(f3490,plain,
( spl21_277
<=> ( sK6 = $product(sK13,sK19(sK13,sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_277])]) ).
tff(f3494,plain,
( ( sK7 = $product(sK13,sK19(sK13,sK7)) )
| ~ spl21_256
| ~ spl21_277 ),
inference(forward_demodulation,[],[f3492,f3113]) ).
tff(f3492,plain,
( ( sK6 = $product(sK13,sK19(sK13,sK6)) )
| ~ spl21_277 ),
inference(avatar_component_clause,[],[f3490]) ).
tff(f3521,plain,
( spl21_282
| ~ spl21_256
| ~ spl21_276 ),
inference(avatar_split_clause,[],[f3488,f3484,f3111,f3518]) ).
tff(f3518,plain,
( spl21_282
<=> ( sK7 = $product(sK12,sK19(sK12,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_282])]) ).
tff(f3484,plain,
( spl21_276
<=> ( sK6 = $product(sK12,sK19(sK12,sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_276])]) ).
tff(f3488,plain,
( ( sK7 = $product(sK12,sK19(sK12,sK7)) )
| ~ spl21_256
| ~ spl21_276 ),
inference(forward_demodulation,[],[f3486,f3113]) ).
tff(f3486,plain,
( ( sK6 = $product(sK12,sK19(sK12,sK6)) )
| ~ spl21_276 ),
inference(avatar_component_clause,[],[f3484]) ).
tff(f3516,plain,
( spl21_281
| ~ spl21_251
| ~ spl21_275 ),
inference(avatar_split_clause,[],[f3482,f3478,f3008,f3513]) ).
tff(f3513,plain,
( spl21_281
<=> ( sK4 = $product(sK13,sK19(sK13,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_281])]) ).
tff(f3478,plain,
( spl21_275
<=> ( sK3 = $product(sK13,sK19(sK13,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_275])]) ).
tff(f3482,plain,
( ( sK4 = $product(sK13,sK19(sK13,sK4)) )
| ~ spl21_251
| ~ spl21_275 ),
inference(forward_demodulation,[],[f3480,f3010]) ).
tff(f3480,plain,
( ( sK3 = $product(sK13,sK19(sK13,sK3)) )
| ~ spl21_275 ),
inference(avatar_component_clause,[],[f3478]) ).
tff(f3511,plain,
( spl21_280
| ~ spl21_251
| ~ spl21_274 ),
inference(avatar_split_clause,[],[f3476,f3472,f3008,f3508]) ).
tff(f3508,plain,
( spl21_280
<=> ( sK4 = $product(sK7,sK19(sK7,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_280])]) ).
tff(f3472,plain,
( spl21_274
<=> ( sK3 = $product(sK7,sK19(sK7,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_274])]) ).
tff(f3476,plain,
( ( sK4 = $product(sK7,sK19(sK7,sK4)) )
| ~ spl21_251
| ~ spl21_274 ),
inference(forward_demodulation,[],[f3474,f3010]) ).
tff(f3474,plain,
( ( sK3 = $product(sK7,sK19(sK7,sK3)) )
| ~ spl21_274 ),
inference(avatar_component_clause,[],[f3472]) ).
tff(f3506,plain,
( spl21_279
| ~ spl21_251
| ~ spl21_272 ),
inference(avatar_split_clause,[],[f3464,f3460,f3008,f3503]) ).
tff(f3503,plain,
( spl21_279
<=> ( sK4 = $product(sK4,div(sK4,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_279])]) ).
tff(f3460,plain,
( spl21_272
<=> ( sK3 = $product(sK4,div(sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_272])]) ).
tff(f3464,plain,
( ( sK4 = $product(sK4,div(sK4,sK4)) )
| ~ spl21_251
| ~ spl21_272 ),
inference(forward_demodulation,[],[f3462,f3010]) ).
tff(f3462,plain,
( ( sK3 = $product(sK4,div(sK3,sK4)) )
| ~ spl21_272 ),
inference(avatar_component_clause,[],[f3460]) ).
tff(f3499,plain,
( spl21_278
| ~ spl21_22
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1773,f1673,f727,f3496]) ).
tff(f3496,plain,
( spl21_278
<=> ( sK6 = $product(sK10,sK19(sK10,sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_278])]) ).
tff(f1673,plain,
( spl21_160
<=> ! [X0: $int,X1: $int] :
( ( $product(X0,sK19(X0,X1)) = X1 )
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_160])]) ).
tff(f1773,plain,
( ( sK6 = $product(sK10,sK19(sK10,sK6)) )
| ~ spl21_22
| ~ spl21_160 ),
inference(resolution,[],[f1674,f729]) ).
tff(f1674,plain,
( ! [X0: $int,X1: $int] :
( ~ divides(X0,X1)
| ( $product(X0,sK19(X0,X1)) = X1 ) )
| ~ spl21_160 ),
inference(avatar_component_clause,[],[f1673]) ).
tff(f3493,plain,
( spl21_277
| ~ spl21_18
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1772,f1673,f707,f3490]) ).
tff(f707,plain,
( spl21_18
<=> divides(sK13,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
tff(f1772,plain,
( ( sK6 = $product(sK13,sK19(sK13,sK6)) )
| ~ spl21_18
| ~ spl21_160 ),
inference(resolution,[],[f1674,f709]) ).
tff(f709,plain,
( divides(sK13,sK6)
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f707]) ).
tff(f3487,plain,
( spl21_276
| ~ spl21_15
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1771,f1673,f692,f3484]) ).
tff(f1771,plain,
( ( sK6 = $product(sK12,sK19(sK12,sK6)) )
| ~ spl21_15
| ~ spl21_160 ),
inference(resolution,[],[f1674,f694]) ).
tff(f3481,plain,
( spl21_275
| ~ spl21_16
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1770,f1673,f697,f3478]) ).
tff(f1770,plain,
( ( sK3 = $product(sK13,sK19(sK13,sK3)) )
| ~ spl21_16
| ~ spl21_160 ),
inference(resolution,[],[f1674,f699]) ).
tff(f3475,plain,
( spl21_274
| ~ spl21_11
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1769,f1673,f672,f3472]) ).
tff(f1769,plain,
( ( sK3 = $product(sK7,sK19(sK7,sK3)) )
| ~ spl21_11
| ~ spl21_160 ),
inference(resolution,[],[f1674,f674]) ).
tff(f3469,plain,
( spl21_273
| ~ spl21_7
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1768,f1673,f652,f3466]) ).
tff(f3466,plain,
( spl21_273
<=> ( sK3 = $product(sK4,sK19(sK4,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_273])]) ).
tff(f652,plain,
( spl21_7
<=> divides(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
tff(f1768,plain,
( ( sK3 = $product(sK4,sK19(sK4,sK3)) )
| ~ spl21_7
| ~ spl21_160 ),
inference(resolution,[],[f1674,f654]) ).
tff(f654,plain,
( divides(sK4,sK3)
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f652]) ).
tff(f3463,plain,
( spl21_272
| ~ spl21_28
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f1264,f1195,f757,f3460]) ).
tff(f1195,plain,
( spl21_104
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).
tff(f1264,plain,
( ( sK3 = $product(sK4,div(sK3,sK4)) )
| ~ spl21_28
| ~ spl21_104 ),
inference(superposition,[],[f1196,f759]) ).
tff(f1196,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl21_104 ),
inference(avatar_component_clause,[],[f1195]) ).
tff(f3423,plain,
( spl21_271
| ~ spl21_256
| ~ spl21_267 ),
inference(avatar_split_clause,[],[f3327,f3324,f3111,f3421]) ).
tff(f3421,plain,
( spl21_271
<=> ! [X0: $int] :
( divides(X0,sK7)
| ~ divides(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_271])]) ).
tff(f3324,plain,
( spl21_267
<=> ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_267])]) ).
tff(f3327,plain,
( ! [X0: $int] :
( divides(X0,sK7)
| ~ divides(X0,sK13) )
| ~ spl21_256
| ~ spl21_267 ),
inference(forward_demodulation,[],[f3325,f3113]) ).
tff(f3325,plain,
( ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK13) )
| ~ spl21_267 ),
inference(avatar_component_clause,[],[f3324]) ).
tff(f3419,plain,
( spl21_270
| ~ spl21_251
| ~ spl21_266 ),
inference(avatar_split_clause,[],[f3322,f3319,f3008,f3417]) ).
tff(f3417,plain,
( spl21_270
<=> ! [X0: $int] :
( divides(X0,sK4)
| ~ divides(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_270])]) ).
tff(f3319,plain,
( spl21_266
<=> ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_266])]) ).
tff(f3322,plain,
( ! [X0: $int] :
( divides(X0,sK4)
| ~ divides(X0,sK13) )
| ~ spl21_251
| ~ spl21_266 ),
inference(forward_demodulation,[],[f3320,f3010]) ).
tff(f3320,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK13) )
| ~ spl21_266 ),
inference(avatar_component_clause,[],[f3319]) ).
tff(f3415,plain,
( spl21_269
| ~ spl21_251
| ~ spl21_265 ),
inference(avatar_split_clause,[],[f3317,f3314,f3008,f3413]) ).
tff(f3413,plain,
( spl21_269
<=> ! [X0: $int] :
( divides(X0,sK4)
| ~ divides(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_269])]) ).
tff(f3314,plain,
( spl21_265
<=> ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_265])]) ).
tff(f3317,plain,
( ! [X0: $int] :
( divides(X0,sK4)
| ~ divides(X0,sK7) )
| ~ spl21_251
| ~ spl21_265 ),
inference(forward_demodulation,[],[f3315,f3010]) ).
tff(f3315,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK7) )
| ~ spl21_265 ),
inference(avatar_component_clause,[],[f3314]) ).
tff(f3332,plain,
( ~ spl21_268
| spl21_161
| ~ spl21_251 ),
inference(avatar_split_clause,[],[f3063,f3008,f1713,f3329]) ).
tff(f3329,plain,
( spl21_268
<=> even(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_268])]) ).
tff(f1713,plain,
( spl21_161
<=> even(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_161])]) ).
tff(f3063,plain,
( ~ even(sK4)
| spl21_161
| ~ spl21_251 ),
inference(superposition,[],[f1715,f3010]) ).
tff(f1715,plain,
( ~ even(sK3)
| spl21_161 ),
inference(avatar_component_clause,[],[f1713]) ).
tff(f3326,plain,
( spl21_267
| ~ spl21_18
| ~ spl21_148 ),
inference(avatar_split_clause,[],[f1618,f1504,f707,f3324]) ).
tff(f1504,plain,
( spl21_148
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_148])]) ).
tff(f1618,plain,
( ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK13) )
| ~ spl21_18
| ~ spl21_148 ),
inference(resolution,[],[f1505,f709]) ).
tff(f1505,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ divides(X1,X2)
| divides(X0,X2)
| ~ divides(X0,X1) )
| ~ spl21_148 ),
inference(avatar_component_clause,[],[f1504]) ).
tff(f3321,plain,
( spl21_266
| ~ spl21_16
| ~ spl21_148 ),
inference(avatar_split_clause,[],[f1616,f1504,f697,f3319]) ).
tff(f1616,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK13) )
| ~ spl21_16
| ~ spl21_148 ),
inference(resolution,[],[f1505,f699]) ).
tff(f3316,plain,
( spl21_265
| ~ spl21_11
| ~ spl21_148 ),
inference(avatar_split_clause,[],[f1615,f1504,f672,f3314]) ).
tff(f1615,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK7) )
| ~ spl21_11
| ~ spl21_148 ),
inference(resolution,[],[f1505,f674]) ).
tff(f3312,plain,
( spl21_264
| ~ spl21_256
| ~ spl21_260
| ~ spl21_261 ),
inference(avatar_split_clause,[],[f3281,f3249,f3219,f3111,f3266]) ).
tff(f3266,plain,
( spl21_264
<=> $less(sK7,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_264])]) ).
tff(f3219,plain,
( spl21_260
<=> $less(sK7,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_260])]) ).
tff(f3249,plain,
( spl21_261
<=> ( sK6 = sK10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_261])]) ).
tff(f3281,plain,
( $less(sK7,sK7)
| ~ spl21_256
| ~ spl21_260
| ~ spl21_261 ),
inference(forward_demodulation,[],[f3221,f3279]) ).
tff(f3279,plain,
( ( sK7 = sK10 )
| ~ spl21_256
| ~ spl21_261 ),
inference(forward_demodulation,[],[f3251,f3113]) ).
tff(f3251,plain,
( ( sK6 = sK10 )
| ~ spl21_261 ),
inference(avatar_component_clause,[],[f3249]) ).
tff(f3221,plain,
( $less(sK7,sK10)
| ~ spl21_260 ),
inference(avatar_component_clause,[],[f3219]) ).
tff(f3282,plain,
( spl21_259
| ~ spl21_256
| ~ spl21_261 ),
inference(avatar_split_clause,[],[f3279,f3249,f3111,f3215]) ).
tff(f3215,plain,
( spl21_259
<=> ( sK7 = sK10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_259])]) ).
tff(f3277,plain,
( ~ spl21_41
| ~ spl21_264 ),
inference(avatar_contradiction_clause,[],[f3272]) ).
tff(f3272,plain,
( $false
| ~ spl21_41
| ~ spl21_264 ),
inference(resolution,[],[f3268,f838]) ).
tff(f838,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f837,plain,
( spl21_41
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_41])]) ).
tff(f3268,plain,
( $less(sK7,sK7)
| ~ spl21_264 ),
inference(avatar_component_clause,[],[f3266]) ).
tff(f3270,plain,
( ~ spl21_256
| ~ spl21_259
| spl21_261 ),
inference(avatar_split_clause,[],[f3259,f3249,f3215,f3111]) ).
tff(f3259,plain,
( ( sK6 != sK7 )
| ~ spl21_259
| spl21_261 ),
inference(forward_demodulation,[],[f3250,f3217]) ).
tff(f3217,plain,
( ( sK7 = sK10 )
| ~ spl21_259 ),
inference(avatar_component_clause,[],[f3215]) ).
tff(f3250,plain,
( ( sK6 != sK10 )
| spl21_261 ),
inference(avatar_component_clause,[],[f3249]) ).
tff(f3269,plain,
( spl21_264
| ~ spl21_256
| ~ spl21_259
| ~ spl21_262 ),
inference(avatar_split_clause,[],[f3258,f3253,f3215,f3111,f3266]) ).
tff(f3258,plain,
( $less(sK7,sK7)
| ~ spl21_256
| ~ spl21_259
| ~ spl21_262 ),
inference(forward_demodulation,[],[f3257,f3217]) ).
tff(f3257,plain,
( $less(sK10,sK7)
| ~ spl21_256
| ~ spl21_262 ),
inference(forward_demodulation,[],[f3255,f3113]) ).
tff(f3255,plain,
( $less(sK10,sK6)
| ~ spl21_262 ),
inference(avatar_component_clause,[],[f3253]) ).
tff(f3264,plain,
( spl21_263
| ~ spl21_155
| ~ spl21_251 ),
inference(avatar_split_clause,[],[f3062,f3008,f1652,f3261]) ).
tff(f3261,plain,
( spl21_263
<=> odd(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_263])]) ).
tff(f1652,plain,
( spl21_155
<=> odd(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_155])]) ).
tff(f3062,plain,
( odd(sK4)
| ~ spl21_155
| ~ spl21_251 ),
inference(superposition,[],[f1654,f3010]) ).
tff(f1654,plain,
( odd(sK3)
| ~ spl21_155 ),
inference(avatar_component_clause,[],[f1652]) ).
tff(f3256,plain,
( spl21_261
| spl21_262
| spl21_23
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1544,f1451,f732,f3253,f3249]) ).
tff(f732,plain,
( spl21_23
<=> $less(sK6,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_23])]) ).
tff(f1451,plain,
( spl21_135
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_135])]) ).
tff(f1544,plain,
( $less(sK10,sK6)
| ( sK6 = sK10 )
| spl21_23
| ~ spl21_135 ),
inference(resolution,[],[f1452,f734]) ).
tff(f734,plain,
( ~ $less(sK6,sK10)
| spl21_23 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f1452,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl21_135 ),
inference(avatar_component_clause,[],[f1451]) ).
tff(f3222,plain,
( spl21_259
| spl21_260
| spl21_24
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1543,f1451,f737,f3219,f3215]) ).
tff(f737,plain,
( spl21_24
<=> $less(sK10,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_24])]) ).
tff(f1543,plain,
( $less(sK7,sK10)
| ( sK7 = sK10 )
| spl21_24
| ~ spl21_135 ),
inference(resolution,[],[f1452,f739]) ).
tff(f739,plain,
( ~ $less(sK10,sK7)
| spl21_24 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f3160,plain,
( spl21_255
| ~ spl21_252
| ~ spl21_253 ),
inference(avatar_split_clause,[],[f3137,f3019,f3012,f3105]) ).
tff(f3105,plain,
( spl21_255
<=> $less(sK4,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_255])]) ).
tff(f3012,plain,
( spl21_252
<=> $less(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_252])]) ).
tff(f3019,plain,
( spl21_253
<=> ( sK3 = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_253])]) ).
tff(f3137,plain,
( $less(sK4,sK7)
| ~ spl21_252
| ~ spl21_253 ),
inference(forward_demodulation,[],[f3014,f3021]) ).
tff(f3021,plain,
( ( sK3 = sK7 )
| ~ spl21_253 ),
inference(avatar_component_clause,[],[f3019]) ).
tff(f3014,plain,
( $less(sK4,sK3)
| ~ spl21_252 ),
inference(avatar_component_clause,[],[f3012]) ).
tff(f3125,plain,
( spl21_258
| ~ spl21_251
| ~ spl21_253
| ~ spl21_256 ),
inference(avatar_split_clause,[],[f3120,f3111,f3019,f3008,f3122]) ).
tff(f3122,plain,
( spl21_258
<=> ( sK4 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_258])]) ).
tff(f3120,plain,
( ( sK4 = sK6 )
| ~ spl21_251
| ~ spl21_253
| ~ spl21_256 ),
inference(forward_demodulation,[],[f3113,f3068]) ).
tff(f3068,plain,
( ( sK4 = sK7 )
| ~ spl21_251
| ~ spl21_253 ),
inference(superposition,[],[f3021,f3010]) ).
tff(f3118,plain,
( spl21_256
| spl21_257
| spl21_14
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1542,f1451,f687,f3115,f3111]) ).
tff(f3115,plain,
( spl21_257
<=> $less(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_257])]) ).
tff(f687,plain,
( spl21_14
<=> $less(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
tff(f1542,plain,
( $less(sK7,sK6)
| ( sK6 = sK7 )
| spl21_14
| ~ spl21_135 ),
inference(resolution,[],[f1452,f689]) ).
tff(f689,plain,
( ~ $less(sK6,sK7)
| spl21_14 ),
inference(avatar_component_clause,[],[f687]) ).
tff(f3108,plain,
( ~ spl21_255
| spl21_252
| ~ spl21_253 ),
inference(avatar_split_clause,[],[f3031,f3019,f3012,f3105]) ).
tff(f3031,plain,
( ~ $less(sK4,sK7)
| spl21_252
| ~ spl21_253 ),
inference(forward_demodulation,[],[f3013,f3021]) ).
tff(f3013,plain,
( ~ $less(sK4,sK3)
| spl21_252 ),
inference(avatar_component_clause,[],[f3012]) ).
tff(f3040,plain,
( spl21_243
| ~ spl21_245
| ~ spl21_251 ),
inference(avatar_split_clause,[],[f3017,f3008,f2915,f2884]) ).
tff(f2884,plain,
( spl21_243
<=> ( 2 = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_243])]) ).
tff(f2915,plain,
( spl21_245
<=> ( 2 = sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_245])]) ).
tff(f3017,plain,
( ( 2 = sK3 )
| ~ spl21_245
| ~ spl21_251 ),
inference(forward_demodulation,[],[f3010,f2917]) ).
tff(f2917,plain,
( ( 2 = sK4 )
| ~ spl21_245 ),
inference(avatar_component_clause,[],[f2915]) ).
tff(f3029,plain,
( spl21_186
| ~ spl21_243
| ~ spl21_253 ),
inference(avatar_split_clause,[],[f3028,f3019,f2884,f2131]) ).
tff(f2131,plain,
( spl21_186
<=> ( 2 = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_186])]) ).
tff(f3028,plain,
( ( 2 = sK7 )
| ~ spl21_243
| ~ spl21_253 ),
inference(forward_demodulation,[],[f3021,f2886]) ).
tff(f2886,plain,
( ( 2 = sK3 )
| ~ spl21_243 ),
inference(avatar_component_clause,[],[f2884]) ).
tff(f3026,plain,
( spl21_253
| spl21_254
| spl21_10
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1541,f1451,f667,f3023,f3019]) ).
tff(f667,plain,
( spl21_10
<=> $less(sK3,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
tff(f1541,plain,
( $less(sK7,sK3)
| ( sK3 = sK7 )
| spl21_10
| ~ spl21_135 ),
inference(resolution,[],[f1452,f669]) ).
tff(f669,plain,
( ~ $less(sK3,sK7)
| spl21_10 ),
inference(avatar_component_clause,[],[f667]) ).
tff(f3015,plain,
( spl21_251
| spl21_252
| spl21_6
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1537,f1451,f647,f3012,f3008]) ).
tff(f647,plain,
( spl21_6
<=> $less(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
tff(f1537,plain,
( $less(sK4,sK3)
| ( sK3 = sK4 )
| spl21_6
| ~ spl21_135 ),
inference(resolution,[],[f1452,f649]) ).
tff(f649,plain,
( ~ $less(sK3,sK4)
| spl21_6 ),
inference(avatar_component_clause,[],[f647]) ).
tff(f2999,plain,
( spl21_186
| spl21_250
| spl21_13
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1534,f1451,f682,f2996,f2131]) ).
tff(f2996,plain,
( spl21_250
<=> $less(2,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_250])]) ).
tff(f682,plain,
( spl21_13
<=> $less(sK7,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).
tff(f1534,plain,
( $less(2,sK7)
| ( 2 = sK7 )
| spl21_13
| ~ spl21_135 ),
inference(resolution,[],[f1452,f684]) ).
tff(f684,plain,
( ~ $less(sK7,2)
| spl21_13 ),
inference(avatar_component_clause,[],[f682]) ).
tff(f2969,plain,
( spl21_249
| ~ spl21_37
| ~ spl21_247 ),
inference(avatar_split_clause,[],[f2947,f2938,f799,f2967]) ).
