TSTP Solution File: NUM924_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:43:13 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 274
% Syntax : Number of formulae : 854 ( 220 unt; 27 typ; 0 def)
% Number of atoms : 1968 ( 403 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1944 ( 803 ~; 804 |; 69 &)
% ( 231 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 16 >; 10 *; 0 +; 0 <<)
% Number of predicates : 174 ( 172 usr; 167 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 848 ( 848 !; 0 ?; 848 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_3,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
times_times_int: ( int * int ) > int ).
tff(func_def_5,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_6,type,
zero_zero_int: int ).
tff(func_def_7,type,
zero_zero_nat: nat ).
tff(func_def_8,type,
bit0: int > int ).
tff(func_def_9,type,
bit1: int > int ).
tff(func_def_10,type,
pls: int ).
tff(func_def_11,type,
number_number_of_int: int > int ).
tff(func_def_12,type,
number_number_of_nat: int > nat ).
tff(func_def_13,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_14,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_15,type,
m: int ).
tff(func_def_16,type,
s: int ).
tff(func_def_17,type,
t: int ).
tff(func_def_18,type,
sK0: int ).
tff(pred_def_1,type,
zprime: int > $o ).
tff(pred_def_2,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_3,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(pred_def_4,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(pred_def_5,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(pred_def_6,type,
twoSqu1431725154sum2sq: int > $o ).
tff(f2030,plain,
$false,
inference(avatar_sat_refutation,[],[f510,f517,f522,f527,f532,f536,f540,f545,f550,f554,f561,f566,f571,f575,f580,f585,f590,f594,f598,f602,f608,f612,f616,f621,f626,f631,f636,f640,f646,f663,f668,f673,f678,f683,f689,f697,f703,f709,f715,f721,f727,f733,f739,f745,f749,f754,f758,f762,f767,f772,f777,f782,f786,f790,f794,f798,f803,f807,f811,f815,f819,f823,f827,f831,f835,f839,f856,f860,f864,f868,f915,f941,f947,f952,f958,f963,f968,f974,f980,f986,f992,f997,f1001,f1005,f1010,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1074,f1078,f1084,f1098,f1167,f1180,f1184,f1188,f1192,f1196,f1200,f1205,f1210,f1216,f1339,f1343,f1347,f1351,f1356,f1360,f1397,f1406,f1412,f1421,f1426,f1432,f1437,f1442,f1447,f1451,f1455,f1459,f1463,f1473,f1586,f1590,f1594,f1603,f1612,f1669,f1673,f1678,f1682,f1686,f1690,f1823,f1829,f1834,f1842,f1848,f1854,f1860,f1864,f1868,f1872,f1876,f1880,f1885,f1889,f1893,f1897,f1965,f1997,f2007,f2025,f2029]) ).
tff(f2029,plain,
( spl1_2
| ~ spl1_18
| ~ spl1_44
| ~ spl1_45
| ~ spl1_166 ),
inference(avatar_split_clause,[],[f2028,f2022,f747,f743,f592,f514]) ).
tff(f514,plain,
( spl1_2
<=> ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f592,plain,
( spl1_18
<=> ! [X0: int] : ( zero_zero_int = times_times_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f743,plain,
( spl1_44
<=> ! [X0: int,X1: int] : ( plus_plus_int(X1,X0) = plus_plus_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f747,plain,
( spl1_45
<=> ! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f2022,plain,
( spl1_166
<=> ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
tff(f2028,plain,
( ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int)
| ~ spl1_18
| ~ spl1_44
| ~ spl1_45
| ~ spl1_166 ),
inference(forward_demodulation,[],[f2027,f744]) ).
tff(f744,plain,
( ! [X0: int,X1: int] : ( plus_plus_int(X1,X0) = plus_plus_int(X0,X1) )
| ~ spl1_44 ),
inference(avatar_component_clause,[],[f743]) ).
tff(f2027,plain,
( ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),zero_zero_int)
| ~ spl1_18
| ~ spl1_45
| ~ spl1_166 ),
inference(forward_demodulation,[],[f2026,f593]) ).
tff(f593,plain,
( ! [X0: int] : ( zero_zero_int = times_times_int(zero_zero_int,X0) )
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f592]) ).
tff(f2026,plain,
( ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ spl1_45
| ~ spl1_166 ),
inference(forward_demodulation,[],[f2024,f748]) ).
tff(f748,plain,
( ! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) )
| ~ spl1_45 ),
inference(avatar_component_clause,[],[f747]) ).
tff(f2024,plain,
( ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ~ spl1_166 ),
inference(avatar_component_clause,[],[f2022]) ).
tff(f2025,plain,
spl1_166,
inference(avatar_split_clause,[],[f443,f2022]) ).
tff(f443,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(forward_demodulation,[],[f285,f442]) ).
tff(f442,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),
inference(forward_demodulation,[],[f284,f281]) ).
tff(f281,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f66]) ).
tff(f66,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_nat__1__add__1) ).
tff(f284,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f285,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f2007,plain,
( spl1_165
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_164 ),
inference(avatar_split_clause,[],[f2002,f1994,f747,f743,f577,f552,f2004]) ).
tff(f2004,plain,
( spl1_165
<=> ( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int))))),t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
tff(f552,plain,
( spl1_10
<=> ! [X0: int] : ( number_number_of_int(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f577,plain,
( spl1_15
<=> ( zero_zero_int = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f1994,plain,
( spl1_164
<=> ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_164])]) ).
tff(f2002,plain,
( ( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int))))),t) )
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_164 ),
inference(forward_demodulation,[],[f2001,f579]) ).
tff(f579,plain,
( ( zero_zero_int = pls )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f577]) ).
tff(f2001,plain,
( ( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),t) )
| ~ spl1_10
| ~ spl1_44
| ~ spl1_45
| ~ spl1_164 ),
inference(forward_demodulation,[],[f2000,f553]) ).
tff(f553,plain,
( ! [X0: int] : ( number_number_of_int(X0) = X0 )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f2000,plain,
( ( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))),t) )
| ~ spl1_44
| ~ spl1_45
| ~ spl1_164 ),
inference(forward_demodulation,[],[f1999,f748]) ).
tff(f1999,plain,
( ( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),t) )
| ~ spl1_44
| ~ spl1_164 ),
inference(forward_demodulation,[],[f1998,f744]) ).
tff(f1998,plain,
( ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) )
| ~ spl1_44
| ~ spl1_164 ),
inference(forward_demodulation,[],[f1996,f744]) ).
tff(f1996,plain,
( ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int) )
| ~ spl1_164 ),
inference(avatar_component_clause,[],[f1994]) ).
tff(f1997,plain,
spl1_164,
inference(avatar_split_clause,[],[f442,f1994]) ).
tff(f1965,plain,
( ~ spl1_163
| ~ spl1_28
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f1469,f1353,f638,f1962]) ).
tff(f1962,plain,
( spl1_163
<=> ord_less_int(bit1(zero_zero_int),one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
tff(f638,plain,
( spl1_28
<=> ! [X0: int,X1: int] :
( ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f1353,plain,
( spl1_119
<=> ord_less_eq_int(one_one_int,bit1(zero_zero_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
tff(f1469,plain,
( ~ ord_less_int(bit1(zero_zero_int),one_one_int)
| ~ spl1_28
| ~ spl1_119 ),
inference(resolution,[],[f1355,f639]) ).
tff(f639,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X1,X0) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f638]) ).
tff(f1355,plain,
( ord_less_eq_int(one_one_int,bit1(zero_zero_int))
| ~ spl1_119 ),
inference(avatar_component_clause,[],[f1353]) ).
tff(f1897,plain,
( spl1_162
| ~ spl1_15
| ~ spl1_152 ),
inference(avatar_split_clause,[],[f1856,f1852,f577,f1895]) ).
tff(f1895,plain,
( spl1_162
<=> ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X1)
| ~ ord_less_eq_int(zero_zero_int,X0)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
tff(f1852,plain,
( spl1_152
<=> ! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_152])]) ).
tff(f1856,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X1)
| ~ ord_less_eq_int(zero_zero_int,X0)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) )
| ~ spl1_15
| ~ spl1_152 ),
inference(forward_demodulation,[],[f1855,f579]) ).
tff(f1855,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X1) )
| ~ spl1_15
| ~ spl1_152 ),
inference(forward_demodulation,[],[f1853,f579]) ).
tff(f1853,plain,
( ! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) )
| ~ spl1_152 ),
inference(avatar_component_clause,[],[f1852]) ).
tff(f1893,plain,
( spl1_161
| ~ spl1_15
| ~ spl1_151 ),
inference(avatar_split_clause,[],[f1850,f1846,f577,f1891]) ).
tff(f1891,plain,
( spl1_161
<=> ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X1)
| ~ ord_less_eq_int(zero_zero_int,X0)
| ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_161])]) ).
tff(f1846,plain,
( spl1_151
<=> ! [X0: int,X1: int] :
( ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
tff(f1850,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X1)
| ~ ord_less_eq_int(zero_zero_int,X0)
| ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) ) )
| ~ spl1_15
| ~ spl1_151 ),
inference(forward_demodulation,[],[f1849,f579]) ).
tff(f1849,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X1) )
| ~ spl1_15
| ~ spl1_151 ),
inference(forward_demodulation,[],[f1847,f579]) ).
tff(f1847,plain,
( ! [X0: int,X1: int] :
( ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) )
| ~ spl1_151 ),
inference(avatar_component_clause,[],[f1846]) ).
tff(f1889,plain,
( spl1_160
| ~ spl1_15
| ~ spl1_150 ),
inference(avatar_split_clause,[],[f1844,f1840,f577,f1887]) ).
tff(f1887,plain,
( spl1_160
<=> ! [X0: int,X1: int] :
( ord_less_int(X1,zero_zero_int)
| ord_less_int(X0,zero_zero_int)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
tff(f1840,plain,
( spl1_150
<=> ! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ord_less_int(X0,pls)
| ord_less_int(X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
tff(f1844,plain,
( ! [X0: int,X1: int] :
( ord_less_int(X1,zero_zero_int)
| ord_less_int(X0,zero_zero_int)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) )
| ~ spl1_15
| ~ spl1_150 ),
inference(forward_demodulation,[],[f1843,f579]) ).
tff(f1843,plain,
( ! [X0: int,X1: int] :
( ord_less_int(X0,zero_zero_int)
| ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ord_less_int(X1,pls) )
| ~ spl1_15
| ~ spl1_150 ),
inference(forward_demodulation,[],[f1841,f579]) ).
tff(f1841,plain,
( ! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ord_less_int(X0,pls)
| ord_less_int(X1,pls) )
| ~ spl1_150 ),
inference(avatar_component_clause,[],[f1840]) ).
tff(f1885,plain,
( spl1_159
| ~ spl1_19
| ~ spl1_119 ),
inference(avatar_split_clause,[],[f1464,f1353,f596,f1882]) ).
tff(f1882,plain,
( spl1_159
<=> ord_less_int(zero_zero_int,bit1(zero_zero_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_159])]) ).
tff(f596,plain,
( spl1_19
<=> ! [X0: int] :
( ord_less_int(zero_zero_int,X0)
| ~ ord_less_eq_int(one_one_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f1464,plain,
( ord_less_int(zero_zero_int,bit1(zero_zero_int))
| ~ spl1_19
| ~ spl1_119 ),
inference(resolution,[],[f1355,f597]) ).
tff(f597,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_int(zero_zero_int,X0) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f596]) ).
tff(f1880,plain,
spl1_158,
inference(avatar_split_clause,[],[f500,f1878]) ).
tff(f1878,plain,
( spl1_158
<=> ! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))))
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
tff(f500,plain,
! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))))
| ( zero_zero_int = X0 ) ),
inference(forward_demodulation,[],[f408,f281]) ).
tff(f408,plain,
! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))))
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: int,X1: int] :
( ( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))))
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(flattening,[],[f265]) ).
tff(f265,plain,
! [X0: int,X1: int] :
( ( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))))
| ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) )
& ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 )
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))))
<=> ( ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X2: int,X3: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X3,number_number_of_nat(bit0(bit1(pls))))))
<=> ( ( zero_zero_int != X3 )
| ( zero_zero_int != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
tff(f1876,plain,
spl1_157,
inference(avatar_split_clause,[],[f499,f1874]) ).
tff(f1874,plain,
( spl1_157
<=> ! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))))
| ( zero_zero_int = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
tff(f499,plain,
! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))))
| ( zero_zero_int = X1 ) ),
inference(forward_demodulation,[],[f409,f281]) ).
tff(f409,plain,
! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))))
| ( zero_zero_int = X1 ) ),
inference(cnf_transformation,[],[f266]) ).
tff(f1872,plain,
spl1_156,
inference(avatar_split_clause,[],[f498,f1870]) ).
tff(f1870,plain,
( spl1_156
<=> ! [X0: int,X1: int] :
( ( zero_zero_int != plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))) )
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
tff(f498,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))) )
| ( zero_zero_int = X0 ) ),
inference(forward_demodulation,[],[f404,f281]) ).
tff(f404,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) ) ) ),
inference(flattening,[],[f263]) ).
tff(f263,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) ) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X2: int,X3: int] :
( ( zero_zero_int = plus_plus_int(power_power_int(X2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X3,number_number_of_nat(bit0(bit1(pls))))) )
<=> ( ( zero_zero_int = X3 )
& ( zero_zero_int = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
tff(f1868,plain,
spl1_155,
inference(avatar_split_clause,[],[f497,f1866]) ).