tff(f2967,plain,
( spl21_249
<=> ! [X11: $int] :
( ~ divides(X11,2)
| ~ $less(X11,sK10)
| $less(X11,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_249])]) ).
tff(f799,plain,
( spl21_37
<=> ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK10)
| $less(X11,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).
tff(f2938,plain,
( spl21_247
<=> ( 2 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_247])]) ).
tff(f2947,plain,
( ! [X11: $int] :
( ~ divides(X11,2)
| ~ $less(X11,sK10)
| $less(X11,2) )
| ~ spl21_37
| ~ spl21_247 ),
inference(forward_demodulation,[],[f800,f2940]) ).
tff(f2940,plain,
( ( 2 = sK6 )
| ~ spl21_247 ),
inference(avatar_component_clause,[],[f2938]) ).
tff(f800,plain,
( ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK10)
| $less(X11,2) )
| ~ spl21_37 ),
inference(avatar_component_clause,[],[f799]) ).
tff(f2946,plain,
( ~ spl21_90
| ~ spl21_80
| ~ spl21_228 ),
inference(avatar_split_clause,[],[f2870,f2717,f1021,f1105]) ).
tff(f1105,plain,
( spl21_90
<=> sP2(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_90])]) ).
tff(f1021,plain,
( spl21_80
<=> ! [X0: $int] :
( ~ $less(X0,2)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_80])]) ).
tff(f2717,plain,
( spl21_228
<=> $less(sK10,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_228])]) ).
tff(f2870,plain,
( ~ sP2(sK10)
| ~ spl21_80
| ~ spl21_228 ),
inference(resolution,[],[f2719,f1022]) ).
tff(f1022,plain,
( ! [X0: $int] :
( ~ $less(X0,2)
| ~ sP2(X0) )
| ~ spl21_80 ),
inference(avatar_component_clause,[],[f1021]) ).
tff(f2719,plain,
( $less(sK10,2)
| ~ spl21_228 ),
inference(avatar_component_clause,[],[f2717]) ).
tff(f2945,plain,
( spl21_247
| spl21_248
| spl21_12
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1533,f1451,f677,f2942,f2938]) ).
tff(f2942,plain,
( spl21_248
<=> $less(2,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_248])]) ).
tff(f677,plain,
( spl21_12
<=> $less(sK6,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
tff(f1533,plain,
( $less(2,sK6)
| ( 2 = sK6 )
| spl21_12
| ~ spl21_135 ),
inference(resolution,[],[f1452,f679]) ).
tff(f679,plain,
( ~ $less(sK6,2)
| spl21_12 ),
inference(avatar_component_clause,[],[f677]) ).
tff(f2922,plain,
( spl21_245
| spl21_246
| spl21_5
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1532,f1451,f642,f2919,f2915]) ).
tff(f2919,plain,
( spl21_246
<=> $less(2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_246])]) ).
tff(f642,plain,
( spl21_5
<=> $less(sK4,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
tff(f1532,plain,
( $less(2,sK4)
| ( 2 = sK4 )
| spl21_5
| ~ spl21_135 ),
inference(resolution,[],[f1452,f644]) ).
tff(f644,plain,
( ~ $less(sK4,2)
| spl21_5 ),
inference(avatar_component_clause,[],[f642]) ).
tff(f2891,plain,
( spl21_243
| spl21_244
| spl21_4
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1531,f1451,f637,f2888,f2884]) ).
tff(f2888,plain,
( spl21_244
<=> $less(2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_244])]) ).
tff(f637,plain,
( spl21_4
<=> $less(sK3,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).
tff(f1531,plain,
( $less(2,sK3)
| ( 2 = sK3 )
| spl21_4
| ~ spl21_135 ),
inference(resolution,[],[f1452,f639]) ).
tff(f639,plain,
( ~ $less(sK3,2)
| spl21_4 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f2865,plain,
( spl21_29
| ~ spl21_3
| ~ spl21_241 ),
inference(avatar_split_clause,[],[f2837,f2829,f632,f762]) ).
tff(f762,plain,
( spl21_29
<=> prime(1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_29])]) ).
tff(f632,plain,
( spl21_3
<=> prime(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
tff(f2829,plain,
( spl21_241
<=> ( 1 = sK10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_241])]) ).
tff(f2837,plain,
( prime(1)
| ~ spl21_3
| ~ spl21_241 ),
inference(superposition,[],[f634,f2831]) ).
tff(f2831,plain,
( ( 1 = sK10 )
| ~ spl21_241 ),
inference(avatar_component_clause,[],[f2829]) ).
tff(f634,plain,
( prime(sK10)
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f2860,plain,
( spl21_222
| ~ spl21_241 ),
inference(avatar_contradiction_clause,[],[f2859]) ).
tff(f2859,plain,
( $false
| spl21_222
| ~ spl21_241 ),
inference(evaluation,[],[f2852]) ).
tff(f2852,plain,
( ~ $less(1,3)
| spl21_222
| ~ spl21_241 ),
inference(superposition,[],[f2671,f2831]) ).
tff(f2671,plain,
( ~ $less(sK10,3)
| spl21_222 ),
inference(avatar_component_clause,[],[f2670]) ).
tff(f2670,plain,
( spl21_222
<=> $less(sK10,3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_222])]) ).
tff(f2858,plain,
( spl21_228
| ~ spl21_241 ),
inference(avatar_contradiction_clause,[],[f2857]) ).
tff(f2857,plain,
( $false
| spl21_228
| ~ spl21_241 ),
inference(evaluation,[],[f2854]) ).
tff(f2854,plain,
( ~ $less(1,2)
| spl21_228
| ~ spl21_241 ),
inference(superposition,[],[f2718,f2831]) ).
tff(f2718,plain,
( ~ $less(sK10,2)
| spl21_228 ),
inference(avatar_component_clause,[],[f2717]) ).
tff(f2836,plain,
( spl21_241
| spl21_242
| spl21_21
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1528,f1451,f722,f2833,f2829]) ).
tff(f1528,plain,
( $less(1,sK10)
| ( 1 = sK10 )
| spl21_21
| ~ spl21_135 ),
inference(resolution,[],[f1452,f724]) ).
tff(f724,plain,
( ~ $less(sK10,1)
| spl21_21 ),
inference(avatar_component_clause,[],[f722]) ).
tff(f2820,plain,
( spl21_12
| ~ spl21_239 ),
inference(avatar_contradiction_clause,[],[f2819]) ).
tff(f2819,plain,
( $false
| spl21_12
| ~ spl21_239 ),
inference(evaluation,[],[f2807]) ).
tff(f2807,plain,
( ~ $less(1,2)
| spl21_12
| ~ spl21_239 ),
inference(superposition,[],[f679,f2799]) ).
tff(f2799,plain,
( ( 1 = sK6 )
| ~ spl21_239 ),
inference(avatar_component_clause,[],[f2797]) ).
tff(f2797,plain,
( spl21_239
<=> ( 1 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_239])]) ).
tff(f2804,plain,
( spl21_239
| spl21_240
| spl21_8
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1527,f1451,f657,f2801,f2797]) ).
tff(f2801,plain,
( spl21_240
<=> $less(1,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_240])]) ).
tff(f657,plain,
( spl21_8
<=> $less(sK6,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).
tff(f1527,plain,
( $less(1,sK6)
| ( 1 = sK6 )
| spl21_8
| ~ spl21_135 ),
inference(resolution,[],[f1452,f659]) ).
tff(f659,plain,
( ~ $less(sK6,1)
| spl21_8 ),
inference(avatar_component_clause,[],[f657]) ).
tff(f2795,plain,
( spl21_238
| ~ spl21_20
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1516,f1447,f717,f2793]) ).
tff(f2793,plain,
( spl21_238
<=> ! [X0: $int] :
( ~ $less(X0,sK10)
| $less(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_238])]) ).
tff(f1447,plain,
( spl21_134
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_134])]) ).
tff(f1516,plain,
( ! [X0: $int] :
( ~ $less(X0,sK10)
| $less(X0,sK13) )
| ~ spl21_20
| ~ spl21_134 ),
inference(resolution,[],[f1448,f719]) ).
tff(f1448,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl21_134 ),
inference(avatar_component_clause,[],[f1447]) ).
tff(f2791,plain,
( spl21_237
| ~ spl21_17
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1515,f1447,f702,f2789]) ).
tff(f2789,plain,
( spl21_237
<=> ! [X0: $int] :
( ~ $less(X0,sK7)
| $less(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_237])]) ).
tff(f1515,plain,
( ! [X0: $int] :
( ~ $less(X0,sK7)
| $less(X0,sK13) )
| ~ spl21_17
| ~ spl21_134 ),
inference(resolution,[],[f1448,f704]) ).
tff(f2787,plain,
( spl21_236
| ~ spl21_28
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1442,f1392,f757,f2785]) ).
tff(f2785,plain,
( spl21_236
<=> ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_236])]) ).
tff(f1392,plain,
( spl21_132
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X2,X1))
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_132])]) ).
tff(f1442,plain,
( ! [X0: $int] :
( divides(X0,sK3)
| ~ divides(X0,sK4) )
| ~ spl21_28
| ~ spl21_132 ),
inference(superposition,[],[f1393,f759]) ).
tff(f1393,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X2,X1))
| ~ divides(X0,X1) )
| ~ spl21_132 ),
inference(avatar_component_clause,[],[f1392]) ).
tff(f2783,plain,
( spl21_235
| ~ spl21_26
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1441,f1392,f747,f2781]) ).
tff(f2781,plain,
( spl21_235
<=> ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_235])]) ).
tff(f1441,plain,
( ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK10) )
| ~ spl21_26
| ~ spl21_132 ),
inference(superposition,[],[f1393,f749]) ).
tff(f2779,plain,
( spl21_234
| ~ spl21_26
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1433,f1387,f747,f2777]) ).
tff(f2777,plain,
( spl21_234
<=> ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_234])]) ).
tff(f1433,plain,
( ! [X0: $int] :
( divides(X0,sK6)
| ~ divides(X0,sK12) )
| ~ spl21_26
| ~ spl21_131 ),
inference(superposition,[],[f1388,f749]) ).
tff(f2765,plain,
( spl21_233
| spl21_12
| ~ spl21_34
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f867,f850,f786,f677,f2762]) ).
tff(f2762,plain,
( spl21_233
<=> divides(sK6,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_233])]) ).
tff(f786,plain,
( spl21_34
<=> ! [X14: $int] :
( divides(X14,sK3)
| $less(X14,2)
| ~ divides(X14,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_34])]) ).
tff(f867,plain,
( $less(sK6,2)
| divides(sK6,sK3)
| ~ spl21_34
| ~ spl21_44 ),
inference(resolution,[],[f851,f787]) ).
tff(f787,plain,
( ! [X14: $int] :
( ~ divides(X14,sK6)
| $less(X14,2)
| divides(X14,sK3) )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f786]) ).
tff(f2758,plain,
( spl21_54
| ~ spl21_232
| ~ spl21_18
| ~ spl21_37 ),
inference(avatar_split_clause,[],[f813,f799,f707,f2755,f903]) ).
tff(f903,plain,
( spl21_54
<=> $less(sK13,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_54])]) ).
tff(f2755,plain,
( spl21_232
<=> $less(sK13,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_232])]) ).
tff(f813,plain,
( ~ $less(sK13,sK10)
| $less(sK13,2)
| ~ spl21_18
| ~ spl21_37 ),
inference(resolution,[],[f800,f709]) ).
tff(f2751,plain,
( spl21_226
| ~ spl21_231
| ~ spl21_15
| ~ spl21_37 ),
inference(avatar_split_clause,[],[f812,f799,f692,f2748,f2696]) ).
tff(f2696,plain,
( spl21_226
<=> $less(sK12,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_226])]) ).
tff(f2748,plain,
( spl21_231
<=> $less(sK12,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_231])]) ).
tff(f812,plain,
( ~ $less(sK12,sK10)
| $less(sK12,2)
| ~ spl21_15
| ~ spl21_37 ),
inference(resolution,[],[f800,f694]) ).
tff(f2744,plain,
( spl21_54
| ~ spl21_230
| ~ spl21_18
| ~ spl21_35 ),
inference(avatar_split_clause,[],[f810,f790,f707,f2741,f903]) ).
tff(f2741,plain,
( spl21_230
<=> $less(sK13,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_230])]) ).
tff(f790,plain,
( spl21_35
<=> ! [X12: $int] :
( ~ divides(X12,sK6)
| ~ $less(X12,sK7)
| $less(X12,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).
tff(f810,plain,
( ~ $less(sK13,sK7)
| $less(sK13,2)
| ~ spl21_18
| ~ spl21_35 ),
inference(resolution,[],[f791,f709]) ).
tff(f791,plain,
( ! [X12: $int] :
( ~ divides(X12,sK6)
| ~ $less(X12,sK7)
| $less(X12,2) )
| ~ spl21_35 ),
inference(avatar_component_clause,[],[f790]) ).
tff(f2737,plain,
( spl21_226
| ~ spl21_229
| ~ spl21_15
| ~ spl21_35 ),
inference(avatar_split_clause,[],[f809,f790,f692,f2734,f2696]) ).
tff(f2734,plain,
( spl21_229
<=> $less(sK12,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_229])]) ).
tff(f809,plain,
( ~ $less(sK12,sK7)
| $less(sK12,2)
| ~ spl21_15
| ~ spl21_35 ),
inference(resolution,[],[f791,f694]) ).
tff(f2720,plain,
( spl21_227
| spl21_228
| ~ spl21_22
| ~ spl21_34 ),
inference(avatar_split_clause,[],[f808,f786,f727,f2717,f2713]) ).
tff(f2713,plain,
( spl21_227
<=> divides(sK10,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_227])]) ).
tff(f808,plain,
( $less(sK10,2)
| divides(sK10,sK3)
| ~ spl21_22
| ~ spl21_34 ),
inference(resolution,[],[f787,f729]) ).
tff(f2699,plain,
( spl21_225
| spl21_226
| ~ spl21_15
| ~ spl21_34 ),
inference(avatar_split_clause,[],[f806,f786,f692,f2696,f2692]) ).
tff(f2692,plain,
( spl21_225
<=> divides(sK12,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_225])]) ).
tff(f806,plain,
( $less(sK12,2)
| divides(sK12,sK3)
| ~ spl21_15
| ~ spl21_34 ),
inference(resolution,[],[f787,f694]) ).
tff(f2686,plain,
( spl21_223
| spl21_224
| ~ spl21_2
| ~ spl21_108 ),
inference(avatar_split_clause,[],[f1295,f1212,f627,f2683,f2679]) ).
tff(f2679,plain,
( spl21_223
<=> odd(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_223])]) ).
tff(f2683,plain,
( spl21_224
<=> $less(sK13,3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_224])]) ).
tff(f1212,plain,
( spl21_108
<=> ! [X0: $int] :
( odd(X0)
| $less(X0,3)
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).
tff(f1295,plain,
( $less(sK13,3)
| odd(sK13)
| ~ spl21_2
| ~ spl21_108 ),
inference(resolution,[],[f1213,f629]) ).
tff(f629,plain,
( prime(sK13)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f627]) ).
tff(f1213,plain,
( ! [X0: $int] :
( ~ prime(X0)
| $less(X0,3)
| odd(X0) )
| ~ spl21_108 ),
inference(avatar_component_clause,[],[f1212]) ).
tff(f2673,plain,
( spl21_221
| spl21_222
| ~ spl21_3
| ~ spl21_108 ),
inference(avatar_split_clause,[],[f1294,f1212,f632,f2670,f2666]) ).
tff(f2666,plain,
( spl21_221
<=> odd(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_221])]) ).
tff(f1294,plain,
( $less(sK10,3)
| odd(sK10)
| ~ spl21_3
| ~ spl21_108 ),
inference(resolution,[],[f1213,f634]) ).
tff(f2660,plain,
( spl21_219
| spl21_220
| ~ spl21_1
| ~ spl21_108 ),
inference(avatar_split_clause,[],[f1293,f1212,f622,f2657,f2653]) ).
tff(f2653,plain,
( spl21_219
<=> odd(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_219])]) ).
tff(f2657,plain,
( spl21_220
<=> $less(sK7,3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_220])]) ).
tff(f622,plain,
( spl21_1
<=> prime(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
tff(f1293,plain,
( $less(sK7,3)
| odd(sK7)
| ~ spl21_1
| ~ spl21_108 ),
inference(resolution,[],[f1213,f624]) ).
tff(f624,plain,
( prime(sK7)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f622]) ).
tff(f2651,plain,
( spl21_217
| ~ spl21_218
| ~ spl21_2
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f1288,f1207,f627,f2648,f2644]) ).
tff(f2644,plain,
( spl21_217
<=> ( 2 = sK13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_217])]) ).
tff(f2648,plain,
( spl21_218
<=> even(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_218])]) ).
tff(f1207,plain,
( spl21_107
<=> ! [X0: $int] :
( ( 2 = X0 )
| ~ even(X0)
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).
tff(f1288,plain,
( ~ even(sK13)
| ( 2 = sK13 )
| ~ spl21_2
| ~ spl21_107 ),
inference(resolution,[],[f1208,f629]) ).
tff(f1208,plain,
( ! [X0: $int] :
( ~ prime(X0)
| ~ even(X0)
| ( 2 = X0 ) )
| ~ spl21_107 ),
inference(avatar_component_clause,[],[f1207]) ).
tff(f2629,plain,
spl21_216,
inference(avatar_split_clause,[],[f592,f2627]) ).
tff(f2627,plain,
( spl21_216
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( div($sum($product(X0,X1),X2),X0) = $sum(X1,div(X2,X0)) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_216])]) ).
tff(f592,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( div($sum($product(X0,X1),X2),X0) = $sum(X1,div(X2,X0)) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f351]) ).
tff(f351,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( div($sum($product(X0,X1),X2),X0) = $sum(X1,div(X2,X0)) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(flattening,[],[f350]) ).
tff(f350,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( div($sum($product(X0,X1),X2),X0) = $sum(X1,div(X2,X0)) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X2,0)
& ~ $less(X1,0)
& $less(0,X0) )
=> ( div($sum($product(X0,X1),X2),X0) = $sum(X1,div(X2,X0)) ) ),
inference(rectify,[],[f140]) ).
tff(f140,plain,
! [X1: $int,X7: $int,X4: $int] :
( ( ~ $less(X4,0)
& ~ $less(X7,0)
& $less(0,X1) )
=> ( div($sum($product(X1,X7),X4),X1) = $sum(X7,div(X4,X1)) ) ),
inference(theory_normalization,[],[f24]) ).
tff(f24,axiom,
! [X1: $int,X7: $int,X4: $int] :
( ( $lesseq(0,X4)
& $lesseq(0,X7)
& $less(0,X1) )
=> ( div($sum($product(X1,X7),X4),X1) = $sum(X7,div(X4,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_mult) ).
tff(f2568,plain,
spl21_215,
inference(avatar_split_clause,[],[f591,f2566]) ).
tff(f2566,plain,
( spl21_215
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( mod($sum($product(X0,X1),X2),X0) = mod(X2,X0) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_215])]) ).
tff(f591,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( mod($sum($product(X0,X1),X2),X0) = mod(X2,X0) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( mod($sum($product(X0,X1),X2),X0) = mod(X2,X0) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(flattening,[],[f348]) ).
tff(f348,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( mod($sum($product(X0,X1),X2),X0) = mod(X2,X0) )
| $less(X2,0)
| $less(X1,0)
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X2,0)
& ~ $less(X1,0)
& $less(0,X0) )
=> ( mod($sum($product(X0,X1),X2),X0) = mod(X2,X0) ) ),
inference(rectify,[],[f139]) ).
tff(f139,plain,
! [X1: $int,X7: $int,X4: $int] :
( ( ~ $less(X4,0)
& ~ $less(X7,0)
& $less(0,X1) )
=> ( mod($sum($product(X1,X7),X4),X1) = mod(X4,X1) ) ),
inference(theory_normalization,[],[f25]) ).
tff(f25,axiom,
! [X1: $int,X7: $int,X4: $int] :
( ( $lesseq(0,X4)
& $lesseq(0,X7)
& $less(0,X1) )
=> ( mod($sum($product(X1,X7),X4),X1) = mod(X4,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_mult) ).
tff(f2564,plain,
spl21_214,
inference(avatar_split_clause,[],[f576,f2562]) ).
tff(f2562,plain,
( spl21_214
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| ~ divides(sK20(X0,X1,X2),X2)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_214])]) ).
tff(f576,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| ~ divides(sK20(X0,X1,X2),X2)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f406,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( gcd(X0,X1) = X2 )
| ( ~ divides(sK20(X0,X1,X2),X2)
& divides(sK20(X0,X1,X2),X1)
& divides(sK20(X0,X1,X2),X0) )
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f327,f405]) ).
tff(f405,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: $int] :
( ~ divides(X3,X2)
& divides(X3,X1)
& divides(X3,X0) )
=> ( ~ divides(sK20(X0,X1,X2),X2)
& divides(sK20(X0,X1,X2),X1)
& divides(sK20(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f327,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( gcd(X0,X1) = X2 )
| ? [X3: $int] :
( ~ divides(X3,X2)
& divides(X3,X1)
& divides(X3,X0) )
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(flattening,[],[f326]) ).
tff(f326,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( gcd(X0,X1) = X2 )
| ? [X3: $int] :
( ~ divides(X3,X2)
& divides(X3,X1)
& divides(X3,X0) )
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(ennf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,0)
=> ( divides(X2,X0)
=> ( divides(X2,X1)
=> ( ! [X3: $int] :
( divides(X3,X0)
=> ( divides(X3,X1)
=> divides(X3,X2) ) )
=> ( gcd(X0,X1) = X2 ) ) ) ) ),
inference(rectify,[],[f136]) ).
tff(f136,plain,
! [X0: $int,X11: $int,X8: $int] :
( ~ $less(X8,0)
=> ( divides(X8,X0)
=> ( divides(X8,X11)
=> ( ! [X1: $int] :
( divides(X1,X0)
=> ( divides(X1,X11)
=> divides(X1,X8) ) )
=> ( gcd(X0,X11) = X8 ) ) ) ) ),
inference(theory_normalization,[],[f77]) ).
tff(f77,axiom,
! [X0: $int,X11: $int,X8: $int] :
( $lesseq(0,X8)
=> ( divides(X8,X0)
=> ( divides(X8,X11)
=> ( ! [X1: $int] :
( divides(X1,X0)
=> ( divides(X1,X11)
=> divides(X1,X8) ) )
=> ( gcd(X0,X11) = X8 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_unique) ).