tff(f1866,plain,
( spl1_155
<=> ! [X0: int,X1: int] :
( ( zero_zero_int != plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))) )
| ( zero_zero_int = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
tff(f497,plain,
! [X0: int,X1: int] :
( ( zero_zero_int != plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))) )
| ( zero_zero_int = X1 ) ),
inference(forward_demodulation,[],[f405,f281]) ).
tff(f405,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(cnf_transformation,[],[f264]) ).
tff(f1864,plain,
spl1_154,
inference(avatar_split_clause,[],[f418,f1862]) ).
tff(f1862,plain,
( spl1_154
<=> ! [X2: int,X0: nat,X1: nat] : ( times_times_nat(plus_plus_nat(X0,X1),number_number_of_nat(X2)) = plus_plus_nat(times_times_nat(X0,number_number_of_nat(X2)),times_times_nat(X1,number_number_of_nat(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
tff(f418,plain,
! [X2: int,X0: nat,X1: nat] : ( times_times_nat(plus_plus_nat(X0,X1),number_number_of_nat(X2)) = plus_plus_nat(times_times_nat(X0,number_number_of_nat(X2)),times_times_nat(X1,number_number_of_nat(X2))) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: nat,X1: nat,X2: int] : ( times_times_nat(plus_plus_nat(X0,X1),number_number_of_nat(X2)) = plus_plus_nat(times_times_nat(X0,number_number_of_nat(X2)),times_times_nat(X1,number_number_of_nat(X2))) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X43: nat,X44: nat,X45: int] : ( times_times_nat(plus_plus_nat(X43,X44),number_number_of_nat(X45)) = plus_plus_nat(times_times_nat(X43,number_number_of_nat(X45)),times_times_nat(X44,number_number_of_nat(X45))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_left__distrib__number__of) ).
tff(f1860,plain,
spl1_153,
inference(avatar_split_clause,[],[f417,f1858]) ).
tff(f1858,plain,
( spl1_153
<=> ! [X2: nat,X0: int,X1: nat] : ( times_times_nat(number_number_of_nat(X0),plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(number_number_of_nat(X0),X1),times_times_nat(number_number_of_nat(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
tff(f417,plain,
! [X2: nat,X0: int,X1: nat] : ( times_times_nat(number_number_of_nat(X0),plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(number_number_of_nat(X0),X1),times_times_nat(number_number_of_nat(X0),X2)) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: int,X1: nat,X2: nat] : ( times_times_nat(number_number_of_nat(X0),plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(number_number_of_nat(X0),X1),times_times_nat(number_number_of_nat(X0),X2)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X46: int,X47: nat,X48: nat] : ( times_times_nat(number_number_of_nat(X46),plus_plus_nat(X47,X48)) = plus_plus_nat(times_times_nat(number_number_of_nat(X46),X47),times_times_nat(number_number_of_nat(X46),X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_right__distrib__number__of) ).
tff(f1854,plain,
spl1_152,
inference(avatar_split_clause,[],[f343,f1852]) ).
tff(f343,plain,
! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(flattening,[],[f203]) ).
tff(f203,plain,
! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(pls,X1)
=> ( ord_less_eq_int(pls,X0)
=> ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X40: int,X41: int] :
( ord_less_eq_int(pls,X41)
=> ( ord_less_eq_int(pls,X40)
=> ( plus_plus_nat(number_number_of_nat(X41),number_number_of_nat(X40)) = number_number_of_nat(plus_plus_int(X41,X40)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_semiring__add__number__of) ).
tff(f1848,plain,
spl1_151,
inference(avatar_split_clause,[],[f342,f1846]) ).
tff(f342,plain,
! [X0: int,X1: int] :
( ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: int,X1: int] :
( ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(flattening,[],[f201]) ).
tff(f201,plain,
! [X0: int,X1: int] :
( ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) )
| ~ ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,X1) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(pls,X1)
=> ( ord_less_eq_int(pls,X0)
=> ( times_times_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(times_times_int(X1,X0)) ) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X25: int,X26: int] :
( ord_less_eq_int(pls,X26)
=> ( ord_less_eq_int(pls,X25)
=> ( times_times_nat(number_number_of_nat(X26),number_number_of_nat(X25)) = number_number_of_nat(times_times_int(X26,X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_semiring__mult__number__of) ).
tff(f1842,plain,
spl1_150,
inference(avatar_split_clause,[],[f338,f1840]) ).
tff(f338,plain,
! [X0: int,X1: int] :
( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ord_less_int(X0,pls)
| ord_less_int(X1,pls) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: int,X1: int] :
( ( ( ( ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) )
| ord_less_int(X0,pls) )
& ( ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X0,pls) ) )
| ord_less_int(X1,pls) )
& ( ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X1,pls) ) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: int,X1: int] :
( ( ~ ord_less_int(X1,pls)
=> ( ( ~ ord_less_int(X0,pls)
=> ( plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) = number_number_of_nat(plus_plus_int(X1,X0)) ) )
& ( ord_less_int(X0,pls)
=> ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) ) ) )
& ( ord_less_int(X1,pls)
=> ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X42: int,X12: int] :
( ( ~ ord_less_int(X12,pls)
=> ( ( ~ ord_less_int(X42,pls)
=> ( plus_plus_nat(number_number_of_nat(X12),number_number_of_nat(X42)) = number_number_of_nat(plus_plus_int(X12,X42)) ) )
& ( ord_less_int(X42,pls)
=> ( number_number_of_nat(X12) = plus_plus_nat(number_number_of_nat(X12),number_number_of_nat(X42)) ) ) ) )
& ( ord_less_int(X12,pls)
=> ( number_number_of_nat(X42) = plus_plus_nat(number_number_of_nat(X12),number_number_of_nat(X42)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__nat__number__of) ).
tff(f1834,plain,
( spl1_149
| ~ spl1_53
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f884,f800,f784,f1831]) ).
tff(f1831,plain,
( spl1_149
<=> ( zero_zero_nat = number_number_of_nat(t) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
tff(f784,plain,
( spl1_53
<=> ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ( zero_zero_nat = number_number_of_nat(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f800,plain,
( spl1_57
<=> ord_less_eq_int(t,zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f884,plain,
( ( zero_zero_nat = number_number_of_nat(t) )
| ~ spl1_53
| ~ spl1_57 ),
inference(resolution,[],[f802,f785]) ).
tff(f785,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ( zero_zero_nat = number_number_of_nat(X0) ) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f784]) ).
tff(f802,plain,
( ord_less_eq_int(t,zero_zero_int)
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f1829,plain,
( spl1_148
| ~ spl1_15
| ~ spl1_147 ),
inference(avatar_split_clause,[],[f1825,f1821,f577,f1827]) ).
tff(f1827,plain,
( spl1_148
<=> ! [X0: int,X1: int] :
( ord_less_int(X1,zero_zero_int)
| ~ ord_less_int(X0,zero_zero_int)
| ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
tff(f1821,plain,
( spl1_147
<=> ! [X0: int,X1: int] :
( ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X0,pls)
| ord_less_int(X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
tff(f1825,plain,
( ! [X0: int,X1: int] :
( ord_less_int(X1,zero_zero_int)
| ~ ord_less_int(X0,zero_zero_int)
| ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) )
| ~ spl1_15
| ~ spl1_147 ),
inference(forward_demodulation,[],[f1824,f579]) ).
tff(f1824,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_int(X0,zero_zero_int)
| ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ord_less_int(X1,pls) )
| ~ spl1_15
| ~ spl1_147 ),
inference(forward_demodulation,[],[f1822,f579]) ).
tff(f1822,plain,
( ! [X0: int,X1: int] :
( ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X0,pls)
| ord_less_int(X1,pls) )
| ~ spl1_147 ),
inference(avatar_component_clause,[],[f1821]) ).
tff(f1823,plain,
spl1_147,
inference(avatar_split_clause,[],[f337,f1821]) ).
tff(f337,plain,
! [X0: int,X1: int] :
( ( number_number_of_nat(X1) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X0,pls)
| ord_less_int(X1,pls) ),
inference(cnf_transformation,[],[f198]) ).
tff(f1690,plain,
spl1_146,
inference(avatar_split_clause,[],[f470,f1688]) ).
tff(f1688,plain,
( spl1_146
<=> ! [X0: int,X1: int] : ~ ord_less_int(plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
tff(f470,plain,
! [X0: int,X1: int] : ~ ord_less_int(plus_plus_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int),
inference(forward_demodulation,[],[f335,f281]) ).
tff(f335,plain,
! [X0: int,X1: int] : ~ ord_less_int(plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: int,X1: int] : ~ ord_less_int(plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
tff(f1686,plain,
spl1_145,
inference(avatar_split_clause,[],[f423,f1684]) ).
tff(f1684,plain,
( spl1_145
<=> ! [X0: int,X3: int,X2: int,X1: int] :
( ord_less_int(plus_plus_int(X2,X0),plus_plus_int(X3,X1))
| ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
tff(f423,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ord_less_int(plus_plus_int(X2,X0),plus_plus_int(X3,X1))
| ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X2,X3) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ord_less_int(plus_plus_int(X2,X0),plus_plus_int(X3,X1))
| ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X2,X3) ),
inference(flattening,[],[f214]) ).
tff(f214,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ord_less_int(plus_plus_int(X2,X0),plus_plus_int(X3,X1))
| ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X2,X3) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ord_less_int(X2,X3)
=> ( ord_less_eq_int(X0,X1)
=> ord_less_int(plus_plus_int(X2,X0),plus_plus_int(X3,X1)) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X36: int,X11: int,X37: int,X9: int] :
( ord_less_int(X37,X9)
=> ( ord_less_eq_int(X36,X11)
=> ord_less_int(plus_plus_int(X37,X36),plus_plus_int(X9,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zadd__zless__mono) ).
tff(f1682,plain,
spl1_144,
inference(avatar_split_clause,[],[f415,f1680]) ).
tff(f1680,plain,
( spl1_144
<=> ! [X2: int,X0: int,X1: int] : ( times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_144])]) ).
tff(f415,plain,
! [X2: int,X0: int,X1: int] : ( times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int,X1: int,X2: int] : ( times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X15: int,X16: int,X9: int] : ( times_times_int(plus_plus_int(X15,X16),X9) = plus_plus_int(times_times_int(X15,X9),times_times_int(X16,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zadd__zmult__distrib) ).
tff(f1678,plain,
( spl1_143
| ~ spl1_8
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f604,f577,f542,f1675]) ).
tff(f1675,plain,
( spl1_143
<=> ( zero_zero_nat = number_number_of_nat(zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_143])]) ).
tff(f542,plain,
( spl1_8
<=> ( zero_zero_nat = number_number_of_nat(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f604,plain,
( ( zero_zero_nat = number_number_of_nat(zero_zero_int) )
| ~ spl1_8
| ~ spl1_15 ),
inference(superposition,[],[f544,f579]) ).
tff(f544,plain,
( ( zero_zero_nat = number_number_of_nat(pls) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f542]) ).
tff(f1673,plain,
spl1_142,
inference(avatar_split_clause,[],[f414,f1671]) ).
tff(f1671,plain,
( spl1_142
<=> ! [X2: int,X0: int,X1: int] : ( times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_142])]) ).
tff(f414,plain,
! [X2: int,X0: int,X1: int] : ( times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: int,X1: int,X2: int] : ( times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X9: int,X15: int,X16: int] : ( times_times_int(X9,plus_plus_int(X15,X16)) = plus_plus_int(times_times_int(X9,X15),times_times_int(X9,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_zadd__zmult__distrib2) ).
tff(f1669,plain,
spl1_141,
inference(avatar_split_clause,[],[f413,f1667]) ).
tff(f1667,plain,
( spl1_141
<=> ! [X2: nat,X0: int,X1: nat] : ( power_power_int(X0,plus_plus_nat(X1,X2)) = times_times_int(power_power_int(X0,X1),power_power_int(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
tff(f413,plain,
! [X2: nat,X0: int,X1: nat] : ( power_power_int(X0,plus_plus_nat(X1,X2)) = times_times_int(power_power_int(X0,X1),power_power_int(X0,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: int,X1: nat,X2: nat] : ( power_power_int(X0,plus_plus_nat(X1,X2)) = times_times_int(power_power_int(X0,X1),power_power_int(X0,X2)) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: int,X1: nat,X11: nat] : ( power_power_int(X0,plus_plus_nat(X1,X11)) = times_times_int(power_power_int(X0,X1),power_power_int(X0,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zpower__zadd__distrib) ).
tff(f1612,plain,
( ~ spl1_139
| spl1_140 ),
inference(avatar_split_clause,[],[f445,f1609,f1605]) ).
tff(f1605,plain,
( spl1_139
<=> ( t = zero_zero_int ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
tff(f1609,plain,
( spl1_140
<=> ( t = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
tff(f445,plain,
( ( t = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int) )
| ( t != zero_zero_int ) ),
inference(inner_rewriting,[],[f444]) ).
tff(f444,plain,
( ( zero_zero_int = plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int) )
| ( t != zero_zero_int ) ),
inference(forward_demodulation,[],[f286,f281]) ).