tff(f2560,plain,
spl21_213,
inference(avatar_split_clause,[],[f575,f2558]) ).
tff(f2558,plain,
( spl21_213
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| divides(sK20(X0,X1,X2),X1)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_213])]) ).
tff(f575,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| divides(sK20(X0,X1,X2),X1)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f2556,plain,
spl21_212,
inference(avatar_split_clause,[],[f574,f2554]) ).
tff(f2554,plain,
( spl21_212
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| divides(sK20(X0,X1,X2),X0)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_212])]) ).
tff(f574,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,X1) = X2 )
| divides(sK20(X0,X1,X2),X0)
| ~ divides(X2,X1)
| ~ divides(X2,X0)
| $less(X2,0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f2519,plain,
spl21_211,
inference(avatar_split_clause,[],[f615,f2517]) ).
tff(f2517,plain,
( spl21_211
<=> ! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( -1 = X1 )
| ( 1 = X1 )
| ~ divides(X1,X0)
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_211])]) ).
tff(f615,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( -1 = X1 )
| ( 1 = X1 )
| ~ divides(X1,X0)
| ~ prime(X0) ),
inference(evaluation,[],[f489]) ).
tff(f489,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( $uminus(1) = X1 )
| ( 1 = X1 )
| ~ divides(X1,X0)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $int] :
( ! [X1: $int] :
( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( $uminus(1) = X1 )
| ( 1 = X1 )
| ~ divides(X1,X0) )
| ~ prime(X0) ),
inference(flattening,[],[f274]) ).
tff(f274,plain,
! [X0: $int] :
( ! [X1: $int] :
( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( $uminus(1) = X1 )
| ( 1 = X1 )
| ~ divides(X1,X0) )
| ~ prime(X0) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $int] :
( prime(X0)
=> ! [X1: $int] :
( divides(X1,X0)
=> ( ( $uminus(X0) = X1 )
| ( X0 = X1 )
| ( $uminus(1) = X1 )
| ( 1 = X1 ) ) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X14: $int] :
( prime(X14)
=> ! [X8: $int] :
( divides(X8,X14)
=> ( ( $uminus(X14) = X8 )
| ( X8 = X14 )
| ( $uminus(1) = X8 )
| ( 1 = X8 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divisors) ).
tff(f2484,plain,
spl21_210,
inference(avatar_split_clause,[],[f573,f2482]) ).
tff(f2482,plain,
( spl21_210
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( gcd($product(X2,X0),$product(X2,X1)) = $product(X2,gcd(X0,X1)) )
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_210])]) ).
tff(f573,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( gcd($product(X2,X0),$product(X2,X1)) = $product(X2,gcd(X0,X1)) )
| $less(X2,0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( gcd($product(X2,X0),$product(X2,X1)) = $product(X2,gcd(X0,X1)) )
| $less(X2,0) ),
inference(ennf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,0)
=> ( gcd($product(X2,X0),$product(X2,X1)) = $product(X2,gcd(X0,X1)) ) ),
inference(rectify,[],[f135]) ).
tff(f135,plain,
! [X0: $int,X11: $int,X12: $int] :
( ~ $less(X12,0)
=> ( gcd($product(X12,X0),$product(X12,X11)) = $product(X12,gcd(X0,X11)) ) ),
inference(theory_normalization,[],[f86]) ).
tff(f86,axiom,
! [X0: $int,X11: $int,X12: $int] :
( $lesseq(0,X12)
=> ( gcd($product(X12,X0),$product(X12,X11)) = $product(X12,gcd(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_mult) ).
tff(f2480,plain,
spl21_209,
inference(avatar_split_clause,[],[f572,f2478]) ).
tff(f2478,plain,
( spl21_209
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $quotient_e($sum($product(X0,X1),X2),X0) = $sum(X1,$quotient_e(X2,X0)) )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_209])]) ).
tff(f572,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( $quotient_e($sum($product(X0,X1),X2),X0) = $sum(X1,$quotient_e(X2,X0)) )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $quotient_e($sum($product(X0,X1),X2),X0) = $sum(X1,$quotient_e(X2,X0)) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(0,X0)
=> ( $quotient_e($sum($product(X0,X1),X2),X0) = $sum(X1,$quotient_e(X2,X0)) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X1: $int,X7: $int,X4: $int] :
( $less(0,X1)
=> ( $quotient_e($sum($product(X1,X7),X4),X1) = $sum(X7,$quotient_e(X4,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_mult1) ).
tff(f2440,plain,
spl21_208,
inference(avatar_split_clause,[],[f597,f2438]) ).
tff(f2438,plain,
( spl21_208
<=> ! [X3: uni,X4: uni,X0: ty,X5: uni,X2: uni,X1: ty] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_208])]) ).
tff(f597,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni,X5: uni] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ),
inference(cnf_transformation,[],[f355]) ).
tff(f355,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 )
| ~ sort(X1,X3) ),
inference(ennf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni,X5: uni] :
( sort(X1,X3)
=> ( match_list(X1,X0,cons(X0,X4,X5),X2,X3) = X3 ) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X0: ty,X15: ty,X4: uni,X5: uni,X6: uni,X16: uni] :
( sort(X15,X5)
=> ( match_list(X15,X0,cons(X0,X6,X16),X4,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_list_Cons) ).
tff(f2436,plain,
spl21_207,
inference(avatar_split_clause,[],[f571,f2434]) ).
tff(f2434,plain,
( spl21_207
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $remainder_e($sum($product(X0,X1),X2),X0) = $remainder_e(X2,X0) )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_207])]) ).
tff(f571,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( $remainder_e($sum($product(X0,X1),X2),X0) = $remainder_e(X2,X0) )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $remainder_e($sum($product(X0,X1),X2),X0) = $remainder_e(X2,X0) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(0,X0)
=> ( $remainder_e($sum($product(X0,X1),X2),X0) = $remainder_e(X2,X0) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X1: $int,X7: $int,X4: $int] :
( $less(0,X1)
=> ( $remainder_e($sum($product(X1,X7),X4),X1) = $remainder_e(X4,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_mult1) ).
tff(f2432,plain,
spl21_206,
inference(avatar_split_clause,[],[f536,f2430]) ).
tff(f2430,plain,
( spl21_206
<=> ! [X0: $int,X1: $int] :
( ( $sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_206])]) ).
tff(f536,plain,
! [X0: $int,X1: $int] :
( ( $sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 )
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $int,X1: $int] :
( ( $sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( $sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X1: $int,X7: $int] :
( ( 0 != X7 )
=> ( $sum($product(X7,div(X1,X7)),mod(X1,X7)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_mod) ).
tff(f2428,plain,
( spl21_204
| ~ spl21_205
| ~ spl21_3
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f1287,f1207,f632,f2425,f2421]) ).
tff(f2421,plain,
( spl21_204
<=> ( 2 = sK10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_204])]) ).
tff(f2425,plain,
( spl21_205
<=> even(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_205])]) ).
tff(f1287,plain,
( ~ even(sK10)
| ( 2 = sK10 )
| ~ spl21_3
| ~ spl21_107 ),
inference(resolution,[],[f1208,f634]) ).
tff(f2419,plain,
spl21_203,
inference(avatar_split_clause,[],[f532,f2417]) ).
tff(f2417,plain,
( spl21_203
<=> ! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_203])]) ).
tff(f532,plain,
! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: ty,X1: uni] :
( ( cons(X0,cons_proj_1(X0,X1),cons_proj_2(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X0: ty,X6: uni] :
( ( cons(X0,cons_proj_1(X0,X6),cons_proj_2(X0,X6)) = X6 )
| ( nil(X0) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',list_inversion) ).
tff(f2415,plain,
spl21_202,
inference(avatar_split_clause,[],[f160,f2413]) ).
tff(f2413,plain,
( spl21_202
<=> ! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ( $sum($remainder_e(X1,X2),$product(X2,$quotient_e(X1,X2))) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_202])]) ).
tff(f160,plain,
! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ( $sum($remainder_e(X1,X2),$product(X2,$quotient_e(X1,X2))) = X1 ) ),
introduced(theory_axiom_152,[]) ).
tff(f2303,plain,
spl21_201,
inference(avatar_split_clause,[],[f610,f2301]) ).
tff(f2301,plain,
( spl21_201
<=> ! [X2: $int,X0: $int,X3: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_201])]) ).
tff(f610,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f157]) ).
tff(f157,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_151,[]) ).
tff(f2299,plain,
spl21_200,
inference(avatar_split_clause,[],[f590,f2297]) ).
tff(f2297,plain,
( spl21_200
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,$product(X1,X2))
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_200])]) ).
tff(f590,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,$product(X1,X2))
| ~ prime(X0) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,$product(X1,X2))
| ~ prime(X0) ),
inference(flattening,[],[f346]) ).
tff(f346,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,$product(X1,X2))
| ~ prime(X0) ),
inference(ennf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( divides(X0,$product(X1,X2))
& prime(X0) )
=> ( divides(X0,X2)
| divides(X0,X1) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X14: $int,X0: $int,X11: $int] :
( ( divides(X14,$product(X0,X11))
& prime(X14) )
=> ( divides(X14,X11)
| divides(X14,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid) ).
tff(f2295,plain,
spl21_199,
inference(avatar_split_clause,[],[f581,f2293]) ).
tff(f2293,plain,
( spl21_199
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_199])]) ).
tff(f581,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f333]) ).
tff(f333,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(flattening,[],[f332]) ).
tff(f332,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X1,X0)
=> ( ~ $less(X2,0)
=> ~ $less($product(X1,X2),$product(X0,X2)) ) ),
inference(rectify,[],[f137]) ).
tff(f137,plain,
! [X1: $int,X7: $int,X4: $int] :
( ~ $less(X7,X1)
=> ( ~ $less(X4,0)
=> ~ $less($product(X7,X4),$product(X1,X4)) ) ),
inference(theory_normalization,[],[f8]) ).
tff(f8,axiom,
! [X1: $int,X7: $int,X4: $int] :
( $lesseq(X1,X7)
=> ( $lesseq(0,X4)
=> $lesseq($product(X1,X4),$product(X7,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatOrderMult) ).
tff(f2291,plain,
spl21_198,
inference(avatar_split_clause,[],[f547,f2289]) ).
tff(f2289,plain,
( spl21_198
<=> ! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( X0 = X1 )
| ~ divides(X1,X0)
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_198])]) ).
tff(f547,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( X0 = X1 )
| ~ divides(X1,X0)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( X0 = X1 )
| ~ divides(X1,X0)
| ~ divides(X0,X1) ),
inference(flattening,[],[f304]) ).
tff(f304,plain,
! [X0: $int,X1: $int] :
( ( $uminus(X1) = X0 )
| ( X0 = X1 )
| ~ divides(X1,X0)
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
=> ( divides(X1,X0)
=> ( ( $uminus(X1) = X0 )
| ( X0 = X1 ) ) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $int,X11: $int] :
( divides(X0,X11)
=> ( divides(X11,X0)
=> ( ( $uminus(X11) = X0 )
| ( X0 = X11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_antisym) ).
tff(f2287,plain,
spl21_197,
inference(avatar_split_clause,[],[f156,f2285]) ).
tff(f2285,plain,
( spl21_197
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_197])]) ).
tff(f156,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f2199,plain,
spl21_196,
inference(avatar_split_clause,[],[f619,f2197]) ).
tff(f2197,plain,
( spl21_196
<=> ! [X0: $int,X1: $int] :
( ~ $less(abs(X0),abs($product(X1,div(X0,X1))))
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_196])]) ).
tff(f619,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X0),abs($product(X1,div(X0,X1))))
| ( 0 = X1 ) ),
inference(forward_demodulation,[],[f535,f152]) ).
tff(f152,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f535,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X0),abs($product(div(X0,X1),X1)))
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X0),abs($product(div(X0,X1),X1)))
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ~ $less(abs(X0),abs($product(div(X0,X1),X1))) ),
inference(rectify,[],[f124]) ).
tff(f124,plain,
! [X1: $int,X7: $int] :
( ( 0 != X7 )
=> ~ $less(abs(X1),abs($product(div(X1,X7),X7))) ),
inference(theory_normalization,[],[f19]) ).
tff(f19,axiom,
! [X1: $int,X7: $int] :
( ( 0 != X7 )
=> $lesseq(abs($product(div(X1,X7),X7)),abs(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rounds_toward_zero) ).
tff(f2195,plain,
spl21_195,
inference(avatar_split_clause,[],[f595,f2193]) ).
tff(f2193,plain,
( spl21_195
<=> ! [X0: ty,X3: uni,X2: uni,X1: ty] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_195])]) ).
tff(f595,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( ( match_list(X1,X0,nil(X0),X2,X3) = X2 )
| ~ sort(X1,X2) ),
inference(ennf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni] :
( sort(X1,X2)
=> ( match_list(X1,X0,nil(X0),X2,X3) = X2 ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: ty,X15: ty,X4: uni,X5: uni] :
( sort(X15,X4)
=> ( match_list(X15,X0,nil(X0),X4,X5) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_list_Nil) ).
tff(f2191,plain,
spl21_194,
inference(avatar_split_clause,[],[f587,f2189]) ).
tff(f2189,plain,
( spl21_194
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$sum(X1,$uminus(X2)))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_194])]) ).
tff(f587,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$sum(X1,$uminus(X2)))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$sum(X1,$uminus(X2)))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(flattening,[],[f340]) ).
tff(f340,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$sum(X1,$uminus(X2)))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> ( divides(X0,X2)
=> divides(X0,$sum(X1,$uminus(X2))) ) ),
inference(rectify,[],[f138]) ).
tff(f138,plain,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> ( divides(X0,X12)
=> divides(X0,$sum(X11,$uminus(X12))) ) ),
inference(theory_normalization,[],[f37]) ).
tff(f37,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> ( divides(X0,X12)
=> divides(X0,$difference(X11,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_minusr) ).
tff(f2187,plain,
spl21_193,
inference(avatar_split_clause,[],[f577,f2185]) ).
tff(f2185,plain,
( spl21_193
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,$product(X1,X2)) = gcd(X0,X2) )
| ~ coprime(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_193])]) ).
tff(f577,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( gcd(X0,$product(X1,X2)) = gcd(X0,X2) )
| ~ coprime(X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( gcd(X0,$product(X1,X2)) = gcd(X0,X2) )
| ~ coprime(X0,X1) ),
inference(ennf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $int,X1: $int,X2: $int] :
( coprime(X0,X1)
=> ( gcd(X0,$product(X1,X2)) = gcd(X0,X2) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $int,X11: $int,X12: $int] :
( coprime(X0,X11)
=> ( gcd(X0,$product(X11,X12)) = gcd(X0,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_coprime) ).
tff(f2183,plain,
spl21_192,
inference(avatar_split_clause,[],[f569,f2181]) ).
tff(f2181,plain,
( spl21_192
<=> ! [X2: $int,X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X0,$sum(X1,$uminus($product(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_192])]) ).
tff(f569,plain,
! [X2: $int,X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X0,$sum(X1,$uminus($product(X2,X0)))) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $int,X1: $int,X2: $int] : ( gcd(X0,X1) = gcd(X0,$sum(X1,$uminus($product(X2,X0)))) ),
inference(rectify,[],[f134]) ).
tff(f134,plain,
! [X0: $int,X11: $int,X10: $int] : ( gcd(X0,X11) = gcd(X0,$sum(X11,$uminus($product(X10,X0)))) ),
inference(theory_normalization,[],[f83]) ).
tff(f83,axiom,
! [X0: $int,X11: $int,X10: $int] : ( gcd(X0,X11) = gcd(X0,$difference(X11,$product(X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_euclid) ).
tff(f2179,plain,
spl21_191,
inference(avatar_split_clause,[],[f534,f2177]) ).
tff(f2177,plain,
( spl21_191
<=> ! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,mod(X0,X1)) )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_191])]) ).
tff(f534,plain,
! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,mod(X0,X1)) )
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,mod(X0,X1)) )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( gcd(X0,X1) = gcd(X1,mod(X0,X1)) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( gcd(X0,X11) = gcd(X11,mod(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_computer_mod) ).
tff(f2175,plain,
spl21_190,
inference(avatar_split_clause,[],[f533,f2173]) ).
tff(f2173,plain,
( spl21_190
<=> ! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,$remainder_e(X0,X1)) )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_190])]) ).
tff(f533,plain,
! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,$remainder_e(X0,X1)) )
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $int,X1: $int] :
( ( gcd(X0,X1) = gcd(X1,$remainder_e(X0,X1)) )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( gcd(X0,X1) = gcd(X1,$remainder_e(X0,X1)) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( gcd(X0,X11) = gcd(X11,$remainder_e(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_euclidean_mod) ).
tff(f2169,plain,
( spl21_189
| ~ spl21_103
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f2165,f2161,f1191,f2167]) ).
tff(f2167,plain,
( spl21_189
<=> ! [X2: $int,X1: $int] :
( ~ $less($sum(-1,$abs(X2)),$remainder_e(X1,X2))
| ( 0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_189])]) ).
tff(f1191,plain,
( spl21_103
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_103])]) ).
tff(f2161,plain,
( spl21_188
<=> ! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($sum($abs(X2),$uminus(1)),$remainder_e(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_188])]) ).
tff(f2165,plain,
( ! [X2: $int,X1: $int] :
( ~ $less($sum(-1,$abs(X2)),$remainder_e(X1,X2))
| ( 0 = X2 ) )
| ~ spl21_103
| ~ spl21_188 ),
inference(forward_demodulation,[],[f2164,f1192]) ).
tff(f1192,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl21_103 ),
inference(avatar_component_clause,[],[f1191]) ).
tff(f2164,plain,
( ! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($sum($abs(X2),-1),$remainder_e(X1,X2)) )
| ~ spl21_188 ),
inference(evaluation,[],[f2162]) ).
tff(f2162,plain,
( ! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($sum($abs(X2),$uminus(1)),$remainder_e(X1,X2)) )
| ~ spl21_188 ),
inference(avatar_component_clause,[],[f2161]) ).
tff(f2163,plain,
spl21_188,
inference(avatar_split_clause,[],[f162,f2161]) ).
tff(f162,plain,
! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($sum($abs(X2),$uminus(1)),$remainder_e(X1,X2)) ),
introduced(theory_axiom_154,[]) ).
tff(f2138,plain,
( spl21_186
| ~ spl21_187
| ~ spl21_1
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f1286,f1207,f622,f2135,f2131]) ).
tff(f2135,plain,
( spl21_187
<=> even(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_187])]) ).
tff(f1286,plain,
( ~ even(sK7)
| ( 2 = sK7 )
| ~ spl21_1
| ~ spl21_107 ),
inference(resolution,[],[f1208,f624]) ).
tff(f1924,plain,
( spl21_137
| spl21_185
| ~ spl21_34
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f1095,f1013,f786,f1921,f1459]) ).
tff(f1921,plain,
( spl21_185
<=> odd(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_185])]) ).
tff(f1013,plain,
( spl21_78
<=> ! [X0: $int] :
( odd(X0)
| divides(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_78])]) ).
tff(f1095,plain,
( odd(sK6)
| divides(2,sK3)
| ~ spl21_34
| ~ spl21_78 ),
inference(evaluation,[],[f1094]) ).
tff(f1094,plain,
( odd(sK6)
| $less(2,2)
| divides(2,sK3)
| ~ spl21_34
| ~ spl21_78 ),
inference(resolution,[],[f1014,f787]) ).
tff(f1014,plain,
( ! [X0: $int] :
( divides(2,X0)
| odd(X0) )
| ~ spl21_78 ),
inference(avatar_component_clause,[],[f1013]) ).
tff(f1870,plain,
spl21_184,
inference(avatar_split_clause,[],[f593,f1868]) ).
tff(f1868,plain,
( spl21_184
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| ~ coprime(X0,X1)
| ~ divides(X0,$product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_184])]) ).
tff(f593,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| ~ coprime(X0,X1)
| ~ divides(X0,$product(X1,X2)) ),
inference(cnf_transformation,[],[f353]) ).
tff(f353,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| ~ coprime(X0,X1)
| ~ divides(X0,$product(X1,X2)) ),
inference(flattening,[],[f352]) ).
tff(f352,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| ~ coprime(X0,X1)
| ~ divides(X0,$product(X1,X2)) ),
inference(ennf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( coprime(X0,X1)
& divides(X0,$product(X1,X2)) )
=> divides(X0,X2) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X0: $int,X11: $int,X12: $int] :
( ( coprime(X0,X11)
& divides(X0,$product(X11,X12)) )
=> divides(X0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gauss) ).
tff(f1866,plain,
spl21_183,
inference(avatar_split_clause,[],[f589,f1864]) ).
tff(f1864,plain,
( spl21_183
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X2,gcd(X0,X1))
| ~ divides(X2,X1)
| ~ divides(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_183])]) ).
tff(f589,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X2,gcd(X0,X1))
| ~ divides(X2,X1)
| ~ divides(X2,X0) ),
inference(cnf_transformation,[],[f345]) ).
tff(f345,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X2,gcd(X0,X1))
| ~ divides(X2,X1)
| ~ divides(X2,X0) ),
inference(flattening,[],[f344]) ).
tff(f344,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X2,gcd(X0,X1))
| ~ divides(X2,X1)
| ~ divides(X2,X0) ),
inference(ennf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X2,X0)
=> ( divides(X2,X1)
=> divides(X2,gcd(X0,X1)) ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $int,X11: $int,X1: $int] :
( divides(X1,X0)
=> ( divides(X1,X11)
=> divides(X1,gcd(X0,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_def3) ).
tff(f1862,plain,
spl21_182,
inference(avatar_split_clause,[],[f588,f1860]) ).
tff(f1860,plain,
( spl21_182
<=> ! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$sum(X1,X2))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_182])]) ).
tff(f588,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$sum(X1,X2))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$sum(X1,X2))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(flattening,[],[f342]) ).
tff(f342,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$sum(X1,X2))
| ~ divides(X0,X2)
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> ( divides(X0,X2)
=> divides(X0,$sum(X1,X2)) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> ( divides(X0,X12)
=> divides(X0,$sum(X11,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_plusr) ).
tff(f1858,plain,
spl21_181,
inference(avatar_split_clause,[],[f580,f1856]) ).
tff(f1856,plain,
( spl21_181
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_181])]) ).
tff(f580,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X1)
=> ( cons_proj_1(X0,cons(X0,X1,X2)) = X1 ) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X0: ty,X6: uni,X16: uni] :
( sort(X0,X6)
=> ( cons_proj_1(X0,cons(X0,X6,X16)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_proj_1_def) ).