tff(f286,plain,
( ( zero_zero_int = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) )
| ( t != zero_zero_int ) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
( ( zero_zero_int = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) )
| ( t != zero_zero_int ) ),
inference(ennf_transformation,[],[f5]) ).
tff(f5,axiom,
( ( t = zero_zero_int )
=> ( zero_zero_int = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
tff(f1603,plain,
spl1_138,
inference(avatar_split_clause,[],[f402,f1601]) ).
tff(f1601,plain,
( spl1_138
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
tff(f402,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int)
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ) ),
inference(flattening,[],[f261]) ).
tff(f261,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int)
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int)
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X2: int,X3: int] :
( ord_less_eq_int(plus_plus_int(times_times_int(X2,X2),times_times_int(X3,X3)),zero_zero_int)
<=> ( ( zero_zero_int = X3 )
& ( zero_zero_int = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_sum__squares__le__zero__iff) ).
tff(f1594,plain,
spl1_137,
inference(avatar_split_clause,[],[f401,f1592]) ).
tff(f1592,plain,
( spl1_137
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
tff(f401,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)),zero_zero_int) ),
inference(cnf_transformation,[],[f262]) ).
tff(f1590,plain,
spl1_136,
inference(avatar_split_clause,[],[f399,f1588]) ).
tff(f1588,plain,
( spl1_136
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
tff(f399,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X1 )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X0: int,X1: int] :
( ( ( zero_zero_int = plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) )
& ( ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) )
<=> ( ( zero_zero_int = X1 )
& ( zero_zero_int = X0 ) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X2: int,X3: int] :
( ( zero_zero_int = plus_plus_int(times_times_int(X2,X2),times_times_int(X3,X3)) )
<=> ( ( zero_zero_int = X3 )
& ( zero_zero_int = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__squares__eq__zero__iff) ).
tff(f1586,plain,
spl1_135,
inference(avatar_split_clause,[],[f398,f1584]) ).
tff(f1584,plain,
( spl1_135
<=> ! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
tff(f398,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f1473,plain,
( spl1_134
| ~ spl1_15
| ~ spl1_128 ),
inference(avatar_split_clause,[],[f1443,f1440,f577,f1471]) ).
tff(f1471,plain,
( spl1_134
<=> ! [X0: int,X1: int] :
( ~ ord_less_int(zero_zero_int,X1)
| ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
tff(f1440,plain,
( spl1_128
<=> ! [X0: int,X1: int] :
( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1)
| ~ ord_less_int(pls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
tff(f1443,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_int(zero_zero_int,X1)
| ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1) )
| ~ spl1_15
| ~ spl1_128 ),
inference(forward_demodulation,[],[f1441,f579]) ).
tff(f1441,plain,
( ! [X0: int,X1: int] :
( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1)
| ~ ord_less_int(pls,X1) )
| ~ spl1_128 ),
inference(avatar_component_clause,[],[f1440]) ).
tff(f1463,plain,
( spl1_133
| ~ spl1_15
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1438,f1435,f577,f1461]) ).
tff(f1461,plain,
( spl1_133
<=> ! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,X1)
| ~ ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
tff(f1435,plain,
( spl1_127
<=> ! [X0: int,X1: int] :
( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
tff(f1438,plain,
( ! [X0: int,X1: int] :
( ord_less_int(zero_zero_int,X1)
| ~ ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) )
| ~ spl1_15
| ~ spl1_127 ),
inference(forward_demodulation,[],[f1436,f579]) ).
tff(f1436,plain,
( ! [X0: int,X1: int] :
( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) )
| ~ spl1_127 ),
inference(avatar_component_clause,[],[f1435]) ).
tff(f1459,plain,
( spl1_132
| ~ spl1_15
| ~ spl1_126 ),
inference(avatar_split_clause,[],[f1433,f1430,f577,f1457]) ).
tff(f1457,plain,
( spl1_132
<=> ! [X0: int,X1: int] :
( ~ ord_less_int(X1,zero_zero_int)
| ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
tff(f1430,plain,
( spl1_126
<=> ! [X0: int,X1: int] :
( ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
tff(f1433,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_int(X1,zero_zero_int)
| ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) )
| ~ spl1_15
| ~ spl1_126 ),
inference(forward_demodulation,[],[f1431,f579]) ).
tff(f1431,plain,
( ! [X0: int,X1: int] :
( ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X1,pls) )
| ~ spl1_126 ),
inference(avatar_component_clause,[],[f1430]) ).
tff(f1455,plain,
spl1_131,
inference(avatar_split_clause,[],[f412,f1453]) ).
tff(f1453,plain,
( spl1_131
<=> ! [X2: int,X0: int,X1: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
tff(f412,plain,
! [X2: int,X0: int,X1: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: int,X1: int,X2: int] : ( times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X1,X2)) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X15: int,X16: int,X17: int] : ( times_times_int(times_times_int(X15,X16),X17) = times_times_int(X15,times_times_int(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zmult__assoc) ).
tff(f1451,plain,
spl1_130,
inference(avatar_split_clause,[],[f411,f1449]) ).
tff(f1449,plain,
( spl1_130
<=> ! [X2: int,X0: int,X1: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
tff(f411,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: int,X1: int,X2: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X15: int,X16: int,X17: int] : ( plus_plus_int(plus_plus_int(X15,X16),X17) = plus_plus_int(X15,plus_plus_int(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_zadd__assoc) ).
tff(f1447,plain,
spl1_129,
inference(avatar_split_clause,[],[f410,f1445]) ).
tff(f1445,plain,
( spl1_129
<=> ! [X2: int,X0: int,X1: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
tff(f410,plain,
! [X2: int,X0: int,X1: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: int,X1: int,X2: int] : ( plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X0: int,X1: int,X11: int] : ( plus_plus_int(X0,plus_plus_int(X1,X11)) = plus_plus_int(X1,plus_plus_int(X0,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zadd__left__commute) ).
tff(f1442,plain,
spl1_128,
inference(avatar_split_clause,[],[f365,f1440]) ).
tff(f365,plain,
! [X0: int,X1: int] :
( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1)
| ~ ord_less_int(pls,X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: int,X1: int] :
( ( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1)
| ( ~ ord_less_int(pls,X1)
& ord_less_int(X0,X1) ) )
& ( ( ord_less_int(X0,X1)
& ( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1) ) )
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
inference(flattening,[],[f241]) ).
tff(f241,plain,
! [X0: int,X1: int] :
( ( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ~ ord_less_int(X0,X1)
| ( ~ ord_less_int(pls,X1)
& ord_less_int(X0,X1) ) )
& ( ( ord_less_int(X0,X1)
& ( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1) ) )
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
inference(nnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: int,X1: int] :
( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
<=> ( ord_less_int(X0,X1)
& ( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1) ) ) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: int,X1: int] :
( ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1))
<=> ( ord_less_int(X0,X1)
& ( ord_less_int(X0,X1)
=> ord_less_int(pls,X1) ) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X24: int,X39: int] :
( ord_less_nat(number_number_of_nat(X24),number_number_of_nat(X39))
<=> ( ord_less_int(X24,X39)
& ( ord_less_int(X24,X39)
=> ord_less_int(pls,X39) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__nat__number__of) ).
tff(f1437,plain,
spl1_127,
inference(avatar_split_clause,[],[f362,f1435]) ).
tff(f362,plain,
! [X0: int,X1: int] :
( ord_less_int(pls,X1)
| ~ ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ),
inference(cnf_transformation,[],[f242]) ).
tff(f1432,plain,
spl1_126,
inference(avatar_split_clause,[],[f336,f1430]) ).
tff(f336,plain,
! [X0: int,X1: int] :
( ( number_number_of_nat(X0) = plus_plus_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
| ~ ord_less_int(X1,pls) ),
inference(cnf_transformation,[],[f198]) ).
tff(f1426,plain,
( spl1_125
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_123 ),
inference(avatar_split_clause,[],[f1416,f1409,f747,f743,f577,f552,f1423]) ).
tff(f1423,plain,
( spl1_125
<=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
tff(f1409,plain,
( spl1_123
<=> ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
tff(f1416,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int))))))
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_123 ),
inference(forward_demodulation,[],[f1415,f579]) ).
tff(f1415,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| ~ spl1_10
| ~ spl1_44
| ~ spl1_45
| ~ spl1_123 ),
inference(forward_demodulation,[],[f1414,f553]) ).
tff(f1414,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))))
| ~ spl1_44
| ~ spl1_45
| ~ spl1_123 ),
inference(forward_demodulation,[],[f1413,f748]) ).
tff(f1413,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)))
| ~ spl1_44
| ~ spl1_123 ),
inference(forward_demodulation,[],[f1411,f744]) ).
tff(f1411,plain,
( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ spl1_123 ),
inference(avatar_component_clause,[],[f1409]) ).
tff(f1421,plain,
( spl1_124
| ~ spl1_6
| ~ spl1_69 ),
inference(avatar_split_clause,[],[f926,f862,f534,f1418]) ).
tff(f1418,plain,
( spl1_124
<=> ord_less_eq_int(bit1(zero_zero_int),one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
tff(f534,plain,
( spl1_6
<=> ! [X0: int] : ord_less_eq_int(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f862,plain,
( spl1_69
<=> ! [X0: int] :
( ~ ord_less_eq_int(X0,bit1(zero_zero_int))
| ord_less_eq_int(X0,one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
tff(f926,plain,
( ord_less_eq_int(bit1(zero_zero_int),one_one_int)
| ~ spl1_6
| ~ spl1_69 ),
inference(resolution,[],[f863,f535]) ).
tff(f535,plain,
( ! [X0: int] : ord_less_eq_int(X0,X0)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f534]) ).
tff(f863,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,bit1(zero_zero_int))
| ord_less_eq_int(X0,one_one_int) )
| ~ spl1_69 ),
inference(avatar_component_clause,[],[f862]) ).
tff(f1412,plain,
spl1_123,
inference(avatar_split_clause,[],[f283,f1409]) ).
tff(f283,plain,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
tff(f1406,plain,
( spl1_122
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f1401,f1394,f747,f743,f577,f552,f1403]) ).
tff(f1403,plain,
( spl1_122
<=> ord_less_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
tff(f1394,plain,
( spl1_121
<=> ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).
tff(f1401,plain,
( ord_less_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int))))))
| ~ spl1_10
| ~ spl1_15
| ~ spl1_44
| ~ spl1_45
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1400,f579]) ).
tff(f1400,plain,
( ord_less_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| ~ spl1_10
| ~ spl1_44
| ~ spl1_45
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1399,f553]) ).
tff(f1399,plain,
( ord_less_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))))
| ~ spl1_44
| ~ spl1_45
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1398,f748]) ).
tff(f1398,plain,
( ord_less_int(t,plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)))
| ~ spl1_44
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1396,f744]) ).
tff(f1396,plain,
( ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ spl1_121 ),
inference(avatar_component_clause,[],[f1394]) ).
tff(f1397,plain,
spl1_121,
inference(avatar_split_clause,[],[f282,f1394]) ).
tff(f282,plain,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_t__l__p) ).
tff(f1360,plain,
spl1_120,
inference(avatar_split_clause,[],[f460,f1358]) ).
tff(f1358,plain,
( spl1_120
<=> ! [X0: int] :
( ord_less_int(zero_zero_int,power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)))
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
tff(f460,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)))
| ( zero_zero_int = X0 ) ),
inference(forward_demodulation,[],[f326,f281]) ).
tff(f326,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
| ( zero_zero_int = X0 ) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: int] :
( ( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
| ( zero_zero_int = X0 ) )
& ( ( zero_zero_int != X0 )
| ~ ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(nnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))))
<=> ( zero_zero_int != X0 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X5: int] :
( ord_less_int(zero_zero_int,power_power_int(X5,number_number_of_nat(bit0(bit1(pls)))))
<=> ( zero_zero_int != X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
tff(f1356,plain,
( spl1_119
| ~ spl1_6
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f917,f854,f534,f1353]) ).
tff(f854,plain,
( spl1_67
<=> ! [X0: int] :
( ~ ord_less_eq_int(bit1(zero_zero_int),X0)
| ord_less_eq_int(one_one_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
tff(f917,plain,
( ord_less_eq_int(one_one_int,bit1(zero_zero_int))
| ~ spl1_6
| ~ spl1_67 ),
inference(resolution,[],[f855,f535]) ).
tff(f855,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(bit1(zero_zero_int),X0)
| ord_less_eq_int(one_one_int,X0) )
| ~ spl1_67 ),
inference(avatar_component_clause,[],[f854]) ).
tff(f1351,plain,
spl1_118,
inference(avatar_split_clause,[],[f459,f1349]) ).
tff(f1349,plain,
( spl1_118
<=> ! [X0: int] :
( ( zero_zero_int != power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)) )
| ( zero_zero_int = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
tff(f459,plain,
! [X0: int] :
( ( zero_zero_int != power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)) )
| ( zero_zero_int = X0 ) ),
inference(forward_demodulation,[],[f323,f281]) ).
tff(f323,plain,
! [X0: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) ) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: int] :
( ( ( zero_zero_int = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) )
| ( zero_zero_int != X0 ) )
& ( ( zero_zero_int = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) ) ) ),
inference(nnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: int] :
( ( zero_zero_int = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_int = X0 ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X5: int] :
( ( zero_zero_int = power_power_int(X5,number_number_of_nat(bit0(bit1(pls)))) )
<=> ( zero_zero_int = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__eq__power2) ).