tff(f1854,plain,
spl21_180,
inference(avatar_split_clause,[],[f570,f1852]) ).
tff(f1852,plain,
( spl21_180
<=> ! [X2: $int,X0: $int,X1: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_180])]) ).
tff(f570,plain,
! [X2: $int,X0: $int,X1: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $int,X1: $int,X2: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X1: $int,X7: $int,X4: $int] : ( gcd(gcd(X1,X7),X4) = gcd(X1,gcd(X7,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assoc) ).
tff(f1850,plain,
spl21_179,
inference(avatar_split_clause,[],[f565,f1848]) ).
tff(f1848,plain,
( spl21_179
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_179])]) ).
tff(f565,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) ),
inference(cnf_transformation,[],[f404]) ).
tff(f404,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) )
& ( ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) )
| $less(X1,abs(X0)) ) ),
inference(flattening,[],[f403]) ).
tff(f403,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,abs(X0))
| $less(X1,X0)
| $less(X0,$uminus(X1)) )
& ( ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) )
| $less(X1,abs(X0)) ) ),
inference(nnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,abs(X0))
<=> ( ~ $less(X1,X0)
& ~ $less(X0,$uminus(X1)) ) ),
inference(rectify,[],[f133]) ).
tff(f133,plain,
! [X1: $int,X7: $int] :
( ~ $less(X7,abs(X1))
<=> ( ~ $less(X7,X1)
& ~ $less(X1,$uminus(X7)) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
! [X1: $int,X7: $int] :
( $lesseq(abs(X1),X7)
<=> ( $lesseq(X1,X7)
& $lesseq($uminus(X7),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_le) ).
tff(f1846,plain,
spl21_178,
inference(avatar_split_clause,[],[f558,f1844]) ).
tff(f1844,plain,
( spl21_178
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,div(X0,X1))
| ~ $less(0,X1)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_178])]) ).
tff(f558,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,div(X0,X1))
| ~ $less(0,X1)
| $less(X0,0) ),
inference(cnf_transformation,[],[f322]) ).
tff(f322,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X0,div(X0,X1))
& ~ $less(div(X0,X1),0) )
| ~ $less(0,X1)
| $less(X0,0) ),
inference(flattening,[],[f321]) ).
tff(f321,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X0,div(X0,X1))
& ~ $less(div(X0,X1),0) )
| ~ $less(0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& ~ $less(X0,0) )
=> ( ~ $less(X0,div(X0,X1))
& ~ $less(div(X0,X1),0) ) ),
inference(rectify,[],[f132]) ).
tff(f132,plain,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& ~ $less(X1,0) )
=> ( ~ $less(X1,div(X1,X7))
& ~ $less(div(X1,X7),0) ) ),
inference(theory_normalization,[],[f13]) ).
tff(f13,axiom,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& $lesseq(0,X1) )
=> ( $lesseq(div(X1,X7),X1)
& $lesseq(0,div(X1,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_bound) ).
tff(f1842,plain,
spl21_177,
inference(avatar_split_clause,[],[f556,f1840]) ).
tff(f1840,plain,
( spl21_177
<=> ! [X0: $int,X1: $int] :
( ~ $less(div(X0,X1),0)
| ~ $less(0,X1)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_177])]) ).
tff(f556,plain,
! [X0: $int,X1: $int] :
( ~ $less(div(X0,X1),0)
| ~ $less(0,X1)
| $less(X0,0) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: $int,X1: $int] :
( ~ $less(div(X0,X1),0)
| ~ $less(0,X1)
| $less(X0,0) ),
inference(flattening,[],[f319]) ).
tff(f319,plain,
! [X0: $int,X1: $int] :
( ~ $less(div(X0,X1),0)
| ~ $less(0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& ~ $less(X0,0) )
=> ~ $less(div(X0,X1),0) ),
inference(rectify,[],[f131]) ).
tff(f131,plain,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& ~ $less(X1,0) )
=> ~ $less(div(X1,X7),0) ),
inference(theory_normalization,[],[f15]) ).
tff(f15,axiom,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& $lesseq(0,X1) )
=> $lesseq(0,div(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_sign_pos) ).
tff(f1838,plain,
spl21_176,
inference(avatar_split_clause,[],[f555,f1836]) ).
tff(f1836,plain,
( spl21_176
<=> ! [X0: $int,X1: $int] :
( ( mod(X0,X1) = X0 )
| ~ $less(X0,X1)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_176])]) ).
tff(f555,plain,
! [X0: $int,X1: $int] :
( ( mod(X0,X1) = X0 )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(cnf_transformation,[],[f318]) ).
tff(f318,plain,
! [X0: $int,X1: $int] :
( ( mod(X0,X1) = X0 )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(flattening,[],[f317]) ).
tff(f317,plain,
! [X0: $int,X1: $int] :
( ( mod(X0,X1) = X0 )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,X1)
& ~ $less(X0,0) )
=> ( mod(X0,X1) = X0 ) ),
inference(rectify,[],[f130]) ).
tff(f130,plain,
! [X1: $int,X7: $int] :
( ( $less(X1,X7)
& ~ $less(X1,0) )
=> ( mod(X1,X7) = X1 ) ),
inference(theory_normalization,[],[f23]) ).
tff(f23,axiom,
! [X1: $int,X7: $int] :
( ( $less(X1,X7)
& $lesseq(0,X1) )
=> ( mod(X1,X7) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_inf) ).
tff(f1834,plain,
spl21_175,
inference(avatar_split_clause,[],[f554,f1832]) ).
tff(f1832,plain,
( spl21_175
<=> ! [X0: $int,X1: $int] :
( ( 0 = div(X0,X1) )
| ~ $less(X0,X1)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_175])]) ).
tff(f554,plain,
! [X0: $int,X1: $int] :
( ( 0 = div(X0,X1) )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: $int,X1: $int] :
( ( 0 = div(X0,X1) )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(flattening,[],[f315]) ).
tff(f315,plain,
! [X0: $int,X1: $int] :
( ( 0 = div(X0,X1) )
| ~ $less(X0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,X1)
& ~ $less(X0,0) )
=> ( 0 = div(X0,X1) ) ),
inference(rectify,[],[f129]) ).
tff(f129,plain,
! [X1: $int,X7: $int] :
( ( $less(X1,X7)
& ~ $less(X1,0) )
=> ( 0 = div(X1,X7) ) ),
inference(theory_normalization,[],[f22]) ).
tff(f22,axiom,
! [X1: $int,X7: $int] :
( ( $less(X1,X7)
& $lesseq(0,X1) )
=> ( 0 = div(X1,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_inf) ).
tff(f1830,plain,
spl21_174,
inference(avatar_split_clause,[],[f553,f1828]) ).
tff(f1828,plain,
( spl21_174
<=> ! [X0: $int,X1: $int] :
( ~ $less(mod(X0,X1),0)
| ( 0 = X1 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_174])]) ).
tff(f553,plain,
! [X0: $int,X1: $int] :
( ~ $less(mod(X0,X1),0)
| ( 0 = X1 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $int,X1: $int] :
( ~ $less(mod(X0,X1),0)
| ( 0 = X1 )
| $less(X0,0) ),
inference(flattening,[],[f313]) ).
tff(f313,plain,
! [X0: $int,X1: $int] :
( ~ $less(mod(X0,X1),0)
| ( 0 = X1 )
| $less(X0,0) ),
inference(ennf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $int,X1: $int] :
( ( ( 0 != X1 )
& ~ $less(X0,0) )
=> ~ $less(mod(X0,X1),0) ),
inference(rectify,[],[f128]) ).
tff(f128,plain,
! [X1: $int,X7: $int] :
( ( ( 0 != X7 )
& ~ $less(X1,0) )
=> ~ $less(mod(X1,X7),0) ),
inference(theory_normalization,[],[f17]) ).
tff(f17,axiom,
! [X1: $int,X7: $int] :
( ( ( 0 != X7 )
& $lesseq(0,X1) )
=> $lesseq(0,mod(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_sign_pos) ).
tff(f1826,plain,
spl21_173,
inference(avatar_split_clause,[],[f552,f1824]) ).
tff(f1824,plain,
( spl21_173
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,div(X0,X1))
| ~ $less(0,X1)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_173])]) ).
tff(f552,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,div(X0,X1))
| ~ $less(0,X1)
| $less(0,X0) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,div(X0,X1))
| ~ $less(0,X1)
| $less(0,X0) ),
inference(flattening,[],[f311]) ).
tff(f311,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,div(X0,X1))
| ~ $less(0,X1)
| $less(0,X0) ),
inference(ennf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& ~ $less(0,X0) )
=> ~ $less(0,div(X0,X1)) ),
inference(rectify,[],[f127]) ).
tff(f127,plain,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& ~ $less(0,X1) )
=> ~ $less(0,div(X1,X7)) ),
inference(theory_normalization,[],[f16]) ).
tff(f16,axiom,
! [X1: $int,X7: $int] :
( ( $less(0,X7)
& $lesseq(X1,0) )
=> $lesseq(div(X1,X7),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_sign_neg) ).
tff(f1822,plain,
spl21_172,
inference(avatar_split_clause,[],[f551,f1820]) ).
tff(f1820,plain,
( spl21_172
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,mod(X0,X1))
| ( 0 = X1 )
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_172])]) ).
tff(f551,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,mod(X0,X1))
| ( 0 = X1 )
| $less(0,X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,mod(X0,X1))
| ( 0 = X1 )
| $less(0,X0) ),
inference(flattening,[],[f309]) ).
tff(f309,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,mod(X0,X1))
| ( 0 = X1 )
| $less(0,X0) ),
inference(ennf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $int,X1: $int] :
( ( ( 0 != X1 )
& ~ $less(0,X0) )
=> ~ $less(0,mod(X0,X1)) ),
inference(rectify,[],[f126]) ).
tff(f126,plain,
! [X1: $int,X7: $int] :
( ( ( 0 != X7 )
& ~ $less(0,X1) )
=> ~ $less(0,mod(X1,X7)) ),
inference(theory_normalization,[],[f18]) ).
tff(f18,axiom,
! [X1: $int,X7: $int] :
( ( ( 0 != X7 )
& $lesseq(X1,0) )
=> $lesseq(mod(X1,X7),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_sign_neg) ).
tff(f1818,plain,
spl21_171,
inference(avatar_split_clause,[],[f548,f1816]) ).
tff(f1816,plain,
( spl21_171
<=> ! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort(ref(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_171])]) ).
tff(f548,plain,
! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort(ref(X0),X1) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort(ref(X0),X1) ),
inference(ennf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: ty,X1: uni] :
( sort(ref(X0),X1)
=> ( mk_ref(X0,contents(X0,X1)) = X1 ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: ty,X6: uni] :
( sort(ref(X0),X6)
=> ( mk_ref(X0,contents(X0,X6)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ref_inversion) ).
tff(f1814,plain,
spl21_170,
inference(avatar_split_clause,[],[f546,f1812]) ).
tff(f1812,plain,
( spl21_170
<=> ! [X0: $int,X1: $int] :
( ~ $less(abs(X1),abs(X0))
| ( 0 = X1 )
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_170])]) ).
tff(f546,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X1),abs(X0))
| ( 0 = X1 )
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X1),abs(X0))
| ( 0 = X1 )
| ~ divides(X0,X1) ),
inference(flattening,[],[f302]) ).
tff(f302,plain,
! [X0: $int,X1: $int] :
( ~ $less(abs(X1),abs(X0))
| ( 0 = X1 )
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
=> ( ( 0 != X1 )
=> ~ $less(abs(X1),abs(X0)) ) ),
inference(rectify,[],[f125]) ).
tff(f125,plain,
! [X0: $int,X11: $int] :
( divides(X0,X11)
=> ( ( 0 != X11 )
=> ~ $less(abs(X11),abs(X0)) ) ),
inference(theory_normalization,[],[f45]) ).
tff(f45,axiom,
! [X0: $int,X11: $int] :
( divides(X0,X11)
=> ( ( 0 != X11 )
=> $lesseq(abs(X0),abs(X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_bounds) ).
tff(f1810,plain,
spl21_169,
inference(avatar_split_clause,[],[f542,f1808]) ).
tff(f1808,plain,
( spl21_169
<=> ! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != mod(X0,X1) )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_169])]) ).
tff(f542,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != mod(X0,X1) )
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != mod(X0,X1) )
| ( 0 = X1 ) ),
inference(flattening,[],[f297]) ).
tff(f297,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != mod(X0,X1) )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( ( 0 = mod(X0,X1) )
=> divides(X1,X0) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( ( 0 = mod(X0,X11) )
=> divides(X11,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_divides_computer) ).
tff(f1806,plain,
spl21_168,
inference(avatar_split_clause,[],[f541,f1804]) ).
tff(f1804,plain,
( spl21_168
<=> ! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != $remainder_e(X0,X1) )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_168])]) ).
tff(f541,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != $remainder_e(X0,X1) )
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != $remainder_e(X0,X1) )
| ( 0 = X1 ) ),
inference(flattening,[],[f295]) ).
tff(f295,plain,
! [X0: $int,X1: $int] :
( divides(X1,X0)
| ( 0 != $remainder_e(X0,X1) )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( ( 0 = $remainder_e(X0,X1) )
=> divides(X1,X0) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( ( 0 = $remainder_e(X0,X11) )
=> divides(X11,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_divides_euclidean) ).
tff(f1802,plain,
spl21_167,
inference(avatar_split_clause,[],[f540,f1800]) ).
tff(f1800,plain,
( spl21_167
<=> ! [X0: $int,X1: $int] :
( ( 0 = mod(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_167])]) ).
tff(f540,plain,
! [X0: $int,X1: $int] :
( ( 0 = mod(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $int,X1: $int] :
( ( 0 = mod(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(flattening,[],[f293]) ).
tff(f293,plain,
! [X0: $int,X1: $int] :
( ( 0 = mod(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( divides(X1,X0)
=> ( 0 = mod(X0,X1) ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( divides(X11,X0)
=> ( 0 = mod(X0,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_mod_computer) ).
tff(f1796,plain,
spl21_166,
inference(avatar_split_clause,[],[f539,f1794]) ).
tff(f1794,plain,
( spl21_166
<=> ! [X0: $int,X1: $int] :
( ( 0 = $remainder_e(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_166])]) ).
tff(f539,plain,
! [X0: $int,X1: $int] :
( ( 0 = $remainder_e(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $int,X1: $int] :
( ( 0 = $remainder_e(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: $int,X1: $int] :
( ( 0 = $remainder_e(X0,X1) )
| ~ divides(X1,X0)
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( divides(X1,X0)
=> ( 0 = $remainder_e(X0,X1) ) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $int,X11: $int] :
( ( 0 != X11 )
=> ( divides(X11,X0)
=> ( 0 = $remainder_e(X0,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_mod_euclidean) ).
tff(f1792,plain,
spl21_165,
inference(avatar_split_clause,[],[f515,f1790]) ).
tff(f515,plain,
! [X2: $int,X0: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f396]) ).
tff(f396,plain,
! [X0: $int] :
( ( sP2(X0)
| ( ~ coprime(sK18(X0),X0)
& $less(sK18(X0),X0)
& ~ $less(sK18(X0),1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ sP2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f394,f395]) ).
tff(f395,plain,
! [X0: $int] :
( ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
=> ( ~ coprime(sK18(X0),X0)
& $less(sK18(X0),X0)
& ~ $less(sK18(X0),1) ) ),
introduced(choice_axiom,[]) ).
tff(f394,plain,
! [X0: $int] :
( ( sP2(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( coprime(X2,X0)
| ~ $less(X2,X0)
| $less(X2,1) )
& ~ $less(X0,2) )
| ~ sP2(X0) ) ),
inference(rectify,[],[f393]) ).
tff(f393,plain,
! [X0: $int] :
( ( sP2(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ sP2(X0) ) ),
inference(flattening,[],[f392]) ).
tff(f392,plain,
! [X0: $int] :
( ( sP2(X0)
| ? [X1: $int] :
( ~ coprime(X1,X0)
& $less(X1,X0)
& ~ $less(X1,1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) )
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f360]) ).
tff(f360,plain,
! [X0: $int] :
( sP2(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f1788,plain,
spl21_164,
inference(avatar_split_clause,[],[f508,f1786]) ).
tff(f508,plain,
! [X2: $int,X0: $int] :
( ~ divides(X2,X0)
| ~ $less(X2,X0)
| ~ $less(1,X2)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f390]) ).
tff(f390,plain,
! [X0: $int] :
( ( sP1(X0)
| ( divides(sK17(X0),X0)
& $less(sK17(X0),X0)
& $less(1,sK17(X0)) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( ~ divides(X2,X0)
| ~ $less(X2,X0)
| ~ $less(1,X2) )
& ~ $less(X0,2) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f388,f389]) ).
tff(f389,plain,
! [X0: $int] :
( ? [X1: $int] :
( divides(X1,X0)
& $less(X1,X0)
& $less(1,X1) )
=> ( divides(sK17(X0),X0)
& $less(sK17(X0),X0)
& $less(1,sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f388,plain,
! [X0: $int] :
( ( sP1(X0)
| ? [X1: $int] :
( divides(X1,X0)
& $less(X1,X0)
& $less(1,X1) )
| $less(X0,2) )
& ( ( ! [X2: $int] :
( ~ divides(X2,X0)
| ~ $less(X2,X0)
| ~ $less(1,X2) )
& ~ $less(X0,2) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f387]) ).
tff(f387,plain,
! [X0: $int] :
( ( sP1(X0)
| ? [X1: $int] :
( divides(X1,X0)
& $less(X1,X0)
& $less(1,X1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,X0)
| ~ $less(1,X1) )
& ~ $less(X0,2) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f386]) ).
tff(f386,plain,
! [X0: $int] :
( ( sP1(X0)
| ? [X1: $int] :
( divides(X1,X0)
& $less(X1,X0)
& $less(1,X1) )
| $less(X0,2) )
& ( ( ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,X0)
| ~ $less(1,X1) )
& ~ $less(X0,2) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f358]) ).
tff(f358,plain,
! [X0: $int] :
( sP1(X0)
<=> ( ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,X0)
| ~ $less(1,X1) )
& ~ $less(X0,2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1784,plain,
spl21_163,
inference(avatar_split_clause,[],[f153,f1782]) ).
tff(f1782,plain,
( spl21_163
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_163])]) ).
tff(f153,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f1780,plain,
spl21_162,
inference(avatar_split_clause,[],[f142,f1778]) ).
tff(f1778,plain,
( spl21_162
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_162])]) ).
tff(f142,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f1716,plain,
( ~ spl21_161
| ~ spl21_74
| spl21_137 ),
inference(avatar_split_clause,[],[f1592,f1459,f996,f1713]) ).
tff(f996,plain,
( spl21_74
<=> ! [X0: $int] :
( divides(2,X0)
| ~ even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).
tff(f1592,plain,
( ~ even(sK3)
| ~ spl21_74
| spl21_137 ),
inference(resolution,[],[f1460,f997]) ).
tff(f997,plain,
( ! [X0: $int] :
( divides(2,X0)
| ~ even(X0) )
| ~ spl21_74 ),
inference(avatar_component_clause,[],[f996]) ).
tff(f1675,plain,
spl21_160,
inference(avatar_split_clause,[],[f620,f1673]) ).
tff(f620,plain,
! [X0: $int,X1: $int] :
( ( $product(X0,sK19(X0,X1)) = X1 )
| ~ divides(X0,X1) ),
inference(forward_demodulation,[],[f561,f152]) ).
tff(f561,plain,
! [X0: $int,X1: $int] :
( ( $product(sK19(X0,X1),X0) = X1 )
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f402]) ).
tff(f402,plain,
! [X0: $int,X1: $int] :
( ( divides(X0,X1)
| ! [X2: $int] : ( $product(X2,X0) != X1 ) )
& ( ( $product(sK19(X0,X1),X0) = X1 )
| ~ divides(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f400,f401]) ).
tff(f401,plain,
! [X0: $int,X1: $int] :
( ? [X3: $int] : ( $product(X3,X0) = X1 )
=> ( $product(sK19(X0,X1),X0) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f400,plain,
! [X0: $int,X1: $int] :
( ( divides(X0,X1)
| ! [X2: $int] : ( $product(X2,X0) != X1 ) )
& ( ? [X3: $int] : ( $product(X3,X0) = X1 )
| ~ divides(X0,X1) ) ),
inference(rectify,[],[f399]) ).
tff(f399,plain,
! [X0: $int,X1: $int] :
( ( divides(X0,X1)
| ! [X2: $int] : ( $product(X2,X0) != X1 ) )
& ( ? [X2: $int] : ( $product(X2,X0) = X1 )
| ~ divides(X0,X1) ) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
<=> ? [X2: $int] : ( $product(X2,X0) = X1 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X8: $int,X9: $int] :
( divides(X8,X9)
<=> ? [X10: $int] : ( $product(X10,X8) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_def) ).
tff(f1671,plain,
spl21_159,
inference(avatar_split_clause,[],[f618,f1669]) ).
tff(f1669,plain,
( spl21_159
<=> ! [X0: $int] :
( ( $sum(1,$product(2,sK16(X0))) = X0 )
| ~ odd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_159])]) ).
tff(f618,plain,
! [X0: $int] :
( ( $sum(1,$product(2,sK16(X0))) = X0 )
| ~ odd(X0) ),
inference(forward_demodulation,[],[f505,f141]) ).
tff(f141,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f505,plain,
! [X0: $int] :
( ( $sum($product(2,sK16(X0)),1) = X0 )
| ~ odd(X0) ),
inference(cnf_transformation,[],[f385]) ).
tff(f385,plain,
! [X0: $int] :
( ( odd(X0)
| ! [X1: $int] : ( $sum($product(2,X1),1) != X0 ) )
& ( ( $sum($product(2,sK16(X0)),1) = X0 )
| ~ odd(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f383,f384]) ).
tff(f384,plain,
! [X0: $int] :
( ? [X2: $int] : ( $sum($product(2,X2),1) = X0 )
=> ( $sum($product(2,sK16(X0)),1) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f383,plain,
! [X0: $int] :
( ( odd(X0)
| ! [X1: $int] : ( $sum($product(2,X1),1) != X0 ) )
& ( ? [X2: $int] : ( $sum($product(2,X2),1) = X0 )
| ~ odd(X0) ) ),
inference(rectify,[],[f382]) ).