tff(f1347,plain,
spl1_117,
inference(avatar_split_clause,[],[f421,f1345]) ).
tff(f1345,plain,
( spl1_117
<=> ! [X2: int,X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,X1),plus_plus_int(X0,X2))
| ~ ord_less_eq_int(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
tff(f421,plain,
! [X2: int,X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,X1),plus_plus_int(X0,X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: int,X1: int,X2: int] :
( ord_less_eq_int(plus_plus_int(X0,X1),plus_plus_int(X0,X2))
| ~ ord_less_eq_int(X1,X2) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: int,X1: int,X2: int] :
( ord_less_eq_int(X1,X2)
=> ord_less_eq_int(plus_plus_int(X0,X1),plus_plus_int(X0,X2)) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X10: int,X18: int,X19: int] :
( ord_less_eq_int(X18,X19)
=> ord_less_eq_int(plus_plus_int(X10,X18),plus_plus_int(X10,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zadd__left__mono) ).
tff(f1343,plain,
spl1_116,
inference(avatar_split_clause,[],[f361,f1341]) ).
tff(f1341,plain,
( spl1_116
<=> ! [X0: int,X1: int] :
( ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
tff(f361,plain,
! [X0: int,X1: int] :
( ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1))
| ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0)) )
& ( ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0))
| ~ ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
inference(nnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: int,X1: int] :
( ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1))
<=> ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0)) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X24: int,X23: int] :
( ord_less_eq_nat(number_number_of_nat(X24),number_number_of_nat(X23))
<=> ~ ord_less_nat(number_number_of_nat(X23),number_number_of_nat(X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of__eq__not__less) ).
tff(f1339,plain,
spl1_115,
inference(avatar_split_clause,[],[f360,f1337]) ).
tff(f1337,plain,
( spl1_115
<=> ! [X0: int,X1: int] :
( ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0))
| ~ ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
tff(f360,plain,
! [X0: int,X1: int] :
( ~ ord_less_nat(number_number_of_nat(X1),number_number_of_nat(X0))
| ~ ord_less_eq_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ),
inference(cnf_transformation,[],[f240]) ).
tff(f1216,plain,
( spl1_114
| ~ spl1_15
| ~ spl1_44
| ~ spl1_105
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1212,f1208,f1165,f743,f577,f1214]) ).
tff(f1214,plain,
( spl1_114
<=> ! [X0: int] : ( plus_plus_int(one_one_int,X0) = number_number_of_int(plus_plus_int(X0,one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
tff(f1165,plain,
( spl1_105
<=> ! [X0: int] : ( plus_plus_int(X0,one_one_int) = plus_plus_int(X0,bit1(zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
tff(f1208,plain,
( spl1_113
<=> ! [X0: int] : ( number_number_of_int(plus_plus_int(bit1(pls),X0)) = plus_plus_int(one_one_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
tff(f1212,plain,
( ! [X0: int] : ( plus_plus_int(one_one_int,X0) = number_number_of_int(plus_plus_int(X0,one_one_int)) )
| ~ spl1_15
| ~ spl1_44
| ~ spl1_105
| ~ spl1_113 ),
inference(forward_demodulation,[],[f1211,f1173]) ).
tff(f1173,plain,
( ! [X0: int] : ( plus_plus_int(X0,one_one_int) = plus_plus_int(bit1(zero_zero_int),X0) )
| ~ spl1_44
| ~ spl1_105 ),
inference(superposition,[],[f1166,f744]) ).
tff(f1166,plain,
( ! [X0: int] : ( plus_plus_int(X0,one_one_int) = plus_plus_int(X0,bit1(zero_zero_int)) )
| ~ spl1_105 ),
inference(avatar_component_clause,[],[f1165]) ).
tff(f1211,plain,
( ! [X0: int] : ( plus_plus_int(one_one_int,X0) = number_number_of_int(plus_plus_int(bit1(zero_zero_int),X0)) )
| ~ spl1_15
| ~ spl1_113 ),
inference(forward_demodulation,[],[f1209,f579]) ).
tff(f1209,plain,
( ! [X0: int] : ( number_number_of_int(plus_plus_int(bit1(pls),X0)) = plus_plus_int(one_one_int,X0) )
| ~ spl1_113 ),
inference(avatar_component_clause,[],[f1208]) ).
tff(f1210,plain,
spl1_113,
inference(avatar_split_clause,[],[f448,f1208]) ).
tff(f448,plain,
! [X0: int] : ( number_number_of_int(plus_plus_int(bit1(pls),X0)) = plus_plus_int(one_one_int,X0) ),
inference(forward_demodulation,[],[f294,f289]) ).
tff(f289,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X10: int] : ( number_number_of_int(X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(f294,plain,
! [X0: int] : ( plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)) ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: int] : ( plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X6: int] : ( plus_plus_int(one_one_int,number_number_of_int(X6)) = number_number_of_int(plus_plus_int(bit1(pls),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__special_I2_J) ).
tff(f1205,plain,
spl1_112,
inference(avatar_split_clause,[],[f435,f1202]) ).
tff(f1202,plain,
( spl1_112
<=> ( zero_zero_int = plus_plus_int(times_times_int(zero_zero_int,zero_zero_int),times_times_int(zero_zero_int,zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
tff(f435,plain,
zero_zero_int = plus_plus_int(times_times_int(zero_zero_int,zero_zero_int),times_times_int(zero_zero_int,zero_zero_int)),
inference(equality_resolution,[],[f434]) ).
tff(f434,plain,
! [X0: int] :
( ( zero_zero_int = plus_plus_int(times_times_int(X0,X0),times_times_int(zero_zero_int,zero_zero_int)) )
| ( zero_zero_int != X0 ) ),
inference(equality_resolution,[],[f400]) ).
tff(f400,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f1200,plain,
spl1_111,
inference(avatar_split_clause,[],[f422,f1198]) ).
tff(f1198,plain,
( spl1_111
<=> ! [X2: int,X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X2,X0)
| ~ ord_less_eq_int(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
tff(f422,plain,
! [X2: int,X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X2,X0)
| ~ ord_less_eq_int(X1,X2) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: int,X1: int,X2: int] :
( ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X2,X0)
| ~ ord_less_eq_int(X1,X2) ),
inference(flattening,[],[f212]) ).
tff(f212,plain,
! [X0: int,X1: int,X2: int] :
( ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X2,X0)
| ~ ord_less_eq_int(X1,X2) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: int,X1: int,X2: int] :
( ord_less_eq_int(X1,X2)
=> ( ord_less_eq_int(X2,X0)
=> ord_less_eq_int(X1,X0) ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X10: int,X18: int,X19: int] :
( ord_less_eq_int(X18,X19)
=> ( ord_less_eq_int(X19,X10)
=> ord_less_eq_int(X18,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zle__trans) ).
tff(f1196,plain,
spl1_110,
inference(avatar_split_clause,[],[f349,f1194]) ).
tff(f1194,plain,
( spl1_110
<=> ! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
tff(f349,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) )
& ( ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) )
| ~ ord_less_int(X0,X1) ) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_eq_int(X0,X1) )
& ( ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) )
| ~ ord_less_int(X0,X1) ) ),
inference(nnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
<=> ( ( X0 != X1 )
& ord_less_eq_int(X0,X1) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X22: int,X23: int] :
( ord_less_int(X22,X23)
<=> ( ( X22 != X23 )
& ord_less_eq_int(X22,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zless__le) ).
tff(f1192,plain,
spl1_109,
inference(avatar_split_clause,[],[f341,f1190]) ).
tff(f1190,plain,
( spl1_109
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
tff(f341,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X0,X1) ),
inference(flattening,[],[f199]) ).
tff(f199,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ~ ord_less_eq_int(X1,X0)
| ~ ord_less_eq_int(X0,X1) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
=> ( ord_less_eq_int(X1,X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X11: int,X9: int] :
( ord_less_eq_int(X11,X9)
=> ( ord_less_eq_int(X9,X11)
=> ( X9 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zle__antisym) ).
tff(f1188,plain,
spl1_108,
inference(avatar_split_clause,[],[f340,f1186]) ).
tff(f1186,plain,
( spl1_108
<=> ! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ( X0 = X1 )
| ord_less_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
tff(f340,plain,
! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ( X0 = X1 )
| ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tff(f97,axiom,
! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ( X0 = X1 )
| ord_less_int(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zless__linear) ).
tff(f1184,plain,
spl1_107,
inference(avatar_split_clause,[],[f330,f1182]) ).
tff(f1182,plain,
( spl1_107
<=> ! [X0: int,X1: int] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
tff(f330,plain,
! [X0: int,X1: int] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1))),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: int,X1: int] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1))),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X34: int,X35: int] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X34,X34),times_times_int(X35,X35))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sum__squares__ge__zero) ).
tff(f1180,plain,
spl1_106,
inference(avatar_split_clause,[],[f329,f1178]) ).
tff(f1178,plain,
( spl1_106
<=> ! [X0: int,X1: int] : ( times_times_int(bit0(X0),X1) = bit0(times_times_int(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
tff(f329,plain,
! [X0: int,X1: int] : ( times_times_int(bit0(X0),X1) = bit0(times_times_int(X0,X1)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: int,X1: int] : ( times_times_int(bit0(X0),X1) = bit0(times_times_int(X0,X1)) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X10: int,X38: int] : ( times_times_int(bit0(X10),X38) = bit0(times_times_int(X10,X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__Bit0) ).
tff(f1167,plain,
( spl1_105
| ~ spl1_15
| ~ spl1_102 ),
inference(avatar_split_clause,[],[f1079,f1076,f577,f1165]) ).
tff(f1076,plain,
( spl1_102
<=> ! [X0: int] : ( plus_plus_int(X0,bit1(pls)) = plus_plus_int(X0,one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).
tff(f1079,plain,
( ! [X0: int] : ( plus_plus_int(X0,one_one_int) = plus_plus_int(X0,bit1(zero_zero_int)) )
| ~ spl1_15
| ~ spl1_102 ),
inference(forward_demodulation,[],[f1077,f579]) ).
tff(f1077,plain,
( ! [X0: int] : ( plus_plus_int(X0,bit1(pls)) = plus_plus_int(X0,one_one_int) )
| ~ spl1_102 ),
inference(avatar_component_clause,[],[f1076]) ).
tff(f1098,plain,
( ~ spl1_104
| ~ spl1_28
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f885,f800,f638,f1095]) ).
tff(f1095,plain,
( spl1_104
<=> ord_less_int(zero_zero_int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
tff(f885,plain,
( ~ ord_less_int(zero_zero_int,t)
| ~ spl1_28
| ~ spl1_57 ),
inference(resolution,[],[f802,f639]) ).
tff(f1084,plain,
( spl1_103
| ~ spl1_15
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f993,f989,f577,f1081]) ).
tff(f1081,plain,
( spl1_103
<=> ( plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(zero_zero_int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
tff(f989,plain,
( spl1_81
<=> ( number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
tff(f993,plain,
( ( plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(zero_zero_int))) )
| ~ spl1_15
| ~ spl1_81 ),
inference(forward_demodulation,[],[f991,f579]) ).
tff(f991,plain,
( ( number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat) )
| ~ spl1_81 ),
inference(avatar_component_clause,[],[f989]) ).
tff(f1078,plain,
spl1_102,
inference(avatar_split_clause,[],[f450,f1076]) ).
tff(f450,plain,
! [X0: int] : ( plus_plus_int(X0,bit1(pls)) = plus_plus_int(X0,one_one_int) ),
inference(forward_demodulation,[],[f449,f289]) ).
tff(f449,plain,
! [X0: int] : ( plus_plus_int(number_number_of_int(X0),one_one_int) = plus_plus_int(X0,bit1(pls)) ),
inference(forward_demodulation,[],[f295,f289]) ).
tff(f295,plain,
! [X0: int] : ( plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))) ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: int] : ( plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X7: int] : ( plus_plus_int(number_number_of_int(X7),one_one_int) = number_number_of_int(plus_plus_int(X7,bit1(pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__special_I3_J) ).
tff(f1074,plain,
spl1_101,
inference(avatar_split_clause,[],[f393,f1072]) ).
tff(f1072,plain,
( spl1_101
<=> ! [X0: int,X1: int] :
( ord_less_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
tff(f393,plain,
! [X0: int,X1: int] :
( ord_less_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: int,X1: int] :
( ( ord_less_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) )
& ( ord_less_eq_int(X0,X1)
| ~ ord_less_int(bit0(X0),bit1(X1)) ) ),
inference(nnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: int,X1: int] :
( ord_less_int(bit0(X0),bit1(X1))
<=> ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X13: int,X14: int] :
( ord_less_int(bit0(X13),bit1(X14))
<=> ord_less_eq_int(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I15_J) ).
tff(f1070,plain,
spl1_100,
inference(avatar_split_clause,[],[f392,f1068]) ).
tff(f1068,plain,
( spl1_100
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(bit0(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
tff(f392,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(bit0(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f256]) ).
tff(f1066,plain,
spl1_99,
inference(avatar_split_clause,[],[f391,f1064]) ).
tff(f1064,plain,
( spl1_99
<=> ! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
tff(f391,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ~ ord_less_eq_int(X0,X1) )
& ( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(nnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
<=> ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X23: int,X22: int] :
( ord_less_int(X23,plus_plus_int(X22,one_one_int))
<=> ord_less_eq_int(X23,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zle__add1__eq__le) ).
tff(f1062,plain,
spl1_98,
inference(avatar_split_clause,[],[f390,f1060]) ).
tff(f1060,plain,
( spl1_98
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
tff(f390,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ),
inference(cnf_transformation,[],[f255]) ).
tff(f1058,plain,
spl1_97,
inference(avatar_split_clause,[],[f388,f1056]) ).
tff(f1056,plain,
( spl1_97
<=> ! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(plus_plus_int(X0,one_one_int),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
tff(f388,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(plus_plus_int(X0,one_one_int),X1) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(plus_plus_int(X0,one_one_int),X1)
| ~ ord_less_int(X0,X1) )
& ( ord_less_int(X0,X1)
| ~ ord_less_eq_int(plus_plus_int(X0,one_one_int),X1) ) ),
inference(nnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,one_one_int),X1)
<=> ord_less_int(X0,X1) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X23: int,X22: int] :
( ord_less_eq_int(plus_plus_int(X23,one_one_int),X22)
<=> ord_less_int(X23,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add1__zle__eq) ).
tff(f1054,plain,
spl1_96,
inference(avatar_split_clause,[],[f379,f1052]) ).
tff(f1052,plain,
( spl1_96
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit0(X1))
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
tff(f379,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit0(X1))
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(bit0(X0),bit0(X1))
| ~ ord_less_eq_int(X0,X1) )
& ( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit0(X1)) ) ),
inference(nnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit0(X1))
<=> ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X20: int,X21: int] :
( ord_less_eq_int(bit0(X20),bit0(X21))
<=> ord_less_eq_int(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__eq__int__code_I13_J) ).
tff(f1050,plain,
spl1_95,
inference(avatar_split_clause,[],[f378,f1048]) ).
tff(f1048,plain,
( spl1_95
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit0(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
tff(f378,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f249]) ).
tff(f1046,plain,
spl1_94,
inference(avatar_split_clause,[],[f375,f1044]) ).
tff(f1044,plain,
( spl1_94
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
tff(f375,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(bit0(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) )
& ( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit1(X1)) ) ),
inference(nnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit0(X0),bit1(X1))
<=> ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X13: int,X14: int] :
( ord_less_eq_int(bit0(X13),bit1(X14))
<=> ord_less_eq_int(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rel__simps_I32_J) ).
tff(f1042,plain,
spl1_93,
inference(avatar_split_clause,[],[f374,f1040]) ).
tff(f1040,plain,
( spl1_93
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).
tff(f374,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit0(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f247]) ).
tff(f1038,plain,
spl1_92,
inference(avatar_split_clause,[],[f371,f1036]) ).
tff(f1036,plain,
( spl1_92
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit0(X1))
| ~ ord_less_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
tff(f371,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit0(X1))
| ~ ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(bit1(X0),bit0(X1))
| ~ ord_less_int(X0,X1) )
& ( ord_less_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit0(X1)) ) ),
inference(nnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit0(X1))
<=> ord_less_int(X0,X1) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X13: int,X14: int] :
( ord_less_eq_int(bit1(X13),bit0(X14))
<=> ord_less_int(X13,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I33_J) ).
tff(f1034,plain,
spl1_91,
inference(avatar_split_clause,[],[f370,f1032]) ).
tff(f1032,plain,
( spl1_91
<=> ! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit0(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
tff(f370,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f1030,plain,
spl1_90,
inference(avatar_split_clause,[],[f367,f1028]) ).
tff(f1028,plain,
( spl1_90
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
tff(f367,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(bit1(X0),bit1(X1))
| ~ ord_less_eq_int(X0,X1) )
& ( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit1(X1)) ) ),
inference(nnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(bit1(X0),bit1(X1))
<=> ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X20: int,X21: int] :
( ord_less_eq_int(bit1(X20),bit1(X21))
<=> ord_less_eq_int(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__eq__int__code_I16_J) ).
tff(f1026,plain,
spl1_89,
inference(avatar_split_clause,[],[f366,f1024]) ).
tff(f1024,plain,
( spl1_89
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
tff(f366,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_eq_int(bit1(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f243]) ).
tff(f1022,plain,
spl1_88,
inference(avatar_split_clause,[],[f363,f1020]) ).
tff(f1020,plain,
( spl1_88
<=> ! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
tff(f363,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
| ~ ord_less_nat(number_number_of_nat(X0),number_number_of_nat(X1)) ),
inference(cnf_transformation,[],[f242]) ).
tff(f1018,plain,
spl1_87,
inference(avatar_split_clause,[],[f358,f1016]) ).
tff(f1016,plain,
( spl1_87
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
tff(f358,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: int,X1: int] :
( ( ( number_number_of_int(X0) = number_number_of_int(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( number_number_of_int(X0) != number_number_of_int(X1) ) ) ),
inference(nnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: int,X1: int] :
( ( number_number_of_int(X0) = number_number_of_int(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X2: int,X3: int] :
( ( number_number_of_int(X2) = number_number_of_int(X3) )
<=> ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_eq__number__of) ).
tff(f1014,plain,
spl1_86,
inference(avatar_split_clause,[],[f356,f1012]) ).
tff(f1012,plain,
( spl1_86
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
tff(f356,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: int,X1: int] :
( ( ( bit0(X0) = bit0(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
inference(nnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: int,X1: int] :
( ( bit0(X0) = bit0(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X13: int,X14: int] :
( ( bit0(X13) = bit0(X14) )
<=> ( X13 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I48_J) ).
tff(f1010,plain,
( ~ spl1_85
| ~ spl1_47
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f975,f971,f756,f1007]) ).
tff(f1007,plain,
( spl1_85
<=> ord_less_int(one_one_int,zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
tff(f756,plain,
( spl1_47
<=> ! [X0: int] : ~ ord_less_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
tff(f971,plain,
( spl1_78
<=> ( one_one_int = power_power_int(one_one_int,plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
tff(f975,plain,
( ~ ord_less_int(one_one_int,zero_zero_int)
| ~ spl1_47
| ~ spl1_78 ),
inference(superposition,[],[f757,f973]) ).
tff(f973,plain,
( ( one_one_int = power_power_int(one_one_int,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl1_78 ),
inference(avatar_component_clause,[],[f971]) ).
tff(f757,plain,
( ! [X0: int] : ~ ord_less_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),zero_zero_int)
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f756]) ).
tff(f1005,plain,
spl1_84,
inference(avatar_split_clause,[],[f354,f1003]) ).
tff(f1003,plain,
( spl1_84
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).
tff(f354,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: int,X1: int] :
( ( ( bit1(X0) = bit1(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
inference(nnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: int,X1: int] :
( ( bit1(X0) = bit1(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X13: int,X14: int] :
( ( bit1(X13) = bit1(X14) )
<=> ( X13 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I51_J) ).
tff(f1001,plain,
spl1_83,
inference(avatar_split_clause,[],[f346,f999]) ).
tff(f999,plain,
( spl1_83
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,one_one_int),X1)
| ~ ord_less_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).
tff(f346,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,one_one_int),X1)
| ~ ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(plus_plus_int(X0,one_one_int),X1)
| ~ ord_less_int(X0,X1) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,X1)
=> ord_less_eq_int(plus_plus_int(X0,one_one_int),X1) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X9: int,X11: int] :
( ord_less_int(X9,X11)
=> ord_less_eq_int(plus_plus_int(X9,one_one_int),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zless__imp__add1__zle) ).
tff(f997,plain,
spl1_82,
inference(avatar_split_clause,[],[f296,f995]) ).
tff(f995,plain,
( spl1_82
<=> ! [X0: int] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,X0))
| ~ ord_less_eq_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
tff(f296,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,X0))
| ~ ord_less_eq_int(zero_zero_int,X0) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,X0))
| ~ ord_less_eq_int(zero_zero_int,X0) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,X0)) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X11: int] :
( ord_less_eq_int(zero_zero_int,X11)
=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_le__imp__0__less) ).
tff(f992,plain,
spl1_81,
inference(avatar_split_clause,[],[f281,f989]) ).
tff(f986,plain,
( spl1_80
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f981,f977,f983]) ).
tff(f983,plain,
( spl1_80
<=> ( zero_zero_int = power_power_int(zero_zero_int,plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
tff(f977,plain,
( spl1_79
<=> ( zero_zero_int = power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
tff(f981,plain,
( ( zero_zero_int = power_power_int(zero_zero_int,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl1_79 ),
inference(forward_demodulation,[],[f979,f281]) ).
tff(f979,plain,
( ( zero_zero_int = power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) )
| ~ spl1_79 ),
inference(avatar_component_clause,[],[f977]) ).
tff(f980,plain,
spl1_79,
inference(avatar_split_clause,[],[f280,f977]) ).
tff(f280,plain,
zero_zero_int = power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
zero_zero_int = power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zero__power2) ).
tff(f974,plain,
( spl1_78
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f969,f965,f971]) ).
tff(f965,plain,
( spl1_77
<=> ( one_one_int = power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
tff(f969,plain,
( ( one_one_int = power_power_int(one_one_int,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl1_77 ),
inference(forward_demodulation,[],[f967,f281]) ).
tff(f967,plain,
( ( one_one_int = power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) )
| ~ spl1_77 ),
inference(avatar_component_clause,[],[f965]) ).
tff(f968,plain,
spl1_77,
inference(avatar_split_clause,[],[f279,f965]) ).
tff(f279,plain,
one_one_int = power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
one_one_int = power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_one__power2) ).
tff(f963,plain,
( ~ spl1_76
| ~ spl1_28
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f840,f751,f638,f960]) ).
tff(f960,plain,
( spl1_76
<=> ord_less_int(one_one_int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_76])]) ).
tff(f751,plain,
( spl1_46
<=> ord_less_eq_int(t,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f840,plain,
( ~ ord_less_int(one_one_int,t)
| ~ spl1_28
| ~ spl1_46 ),
inference(resolution,[],[f753,f639]) ).
tff(f753,plain,
( ord_less_eq_int(t,one_one_int)
| ~ spl1_46 ),
inference(avatar_component_clause,[],[f751]) ).
tff(f958,plain,
( spl1_75
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f953,f949,f955]) ).
tff(f955,plain,
( spl1_75
<=> ( zero_zero_nat = power_power_nat(zero_zero_nat,plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
tff(f949,plain,
( spl1_74
<=> ( zero_zero_nat = power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
tff(f953,plain,
( ( zero_zero_nat = power_power_nat(zero_zero_nat,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl1_74 ),
inference(forward_demodulation,[],[f951,f281]) ).
tff(f951,plain,
( ( zero_zero_nat = power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) )
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f949]) ).
tff(f952,plain,
spl1_74,
inference(avatar_split_clause,[],[f278,f949]) ).
tff(f278,plain,
zero_zero_nat = power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
zero_zero_nat = power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__power2) ).
tff(f947,plain,
( spl1_73
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f942,f938,f944]) ).
tff(f944,plain,
( spl1_73
<=> ( one_one_nat = power_power_nat(one_one_nat,plus_plus_nat(one_one_nat,one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
tff(f938,plain,
( spl1_72
<=> ( one_one_nat = power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
tff(f942,plain,
( ( one_one_nat = power_power_nat(one_one_nat,plus_plus_nat(one_one_nat,one_one_nat)) )
| ~ spl1_72 ),
inference(forward_demodulation,[],[f940,f281]) ).
tff(f940,plain,
( ( one_one_nat = power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) )
| ~ spl1_72 ),
inference(avatar_component_clause,[],[f938]) ).
tff(f941,plain,
spl1_72,
inference(avatar_split_clause,[],[f277,f938]) ).
tff(f277,plain,
one_one_nat = power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
one_one_nat = power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
tff(f915,plain,
( spl1_71
| ~ spl1_22
| ~ spl1_29 ),
inference(avatar_split_clause,[],[f693,f643,f610,f912]) ).
tff(f912,plain,
( spl1_71
<=> ord_less_eq_int(zero_zero_int,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
tff(f610,plain,
( spl1_22
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f643,plain,
( spl1_29
<=> ord_less_int(zero_zero_int,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f693,plain,
( ord_less_eq_int(zero_zero_int,one_one_int)
| ~ spl1_22
| ~ spl1_29 ),
inference(resolution,[],[f645,f611]) ).
tff(f611,plain,
( ! [X0: int,X1: int] :
( ~ ord_less_int(X0,X1)
| ord_less_eq_int(X0,X1) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f610]) ).
tff(f645,plain,
( ord_less_int(zero_zero_int,one_one_int)
| ~ spl1_29 ),
inference(avatar_component_clause,[],[f643]) ).
tff(f868,plain,
( spl1_70
| ~ spl1_15
| ~ spl1_51 ),
inference(avatar_split_clause,[],[f778,f775,f577,f866]) ).
tff(f866,plain,
( spl1_70
<=> ! [X0: int] :
( ord_less_eq_int(X0,bit1(zero_zero_int))
| ~ ord_less_eq_int(X0,one_one_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
tff(f775,plain,
( spl1_51
<=> ! [X0: int] :
( ~ ord_less_eq_int(X0,one_one_int)
| ord_less_eq_int(X0,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f778,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,bit1(zero_zero_int))
| ~ ord_less_eq_int(X0,one_one_int) )
| ~ spl1_15
| ~ spl1_51 ),
inference(forward_demodulation,[],[f776,f579]) ).