tff(f382,plain,
! [X0: $int] :
( ( odd(X0)
| ! [X1: $int] : ( $sum($product(2,X1),1) != X0 ) )
& ( ? [X1: $int] : ( $sum($product(2,X1),1) = X0 )
| ~ odd(X0) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $int] :
( odd(X0)
<=> ? [X1: $int] : ( $sum($product(2,X1),1) = X0 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X9: $int] :
( odd(X9)
<=> ? [X13: $int] : ( $sum($product(2,X13),1) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_def) ).
tff(f1667,plain,
spl21_158,
inference(avatar_split_clause,[],[f585,f1665]) ).
tff(f585,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides($product(X2,X0),$product(X2,X1))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f337]) ).
tff(f337,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides($product(X2,X0),$product(X2,X1))
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> divides($product(X2,X0),$product(X2,X1)) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> divides($product(X12,X0),$product(X12,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_left) ).
tff(f1663,plain,
spl21_157,
inference(avatar_split_clause,[],[f584,f1661]) ).
tff(f584,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides($product(X0,X2),$product(X1,X2))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f336]) ).
tff(f336,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides($product(X0,X2),$product(X1,X2))
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> divides($product(X0,X2),$product(X1,X2)) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> divides($product(X0,X12),$product(X11,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_right) ).
tff(f1659,plain,
spl21_156,
inference(avatar_split_clause,[],[f579,f1657]) ).
tff(f1657,plain,
( spl21_156
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_156])]) ).
tff(f579,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool(X0,true,X1,X2) = X1 )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X1)
=> ( match_bool(X0,true,X1,X2) = X1 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort(X0,X4)
=> ( match_bool(X0,true,X4,X5) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_bool_True) ).
tff(f1655,plain,
( spl21_155
| ~ spl21_78
| spl21_137 ),
inference(avatar_split_clause,[],[f1591,f1459,f1013,f1652]) ).
tff(f1591,plain,
( odd(sK3)
| ~ spl21_78
| spl21_137 ),
inference(resolution,[],[f1460,f1014]) ).
tff(f1650,plain,
spl21_154,
inference(avatar_split_clause,[],[f578,f1648]) ).
tff(f1648,plain,
( spl21_154
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_154])]) ).
tff(f578,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool(X0,false,X1,X2) = X2 )
| ~ sort(X0,X2) ),
inference(ennf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort(X0,X2)
=> ( match_bool(X0,false,X1,X2) = X2 ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort(X0,X5)
=> ( match_bool(X0,false,X4,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_bool_False) ).
tff(f1646,plain,
spl21_153,
inference(avatar_split_clause,[],[f543,f1644]) ).
tff(f1644,plain,
( spl21_153
<=> ! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_153])]) ).
tff(f543,plain,
! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort(X0,X1) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort(X0,X1) ),
inference(ennf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: ty,X1: uni] :
( sort(X0,X1)
=> ( contents(X0,mk_ref(X0,X1)) = X1 ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: ty,X6: uni] :
( sort(X0,X6)
=> ( contents(X0,mk_ref(X0,X6)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contents_def) ).
tff(f1642,plain,
spl21_152,
inference(avatar_split_clause,[],[f537,f1640]) ).
tff(f1640,plain,
( spl21_152
<=> ! [X0: $int,X1: $int] :
( $less($uminus(abs(X1)),mod(X0,X1))
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_152])]) ).
tff(f537,plain,
! [X0: $int,X1: $int] :
( $less($uminus(abs(X1)),mod(X0,X1))
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $int,X1: $int] :
( ( $less(mod(X0,X1),abs(X1))
& $less($uminus(abs(X1)),mod(X0,X1)) )
| ( 0 = X1 ) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
=> ( $less(mod(X0,X1),abs(X1))
& $less($uminus(abs(X1)),mod(X0,X1)) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X1: $int,X7: $int] :
( ( 0 != X7 )
=> ( $less(mod(X1,X7),abs(X7))
& $less($uminus(abs(X7)),mod(X1,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_bound) ).
tff(f1638,plain,
spl21_151,
inference(avatar_split_clause,[],[f149,f1636]) ).
tff(f1636,plain,
( spl21_151
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_151])]) ).
tff(f149,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f1634,plain,
spl21_150,
inference(avatar_split_clause,[],[f144,f1632]) ).
tff(f1632,plain,
( spl21_150
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_150])]) ).
tff(f144,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f1510,plain,
spl21_149,
inference(avatar_split_clause,[],[f614,f1508]) ).
tff(f1508,plain,
( spl21_149
<=> ! [X0: $int] :
( ( -1 = X0 )
| ( 1 = X0 )
| ~ divides(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_149])]) ).
tff(f614,plain,
! [X0: $int] :
( ( -1 = X0 )
| ( 1 = X0 )
| ~ divides(X0,1) ),
inference(evaluation,[],[f498]) ).
tff(f498,plain,
! [X0: $int] :
( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ~ divides(X0,1) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $int] :
( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ~ divides(X0,1) ),
inference(flattening,[],[f280]) ).
tff(f280,plain,
! [X0: $int] :
( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ~ divides(X0,1) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $int] :
( divides(X0,1)
=> ( ( $uminus(1) = X0 )
| ( 1 = X0 ) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X9: $int] :
( divides(X9,1)
=> ( ( $uminus(1) = X9 )
| ( 1 = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_n_1) ).
tff(f1506,plain,
spl21_148,
inference(avatar_split_clause,[],[f586,f1504]) ).
tff(f586,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f339]) ).
tff(f339,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(flattening,[],[f338]) ).
tff(f338,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> ( divides(X1,X2)
=> divides(X0,X2) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> ( divides(X11,X12)
=> divides(X0,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_trans) ).
tff(f1502,plain,
spl21_147,
inference(avatar_split_clause,[],[f538,f1500]) ).
tff(f1500,plain,
( spl21_147
<=> ! [X0: $int,X1: $int] :
( $less(mod(X0,X1),abs(X1))
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_147])]) ).
tff(f538,plain,
! [X0: $int,X1: $int] :
( $less(mod(X0,X1),abs(X1))
| ( 0 = X1 ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f1498,plain,
spl21_146,
inference(avatar_split_clause,[],[f518,f1496]) ).
tff(f1496,plain,
( spl21_146
<=> ! [X0: $int] :
( sP2(X0)
| ~ coprime(sK18(X0),X0)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_146])]) ).
tff(f518,plain,
! [X0: $int] :
( sP2(X0)
| ~ coprime(sK18(X0),X0)
| $less(X0,2) ),
inference(cnf_transformation,[],[f396]) ).
tff(f1494,plain,
spl21_145,
inference(avatar_split_clause,[],[f517,f1492]) ).
tff(f1492,plain,
( spl21_145
<=> ! [X0: $int] :
( sP2(X0)
| $less(sK18(X0),X0)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_145])]) ).
tff(f517,plain,
! [X0: $int] :
( sP2(X0)
| $less(sK18(X0),X0)
| $less(X0,2) ),
inference(cnf_transformation,[],[f396]) ).
tff(f1490,plain,
spl21_144,
inference(avatar_split_clause,[],[f516,f1488]) ).
tff(f1488,plain,
( spl21_144
<=> ! [X0: $int] :
( sP2(X0)
| ~ $less(sK18(X0),1)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_144])]) ).
tff(f516,plain,
! [X0: $int] :
( sP2(X0)
| ~ $less(sK18(X0),1)
| $less(X0,2) ),
inference(cnf_transformation,[],[f396]) ).
tff(f1486,plain,
spl21_143,
inference(avatar_split_clause,[],[f511,f1484]) ).
tff(f1484,plain,
( spl21_143
<=> ! [X0: $int] :
( sP1(X0)
| divides(sK17(X0),X0)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_143])]) ).
tff(f511,plain,
! [X0: $int] :
( sP1(X0)
| divides(sK17(X0),X0)
| $less(X0,2) ),
inference(cnf_transformation,[],[f390]) ).
tff(f1482,plain,
spl21_142,
inference(avatar_split_clause,[],[f510,f1480]) ).
tff(f1480,plain,
( spl21_142
<=> ! [X0: $int] :
( sP1(X0)
| $less(sK17(X0),X0)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_142])]) ).
tff(f510,plain,
! [X0: $int] :
( sP1(X0)
| $less(sK17(X0),X0)
| $less(X0,2) ),
inference(cnf_transformation,[],[f390]) ).
tff(f1478,plain,
spl21_141,
inference(avatar_split_clause,[],[f509,f1476]) ).
tff(f1476,plain,
( spl21_141
<=> ! [X0: $int] :
( sP1(X0)
| $less(1,sK17(X0))
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_141])]) ).
tff(f509,plain,
! [X0: $int] :
( sP1(X0)
| $less(1,sK17(X0))
| $less(X0,2) ),
inference(cnf_transformation,[],[f390]) ).
tff(f1474,plain,
spl21_140,
inference(avatar_split_clause,[],[f494,f1472]) ).
tff(f1472,plain,
( spl21_140
<=> ! [X0: $int] :
( ~ $less(X0,$product(sK14(X0),sK14(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_140])]) ).
tff(f494,plain,
! [X0: $int] :
( ~ $less(X0,$product(sK14(X0),sK14(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f375]) ).
tff(f375,plain,
! [X0: $int] :
( ( divides(sK14(X0),X0)
& ~ $less(X0,$product(sK14(X0),sK14(X0)))
& $less(1,$product(sK14(X0),sK14(X0)))
& prime(sK14(X0))
& ~ $less(sK14(X0),2) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f373,f374]) ).
tff(f374,plain,
! [X0: $int] :
( ? [X1: $int] :
( divides(X1,X0)
& ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1))
& prime(X1)
& ~ $less(X1,2) )
=> ( divides(sK14(X0),X0)
& ~ $less(X0,$product(sK14(X0),sK14(X0)))
& $less(1,$product(sK14(X0),sK14(X0)))
& prime(sK14(X0))
& ~ $less(sK14(X0),2) ) ),
introduced(choice_axiom,[]) ).
tff(f373,plain,
! [X0: $int] :
( ? [X1: $int] :
( divides(X1,X0)
& ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1))
& prime(X1)
& ~ $less(X1,2) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f356]) ).
tff(f356,plain,
! [X0: $int] :
( ? [X1: $int] :
( divides(X1,X0)
& ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1))
& prime(X1)
& ~ $less(X1,2) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1470,plain,
spl21_139,
inference(avatar_split_clause,[],[f493,f1468]) ).
tff(f1468,plain,
( spl21_139
<=> ! [X0: $int] :
( $less(1,$product(sK14(X0),sK14(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_139])]) ).
tff(f493,plain,
! [X0: $int] :
( $less(1,$product(sK14(X0),sK14(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f375]) ).
tff(f1466,plain,
( spl21_137
| ~ spl21_138
| ~ spl21_34
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f1075,f996,f786,f1463,f1459]) ).
tff(f1463,plain,
( spl21_138
<=> even(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_138])]) ).
tff(f1075,plain,
( ~ even(sK6)
| divides(2,sK3)
| ~ spl21_34
| ~ spl21_74 ),
inference(evaluation,[],[f1074]) ).
tff(f1074,plain,
( ~ even(sK6)
| $less(2,2)
| divides(2,sK3)
| ~ spl21_34
| ~ spl21_74 ),
inference(resolution,[],[f997,f787]) ).
tff(f1457,plain,
spl21_136,
inference(avatar_split_clause,[],[f490,f1455]) ).
tff(f1455,plain,
( spl21_136
<=> ! [X0: $int] :
( ( $uminus(X0) = gcd(X0,0) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_136])]) ).
tff(f490,plain,
! [X0: $int] :
( ( $uminus(X0) = gcd(X0,0) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $int] :
( ( $uminus(X0) = gcd(X0,0) )
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f81]) ).
tff(f81,axiom,
! [X0: $int] :
( $less(X0,0)
=> ( $uminus(X0) = gcd(X0,0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_0_neg) ).
tff(f1453,plain,
spl21_135,
inference(avatar_split_clause,[],[f148,f1451]) ).
tff(f148,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f1449,plain,
spl21_134,
inference(avatar_split_clause,[],[f147,f1447]) ).
tff(f147,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f1398,plain,
spl21_133,
inference(avatar_split_clause,[],[f596,f1396]) ).
tff(f1396,plain,
( spl21_133
<=> ! [X4: uni,X0: ty,X3: uni,X2: uni,X1: ty] : sort(X1,match_list(X1,X0,X2,X3,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_133])]) ).
tff(f596,plain,
! [X2: uni,X3: uni,X0: ty,X1: ty,X4: uni] : sort(X1,match_list(X1,X0,X2,X3,X4)),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: ty,X1: ty,X2: uni,X3: uni,X4: uni] : sort(X1,match_list(X1,X0,X2,X3,X4)),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: ty,X15: ty,X1: uni,X2: uni,X3: uni] : sort(X15,match_list(X15,X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_list_sort) ).
tff(f1394,plain,
spl21_132,
inference(avatar_split_clause,[],[f583,f1392]) ).
tff(f583,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X2,X1))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$product(X2,X1))
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> divides(X0,$product(X2,X1)) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> divides(X0,$product(X12,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_multl) ).
tff(f1389,plain,
spl21_131,
inference(avatar_split_clause,[],[f582,f1387]) ).
tff(f582,plain,
! [X2: $int,X0: $int,X1: $int] :
( divides(X0,$product(X1,X2))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,$product(X1,X2))
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $int,X1: $int,X2: $int] :
( divides(X0,X1)
=> divides(X0,$product(X1,X2)) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $int,X11: $int,X12: $int] :
( divides(X0,X11)
=> divides(X0,$product(X11,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_multr) ).
tff(f1385,plain,
spl21_130,
inference(avatar_split_clause,[],[f568,f1383]) ).
tff(f1383,plain,
( spl21_130
<=> ! [X2: uni,X0: ty,X1: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_130])]) ).
tff(f568,plain,
! [X2: uni,X0: ty,X1: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: ty,X1: uni,X2: uni] : ( cons_proj_2(X0,cons(X0,X1,X2)) = X2 ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X0: ty,X6: uni,X16: uni] : ( cons_proj_2(X0,cons(X0,X6,X16)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_proj_2_def) ).
tff(f1381,plain,
spl21_129,
inference(avatar_split_clause,[],[f563,f1379]) ).
tff(f1379,plain,
( spl21_129
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| $less(X1,abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_129])]) ).
tff(f563,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| $less(X1,abs(X0)) ),
inference(cnf_transformation,[],[f404]) ).
tff(f1377,plain,
spl21_128,
inference(avatar_split_clause,[],[f560,f1375]) ).
tff(f1375,plain,
( spl21_128
<=> ! [X0: $int,X1: $int] :
( coprime(X0,X1)
| ( 1 != gcd(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_128])]) ).
tff(f560,plain,
! [X0: $int,X1: $int] :
( coprime(X0,X1)
| ( 1 != gcd(X0,X1) ) ),
inference(cnf_transformation,[],[f398]) ).
tff(f398,plain,
! [X0: $int,X1: $int] :
( ( coprime(X0,X1)
| ( 1 != gcd(X0,X1) ) )
& ( ( 1 = gcd(X0,X1) )
| ~ coprime(X0,X1) ) ),
inference(nnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $int,X1: $int] :
( coprime(X0,X1)
<=> ( 1 = gcd(X0,X1) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $int,X11: $int] :
( coprime(X0,X11)
<=> ( 1 = gcd(X0,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coprime_def) ).
tff(f1373,plain,
spl21_127,
inference(avatar_split_clause,[],[f559,f1371]) ).
tff(f1371,plain,
( spl21_127
<=> ! [X0: $int,X1: $int] :
( ( 1 = gcd(X0,X1) )
| ~ coprime(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_127])]) ).
tff(f559,plain,
! [X0: $int,X1: $int] :
( ( 1 = gcd(X0,X1) )
| ~ coprime(X0,X1) ),
inference(cnf_transformation,[],[f398]) ).
tff(f1369,plain,
spl21_126,
inference(avatar_split_clause,[],[f531,f1367]) ).
tff(f1367,plain,
( spl21_126
<=> ! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_126])]) ).
tff(f531,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd($uminus(X0),X1) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd($uminus(X0),X1) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $int,X11: $int] : ( gcd(X0,X11) = gcd($uminus(X0),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_opp) ).
tff(f1365,plain,
spl21_125,
inference(avatar_split_clause,[],[f501,f1363]) ).
tff(f1363,plain,
( spl21_125
<=> ! [X0: $int] :
( ( $product(2,sK15(X0)) = X0 )
| ~ even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_125])]) ).
tff(f501,plain,
! [X0: $int] :
( ( $product(2,sK15(X0)) = X0 )
| ~ even(X0) ),
inference(cnf_transformation,[],[f380]) ).
tff(f380,plain,
! [X0: $int] :
( ( even(X0)
| ! [X1: $int] : ( $product(2,X1) != X0 ) )
& ( ( $product(2,sK15(X0)) = X0 )
| ~ even(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f378,f379]) ).
tff(f379,plain,
! [X0: $int] :
( ? [X2: $int] : ( $product(2,X2) = X0 )
=> ( $product(2,sK15(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f378,plain,
! [X0: $int] :
( ( even(X0)
| ! [X1: $int] : ( $product(2,X1) != X0 ) )
& ( ? [X2: $int] : ( $product(2,X2) = X0 )
| ~ even(X0) ) ),
inference(rectify,[],[f377]) ).
tff(f377,plain,
! [X0: $int] :
( ( even(X0)
| ! [X1: $int] : ( $product(2,X1) != X0 ) )
& ( ? [X1: $int] : ( $product(2,X1) = X0 )
| ~ even(X0) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $int] :
( even(X0)
<=> ? [X1: $int] : ( $product(2,X1) = X0 ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X9: $int] :
( even(X9)
<=> ? [X13: $int] : ( $product(2,X13) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_def) ).
tff(f1361,plain,
spl21_124,
inference(avatar_split_clause,[],[f497,f1359]) ).
tff(f1359,plain,
( spl21_124
<=> ! [X0: $int] :
( ( gcd(X0,0) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_124])]) ).
tff(f497,plain,
! [X0: $int] :
( ( gcd(X0,0) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $int] :
( ( gcd(X0,0) = X0 )
| $less(X0,0) ),
inference(ennf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: $int] :
( ~ $less(X0,0)
=> ( gcd(X0,0) = X0 ) ),
inference(theory_normalization,[],[f80]) ).
tff(f80,axiom,
! [X0: $int] :
( $lesseq(0,X0)
=> ( gcd(X0,0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_0_pos) ).
tff(f1357,plain,
spl21_123,
inference(avatar_split_clause,[],[f478,f1355]) ).
tff(f1355,plain,
( spl21_123
<=> ! [X0: $int] :
( ( $uminus(X0) = abs(X0) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_123])]) ).
tff(f478,plain,
! [X0: $int] :
( ( $uminus(X0) = abs(X0) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $int] :
( ( ( $uminus(X0) = abs(X0) )
| ~ $less(X0,0) )
& ( ( abs(X0) = X0 )
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $int] :
( ( $less(X0,0)
=> ( $uminus(X0) = abs(X0) ) )
& ( ~ $less(X0,0)
=> ( abs(X0) = X0 ) ) ),
inference(rectify,[],[f117]) ).
tff(f117,plain,
! [X1: $int] :
( ( $less(X1,0)
=> ( abs(X1) = $uminus(X1) ) )
& ( ~ $less(X1,0)
=> ( abs(X1) = X1 ) ) ),
inference(theory_normalization,[],[f9]) ).
tff(f9,axiom,
! [X1: $int] :
( ( ~ $lesseq(0,X1)
=> ( abs(X1) = $uminus(X1) ) )
& ( $lesseq(0,X1)
=> ( abs(X1) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_def) ).
tff(f1353,plain,
spl21_122,
inference(avatar_split_clause,[],[f163,f1351]) ).
tff(f1351,plain,
( spl21_122
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).
tff(f163,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f1348,plain,
spl21_121,
inference(avatar_split_clause,[],[f161,f1346]) ).
tff(f1346,plain,
( spl21_121
<=> ! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($remainder_e(X1,X2),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).
tff(f161,plain,
! [X2: $int,X1: $int] :
( ( 0 = X2 )
| ~ $less($remainder_e(X1,X2),0) ),
introduced(theory_axiom_153,[]) ).
tff(f1344,plain,
spl21_120,
inference(avatar_split_clause,[],[f159,f1342]) ).
tff(f1342,plain,
( spl21_120
<=> ! [X1: $int] :
( ~ $less(X1,0)
| ( $uminus(X1) = $abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).
tff(f159,plain,
! [X1: $int] :
( ~ $less(X1,0)
| ( $uminus(X1) = $abs(X1) ) ),
introduced(theory_axiom_158,[]) ).
tff(f1340,plain,
spl21_119,
inference(avatar_split_clause,[],[f150,f1338]) ).
tff(f1338,plain,
( spl21_119
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_119])]) ).
tff(f150,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f1255,plain,
spl21_118,
inference(avatar_split_clause,[],[f594,f1253]) ).
tff(f1253,plain,
( spl21_118
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool] : sort(X0,match_bool(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).
tff(f594,plain,
! [X2: uni,X3: uni,X0: ty,X1: bool] : sort(X0,match_bool(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: ty,X1: bool,X2: uni,X3: uni] : sort(X0,match_bool(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',match_bool_sort) ).
tff(f1250,plain,
spl21_117,
inference(avatar_split_clause,[],[f567,f1248]) ).
tff(f1248,plain,
( spl21_117
<=> ! [X2: uni,X0: ty,X1: uni] : sort(list(X0),cons(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).
tff(f567,plain,
! [X2: uni,X0: ty,X1: uni] : sort(list(X0),cons(X0,X1,X2)),
inference(cnf_transformation,[],[f97]) ).
tff(f97,axiom,
! [X0: ty,X1: uni,X2: uni] : sort(list(X0),cons(X0,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_sort) ).
tff(f1246,plain,
spl21_116,
inference(avatar_split_clause,[],[f566,f1244]) ).
tff(f1244,plain,
( spl21_116
<=> ! [X2: uni,X0: ty,X1: uni] : ( nil(X0) != cons(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).
tff(f566,plain,
! [X2: uni,X0: ty,X1: uni] : ( nil(X0) != cons(X0,X1,X2) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: ty,X1: uni,X2: uni] : ( nil(X0) != cons(X0,X1,X2) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X0: ty,X17: uni,X18: uni] : ( nil(X0) != cons(X0,X17,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nil_Cons) ).
tff(f1242,plain,
spl21_115,
inference(avatar_split_clause,[],[f564,f1240]) ).
tff(f1240,plain,
( spl21_115
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,abs(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_115])]) ).
tff(f564,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,abs(X0)) ),
inference(cnf_transformation,[],[f404]) ).
tff(f1238,plain,
spl21_114,
inference(avatar_split_clause,[],[f550,f1236]) ).
tff(f1236,plain,
( spl21_114
<=> ! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_114])]) ).
tff(f550,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides($uminus(X0),X1) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides($uminus(X0),X1) ),
inference(ennf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $int,X1: $int] :
( divides($uminus(X0),X1)
=> divides(X0,X1) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $int,X11: $int] :
( divides($uminus(X0),X11)
=> divides(X0,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_oppr_rev) ).
tff(f1234,plain,
spl21_113,
inference(avatar_split_clause,[],[f549,f1232]) ).
tff(f1232,plain,
( spl21_113
<=> ! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides(X0,$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_113])]) ).
tff(f549,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides(X0,$uminus(X1)) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
| ~ divides(X0,$uminus(X1)) ),
inference(ennf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $int,X1: $int] :
( divides(X0,$uminus(X1))
=> divides(X0,X1) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: $int,X11: $int] :
( divides(X0,$uminus(X11))
=> divides(X0,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_oppl_rev) ).
tff(f1230,plain,
spl21_112,
inference(avatar_split_clause,[],[f545,f1228]) ).
tff(f1228,plain,
( spl21_112
<=> ! [X0: $int,X1: $int] :
( divides($uminus(X0),X1)
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_112])]) ).
tff(f545,plain,
! [X0: $int,X1: $int] :
( divides($uminus(X0),X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: $int,X1: $int] :
( divides($uminus(X0),X1)
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
=> divides($uminus(X0),X1) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $int,X11: $int] :
( divides(X0,X11)
=> divides($uminus(X0),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_oppl) ).
tff(f1226,plain,
spl21_111,
inference(avatar_split_clause,[],[f544,f1224]) ).
tff(f1224,plain,
( spl21_111
<=> ! [X0: $int,X1: $int] :
( divides(X0,$uminus(X1))
| ~ divides(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_111])]) ).
tff(f544,plain,
! [X0: $int,X1: $int] :
( divides(X0,$uminus(X1))
| ~ divides(X0,X1) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $int,X1: $int] :
( divides(X0,$uminus(X1))
| ~ divides(X0,X1) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $int,X1: $int] :
( divides(X0,X1)
=> divides(X0,$uminus(X1)) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $int,X11: $int] :
( divides(X0,X11)
=> divides(X0,$uminus(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_oppr) ).
tff(f1222,plain,
spl21_110,
inference(avatar_split_clause,[],[f530,f1220]) ).
tff(f1220,plain,
( spl21_110
<=> ! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_110])]) ).
tff(f530,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X1: $int,X7: $int] : ( gcd(X1,X7) = gcd(X7,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comm) ).
tff(f1218,plain,
spl21_109,
inference(avatar_split_clause,[],[f496,f1216]) ).
tff(f1216,plain,
( spl21_109
<=> ! [X0: $int] :
( prime(X0)
| sP0(X0)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_109])]) ).
tff(f496,plain,
! [X0: $int] :
( prime(X0)
| sP0(X0)
| $less(X0,2) ),
inference(cnf_transformation,[],[f357]) ).
tff(f357,plain,
! [X0: $int] :
( prime(X0)
| sP0(X0)
| $less(X0,2) ),
inference(definition_folding,[],[f278,f356]) ).
tff(f278,plain,
! [X0: $int] :
( prime(X0)
| ? [X1: $int] :
( divides(X1,X0)
& ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1))
& prime(X1)
& ~ $less(X1,2) )
| $less(X0,2) ),
inference(flattening,[],[f277]) ).
tff(f277,plain,
! [X0: $int] :
( prime(X0)
| ? [X1: $int] :
( divides(X1,X0)
& ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1))
& prime(X1)
& ~ $less(X1,2) )
| $less(X0,2) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $int] :
( ~ $less(X0,2)
=> ( ! [X1: $int] :
( ~ $less(X1,2)
=> ( prime(X1)
=> ( ( ~ $less(X0,$product(X1,X1))
& $less(1,$product(X1,X1)) )
=> ~ divides(X1,X0) ) ) )
=> prime(X0) ) ),
inference(rectify,[],[f119]) ).
tff(f119,plain,
! [X14: $int] :
( ~ $less(X14,2)
=> ( ! [X8: $int] :
( ~ $less(X8,2)
=> ( prime(X8)
=> ( ( ~ $less(X14,$product(X8,X8))
& $less(1,$product(X8,X8)) )
=> ~ divides(X8,X14) ) ) )
=> prime(X14) ) ),
inference(theory_normalization,[],[f70]) ).
tff(f70,axiom,
! [X14: $int] :
( $lesseq(2,X14)
=> ( ! [X8: $int] :
( $lesseq(2,X8)
=> ( prime(X8)
=> ( ( $lesseq($product(X8,X8),X14)
& $less(1,$product(X8,X8)) )
=> ~ divides(X8,X14) ) ) )
=> prime(X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',small_divisors) ).
tff(f1214,plain,
spl21_108,
inference(avatar_split_clause,[],[f488,f1212]) ).
tff(f488,plain,
! [X0: $int] :
( odd(X0)
| $less(X0,3)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $int] :
( odd(X0)
| $less(X0,3)
| ~ prime(X0) ),
inference(flattening,[],[f272]) ).
tff(f272,plain,
! [X0: $int] :
( odd(X0)
| $less(X0,3)
| ~ prime(X0) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $int] :
( prime(X0)
=> ( ~ $less(X0,3)
=> odd(X0) ) ),
inference(rectify,[],[f118]) ).
tff(f118,plain,
! [X14: $int] :
( prime(X14)
=> ( ~ $less(X14,3)
=> odd(X14) ) ),
inference(theory_normalization,[],[f72]) ).
tff(f72,axiom,
! [X14: $int] :
( prime(X14)
=> ( $lesseq(3,X14)
=> odd(X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_prime) ).
tff(f1209,plain,
spl21_107,
inference(avatar_split_clause,[],[f487,f1207]) ).
tff(f487,plain,
! [X0: $int] :
( ( 2 = X0 )
| ~ even(X0)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $int] :
( ( 2 = X0 )
| ~ even(X0)
| ~ prime(X0) ),
inference(flattening,[],[f270]) ).
tff(f270,plain,
! [X0: $int] :
( ( 2 = X0 )
| ~ even(X0)
| ~ prime(X0) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $int] :
( prime(X0)
=> ( even(X0)
=> ( 2 = X0 ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X14: $int] :
( prime(X14)
=> ( even(X14)
=> ( 2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_prime) ).
tff(f1205,plain,
spl21_106,
inference(avatar_split_clause,[],[f477,f1203]) ).
tff(f1203,plain,
( spl21_106
<=> ! [X0: $int] :
( ( abs(X0) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).
tff(f477,plain,
! [X0: $int] :
( ( abs(X0) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f1201,plain,
spl21_105,
inference(avatar_split_clause,[],[f158,f1199]) ).
tff(f1199,plain,
( spl21_105
<=> ! [X1: $int] :
( ~ $less(0,X1)
| ( $abs(X1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).
tff(f158,plain,
! [X1: $int] :
( ~ $less(0,X1)
| ( $abs(X1) = X1 ) ),
introduced(theory_axiom_157,[]) ).
tff(f1197,plain,
spl21_104,
inference(avatar_split_clause,[],[f152,f1195]) ).
tff(f1193,plain,
spl21_103,
inference(avatar_split_clause,[],[f141,f1191]) ).
tff(f1174,plain,
spl21_102,
inference(avatar_split_clause,[],[f616,f1172]) ).
tff(f1172,plain,
( spl21_102
<=> ! [X0: $int] : odd($sum(1,$product(2,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_102])]) ).
tff(f616,plain,
! [X0: $int] : odd($sum(1,$product(2,X0))),
inference(forward_demodulation,[],[f476,f141]) ).
tff(f476,plain,
! [X0: $int] : odd($sum($product(2,X0),1)),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $int] : odd($sum($product(2,X0),1)),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X13: $int] : odd($sum($product(2,X13),1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_2k1) ).
tff(f1170,plain,
spl21_101,
inference(avatar_split_clause,[],[f529,f1168]) ).
tff(f1168,plain,
( spl21_101
<=> ! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_101])]) ).
tff(f529,plain,
! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
! [X0: ty,X1: uni] : sort(list(X0),cons_proj_2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_proj_2_sort) ).
tff(f1166,plain,
spl21_100,
inference(avatar_split_clause,[],[f528,f1164]) ).
tff(f1164,plain,
( spl21_100
<=> ! [X0: ty,X1: uni] : sort(ref(X0),mk_ref(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_100])]) ).
tff(f528,plain,
! [X0: ty,X1: uni] : sort(ref(X0),mk_ref(X0,X1)),
inference(cnf_transformation,[],[f92]) ).
tff(f92,axiom,
! [X0: ty,X1: uni] : sort(ref(X0),mk_ref(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mk_ref_sort) ).
tff(f1162,plain,
spl21_99,
inference(avatar_split_clause,[],[f495,f1160]) ).
tff(f1160,plain,
( spl21_99
<=> ! [X0: $int] :
( divides(sK14(X0),X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_99])]) ).
tff(f495,plain,
! [X0: $int] :
( divides(sK14(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f375]) ).
tff(f1158,plain,
( spl21_98
| ~ spl21_2
| ~ spl21_58 ),
inference(avatar_split_clause,[],[f937,f920,f627,f1155]) ).
tff(f920,plain,
( spl21_58
<=> ! [X0: $int] :
( sP2(X0)
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).
tff(f937,plain,
( sP2(sK13)
| ~ spl21_2
| ~ spl21_58 ),
inference(resolution,[],[f921,f629]) ).
tff(f921,plain,
( ! [X0: $int] :
( ~ prime(X0)
| sP2(X0) )
| ~ spl21_58 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f1153,plain,
spl21_97,
inference(avatar_split_clause,[],[f491,f1151]) ).
tff(f1151,plain,
( spl21_97
<=> ! [X0: $int] :
( ~ $less(sK14(X0),2)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_97])]) ).
tff(f491,plain,
! [X0: $int] :
( ~ $less(sK14(X0),2)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f375]) ).
tff(f1149,plain,
spl21_96,
inference(avatar_split_clause,[],[f486,f1147]) ).
tff(f1147,plain,
( spl21_96
<=> ! [X0: $int] :
( odd($sum(X0,2))
| ~ odd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).
tff(f486,plain,
! [X0: $int] :
( odd($sum(X0,2))
| ~ odd(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $int] :
( odd($sum(X0,2))
| ~ odd(X0) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $int] :
( odd(X0)
=> odd($sum(X0,2)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X9: $int] :
( odd(X9)
=> odd($sum(X9,2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_odd) ).
tff(f1145,plain,
spl21_95,
inference(avatar_split_clause,[],[f485,f1143]) ).
tff(f1143,plain,
( spl21_95
<=> ! [X0: $int] :
( even($sum(X0,1))
| ~ odd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_95])]) ).
tff(f485,plain,
! [X0: $int] :
( even($sum(X0,1))
| ~ odd(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $int] :
( even($sum(X0,1))
| ~ odd(X0) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $int] :
( odd(X0)
=> even($sum(X0,1)) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X9: $int] :
( odd(X9)
=> even($sum(X9,1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_even) ).
tff(f1141,plain,
spl21_94,
inference(avatar_split_clause,[],[f483,f1139]) ).
tff(f1139,plain,
( spl21_94
<=> ! [X0: $int] :
( odd($sum(X0,1))
| ~ even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).
tff(f483,plain,
! [X0: $int] :
( odd($sum(X0,1))
| ~ even(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $int] :
( odd($sum(X0,1))
| ~ even(X0) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $int] :
( even(X0)
=> odd($sum(X0,1)) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X9: $int] :
( even(X9)
=> odd($sum(X9,1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_odd) ).
tff(f1137,plain,
spl21_93,
inference(avatar_split_clause,[],[f482,f1135]) ).
tff(f1135,plain,
( spl21_93
<=> ! [X0: $int] :
( even($sum(X0,2))
| ~ even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_93])]) ).
tff(f482,plain,
! [X0: $int] :
( even($sum(X0,2))
| ~ even(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $int] :
( even($sum(X0,2))
| ~ even(X0) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $int] :
( even(X0)
=> even($sum(X0,2)) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X9: $int] :
( even(X9)
=> even($sum(X9,2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_even) ).
tff(f1133,plain,
spl21_92,
inference(avatar_split_clause,[],[f480,f1131]) ).
tff(f1131,plain,
( spl21_92
<=> ! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_92])]) ).
tff(f480,plain,
! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: bool] :
( ( false = X0 )
| ( true = X0 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X6: bool] :
( ( false = X6 )
| ( true = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_inversion) ).
tff(f1129,plain,
spl21_91,
inference(avatar_split_clause,[],[f145,f1127]) ).
tff(f1127,plain,
( spl21_91
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_91])]) ).
tff(f145,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f1108,plain,
( spl21_90
| ~ spl21_3
| ~ spl21_58 ),
inference(avatar_split_clause,[],[f936,f920,f632,f1105]) ).
tff(f936,plain,
( sP2(sK10)
| ~ spl21_3
| ~ spl21_58 ),
inference(resolution,[],[f921,f634]) ).
tff(f1068,plain,
( spl21_89
| ~ spl21_1
| ~ spl21_58 ),
inference(avatar_split_clause,[],[f935,f920,f622,f1065]) ).
tff(f1065,plain,
( spl21_89
<=> sP2(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_89])]) ).
tff(f935,plain,
( sP2(sK7)
| ~ spl21_1
| ~ spl21_58 ),
inference(resolution,[],[f921,f624]) ).
tff(f1056,plain,
( spl21_88
| ~ spl21_2
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f932,f912,f627,f1053]) ).
tff(f1053,plain,
( spl21_88
<=> sP1(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_88])]) ).
tff(f912,plain,
( spl21_56
<=> ! [X0: $int] :
( sP1(X0)
| ~ prime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_56])]) ).
tff(f932,plain,
( sP1(sK13)
| ~ spl21_2
| ~ spl21_56 ),
inference(resolution,[],[f913,f629]) ).
tff(f913,plain,
( ! [X0: $int] :
( ~ prime(X0)
| sP1(X0) )
| ~ spl21_56 ),
inference(avatar_component_clause,[],[f912]) ).
tff(f1051,plain,
spl21_87,
inference(avatar_split_clause,[],[f527,f1049]) ).
tff(f1049,plain,
( spl21_87
<=> ! [X0: $int,X1: $int] : divides(gcd(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_87])]) ).
tff(f527,plain,
! [X0: $int,X1: $int] : divides(gcd(X0,X1),X1),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $int,X1: $int] : divides(gcd(X0,X1),X1),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $int,X11: $int] : divides(gcd(X0,X11),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_def2) ).
tff(f1047,plain,
spl21_86,
inference(avatar_split_clause,[],[f526,f1045]) ).
tff(f1045,plain,
( spl21_86
<=> ! [X0: $int,X1: $int] : divides(gcd(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_86])]) ).
tff(f526,plain,
! [X0: $int,X1: $int] : divides(gcd(X0,X1),X0),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $int,X1: $int] : divides(gcd(X0,X1),X0),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $int,X11: $int] : divides(gcd(X0,X11),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_def1) ).
tff(f1043,plain,
spl21_85,
inference(avatar_split_clause,[],[f525,f1041]) ).
tff(f1041,plain,
( spl21_85
<=> ! [X0: $int,X1: $int] : divides(X0,$product(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_85])]) ).
tff(f525,plain,
! [X0: $int,X1: $int] : divides(X0,$product(X1,X0)),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $int,X1: $int] : divides(X0,$product(X1,X0)),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $int,X11: $int] : divides(X0,$product(X11,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_factorl) ).
tff(f1039,plain,
spl21_84,
inference(avatar_split_clause,[],[f524,f1037]) ).
tff(f1037,plain,
( spl21_84
<=> ! [X0: $int,X1: $int] : divides(X0,$product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_84])]) ).
tff(f524,plain,
! [X0: $int,X1: $int] : divides(X0,$product(X0,X1)),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $int,X1: $int] : divides(X0,$product(X0,X1)),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $int,X11: $int] : divides(X0,$product(X0,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_factorr) ).
tff(f1035,plain,
spl21_83,
inference(avatar_split_clause,[],[f523,f1033]) ).
tff(f1033,plain,
( spl21_83
<=> ! [X0: ty,X1: uni] : sort(X0,contents(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_83])]) ).
tff(f523,plain,
! [X0: ty,X1: uni] : sort(X0,contents(X0,X1)),
inference(cnf_transformation,[],[f93]) ).
tff(f93,axiom,
! [X0: ty,X1: uni] : sort(X0,contents(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contents_sort) ).
tff(f1031,plain,
spl21_82,
inference(avatar_split_clause,[],[f522,f1029]) ).
tff(f1029,plain,
( spl21_82
<=> ! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_82])]) ).
tff(f522,plain,
! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
! [X0: ty,X1: uni] : sort(X0,cons_proj_1(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cons_proj_1_sort) ).
tff(f1027,plain,
spl21_81,
inference(avatar_split_clause,[],[f521,f1025]) ).
tff(f1025,plain,
( spl21_81
<=> ! [X0: $int,X1: $int] : ~ $less(gcd(X0,X1),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_81])]) ).
tff(f521,plain,
! [X0: $int,X1: $int] : ~ $less(gcd(X0,X1),0),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $int,X1: $int] : ~ $less(gcd(X0,X1),0),
inference(rectify,[],[f123]) ).
tff(f123,plain,
! [X0: $int,X11: $int] : ~ $less(gcd(X0,X11),0),
inference(theory_normalization,[],[f73]) ).
tff(f73,axiom,
! [X0: $int,X11: $int] : $lesseq(0,gcd(X0,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gcd_nonneg) ).
tff(f1023,plain,
spl21_80,
inference(avatar_split_clause,[],[f514,f1021]) ).
tff(f514,plain,
! [X0: $int] :
( ~ $less(X0,2)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f396]) ).
tff(f1019,plain,
spl21_79,
inference(avatar_split_clause,[],[f507,f1017]) ).
tff(f1017,plain,
( spl21_79
<=> ! [X0: $int] :
( ~ $less(X0,2)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_79])]) ).
tff(f507,plain,
! [X0: $int] :
( ~ $less(X0,2)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f390]) ).
tff(f1015,plain,
spl21_78,
inference(avatar_split_clause,[],[f504,f1013]) ).
tff(f504,plain,
! [X0: $int] :
( odd(X0)
| divides(2,X0) ),
inference(cnf_transformation,[],[f381]) ).
tff(f381,plain,
! [X0: $int] :
( ( odd(X0)
| divides(2,X0) )
& ( ~ divides(2,X0)
| ~ odd(X0) ) ),
inference(nnf_transformation,[],[f64]) ).
tff(f64,axiom,
! [X0: $int] :
( odd(X0)
<=> ~ divides(2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odd_divides) ).
tff(f1011,plain,
( spl21_77
| ~ spl21_3
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f931,f912,f632,f1008]) ).
tff(f1008,plain,
( spl21_77
<=> sP1(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_77])]) ).
tff(f931,plain,
( sP1(sK10)
| ~ spl21_3
| ~ spl21_56 ),
inference(resolution,[],[f913,f634]) ).
tff(f1006,plain,
spl21_76,
inference(avatar_split_clause,[],[f503,f1004]) ).
tff(f1004,plain,
( spl21_76
<=> ! [X0: $int] :
( ~ divides(2,X0)
| ~ odd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_76])]) ).
tff(f503,plain,
! [X0: $int] :
( ~ divides(2,X0)
| ~ odd(X0) ),
inference(cnf_transformation,[],[f381]) ).
tff(f1002,plain,
spl21_75,
inference(avatar_split_clause,[],[f500,f1000]) ).
tff(f1000,plain,
( spl21_75
<=> ! [X0: $int] :
( even(X0)
| ~ divides(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_75])]) ).
tff(f500,plain,
! [X0: $int] :
( even(X0)
| ~ divides(2,X0) ),
inference(cnf_transformation,[],[f376]) ).
tff(f376,plain,
! [X0: $int] :
( ( even(X0)
| ~ divides(2,X0) )
& ( divides(2,X0)
| ~ even(X0) ) ),
inference(nnf_transformation,[],[f63]) ).
tff(f63,axiom,
! [X0: $int] :
( even(X0)
<=> divides(2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_divides) ).
tff(f998,plain,
spl21_74,
inference(avatar_split_clause,[],[f499,f996]) ).
tff(f499,plain,
! [X0: $int] :
( divides(2,X0)
| ~ even(X0) ),
inference(cnf_transformation,[],[f376]) ).
tff(f994,plain,
spl21_73,
inference(avatar_split_clause,[],[f492,f992]) ).
tff(f992,plain,
( spl21_73
<=> ! [X0: $int] :
( prime(sK14(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).
tff(f492,plain,
! [X0: $int] :
( prime(sK14(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f375]) ).
tff(f990,plain,
spl21_72,
inference(avatar_split_clause,[],[f475,f988]) ).
tff(f988,plain,
( spl21_72
<=> ! [X0: ty] : sort(list(X0),nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).
tff(f475,plain,
! [X0: ty] : sort(list(X0),nil(X0)),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: ty] : sort(list(X0),nil(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nil_sort) ).
tff(f986,plain,
spl21_71,
inference(avatar_split_clause,[],[f474,f984]) ).
tff(f984,plain,
( spl21_71
<=> ! [X0: list_int] : sort(list(int),t2tb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).
tff(f474,plain,
! [X0: list_int] : sort(list(int),t2tb(X0)),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: list_int] : sort(list(int),t2tb(X0)),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X1: list_int] : sort(list(int),t2tb(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort) ).
tff(f982,plain,
spl21_70,
inference(avatar_split_clause,[],[f473,f980]) ).
tff(f980,plain,
( spl21_70
<=> ! [X0: $int] : ( div(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).
tff(f473,plain,
! [X0: $int] : ( div(X0,1) = X0 ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $int] : ( div(X0,1) = X0 ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X1: $int] : ( div(X1,1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_1) ).
tff(f978,plain,
spl21_69,
inference(avatar_split_clause,[],[f472,f976]) ).
tff(f976,plain,
( spl21_69
<=> ! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_69])]) ).