tff(f776,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,one_one_int)
| ord_less_eq_int(X0,bit1(pls)) )
| ~ spl1_51 ),
inference(avatar_component_clause,[],[f775]) ).
tff(f864,plain,
( spl1_69
| ~ spl1_15
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f773,f770,f577,f862]) ).
tff(f770,plain,
( spl1_50
<=> ! [X0: int] :
( ord_less_eq_int(X0,one_one_int)
| ~ ord_less_eq_int(X0,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f773,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,bit1(zero_zero_int))
| ord_less_eq_int(X0,one_one_int) )
| ~ spl1_15
| ~ spl1_50 ),
inference(forward_demodulation,[],[f771,f579]) ).
tff(f771,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,one_one_int)
| ~ ord_less_eq_int(X0,bit1(pls)) )
| ~ spl1_50 ),
inference(avatar_component_clause,[],[f770]) ).
tff(f860,plain,
( spl1_68
| ~ spl1_15
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f768,f765,f577,f858]) ).
tff(f858,plain,
( spl1_68
<=> ! [X0: int] :
( ord_less_eq_int(bit1(zero_zero_int),X0)
| ~ ord_less_eq_int(one_one_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
tff(f765,plain,
( spl1_49
<=> ! [X0: int] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_eq_int(bit1(pls),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f768,plain,
( ! [X0: int] :
( ord_less_eq_int(bit1(zero_zero_int),X0)
| ~ ord_less_eq_int(one_one_int,X0) )
| ~ spl1_15
| ~ spl1_49 ),
inference(forward_demodulation,[],[f766,f579]) ).
tff(f766,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_eq_int(bit1(pls),X0) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f765]) ).
tff(f856,plain,
( spl1_67
| ~ spl1_15
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f763,f760,f577,f854]) ).
tff(f760,plain,
( spl1_48
<=> ! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_eq_int(bit1(pls),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f763,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(bit1(zero_zero_int),X0)
| ord_less_eq_int(one_one_int,X0) )
| ~ spl1_15
| ~ spl1_48 ),
inference(forward_demodulation,[],[f761,f579]) ).
tff(f761,plain,
( ! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_eq_int(bit1(pls),X0) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f760]) ).
tff(f839,plain,
( spl1_66
| ~ spl1_15
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f741,f737,f577,f837]) ).
tff(f837,plain,
( spl1_66
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_int(zero_zero_int,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
tff(f737,plain,
( spl1_43
<=> ! [X0: int] :
( ord_less_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f741,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_int(zero_zero_int,bit1(X0)) )
| ~ spl1_15
| ~ spl1_43 ),
inference(forward_demodulation,[],[f740,f579]) ).
tff(f740,plain,
( ! [X0: int] :
( ord_less_int(zero_zero_int,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_15
| ~ spl1_43 ),
inference(forward_demodulation,[],[f738,f579]) ).
tff(f738,plain,
( ! [X0: int] :
( ord_less_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_43 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f835,plain,
( spl1_65
| ~ spl1_15
| ~ spl1_42 ),
inference(avatar_split_clause,[],[f735,f731,f577,f833]) ).
tff(f833,plain,
( spl1_65
<=> ! [X0: int] :
( ~ ord_less_int(zero_zero_int,bit1(X0))
| ord_less_eq_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
tff(f731,plain,
( spl1_42
<=> ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_int(pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
tff(f735,plain,
( ! [X0: int] :
( ~ ord_less_int(zero_zero_int,bit1(X0))
| ord_less_eq_int(zero_zero_int,X0) )
| ~ spl1_15
| ~ spl1_42 ),
inference(forward_demodulation,[],[f734,f579]) ).
tff(f734,plain,
( ! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
| ~ ord_less_int(pls,bit1(X0)) )
| ~ spl1_15
| ~ spl1_42 ),
inference(forward_demodulation,[],[f732,f579]) ).
tff(f732,plain,
( ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_int(pls,bit1(X0)) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f731]) ).
tff(f831,plain,
( spl1_64
| ~ spl1_15
| ~ spl1_41 ),
inference(avatar_split_clause,[],[f729,f725,f577,f829]) ).
tff(f829,plain,
( spl1_64
<=> ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ord_less_eq_int(bit0(X0),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
tff(f725,plain,
( spl1_41
<=> ! [X0: int] :
( ord_less_eq_int(bit0(X0),pls)
| ~ ord_less_eq_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
tff(f729,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ord_less_eq_int(bit0(X0),zero_zero_int) )
| ~ spl1_15
| ~ spl1_41 ),
inference(forward_demodulation,[],[f728,f579]) ).
tff(f728,plain,
( ! [X0: int] :
( ord_less_eq_int(bit0(X0),zero_zero_int)
| ~ ord_less_eq_int(X0,pls) )
| ~ spl1_15
| ~ spl1_41 ),
inference(forward_demodulation,[],[f726,f579]) ).
tff(f726,plain,
( ! [X0: int] :
( ord_less_eq_int(bit0(X0),pls)
| ~ ord_less_eq_int(X0,pls) )
| ~ spl1_41 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f827,plain,
( spl1_63
| ~ spl1_15
| ~ spl1_40 ),
inference(avatar_split_clause,[],[f723,f719,f577,f825]) ).
tff(f825,plain,
( spl1_63
<=> ! [X0: int] :
( ~ ord_less_eq_int(bit0(X0),zero_zero_int)
| ord_less_eq_int(X0,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f719,plain,
( spl1_40
<=> ! [X0: int] :
( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(bit0(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
tff(f723,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(bit0(X0),zero_zero_int)
| ord_less_eq_int(X0,zero_zero_int) )
| ~ spl1_15
| ~ spl1_40 ),
inference(forward_demodulation,[],[f722,f579]) ).
tff(f722,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,zero_zero_int)
| ~ ord_less_eq_int(bit0(X0),pls) )
| ~ spl1_15
| ~ spl1_40 ),
inference(forward_demodulation,[],[f720,f579]) ).
tff(f720,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(bit0(X0),pls) )
| ~ spl1_40 ),
inference(avatar_component_clause,[],[f719]) ).
tff(f823,plain,
( spl1_62
| ~ spl1_15
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f717,f713,f577,f821]) ).
tff(f821,plain,
( spl1_62
<=> ! [X0: int] :
( ~ ord_less_int(X0,zero_zero_int)
| ord_less_eq_int(bit1(X0),zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
tff(f713,plain,
( spl1_39
<=> ! [X0: int] :
( ord_less_eq_int(bit1(X0),pls)
| ~ ord_less_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
tff(f717,plain,
( ! [X0: int] :
( ~ ord_less_int(X0,zero_zero_int)
| ord_less_eq_int(bit1(X0),zero_zero_int) )
| ~ spl1_15
| ~ spl1_39 ),
inference(forward_demodulation,[],[f716,f579]) ).
tff(f716,plain,
( ! [X0: int] :
( ord_less_eq_int(bit1(X0),zero_zero_int)
| ~ ord_less_int(X0,pls) )
| ~ spl1_15
| ~ spl1_39 ),
inference(forward_demodulation,[],[f714,f579]) ).
tff(f714,plain,
( ! [X0: int] :
( ord_less_eq_int(bit1(X0),pls)
| ~ ord_less_int(X0,pls) )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f713]) ).
tff(f819,plain,
( spl1_61
| ~ spl1_15
| ~ spl1_38 ),
inference(avatar_split_clause,[],[f711,f707,f577,f817]) ).
tff(f817,plain,
( spl1_61
<=> ! [X0: int] :
( ~ ord_less_eq_int(bit1(X0),zero_zero_int)
| ord_less_int(X0,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
tff(f707,plain,
( spl1_38
<=> ! [X0: int] :
( ord_less_int(X0,pls)
| ~ ord_less_eq_int(bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
tff(f711,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(bit1(X0),zero_zero_int)
| ord_less_int(X0,zero_zero_int) )
| ~ spl1_15
| ~ spl1_38 ),
inference(forward_demodulation,[],[f710,f579]) ).
tff(f710,plain,
( ! [X0: int] :
( ord_less_int(X0,zero_zero_int)
| ~ ord_less_eq_int(bit1(X0),pls) )
| ~ spl1_15
| ~ spl1_38 ),
inference(forward_demodulation,[],[f708,f579]) ).
tff(f708,plain,
( ! [X0: int] :
( ord_less_int(X0,pls)
| ~ ord_less_eq_int(bit1(X0),pls) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f707]) ).
tff(f815,plain,
( spl1_60
| ~ spl1_15
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f705,f701,f577,f813]) ).
tff(f813,plain,
( spl1_60
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(zero_zero_int,bit0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f701,plain,
( spl1_37
<=> ! [X0: int] :
( ord_less_eq_int(pls,bit0(X0))
| ~ ord_less_eq_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
tff(f705,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(zero_zero_int,bit0(X0)) )
| ~ spl1_15
| ~ spl1_37 ),
inference(forward_demodulation,[],[f704,f579]) ).
tff(f704,plain,
( ! [X0: int] :
( ord_less_eq_int(zero_zero_int,bit0(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_15
| ~ spl1_37 ),
inference(forward_demodulation,[],[f702,f579]) ).
tff(f702,plain,
( ! [X0: int] :
( ord_less_eq_int(pls,bit0(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f701]) ).
tff(f811,plain,
( spl1_59
| ~ spl1_15
| ~ spl1_36 ),
inference(avatar_split_clause,[],[f699,f695,f577,f809]) ).
tff(f809,plain,
( spl1_59
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,bit0(X0))
| ord_less_eq_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
tff(f695,plain,
( spl1_36
<=> ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f699,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,bit0(X0))
| ord_less_eq_int(zero_zero_int,X0) )
| ~ spl1_15
| ~ spl1_36 ),
inference(forward_demodulation,[],[f698,f579]) ).
tff(f698,plain,
( ! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
| ~ ord_less_eq_int(pls,bit0(X0)) )
| ~ spl1_15
| ~ spl1_36 ),
inference(forward_demodulation,[],[f696,f579]) ).
tff(f696,plain,
( ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit0(X0)) )
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f695]) ).
tff(f807,plain,
( spl1_58
| ~ spl1_15
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f691,f687,f577,f805]) ).
tff(f805,plain,
( spl1_58
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(zero_zero_int,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
tff(f687,plain,
( spl1_35
<=> ! [X0: int] :
( ord_less_eq_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f691,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(zero_zero_int,bit1(X0)) )
| ~ spl1_15
| ~ spl1_35 ),
inference(forward_demodulation,[],[f690,f579]) ).
tff(f690,plain,
( ! [X0: int] :
( ord_less_eq_int(zero_zero_int,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_15
| ~ spl1_35 ),
inference(forward_demodulation,[],[f688,f579]) ).
tff(f688,plain,
( ! [X0: int] :
( ord_less_eq_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f687]) ).
tff(f803,plain,
( spl1_57
| ~ spl1_5
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f653,f610,f529,f800]) ).
tff(f529,plain,
( spl1_5
<=> ord_less_int(t,zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f653,plain,
( ord_less_eq_int(t,zero_zero_int)
| ~ spl1_5
| ~ spl1_22 ),
inference(resolution,[],[f611,f531]) ).
tff(f531,plain,
( ord_less_int(t,zero_zero_int)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f529]) ).
tff(f798,plain,
( spl1_56
| ~ spl1_15
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f685,f681,f577,f796]) ).
tff(f796,plain,
( spl1_56
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,bit1(X0))
| ord_less_eq_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f681,plain,
( spl1_34
<=> ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f685,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,bit1(X0))
| ord_less_eq_int(zero_zero_int,X0) )
| ~ spl1_15
| ~ spl1_34 ),
inference(forward_demodulation,[],[f684,f579]) ).
tff(f684,plain,
( ! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
| ~ ord_less_eq_int(pls,bit1(X0)) )
| ~ spl1_15
| ~ spl1_34 ),
inference(forward_demodulation,[],[f682,f579]) ).
tff(f682,plain,
( ! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit1(X0)) )
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f681]) ).
tff(f794,plain,
( spl1_55
| ~ spl1_15
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f679,f676,f577,f792]) ).
tff(f792,plain,
( spl1_55
<=> ! [X0: int] :
( ~ ord_less_int(zero_zero_int,X0)
| ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f676,plain,
( spl1_33
<=> ! [X0: int] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(X0))
| ~ ord_less_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f679,plain,
( ! [X0: int] :
( ~ ord_less_int(zero_zero_int,X0)
| ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) )
| ~ spl1_15
| ~ spl1_33 ),
inference(forward_demodulation,[],[f677,f579]) ).
tff(f677,plain,
( ! [X0: int] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(X0))
| ~ ord_less_int(pls,X0) )
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f790,plain,
( spl1_54
| ~ spl1_15
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f674,f671,f577,f788]) ).
tff(f788,plain,
( spl1_54
<=> ! [X0: int] :
( ord_less_int(zero_zero_int,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f671,plain,
( spl1_32
<=> ! [X0: int] :
( ord_less_int(pls,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f674,plain,
( ! [X0: int] :
( ord_less_int(zero_zero_int,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) )
| ~ spl1_15
| ~ spl1_32 ),
inference(forward_demodulation,[],[f672,f579]) ).