tff(f472,plain,
! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: uni] : ( t2tb1(tb2t1(X0)) = X0 ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X20: uni] : ( t2tb1(tb2t1(X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR1) ).
tff(f974,plain,
spl21_68,
inference(avatar_split_clause,[],[f471,f972]) ).
tff(f972,plain,
( spl21_68
<=> ! [X0: list_int] : ( tb2t(t2tb(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).
tff(f471,plain,
! [X0: list_int] : ( tb2t(t2tb(X0)) = X0 ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: list_int] : ( tb2t(t2tb(X0)) = X0 ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X19: list_int] : ( tb2t(t2tb(X19)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL) ).
tff(f970,plain,
spl21_67,
inference(avatar_split_clause,[],[f470,f968]) ).
tff(f968,plain,
( spl21_67
<=> ! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).
tff(f470,plain,
! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: uni] : ( t2tb(tb2t(X0)) = X0 ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X20: uni] : ( t2tb(tb2t(X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeR) ).
tff(f966,plain,
( spl21_66
| ~ spl21_1
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f930,f912,f622,f963]) ).
tff(f930,plain,
( sP1(sK7)
| ~ spl21_1
| ~ spl21_56 ),
inference(resolution,[],[f913,f624]) ).
tff(f961,plain,
spl21_65,
inference(avatar_split_clause,[],[f469,f959]) ).
tff(f959,plain,
( spl21_65
<=> ! [X0: $int] : ( tb2t1(t2tb1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).
tff(f469,plain,
! [X0: $int] : ( tb2t1(t2tb1(X0)) = X0 ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $int] : ( tb2t1(t2tb1(X0)) = X0 ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X19: $int] : ( tb2t1(t2tb1(X19)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bridgeL1) ).
tff(f957,plain,
spl21_64,
inference(avatar_split_clause,[],[f468,f955]) ).
tff(f955,plain,
( spl21_64
<=> ! [X0: $int] : ( 0 = mod(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).
tff(f468,plain,
! [X0: $int] : ( 0 = mod(X0,1) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $int] : ( 0 = mod(X0,1) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X1: $int] : ( 0 = mod(X1,1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_1) ).
tff(f953,plain,
spl21_63,
inference(avatar_split_clause,[],[f155,f951]) ).
tff(f951,plain,
( spl21_63
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_63])]) ).
tff(f155,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f949,plain,
spl21_62,
inference(avatar_split_clause,[],[f154,f947]) ).
tff(f947,plain,
( spl21_62
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).
tff(f154,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f945,plain,
spl21_61,
inference(avatar_split_clause,[],[f151,f943]) ).
tff(f943,plain,
( spl21_61
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).
tff(f151,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f941,plain,
spl21_60,
inference(avatar_split_clause,[],[f143,f939]) ).
tff(f939,plain,
( spl21_60
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_60])]) ).
tff(f143,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f926,plain,
spl21_59,
inference(avatar_split_clause,[],[f520,f924]) ).
tff(f924,plain,
( spl21_59
<=> ! [X0: $int] :
( prime(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_59])]) ).
tff(f520,plain,
! [X0: $int] :
( prime(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f397]) ).
tff(f397,plain,
! [X0: $int] :
( ( prime(X0)
| ~ sP2(X0) )
& ( sP2(X0)
| ~ prime(X0) ) ),
inference(nnf_transformation,[],[f361]) ).
tff(f361,plain,
! [X0: $int] :
( prime(X0)
<=> sP2(X0) ),
inference(definition_folding,[],[f285,f360]) ).
tff(f285,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
inference(flattening,[],[f284]) ).
tff(f284,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( coprime(X1,X0)
| ~ $less(X1,X0)
| $less(X1,1) )
& ~ $less(X0,2) ) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ( $less(X1,X0)
& ~ $less(X1,1) )
=> coprime(X1,X0) )
& ~ $less(X0,2) ) ),
inference(rectify,[],[f122]) ).
tff(f122,plain,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& ~ $less(X9,1) )
=> coprime(X9,X14) )
& ~ $less(X14,2) ) ),
inference(theory_normalization,[],[f88]) ).
tff(f88,axiom,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& $lesseq(1,X9) )
=> coprime(X9,X14) )
& $lesseq(2,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_coprime) ).
tff(f922,plain,
spl21_58,
inference(avatar_split_clause,[],[f519,f920]) ).
tff(f519,plain,
! [X0: $int] :
( sP2(X0)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f397]) ).
tff(f918,plain,
spl21_57,
inference(avatar_split_clause,[],[f513,f916]) ).
tff(f916,plain,
( spl21_57
<=> ! [X0: $int] :
( prime(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).
tff(f513,plain,
! [X0: $int] :
( prime(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f391]) ).
tff(f391,plain,
! [X0: $int] :
( ( prime(X0)
| ~ sP1(X0) )
& ( sP1(X0)
| ~ prime(X0) ) ),
inference(nnf_transformation,[],[f359]) ).
tff(f359,plain,
! [X0: $int] :
( prime(X0)
<=> sP1(X0) ),
inference(definition_folding,[],[f283,f358]) ).
tff(f283,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,X0)
| ~ $less(1,X1) )
& ~ $less(X0,2) ) ),
inference(flattening,[],[f282]) ).
tff(f282,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,X0)
| ~ $less(1,X1) )
& ~ $less(X0,2) ) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $int] :
( prime(X0)
<=> ( ! [X1: $int] :
( ( $less(X1,X0)
& $less(1,X1) )
=> ~ divides(X1,X0) )
& ~ $less(X0,2) ) ),
inference(rectify,[],[f121]) ).
tff(f121,plain,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& $less(1,X9) )
=> ~ divides(X9,X14) )
& ~ $less(X14,2) ) ),
inference(theory_normalization,[],[f65]) ).
tff(f65,axiom,
! [X14: $int] :
( prime(X14)
<=> ( ! [X9: $int] :
( ( $less(X9,X14)
& $less(1,X9) )
=> ~ divides(X9,X14) )
& $lesseq(2,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_def) ).
tff(f914,plain,
spl21_56,
inference(avatar_split_clause,[],[f512,f912]) ).
tff(f512,plain,
! [X0: $int] :
( sP1(X0)
| ~ prime(X0) ),
inference(cnf_transformation,[],[f391]) ).
tff(f910,plain,
( spl21_54
| ~ spl21_55
| ~ spl21_16
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f805,f777,f697,f907,f903]) ).
tff(f907,plain,
( spl21_55
<=> $less(sK13,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_55])]) ).
tff(f777,plain,
( spl21_32
<=> ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,sK4)
| $less(X16,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).
tff(f805,plain,
( ~ $less(sK13,sK4)
| $less(sK13,2)
| ~ spl21_16
| ~ spl21_32 ),
inference(resolution,[],[f778,f699]) ).
tff(f778,plain,
( ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,sK4)
| $less(X16,2) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f777]) ).
tff(f901,plain,
spl21_53,
inference(avatar_split_clause,[],[f481,f899]) ).
tff(f899,plain,
( spl21_53
<=> ! [X0: $int] :
( ~ odd(X0)
| ~ even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_53])]) ).
tff(f481,plain,
! [X0: $int] :
( ~ odd(X0)
| ~ even(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $int] :
( ~ odd(X0)
| ~ even(X0) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $int] :
( even(X0)
=> ~ odd(X0) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X9: $int] :
( even(X9)
=> ~ odd(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_not_odd) ).
tff(f897,plain,
spl21_52,
inference(avatar_split_clause,[],[f479,f895]) ).
tff(f895,plain,
( spl21_52
<=> ! [X0: $int] :
( odd(X0)
| even(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_52])]) ).
tff(f479,plain,
! [X0: $int] :
( odd(X0)
| even(X0) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $int] :
( odd(X0)
| even(X0) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X9: $int] :
( odd(X9)
| even(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_or_odd) ).
tff(f893,plain,
spl21_51,
inference(avatar_split_clause,[],[f467,f891]) ).
tff(f891,plain,
( spl21_51
<=> ! [X0: $int] : ~ $less(abs(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_51])]) ).
tff(f467,plain,
! [X0: $int] : ~ $less(abs(X0),0),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $int] : ~ $less(abs(X0),0),
inference(rectify,[],[f116]) ).
tff(f116,plain,
! [X1: $int] : ~ $less(abs(X1),0),
inference(theory_normalization,[],[f11]) ).
tff(f11,axiom,
! [X1: $int] : $lesseq(0,abs(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_pos) ).
tff(f889,plain,
spl21_50,
inference(avatar_split_clause,[],[f466,f887]) ).
tff(f887,plain,
( spl21_50
<=> ! [X0: $int] : sort(int,t2tb1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_50])]) ).
tff(f466,plain,
! [X0: $int] : sort(int,t2tb1(X0)),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $int] : sort(int,t2tb1(X0)),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X1: $int] : sort(int,t2tb1(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2tb_sort1) ).
tff(f885,plain,
spl21_49,
inference(avatar_split_clause,[],[f465,f883]) ).
tff(f883,plain,
( spl21_49
<=> ! [X0: ty] : sort(X0,witness(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_49])]) ).
tff(f465,plain,
! [X0: ty] : sort(X0,witness(X0)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: ty] : sort(X0,witness(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',witness_sort) ).
tff(f881,plain,
spl21_48,
inference(avatar_split_clause,[],[f464,f879]) ).
tff(f879,plain,
( spl21_48
<=> ! [X0: $int] : even($product(2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_48])]) ).
tff(f464,plain,
! [X0: $int] : even($product(2,X0)),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $int] : even($product(2,X0)),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X13: $int] : even($product(2,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',even_2k) ).
tff(f877,plain,
spl21_47,
inference(avatar_split_clause,[],[f420,f875]) ).
tff(f875,plain,
( spl21_47
<=> ! [X15: $int] :
( divides(X15,div(sK3,sK4))
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_47])]) ).
tff(f420,plain,
! [X15: $int] :
( divides(X15,div(sK3,sK4))
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) ),
inference(cnf_transformation,[],[f372]) ).
tff(f372,plain,
( ~ coprime(sK9,sK13)
& $less(sK9,sK13)
& ~ $less(sK9,1)
& divides(sK13,sK6)
& $less(sK7,sK13)
& $less(sK9,sK13)
& divides(sK13,sK3)
& prime(sK13)
& divides(sK12,sK6)
& ( sK6 = $product(sK12,sK9) )
& ( div(sK6,sK9) = sK12 )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = sK11 )
& ( sK9 = sK10 )
& prime(sK9)
& ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK9)
| $less(X11,2) )
& divides(sK9,sK6)
& ~ $less(sK6,sK9)
& ~ $less(sK9,sK7)
& ! [X12: $int] :
( ~ divides(X12,sK6)
| ~ $less(X12,sK7)
| $less(X12,2) )
& ~ $less(sK6,sK7)
& ~ $less(sK7,2)
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ~ $less(sK6,2)
& divides(sK6,sK6)
& ~ $less(sK6,2)
& ! [X13: $int] :
( divides(X13,sK6)
| ~ $less(sK7,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,sK7) )
| $less(X14,2)
| ~ divides(X14,sK6) )
& prime(sK7)
& divides(sK7,sK3)
& ~ $less(sK3,sK7)
& ~ $less(sK7,2)
& ~ $less(sK3,sK6)
& ~ $less(sK6,1)
& ! [X15: $int] :
( ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,sK4),sK3)
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 )
& ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,sK4)
| $less(X16,2) )
& divides(sK4,sK3)
& ~ $less(sK3,sK4)
& ~ $less(sK4,2)
& ! [X17: $int] :
( ~ divides(X17,sK3)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(sK3,2)
& ~ $less(2,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f362,f371,f370,f369,f368,f367,f366,f365,f364,f363]) ).
tff(f363,plain,
( ? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: $int,X5: list_int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,X0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,X0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,X0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,X0)
& ~ $less(X0,X4)
& ~ $less(X4,2)
& ~ $less(X0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,X0)
| ~ prime(X15) )
& divides(div(X0,X1),X0)
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,X0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,X0)
& ~ $less(X0,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,X0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) )
=> ( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,X1),sK3)
& ( sK3 = $product(div(sK3,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,sK3)
& ~ $less(sK3,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,sK3)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(sK3,2)
& ~ $less(2,2)
& ~ $less(sK3,2)
& ~ $less(sK3,2) ) ),
introduced(choice_axiom,[]) ).
tff(f364,plain,
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK3,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,X1),sK3)
& ( sK3 = $product(div(sK3,X1),X1) )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,sK3)
& ~ $less(sK3,X1)
& ~ $less(X1,2) )
=> ( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,sK4),sK3)
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,sK4)
| $less(X16,2) )
& divides(sK4,sK3)
& ~ $less(sK3,sK4)
& ~ $less(sK4,2) ) ),
introduced(choice_axiom,[]) ).
tff(f365,plain,
( ? [X2: list_int] :
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,sK4),sK3)
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = X2 ) )
=> ( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(sK3,sK4))
& coprime(sK4,X15) )
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) )
& divides(div(sK3,sK4),sK3)
& ( sK3 = $product(div(sK3,sK4),sK4) )
& ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 ) ) ),
introduced(choice_axiom,[]) ).
tff(f366,plain,
( ? [X5: list_int,X4: $int,X3: $int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,sK3)
& ~ $less(sK3,X4)
& ~ $less(X4,2)
& ~ $less(sK3,X3)
& ~ $less(X3,1) )
=> ( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( $product(X9,X6) = sK6 )
& ( div(sK6,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(sK8))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,sK6)
& ~ $less(sK6,X6)
& ~ $less(X6,sK7) )
& ! [X12: $int] :
( ~ divides(X12,sK6)
| ~ $less(X12,sK7)
| $less(X12,2) )
& ~ $less(sK6,sK7)
& ~ $less(sK7,2)
& ~ $less(sK6,2)
& ~ $less(sK6,sK7)
& ~ $less(sK6,2)
& divides(sK6,sK6)
& ~ $less(sK6,2)
& ! [X13: $int] :
( divides(X13,sK6)
| ~ $less(sK7,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,sK3)
& ~ $less(X14,sK7) )
| $less(X14,2)
| ~ divides(X14,sK6) )
& prime(sK7)
& divides(sK7,sK3)
& ~ $less(sK3,sK7)
& ~ $less(sK7,2)
& ~ $less(sK3,sK6)
& ~ $less(sK6,1) ) ),
introduced(choice_axiom,[]) ).
tff(f367,plain,
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(X6,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( $product(X9,X6) = sK6 )
& ( div(sK6,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(sK8))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,sK6)
& ~ $less(sK6,X6)
& ~ $less(X6,sK7) )
=> ( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 ) )
& ( sK9 = X7 ) )
& prime(sK9)
& ! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK9)
| $less(X11,2) )
& divides(sK9,sK6)
& ~ $less(sK6,sK9)
& ~ $less(sK9,sK7) ) ),
introduced(choice_axiom,[]) ).
tff(f368,plain,
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 ) )
& ( sK9 = X7 ) )
=> ( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 ) )
& ( sK9 = sK10 ) ) ),
introduced(choice_axiom,[]) ).
tff(f369,plain,
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = X8 ) )
=> ( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
& ( tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = sK11 ) ) ),
introduced(choice_axiom,[]) ).
tff(f370,plain,
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(X9,sK6)
& ( sK6 = $product(X9,sK9) )
& ( div(sK6,sK9) = X9 ) )
=> ( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
& divides(sK12,sK6)
& ( sK6 = $product(sK12,sK9) )
& ( div(sK6,sK9) = sK12 ) ) ),
introduced(choice_axiom,[]) ).
tff(f371,plain,
( ? [X10: $int] :
( ~ coprime(sK9,X10)
& $less(sK9,X10)
& ~ $less(sK9,1)
& divides(X10,sK6)
& $less(sK7,X10)
& $less(sK9,X10)
& divides(X10,sK3)
& prime(X10) )
=> ( ~ coprime(sK9,sK13)
& $less(sK9,sK13)
& ~ $less(sK9,1)
& divides(sK13,sK6)
& $less(sK7,sK13)
& $less(sK9,sK13)
& divides(sK13,sK3)
& prime(sK13) ) ),
introduced(choice_axiom,[]) ).
tff(f362,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: list_int] :
( ? [X3: $int,X4: $int,X5: list_int] :
( ? [X6: $int] :
( ? [X7: $int] :
( ? [X8: list_int] :
( ? [X9: $int] :
( ? [X10: $int] :
( ~ coprime(X6,X10)
& $less(X6,X10)
& ~ $less(X6,1)
& divides(X10,X3)
& $less(X4,X10)
& $less(X6,X10)
& divides(X10,X0)
& prime(X10) )
& divides(X9,X3)
& ( $product(X9,X6) = X3 )
& ( div(X3,X6) = X9 ) )
& ( tb2t(cons(int,t2tb1(X6),t2tb(X5))) = X8 ) )
& ( X6 = X7 ) )
& prime(X6)
& ! [X11: $int] :
( ~ divides(X11,X3)
| ~ $less(X11,X6)
| $less(X11,2) )
& divides(X6,X3)
& ~ $less(X3,X6)
& ~ $less(X6,X4) )
& ! [X12: $int] :
( ~ divides(X12,X3)
| ~ $less(X12,X4)
| $less(X12,2) )
& ~ $less(X3,X4)
& ~ $less(X4,2)
& ~ $less(X3,2)
& ~ $less(X3,X4)
& ~ $less(X3,2)
& divides(X3,X3)
& ~ $less(X3,2)
& ! [X13: $int] :
( divides(X13,X3)
| ~ $less(X4,X13)
| ~ divides(X13,X0)
| ~ prime(X13) )
& ! [X14: $int] :
( ( divides(X14,X0)
& ~ $less(X14,X4) )
| $less(X14,2)
| ~ divides(X14,X3) )
& prime(X4)
& divides(X4,X0)
& ~ $less(X0,X4)
& ~ $less(X4,2)
& ~ $less(X0,X3)
& ~ $less(X3,1) )
& ! [X15: $int] :
( ( divides(X15,div(X0,X1))
& coprime(X1,X15) )
| ~ $less(X1,X15)
| ~ divides(X15,X0)
| ~ prime(X15) )
& divides(div(X0,X1),X0)
& ( $product(div(X0,X1),X1) = X0 )
& ( tb2t(cons(int,t2tb1(X1),nil(int))) = X2 ) )
& ! [X16: $int] :
( ~ divides(X16,X0)
| ~ $less(X16,X1)
| $less(X16,2) )
& divides(X1,X0)
& ~ $less(X0,X1)
& ~ $less(X1,2) )
& ! [X17: $int] :
( ~ divides(X17,X0)
| ~ $less(X17,2)
| $less(X17,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(rectify,[],[f262]) ).
tff(f262,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X6: $int,X7: $int,X8: list_int] :
( ? [X12: $int] :
( ? [X14: $int] :
( ? [X15: list_int] :
( ? [X16: $int] :
( ? [X17: $int] :
( ~ coprime(X12,X17)
& $less(X12,X17)
& ~ $less(X12,1)
& divides(X17,X6)
& $less(X7,X17)
& $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
& divides(X16,X6)
& ( $product(X16,X12) = X6 )
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X6)
| ~ $less(X13,X12)
| $less(X13,2) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
& ! [X11: $int] :
( ~ divides(X11,X6)
| ~ $less(X11,X7)
| $less(X11,2) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6)
& ~ $less(X6,2)
& ! [X9: $int] :
( divides(X9,X6)
| ~ $less(X7,X9)
| ~ divides(X9,X0)
| ~ prime(X9) )
& ! [X10: $int] :
( ( divides(X10,X0)
& ~ $less(X10,X7) )
| $less(X10,2)
| ~ divides(X10,X6) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ $less(X2,X5)
| ~ divides(X5,X0)
| ~ prime(X5) )
& divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 )
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ! [X3: $int] :
( ~ divides(X3,X0)
| ~ $less(X3,X2)
| $less(X3,2) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
? [X0: $int] :
( ? [X2: $int] :
( ? [X4: list_int] :
( ? [X6: $int,X7: $int,X8: list_int] :
( ? [X12: $int] :
( ? [X14: $int] :
( ? [X15: list_int] :
( ? [X16: $int] :
( ? [X17: $int] :
( ~ coprime(X12,X17)
& $less(X12,X17)
& ~ $less(X12,1)
& divides(X17,X6)
& $less(X7,X17)
& $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
& divides(X16,X6)
& ( $product(X16,X12) = X6 )
& ( div(X6,X12) = X16 ) )
& ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 ) )
& ( X12 = X14 ) )
& prime(X12)
& ! [X13: $int] :
( ~ divides(X13,X6)
| ~ $less(X13,X12)
| $less(X13,2) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
& ! [X11: $int] :
( ~ divides(X11,X6)
| ~ $less(X11,X7)
| $less(X11,2) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2)
& ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6)
& ~ $less(X6,2)
& ! [X9: $int] :
( divides(X9,X6)
| ~ $less(X7,X9)
| ~ divides(X9,X0)
| ~ prime(X9) )
& ! [X10: $int] :
( ( divides(X10,X0)
& ~ $less(X10,X7) )
| $less(X10,2)
| ~ divides(X10,X6) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
& ! [X5: $int] :
( ( divides(X5,div(X0,X2))
& coprime(X2,X5) )
| ~ $less(X2,X5)
| ~ divides(X5,X0)
| ~ prime(X5) )
& divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 )
& ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 ) )
& ! [X3: $int] :
( ~ divides(X3,X0)
| ~ $less(X3,X2)
| $less(X3,2) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
& ! [X1: $int] :
( ~ divides(X1,X0)
| ~ $less(X1,2)
| $less(X1,2) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2)
& ~ $less(X0,2) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
~ ! [X0: $int] :
( ~ $less(X0,2)
=> ( ( ! [X1: $int] :
( ( $less(X1,2)
& ~ $less(X1,2) )
=> ~ divides(X1,X0) )
& ~ $less(X0,2)
& ~ $less(2,2)
& ~ $less(X0,2) )
=> ! [X2: $int] :
( ( ! [X3: $int] :
( ( $less(X3,X2)
& ~ $less(X3,2) )
=> ~ divides(X3,X0) )
& divides(X2,X0)
& ~ $less(X0,X2)
& ~ $less(X2,2) )
=> ! [X4: list_int] :
( ( tb2t(cons(int,t2tb1(X2),nil(int))) = X4 )
=> ( ( divides(div(X0,X2),X0)
& ( $product(div(X0,X2),X2) = X0 ) )
=> ( ! [X5: $int] :
( ( $less(X2,X5)
& divides(X5,X0)
& prime(X5) )
=> ( divides(X5,div(X0,X2))
& coprime(X2,X5) ) )
=> ! [X6: $int,X7: $int,X8: list_int] :
( ( ! [X9: $int] :
( ( $less(X7,X9)
& divides(X9,X0)
& prime(X9) )
=> divides(X9,X6) )
& ! [X10: $int] :
( ( ~ $less(X10,2)
& divides(X10,X6) )
=> ( divides(X10,X0)
& ~ $less(X10,X7) ) )
& prime(X7)
& divides(X7,X0)
& ~ $less(X0,X7)
& ~ $less(X7,2)
& ~ $less(X0,X6)
& ~ $less(X6,1) )
=> ( ~ $less(X6,2)
=> ( ( ~ $less(X6,X7)
& ~ $less(X6,2)
& divides(X6,X6) )
=> ( ( ! [X11: $int] :
( ( $less(X11,X7)
& ~ $less(X11,2) )
=> ~ divides(X11,X6) )
& ~ $less(X6,X7)
& ~ $less(X7,2)
& ~ $less(X6,2) )
=> ! [X12: $int] :
( ( ! [X13: $int] :
( ( $less(X13,X12)
& ~ $less(X13,2) )
=> ~ divides(X13,X6) )
& divides(X12,X6)
& ~ $less(X6,X12)
& ~ $less(X12,X7) )
=> ( prime(X12)
=> ! [X14: $int] :
( ( X12 = X14 )
=> ! [X15: list_int] :
( ( tb2t(cons(int,t2tb1(X12),t2tb(X8))) = X15 )
=> ! [X16: $int] :
( ( div(X6,X12) = X16 )
=> ( ( divides(X16,X6)
& ( $product(X16,X12) = X6 ) )
=> ! [X17: $int] :
( ( $less(X12,X17)
& divides(X17,X0)
& prime(X17) )
=> ( $less(X7,X17)
=> ( divides(X17,X6)
=> ( ( $less(X12,X17)
& ~ $less(X12,1) )
=> coprime(X12,X17) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f115]) ).