tff(f672,plain,
( ! [X0: int] :
( ord_less_int(pls,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) )
| ~ spl1_32 ),
inference(avatar_component_clause,[],[f671]) ).
tff(f786,plain,
( spl1_53
| ~ spl1_15
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f669,f666,f577,f784]) ).
tff(f666,plain,
( spl1_31
<=> ! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ ord_less_eq_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f669,plain,
( ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ( zero_zero_nat = number_number_of_nat(X0) ) )
| ~ spl1_15
| ~ spl1_31 ),
inference(forward_demodulation,[],[f667,f579]) ).
tff(f667,plain,
( ! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ ord_less_eq_int(X0,pls) )
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f666]) ).
tff(f782,plain,
( spl1_52
| ~ spl1_15
| ~ spl1_30 ),
inference(avatar_split_clause,[],[f664,f661,f577,f780]) ).
tff(f780,plain,
( spl1_52
<=> ! [X0: int] :
( ord_less_eq_int(X0,zero_zero_int)
| ( zero_zero_nat != number_number_of_nat(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f661,plain,
( spl1_30
<=> ! [X0: int] :
( ord_less_eq_int(X0,pls)
| ( zero_zero_nat != number_number_of_nat(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f664,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,zero_zero_int)
| ( zero_zero_nat != number_number_of_nat(X0) ) )
| ~ spl1_15
| ~ spl1_30 ),
inference(forward_demodulation,[],[f662,f579]) ).
tff(f662,plain,
( ! [X0: int] :
( ord_less_eq_int(X0,pls)
| ( zero_zero_nat != number_number_of_nat(X0) ) )
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f777,plain,
spl1_51,
inference(avatar_split_clause,[],[f456,f775]) ).
tff(f456,plain,
! [X0: int] :
( ~ ord_less_eq_int(X0,one_one_int)
| ord_less_eq_int(X0,bit1(pls)) ),
inference(forward_demodulation,[],[f317,f289]) ).
tff(f317,plain,
! [X0: int] :
( ord_less_eq_int(X0,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(X0),one_one_int) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: int] :
( ( ord_less_eq_int(number_number_of_int(X0),one_one_int)
| ~ ord_less_eq_int(X0,bit1(pls)) )
& ( ord_less_eq_int(X0,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(X0),one_one_int) ) ),
inference(nnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: int] :
( ord_less_eq_int(number_number_of_int(X0),one_one_int)
<=> ord_less_eq_int(X0,bit1(pls)) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X2: int] :
( ord_less_eq_int(number_number_of_int(X2),one_one_int)
<=> ord_less_eq_int(X2,bit1(pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__special_I4_J) ).
tff(f772,plain,
spl1_50,
inference(avatar_split_clause,[],[f455,f770]) ).
tff(f455,plain,
! [X0: int] :
( ord_less_eq_int(X0,one_one_int)
| ~ ord_less_eq_int(X0,bit1(pls)) ),
inference(forward_demodulation,[],[f318,f289]) ).
tff(f318,plain,
! [X0: int] :
( ord_less_eq_int(number_number_of_int(X0),one_one_int)
| ~ ord_less_eq_int(X0,bit1(pls)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f767,plain,
spl1_49,
inference(avatar_split_clause,[],[f452,f765]) ).
tff(f452,plain,
! [X0: int] :
( ~ ord_less_eq_int(one_one_int,X0)
| ord_less_eq_int(bit1(pls),X0) ),
inference(forward_demodulation,[],[f305,f289]) ).
tff(f305,plain,
! [X0: int] :
( ord_less_eq_int(bit1(pls),X0)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(X0)) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: int] :
( ( ord_less_eq_int(one_one_int,number_number_of_int(X0))
| ~ ord_less_eq_int(bit1(pls),X0) )
& ( ord_less_eq_int(bit1(pls),X0)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(X0)) ) ),
inference(nnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: int] :
( ord_less_eq_int(one_one_int,number_number_of_int(X0))
<=> ord_less_eq_int(bit1(pls),X0) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X3: int] :
( ord_less_eq_int(one_one_int,number_number_of_int(X3))
<=> ord_less_eq_int(bit1(pls),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__special_I2_J) ).
tff(f762,plain,
spl1_48,
inference(avatar_split_clause,[],[f451,f760]) ).
tff(f451,plain,
! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_eq_int(bit1(pls),X0) ),
inference(forward_demodulation,[],[f306,f289]) ).
tff(f306,plain,
! [X0: int] :
( ord_less_eq_int(one_one_int,number_number_of_int(X0))
| ~ ord_less_eq_int(bit1(pls),X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f758,plain,
spl1_47,
inference(avatar_split_clause,[],[f447,f756]) ).
tff(f447,plain,
! [X0: int] : ~ ord_less_int(power_power_int(X0,plus_plus_nat(one_one_nat,one_one_nat)),zero_zero_int),
inference(forward_demodulation,[],[f293,f281]) ).
tff(f293,plain,
! [X0: int] : ~ ord_less_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: int] : ~ ord_less_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X4: int] : ~ ord_less_int(power_power_int(X4,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
tff(f754,plain,
( spl1_46
| spl1_3
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f647,f606,f519,f751]) ).
tff(f519,plain,
( spl1_3
<=> ord_less_eq_int(one_one_int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f606,plain,
( spl1_21
<=> ! [X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f647,plain,
( ord_less_eq_int(t,one_one_int)
| spl1_3
| ~ spl1_21 ),
inference(resolution,[],[f607,f521]) ).
tff(f521,plain,
( ~ ord_less_eq_int(one_one_int,t)
| spl1_3 ),
inference(avatar_component_clause,[],[f519]) ).
tff(f607,plain,
( ! [X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ord_less_eq_int(X0,X1) )
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f606]) ).
tff(f749,plain,
spl1_45,
inference(avatar_split_clause,[],[f328,f747]) ).
tff(f328,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X11: int,X9: int] : ( times_times_int(X11,X9) = times_times_int(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(f745,plain,
spl1_44,
inference(avatar_split_clause,[],[f327,f743]) ).
tff(f327,plain,
! [X0: int,X1: int] : ( plus_plus_int(X1,X0) = plus_plus_int(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: int,X1: int] : ( plus_plus_int(X1,X0) = plus_plus_int(X0,X1) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X11: int,X9: int] : ( plus_plus_int(X9,X11) = plus_plus_int(X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
tff(f739,plain,
spl1_43,
inference(avatar_split_clause,[],[f322,f737]) ).
tff(f322,plain,
! [X0: int] :
( ord_less_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: int] :
( ( ord_less_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
& ( ord_less_eq_int(pls,X0)
| ~ ord_less_int(pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: int] :
( ord_less_int(pls,bit1(X0))
<=> ord_less_eq_int(pls,X0) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X13: int] :
( ord_less_int(pls,bit1(X13))
<=> ord_less_eq_int(pls,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I5_J) ).
tff(f733,plain,
spl1_42,
inference(avatar_split_clause,[],[f321,f731]) ).
tff(f321,plain,
! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_int(pls,bit1(X0)) ),
inference(cnf_transformation,[],[f230]) ).
tff(f727,plain,
spl1_41,
inference(avatar_split_clause,[],[f316,f725]) ).
tff(f316,plain,
! [X0: int] :
( ord_less_eq_int(bit0(X0),pls)
| ~ ord_less_eq_int(X0,pls) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: int] :
( ( ord_less_eq_int(bit0(X0),pls)
| ~ ord_less_eq_int(X0,pls) )
& ( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: int] :
( ord_less_eq_int(bit0(X0),pls)
<=> ord_less_eq_int(X0,pls) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X13: int] :
( ord_less_eq_int(bit0(X13),pls)
<=> ord_less_eq_int(X13,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I27_J) ).
tff(f721,plain,
spl1_40,
inference(avatar_split_clause,[],[f315,f719]) ).
tff(f315,plain,
! [X0: int] :
( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(bit0(X0),pls) ),
inference(cnf_transformation,[],[f227]) ).
tff(f715,plain,
spl1_39,
inference(avatar_split_clause,[],[f314,f713]) ).
tff(f314,plain,
! [X0: int] :
( ord_less_eq_int(bit1(X0),pls)
| ~ ord_less_int(X0,pls) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: int] :
( ( ord_less_eq_int(bit1(X0),pls)
| ~ ord_less_int(X0,pls) )
& ( ord_less_int(X0,pls)
| ~ ord_less_eq_int(bit1(X0),pls) ) ),
inference(nnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: int] :
( ord_less_eq_int(bit1(X0),pls)
<=> ord_less_int(X0,pls) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X13: int] :
( ord_less_eq_int(bit1(X13),pls)
<=> ord_less_int(X13,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rel__simps_I29_J) ).
tff(f709,plain,
spl1_38,
inference(avatar_split_clause,[],[f313,f707]) ).
tff(f313,plain,
! [X0: int] :
( ord_less_int(X0,pls)
| ~ ord_less_eq_int(bit1(X0),pls) ),
inference(cnf_transformation,[],[f226]) ).
tff(f703,plain,
spl1_37,
inference(avatar_split_clause,[],[f312,f701]) ).
tff(f312,plain,
! [X0: int] :
( ord_less_eq_int(pls,bit0(X0))
| ~ ord_less_eq_int(pls,X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: int] :
( ( ord_less_eq_int(pls,bit0(X0))
| ~ ord_less_eq_int(pls,X0) )
& ( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: int] :
( ord_less_eq_int(pls,bit0(X0))
<=> ord_less_eq_int(pls,X0) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X13: int] :
( ord_less_eq_int(pls,bit0(X13))
<=> ord_less_eq_int(pls,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__simps_I21_J) ).
tff(f697,plain,
spl1_36,
inference(avatar_split_clause,[],[f311,f695]) ).
tff(f311,plain,
! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit0(X0)) ),
inference(cnf_transformation,[],[f225]) ).
tff(f689,plain,
spl1_35,
inference(avatar_split_clause,[],[f310,f687]) ).
tff(f310,plain,
! [X0: int] :
( ord_less_eq_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: int] :
( ( ord_less_eq_int(pls,bit1(X0))
| ~ ord_less_eq_int(pls,X0) )
& ( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit1(X0)) ) ),
inference(nnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: int] :
( ord_less_eq_int(pls,bit1(X0))
<=> ord_less_eq_int(pls,X0) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X13: int] :
( ord_less_eq_int(pls,bit1(X13))
<=> ord_less_eq_int(pls,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I22_J) ).
tff(f683,plain,
spl1_34,
inference(avatar_split_clause,[],[f309,f681]) ).
tff(f309,plain,
! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(pls,bit1(X0)) ),
inference(cnf_transformation,[],[f224]) ).
tff(f678,plain,
spl1_33,
inference(avatar_split_clause,[],[f304,f676]) ).
tff(f304,plain,
! [X0: int] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(X0))
| ~ ord_less_int(pls,X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: int] :
( ( ord_less_nat(zero_zero_nat,number_number_of_nat(X0))
| ~ ord_less_int(pls,X0) )
& ( ord_less_int(pls,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) ) ),
inference(nnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: int] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(X0))
<=> ord_less_int(pls,X0) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X24: int] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(X24))
<=> ord_less_int(pls,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__0__number__of) ).
tff(f673,plain,
spl1_32,
inference(avatar_split_clause,[],[f303,f671]) ).
tff(f303,plain,
! [X0: int] :
( ord_less_int(pls,X0)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(X0)) ),
inference(cnf_transformation,[],[f221]) ).
tff(f668,plain,
spl1_31,
inference(avatar_split_clause,[],[f300,f666]) ).
tff(f300,plain,
! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ ord_less_eq_int(X0,pls) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: int] :
( ( ( zero_zero_nat = number_number_of_nat(X0) )
| ~ ord_less_eq_int(X0,pls) )
& ( ord_less_eq_int(X0,pls)
| ( zero_zero_nat != number_number_of_nat(X0) ) ) ),
inference(nnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: int] :
( ( zero_zero_nat = number_number_of_nat(X0) )
<=> ord_less_eq_int(X0,pls) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X24: int] :
( ( zero_zero_nat = number_number_of_nat(X24) )
<=> ord_less_eq_int(X24,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_eq__0__number__of) ).
tff(f663,plain,
spl1_30,
inference(avatar_split_clause,[],[f299,f661]) ).
tff(f299,plain,
! [X0: int] :
( ord_less_eq_int(X0,pls)
| ( zero_zero_nat != number_number_of_nat(X0) ) ),
inference(cnf_transformation,[],[f219]) ).
tff(f646,plain,
( spl1_29
| ~ spl1_6
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f641,f596,f534,f643]) ).
tff(f641,plain,
( ord_less_int(zero_zero_int,one_one_int)
| ~ spl1_6
| ~ spl1_19 ),
inference(resolution,[],[f597,f535]) ).
tff(f640,plain,
spl1_28,
inference(avatar_split_clause,[],[f490,f638]) ).
tff(f490,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq_int(X0,X1)
| ~ ord_less_int(X1,X0) ),
inference(forward_demodulation,[],[f489,f289]) ).
tff(f489,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq_int(number_number_of_int(X0),X1)
| ~ ord_less_int(X1,X0) ),
inference(forward_demodulation,[],[f488,f289]) ).
tff(f488,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(X1,X0)
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(forward_demodulation,[],[f487,f289]) ).
tff(f487,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(number_number_of_int(X1),X0)
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(forward_demodulation,[],[f386,f289]) ).
tff(f386,plain,
! [X0: int,X1: int] :
( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: int,X1: int] :
( ( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
| ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) )
& ( ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0))
| ~ ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1)) ) ),
inference(nnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
<=> ~ ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X24: int,X23: int] :
( ord_less_eq_int(number_number_of_int(X24),number_number_of_int(X23))
<=> ~ ord_less_int(number_number_of_int(X23),number_number_of_int(X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__number__of__eq__not__less) ).
tff(f636,plain,
spl1_27,
inference(avatar_split_clause,[],[f486,f634]) ).
tff(f634,plain,
( spl1_27
<=> ! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ord_less_eq_int(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f486,plain,
! [X0: int,X1: int] :
( ord_less_int(X1,X0)
| ord_less_eq_int(X0,X1) ),
inference(forward_demodulation,[],[f485,f289]) ).
tff(f485,plain,
! [X0: int,X1: int] :
( ord_less_int(number_number_of_int(X1),X0)
| ord_less_eq_int(X0,X1) ),
inference(forward_demodulation,[],[f484,f289]) ).
tff(f484,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
inference(forward_demodulation,[],[f483,f289]) ).
tff(f483,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(number_number_of_int(X0),X1)
| ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
inference(forward_demodulation,[],[f387,f289]) ).
tff(f387,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(number_number_of_int(X0),number_number_of_int(X1))
| ord_less_int(number_number_of_int(X1),number_number_of_int(X0)) ),
inference(cnf_transformation,[],[f253]) ).
tff(f631,plain,
spl1_26,
inference(avatar_split_clause,[],[f458,f629]) ).
tff(f629,plain,
( spl1_26
<=> ! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ord_less_eq_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f458,plain,
! [X0: int] :
( ~ ord_less_eq_int(X0,zero_zero_int)
| ord_less_eq_int(X0,pls) ),
inference(forward_demodulation,[],[f319,f289]) ).
tff(f319,plain,
! [X0: int] :
( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(number_number_of_int(X0),zero_zero_int) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: int] :
( ( ord_less_eq_int(number_number_of_int(X0),zero_zero_int)
| ~ ord_less_eq_int(X0,pls) )
& ( ord_less_eq_int(X0,pls)
| ~ ord_less_eq_int(number_number_of_int(X0),zero_zero_int) ) ),
inference(nnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: int] :
( ord_less_eq_int(number_number_of_int(X0),zero_zero_int)
<=> ord_less_eq_int(X0,pls) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X2: int] :
( ord_less_eq_int(number_number_of_int(X2),zero_zero_int)
<=> ord_less_eq_int(X2,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__special_I3_J) ).
tff(f626,plain,
spl1_25,
inference(avatar_split_clause,[],[f457,f624]) ).
tff(f624,plain,
( spl1_25
<=> ! [X0: int] :
( ord_less_eq_int(X0,zero_zero_int)
| ~ ord_less_eq_int(X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f457,plain,
! [X0: int] :
( ord_less_eq_int(X0,zero_zero_int)
| ~ ord_less_eq_int(X0,pls) ),
inference(forward_demodulation,[],[f320,f289]) ).
tff(f320,plain,
! [X0: int] :
( ord_less_eq_int(number_number_of_int(X0),zero_zero_int)
| ~ ord_less_eq_int(X0,pls) ),
inference(cnf_transformation,[],[f229]) ).
tff(f621,plain,
spl1_24,
inference(avatar_split_clause,[],[f454,f619]) ).
tff(f619,plain,
( spl1_24
<=> ! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f454,plain,
! [X0: int] :
( ~ ord_less_eq_int(zero_zero_int,X0)
| ord_less_eq_int(pls,X0) ),
inference(forward_demodulation,[],[f307,f289]) ).
tff(f307,plain,
! [X0: int] :
( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(X0)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: int] :
( ( ord_less_eq_int(zero_zero_int,number_number_of_int(X0))
| ~ ord_less_eq_int(pls,X0) )
& ( ord_less_eq_int(pls,X0)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(X0)) ) ),
inference(nnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: int] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(X0))
<=> ord_less_eq_int(pls,X0) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X3: int] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(X3))
<=> ord_less_eq_int(pls,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__special_I1_J) ).
tff(f616,plain,
spl1_23,
inference(avatar_split_clause,[],[f453,f614]) ).
tff(f614,plain,
( spl1_23
<=> ! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
| ~ ord_less_eq_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f453,plain,
! [X0: int] :
( ord_less_eq_int(zero_zero_int,X0)
| ~ ord_less_eq_int(pls,X0) ),
inference(forward_demodulation,[],[f308,f289]) ).
tff(f308,plain,
! [X0: int] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(X0))
| ~ ord_less_eq_int(pls,X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f612,plain,
spl1_22,
inference(avatar_split_clause,[],[f347,f610]) ).
tff(f347,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X0,X1)
| ~ ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tff(f608,plain,
spl1_21,
inference(avatar_split_clause,[],[f339,f606]) ).
tff(f339,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ord_less_eq_int(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: int,X1: int] :
( ord_less_eq_int(X1,X0)
| ord_less_eq_int(X0,X1) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X11: int,X9: int] :
( ord_less_eq_int(X9,X11)
| ord_less_eq_int(X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_zle__linear) ).
tff(f602,plain,
spl1_20,
inference(avatar_split_clause,[],[f298,f600]) ).
tff(f600,plain,
( spl1_20
<=> ! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_int(zero_zero_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f298,plain,
! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_int(zero_zero_int,X0) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: int] :
( ( ord_less_eq_int(one_one_int,X0)
| ~ ord_less_int(zero_zero_int,X0) )
& ( ord_less_int(zero_zero_int,X0)
| ~ ord_less_eq_int(one_one_int,X0) ) ),
inference(nnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: int] :
( ord_less_eq_int(one_one_int,X0)
<=> ord_less_int(zero_zero_int,X0) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X22: int] :
( ord_less_eq_int(one_one_int,X22)
<=> ord_less_int(zero_zero_int,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__one__le__iff__zero__less) ).
tff(f598,plain,
spl1_19,
inference(avatar_split_clause,[],[f297,f596]) ).
tff(f297,plain,
! [X0: int] :
( ord_less_int(zero_zero_int,X0)
| ~ ord_less_eq_int(one_one_int,X0) ),
inference(cnf_transformation,[],[f218]) ).
tff(f594,plain,
( spl1_18
| ~ spl1_9
| ~ spl1_10
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f567,f564,f552,f547,f592]) ).
tff(f547,plain,
( spl1_9
<=> ( zero_zero_int = number_number_of_int(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f564,plain,
( spl1_12
<=> ! [X0: int] : ( pls = times_times_int(pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f567,plain,
( ! [X0: int] : ( zero_zero_int = times_times_int(zero_zero_int,X0) )
| ~ spl1_9
| ~ spl1_10
| ~ spl1_12 ),
inference(forward_demodulation,[],[f565,f555]) ).
tff(f555,plain,
( ( zero_zero_int = pls )
| ~ spl1_9
| ~ spl1_10 ),
inference(superposition,[],[f553,f549]) ).
tff(f549,plain,
( ( zero_zero_int = number_number_of_int(pls) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f547]) ).
tff(f565,plain,
( ! [X0: int] : ( pls = times_times_int(pls,X0) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f590,plain,
( spl1_17
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f562,f558,f552,f547,f587]) ).
tff(f587,plain,
( spl1_17
<=> ( one_one_nat = number_number_of_nat(bit1(zero_zero_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f558,plain,
( spl1_11
<=> ( one_one_nat = number_number_of_nat(bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f562,plain,
( ( one_one_nat = number_number_of_nat(bit1(zero_zero_int)) )
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(forward_demodulation,[],[f560,f555]) ).
tff(f560,plain,
( ( one_one_nat = number_number_of_nat(bit1(pls)) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f558]) ).
tff(f585,plain,
spl1_16,
inference(avatar_split_clause,[],[f496,f582]) ).
tff(f582,plain,
( spl1_16
<=> ( zero_zero_int = plus_plus_int(zero_zero_int,zero_zero_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f496,plain,
zero_zero_int = plus_plus_int(zero_zero_int,zero_zero_int),
inference(forward_demodulation,[],[f439,f280]) ).
tff(f439,plain,
zero_zero_int = plus_plus_int(power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))),power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls))))),
inference(equality_resolution,[],[f438]) ).
tff(f438,plain,
! [X0: int] :
( ( zero_zero_int = plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls))))) )
| ( zero_zero_int != X0 ) ),
inference(equality_resolution,[],[f406]) ).
tff(f406,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) )
| ( zero_zero_int != X1 )
| ( zero_zero_int != X0 ) ),
inference(cnf_transformation,[],[f264]) ).
tff(f580,plain,
( spl1_15
| ~ spl1_9
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f555,f552,f547,f577]) ).
tff(f575,plain,
spl1_14,
inference(avatar_split_clause,[],[f292,f573]) ).
tff(f573,plain,
( spl1_14
<=> ! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f292,plain,
! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: int] : ( times_times_int(one_one_int,X0) = X0 ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X11: int] : ( times_times_int(one_one_int,X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_zmult__1) ).
tff(f571,plain,
spl1_13,
inference(avatar_split_clause,[],[f291,f569]) ).
tff(f569,plain,
( spl1_13
<=> ! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f291,plain,
! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: int] : ( times_times_int(X0,one_one_int) = X0 ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X11: int] : ( times_times_int(X11,one_one_int) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zmult__1__right) ).
tff(f566,plain,
spl1_12,
inference(avatar_split_clause,[],[f290,f564]) ).
tff(f290,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X9: int] : ( pls = times_times_int(pls,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(f561,plain,
spl1_11,
inference(avatar_split_clause,[],[f275,f558]) ).
tff(f275,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(cnf_transformation,[],[f83]) ).
tff(f83,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat__numeral__1__eq__1) ).
tff(f554,plain,
spl1_10,
inference(avatar_split_clause,[],[f289,f552]) ).
tff(f550,plain,
spl1_9,
inference(avatar_split_clause,[],[f274,f547]) ).
tff(f274,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(f545,plain,
spl1_8,
inference(avatar_split_clause,[],[f272,f542]) ).
tff(f272,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(cnf_transformation,[],[f62]) ).
tff(f62,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__number__of__Pls) ).
tff(f540,plain,
spl1_7,
inference(avatar_split_clause,[],[f426,f538]) ).
tff(f538,plain,
( spl1_7
<=> ! [X1: int] : ~ ord_less_int(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f426,plain,
! [X1: int] : ~ ord_less_int(X1,X1),
inference(equality_resolution,[],[f348]) ).
tff(f348,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ~ ord_less_int(X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tff(f536,plain,
spl1_6,
inference(avatar_split_clause,[],[f288,f534]) ).
tff(f288,plain,
! [X0: int] : ord_less_eq_int(X0,X0),
inference(cnf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: int] : ord_less_eq_int(X0,X0),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X9: int] : ord_less_eq_int(X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zle__refl) ).
tff(f532,plain,
spl1_5,
inference(avatar_split_clause,[],[f271,f529]) ).
tff(f271,plain,
ord_less_int(t,zero_zero_int),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less_int(t,zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
tff(f527,plain,
spl1_4,
inference(avatar_split_clause,[],[f270,f524]) ).
tff(f524,plain,
( spl1_4
<=> ord_less_int(t,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f270,plain,
ord_less_int(t,one_one_int),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less_int(t,one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
tff(f522,plain,
~ spl1_3,
inference(avatar_split_clause,[],[f268,f519]) ).
tff(f268,plain,
~ ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
~ ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(f517,plain,
( ~ spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f512,f507,f514]) ).
tff(f507,plain,
( spl1_1
<=> ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f512,plain,
( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int)
| spl1_1 ),
inference(forward_demodulation,[],[f511,f281]) ).
tff(f511,plain,
( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| spl1_1 ),
inference(forward_demodulation,[],[f509,f327]) ).
tff(f509,plain,
( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int)
| spl1_1 ),
inference(avatar_component_clause,[],[f507]) ).
tff(f510,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f267,f507]) ).
tff(f267,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f108]) ).
tff(f108,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(negated_conjecture,[],[f107]) ).
tff(f107,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.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 : Fri May 3 14:54:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (15389)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (15392)WARNING: value z3 for option sas not known
% 0.20/0.38 % (15393)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (15390)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (15394)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.38 % (15395)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.38 % (15392)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38 % (15396)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38 % (15391)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39 TRYING [1,1]
% 0.20/0.39 TRYING [2,1]
% 0.20/0.40 TRYING [3,1]
% 0.20/0.41 TRYING [1]
% 0.20/0.42 % (15394)First to succeed.
% 0.20/0.42 TRYING [2]
% 0.20/0.42 % (15395)Also succeeded, but the first one will report.
% 0.20/0.43 % (15394)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15389"
% 0.20/0.43 % (15394)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (15394)------------------------------
% 0.20/0.44 % (15394)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.44 % (15394)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (15394)Memory used [KB]: 1673
% 0.20/0.44 % (15394)Time elapsed: 0.055 s
% 0.20/0.44 % (15394)Instructions burned: 89 (million)
% 0.20/0.44 % (15389)Success in time 0.073 s
%------------------------------------------------------------------------------