tff(f115,plain,
~ ! [X9: $int] :
( ~ $less(X9,2)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) )
& ~ $less(X9,2)
& ~ $less(2,2)
& ~ $less(X9,2) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& ~ $less(X19,2) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& ~ $less(X9,X8)
& ~ $less(X8,2) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( ~ $less(X19,2)
& divides(X19,X22) )
=> ( divides(X19,X9)
& ~ $less(X19,X23) ) )
& prime(X23)
& divides(X23,X9)
& ~ $less(X9,X23)
& ~ $less(X23,2)
& ~ $less(X9,X22)
& ~ $less(X22,1) )
=> ( ~ $less(X22,2)
=> ( ( ~ $less(X22,X23)
& ~ $less(X22,2)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& ~ $less(X19,2) )
=> ~ divides(X19,X22) )
& ~ $less(X22,X23)
& ~ $less(X23,2)
& ~ $less(X22,2) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& ~ $less(X19,2) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& ~ $less(X22,X25)
& ~ $less(X25,X23) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( $less(X25,X19)
& divides(X19,X9)
& prime(X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& ~ $less(X25,1) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f114]) ).
tff(f114,negated_conjecture,
~ ! [X9: $int] :
( $lesseq(2,X9)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& prime(X23)
& divides(X23,X9)
& $lesseq(X23,X9)
& $lesseq(2,X23)
& $lesseq(X22,X9)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& $lesseq(2,X22)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& $lesseq(X23,X22)
& $lesseq(2,X23)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& $lesseq(X25,X22)
& $lesseq(X23,X25) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( $less(X25,X19)
& divides(X19,X9)
& prime(X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f113]) ).
tff(f113,conjecture,
! [X9: $int] :
( $lesseq(2,X9)
=> ( ( ! [X19: $int] :
( ( $less(X19,2)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& $lesseq(2,X9)
& $lesseq(2,2)
& $lesseq(2,X9) )
=> ! [X8: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X8)
& $lesseq(2,X19) )
=> ~ divides(X19,X9) )
& divides(X8,X9)
& $lesseq(X8,X9)
& $lesseq(2,X8) )
=> ! [X21: list_int] :
( ( tb2t(cons(int,t2tb1(X8),nil(int))) = X21 )
=> ( ( divides(div(X9,X8),X9)
& ( $product(div(X9,X8),X8) = X9 ) )
=> ( ! [X19: $int] :
( ( $less(X8,X19)
& divides(X19,X9)
& prime(X19) )
=> ( divides(X19,div(X9,X8))
& coprime(X8,X19) ) )
=> ! [X22: $int,X23: $int,X24: list_int] :
( ( ! [X19: $int] :
( ( $less(X23,X19)
& divides(X19,X9)
& prime(X19) )
=> divides(X19,X22) )
& ! [X19: $int] :
( ( $lesseq(2,X19)
& divides(X19,X22) )
=> ( divides(X19,X9)
& $lesseq(X23,X19) ) )
& prime(X23)
& divides(X23,X9)
& $lesseq(X23,X9)
& $lesseq(2,X23)
& $lesseq(X22,X9)
& $lesseq(1,X22) )
=> ( $lesseq(2,X22)
=> ( ( $lesseq(X23,X22)
& $lesseq(2,X22)
& divides(X22,X22) )
=> ( ( ! [X19: $int] :
( ( $less(X19,X23)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& $lesseq(X23,X22)
& $lesseq(2,X23)
& $lesseq(2,X22) )
=> ! [X25: $int] :
( ( ! [X19: $int] :
( ( $less(X19,X25)
& $lesseq(2,X19) )
=> ~ divides(X19,X22) )
& divides(X25,X22)
& $lesseq(X25,X22)
& $lesseq(X23,X25) )
=> ( prime(X25)
=> ! [X26: $int] :
( ( X25 = X26 )
=> ! [X27: list_int] :
( ( tb2t(cons(int,t2tb1(X25),t2tb(X24))) = X27 )
=> ! [X28: $int] :
( ( div(X22,X25) = X28 )
=> ( ( divides(X28,X22)
& ( $product(X28,X25) = X22 ) )
=> ! [X19: $int] :
( ( $less(X25,X19)
& divides(X19,X9)
& prime(X19) )
=> ( $less(X23,X19)
=> ( divides(X19,X22)
=> ( ( $less(X25,X19)
& $lesseq(1,X25) )
=> coprime(X25,X19) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_largest_prime_factor) ).
tff(f860,plain,
spl21_46,
inference(avatar_split_clause,[],[f463,f858]) ).
tff(f858,plain,
( spl21_46
<=> ! [X0: $int] : divides(1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_46])]) ).
tff(f463,plain,
! [X0: $int] : divides(1,X0),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $int] : divides(1,X0),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X9: $int] : divides(1,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_1_n) ).
tff(f856,plain,
spl21_45,
inference(avatar_split_clause,[],[f462,f854]) ).
tff(f854,plain,
( spl21_45
<=> ! [X0: $int] : divides(X0,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_45])]) ).
tff(f462,plain,
! [X0: $int] : divides(X0,0),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $int] : divides(X0,0),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X9: $int] : divides(X9,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_0) ).
tff(f852,plain,
spl21_44,
inference(avatar_split_clause,[],[f461,f850]) ).
tff(f461,plain,
! [X0: $int] : divides(X0,X0),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $int] : divides(X0,X0),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X9: $int] : divides(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_refl) ).
tff(f848,plain,
spl21_43,
inference(avatar_split_clause,[],[f460,f846]) ).
tff(f846,plain,
( spl21_43
<=> ! [X0: tuple0] : ( tuple02 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_43])]) ).
tff(f460,plain,
! [X0: tuple0] : ( tuple02 = X0 ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: tuple0] : ( tuple02 = X0 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: tuple0] : ( tuple02 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuple0_inversion) ).
tff(f844,plain,
~ spl21_42,
inference(avatar_split_clause,[],[f459,f841]) ).
tff(f841,plain,
( spl21_42
<=> ( true = false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_42])]) ).
tff(f459,plain,
true != false,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
true != false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_False) ).
tff(f839,plain,
spl21_41,
inference(avatar_split_clause,[],[f146,f837]) ).
tff(f146,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f835,plain,
( spl21_13
| ~ spl21_40
| ~ spl21_11
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f804,f777,f672,f832,f682]) ).
tff(f832,plain,
( spl21_40
<=> $less(sK7,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_40])]) ).
tff(f804,plain,
( ~ $less(sK7,sK4)
| $less(sK7,2)
| ~ spl21_11
| ~ spl21_32 ),
inference(resolution,[],[f778,f674]) ).
tff(f822,plain,
spl21_39,
inference(avatar_split_clause,[],[f429,f820]) ).
tff(f429,plain,
! [X13: $int] :
( divides(X13,sK6)
| ~ $less(sK7,X13)
| ~ divides(X13,sK3)
| ~ prime(X13) ),
inference(cnf_transformation,[],[f372]) ).
tff(f818,plain,
spl21_38,
inference(avatar_split_clause,[],[f419,f816]) ).
tff(f419,plain,
! [X15: $int] :
( coprime(sK4,X15)
| ~ $less(sK4,X15)
| ~ divides(X15,sK3)
| ~ prime(X15) ),
inference(cnf_transformation,[],[f372]) ).
tff(f801,plain,
spl21_37,
inference(avatar_split_clause,[],[f606,f799]) ).
tff(f606,plain,
! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK10)
| $less(X11,2) ),
inference(definition_unfolding,[],[f441,f443]) ).
tff(f443,plain,
sK9 = sK10,
inference(cnf_transformation,[],[f372]) ).
tff(f441,plain,
! [X11: $int] :
( ~ divides(X11,sK6)
| ~ $less(X11,sK9)
| $less(X11,2) ),
inference(cnf_transformation,[],[f372]) ).
tff(f797,plain,
spl21_36,
inference(avatar_split_clause,[],[f604,f794]) ).
tff(f794,plain,
( spl21_36
<=> ( sK11 = tb2t(cons(int,t2tb1(sK10),t2tb(sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).
tff(f604,plain,
sK11 = tb2t(cons(int,t2tb1(sK10),t2tb(sK8))),
inference(definition_unfolding,[],[f444,f443]) ).
tff(f444,plain,
tb2t(cons(int,t2tb1(sK9),t2tb(sK8))) = sK11,
inference(cnf_transformation,[],[f372]) ).
tff(f792,plain,
spl21_35,
inference(avatar_split_clause,[],[f437,f790]) ).
tff(f437,plain,
! [X12: $int] :
( ~ divides(X12,sK6)
| ~ $less(X12,sK7)
| $less(X12,2) ),
inference(cnf_transformation,[],[f372]) ).
tff(f788,plain,
spl21_34,
inference(avatar_split_clause,[],[f428,f786]) ).
tff(f428,plain,
! [X14: $int] :
( divides(X14,sK3)
| $less(X14,2)
| ~ divides(X14,sK6) ),
inference(cnf_transformation,[],[f372]) ).
tff(f784,plain,
spl21_33,
inference(avatar_split_clause,[],[f416,f781]) ).
tff(f781,plain,
( spl21_33
<=> ( tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_33])]) ).
tff(f416,plain,
tb2t(cons(int,t2tb1(sK4),nil(int))) = sK5,
inference(cnf_transformation,[],[f372]) ).
tff(f779,plain,
spl21_32,
inference(avatar_split_clause,[],[f415,f777]) ).
tff(f415,plain,
! [X16: $int] :
( ~ divides(X16,sK3)
| ~ $less(X16,sK4)
| $less(X16,2) ),
inference(cnf_transformation,[],[f372]) ).
tff(f775,plain,
spl21_31,
inference(avatar_split_clause,[],[f458,f772]) ).
tff(f772,plain,
( spl21_31
<=> prime(2) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_31])]) ).
tff(f458,plain,
prime(2),
inference(cnf_transformation,[],[f67]) ).
tff(f67,axiom,
prime(2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_2) ).
tff(f770,plain,
spl21_30,
inference(avatar_split_clause,[],[f457,f767]) ).
tff(f767,plain,
( spl21_30
<=> prime(3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_30])]) ).
tff(f457,plain,
prime(3),
inference(cnf_transformation,[],[f68]) ).
tff(f68,axiom,
prime(3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_3) ).
tff(f765,plain,
~ spl21_29,
inference(avatar_split_clause,[],[f456,f762]) ).
tff(f456,plain,
~ prime(1),
inference(cnf_transformation,[],[f66]) ).
tff(f66,axiom,
~ prime(1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_prime_1) ).
tff(f760,plain,
spl21_28,
inference(avatar_split_clause,[],[f417,f757]) ).
tff(f417,plain,
sK3 = $product(div(sK3,sK4),sK4),
inference(cnf_transformation,[],[f372]) ).
tff(f755,plain,
spl21_27,
inference(avatar_split_clause,[],[f603,f752]) ).
tff(f752,plain,
( spl21_27
<=> ( sK12 = div(sK6,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_27])]) ).
tff(f603,plain,
sK12 = div(sK6,sK10),
inference(definition_unfolding,[],[f445,f443]) ).
tff(f445,plain,
div(sK6,sK9) = sK12,
inference(cnf_transformation,[],[f372]) ).
tff(f750,plain,
spl21_26,
inference(avatar_split_clause,[],[f602,f747]) ).
tff(f602,plain,
sK6 = $product(sK12,sK10),
inference(definition_unfolding,[],[f446,f443]) ).
tff(f446,plain,
sK6 = $product(sK12,sK9),
inference(cnf_transformation,[],[f372]) ).
tff(f745,plain,
spl21_25,
inference(avatar_split_clause,[],[f418,f742]) ).
tff(f742,plain,
( spl21_25
<=> divides(div(sK3,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).
tff(f418,plain,
divides(div(sK3,sK4),sK3),
inference(cnf_transformation,[],[f372]) ).
tff(f740,plain,
~ spl21_24,
inference(avatar_split_clause,[],[f609,f737]) ).
tff(f609,plain,
~ $less(sK10,sK7),
inference(definition_unfolding,[],[f438,f443]) ).
tff(f438,plain,
~ $less(sK9,sK7),
inference(cnf_transformation,[],[f372]) ).
tff(f735,plain,
~ spl21_23,
inference(avatar_split_clause,[],[f608,f732]) ).
tff(f608,plain,
~ $less(sK6,sK10),
inference(definition_unfolding,[],[f439,f443]) ).
tff(f439,plain,
~ $less(sK6,sK9),
inference(cnf_transformation,[],[f372]) ).
tff(f730,plain,
spl21_22,
inference(avatar_split_clause,[],[f607,f727]) ).
tff(f607,plain,
divides(sK10,sK6),
inference(definition_unfolding,[],[f440,f443]) ).
tff(f440,plain,
divides(sK9,sK6),
inference(cnf_transformation,[],[f372]) ).
tff(f725,plain,
~ spl21_21,
inference(avatar_split_clause,[],[f600,f722]) ).
tff(f600,plain,
~ $less(sK10,1),
inference(definition_unfolding,[],[f453,f443]) ).
tff(f453,plain,
~ $less(sK9,1),
inference(cnf_transformation,[],[f372]) ).
tff(f720,plain,
spl21_20,
inference(avatar_split_clause,[],[f599,f717]) ).
tff(f599,plain,
$less(sK10,sK13),
inference(definition_unfolding,[],[f454,f443]) ).
tff(f454,plain,
$less(sK9,sK13),
inference(cnf_transformation,[],[f372]) ).
tff(f715,plain,
~ spl21_19,
inference(avatar_split_clause,[],[f598,f712]) ).
tff(f598,plain,
~ coprime(sK10,sK13),
inference(definition_unfolding,[],[f455,f443]) ).
tff(f455,plain,
~ coprime(sK9,sK13),
inference(cnf_transformation,[],[f372]) ).
tff(f710,plain,
spl21_18,
inference(avatar_split_clause,[],[f452,f707]) ).
tff(f452,plain,
divides(sK13,sK6),
inference(cnf_transformation,[],[f372]) ).
tff(f705,plain,
spl21_17,
inference(avatar_split_clause,[],[f451,f702]) ).
tff(f451,plain,
$less(sK7,sK13),
inference(cnf_transformation,[],[f372]) ).
tff(f700,plain,
spl21_16,
inference(avatar_split_clause,[],[f449,f697]) ).
tff(f449,plain,
divides(sK13,sK3),
inference(cnf_transformation,[],[f372]) ).
tff(f695,plain,
spl21_15,
inference(avatar_split_clause,[],[f447,f692]) ).
tff(f447,plain,
divides(sK12,sK6),
inference(cnf_transformation,[],[f372]) ).
tff(f690,plain,
~ spl21_14,
inference(avatar_split_clause,[],[f436,f687]) ).
tff(f436,plain,
~ $less(sK6,sK7),
inference(cnf_transformation,[],[f372]) ).
tff(f685,plain,
~ spl21_13,
inference(avatar_split_clause,[],[f435,f682]) ).
tff(f435,plain,
~ $less(sK7,2),
inference(cnf_transformation,[],[f372]) ).
tff(f680,plain,
~ spl21_12,
inference(avatar_split_clause,[],[f434,f677]) ).
tff(f434,plain,
~ $less(sK6,2),
inference(cnf_transformation,[],[f372]) ).
tff(f675,plain,
spl21_11,
inference(avatar_split_clause,[],[f425,f672]) ).
tff(f425,plain,
divides(sK7,sK3),
inference(cnf_transformation,[],[f372]) ).
tff(f670,plain,
~ spl21_10,
inference(avatar_split_clause,[],[f424,f667]) ).
tff(f424,plain,
~ $less(sK3,sK7),
inference(cnf_transformation,[],[f372]) ).
tff(f665,plain,
~ spl21_9,
inference(avatar_split_clause,[],[f422,f662]) ).
tff(f662,plain,
( spl21_9
<=> $less(sK3,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
tff(f422,plain,
~ $less(sK3,sK6),
inference(cnf_transformation,[],[f372]) ).
tff(f660,plain,
~ spl21_8,
inference(avatar_split_clause,[],[f421,f657]) ).
tff(f421,plain,
~ $less(sK6,1),
inference(cnf_transformation,[],[f372]) ).
tff(f655,plain,
spl21_7,
inference(avatar_split_clause,[],[f414,f652]) ).
tff(f414,plain,
divides(sK4,sK3),
inference(cnf_transformation,[],[f372]) ).
tff(f650,plain,
~ spl21_6,
inference(avatar_split_clause,[],[f413,f647]) ).
tff(f413,plain,
~ $less(sK3,sK4),
inference(cnf_transformation,[],[f372]) ).
tff(f645,plain,
~ spl21_5,
inference(avatar_split_clause,[],[f412,f642]) ).
tff(f412,plain,
~ $less(sK4,2),
inference(cnf_transformation,[],[f372]) ).
tff(f640,plain,
~ spl21_4,
inference(avatar_split_clause,[],[f410,f637]) ).
tff(f410,plain,
~ $less(sK3,2),
inference(cnf_transformation,[],[f372]) ).
tff(f635,plain,
spl21_3,
inference(avatar_split_clause,[],[f605,f632]) ).
tff(f605,plain,
prime(sK10),
inference(definition_unfolding,[],[f442,f443]) ).
tff(f442,plain,
prime(sK9),
inference(cnf_transformation,[],[f372]) ).
tff(f630,plain,
spl21_2,
inference(avatar_split_clause,[],[f448,f627]) ).
tff(f448,plain,
prime(sK13),
inference(cnf_transformation,[],[f372]) ).
tff(f625,plain,
spl21_1,
inference(avatar_split_clause,[],[f426,f622]) ).
tff(f426,plain,
prime(sK7),
inference(cnf_transformation,[],[f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW613_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 03:01:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (8549)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (8552)WARNING: value z3 for option sas not known
% 0.14/0.37 % (8550)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (8553)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (8551)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (8552)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)
% 0.14/0.37 % (8554)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)
% 0.14/0.37 % (8555)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)
% 0.14/0.37 % (8556)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)
% 0.14/0.38 % (8550)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (8550)Terminated due to inappropriate strategy.
% 0.14/0.38 % (8550)------------------------------
% 0.14/0.38 % (8550)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (8550)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (8550)Memory used [KB]: 1109
% 0.14/0.38 % (8550)Time elapsed: 0.008 s
% 0.14/0.38 % (8550)Instructions burned: 14 (million)
% 0.14/0.38 % (8550)------------------------------
% 0.14/0.38 % (8550)------------------------------
% 0.14/0.38 % (8551)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (8551)Terminated due to inappropriate strategy.
% 0.14/0.38 % (8551)------------------------------
% 0.14/0.38 % (8551)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (8551)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (8551)Memory used [KB]: 1110
% 0.14/0.38 % (8551)Time elapsed: 0.008 s
% 0.14/0.38 % (8551)Instructions burned: 14 (million)
% 0.14/0.38 % (8551)------------------------------
% 0.14/0.38 % (8551)------------------------------
% 0.14/0.38 % (8553)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (8553)Terminated due to inappropriate strategy.
% 0.14/0.38 % (8553)------------------------------
% 0.14/0.38 % (8553)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (8553)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (8553)Memory used [KB]: 1111
% 0.14/0.38 % (8553)Time elapsed: 0.008 s
% 0.14/0.38 % (8553)Instructions burned: 14 (million)
% 0.14/0.38 % (8553)------------------------------
% 0.14/0.38 % (8553)------------------------------
% 0.14/0.40 % (8557)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (8559)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)
% 0.14/0.40 % (8558)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)
% 0.14/0.40 % (8557)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (8557)Terminated due to inappropriate strategy.
% 0.14/0.40 % (8557)------------------------------
% 0.14/0.40 % (8557)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40 % (8557)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (8557)Memory used [KB]: 1097
% 0.14/0.40 % (8557)Time elapsed: 0.007 s
% 0.14/0.40 % (8557)Instructions burned: 12 (million)
% 0.14/0.40 % (8557)------------------------------
% 0.14/0.40 % (8557)------------------------------
% 0.20/0.42 % (8560)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.47 % (8554)First to succeed.
% 0.20/0.49 % (8554)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (8554)------------------------------
% 0.20/0.49 % (8554)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.49 % (8554)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (8554)Memory used [KB]: 2668
% 0.20/0.49 % (8554)Time elapsed: 0.112 s
% 0.20/0.49 % (8554)Instructions burned: 186 (million)
% 0.20/0.49 % (8554)------------------------------
% 0.20/0.49 % (8554)------------------------------
% 0.20/0.49 % (8549)Success in time 0.136 s
%------------------------------------------------------------------------------