TSTP Solution File: NUM924+5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM924+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:14:27 EDT 2024
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 350
% Syntax : Number of formulae : 1072 ( 319 unt; 0 def)
% Number of atoms : 2648 ( 538 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2577 (1001 ~; 990 |; 120 &)
% ( 327 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 227 ( 225 usr; 211 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 1493 (1491 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3100,plain,
$false,
inference(avatar_sat_refutation,[],[f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f741,f745,f749,f754,f759,f764,f769,f774,f779,f784,f788,f793,f798,f804,f810,f814,f818,f822,f826,f835,f853,f857,f861,f865,f880,f884,f888,f892,f900,f905,f909,f913,f917,f933,f937,f941,f946,f950,f954,f958,f962,f966,f970,f974,f978,f982,f987,f991,f995,f999,f1058,f1064,f1068,f1075,f1080,f1086,f1090,f1094,f1098,f1102,f1107,f1111,f1115,f1119,f1123,f1127,f1131,f1135,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1213,f1245,f1304,f1308,f1312,f1316,f1320,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1361,f1365,f1515,f1519,f1523,f1527,f1531,f1536,f1540,f1544,f1548,f1552,f1572,f1580,f1584,f1588,f1592,f1596,f1600,f1604,f1608,f1612,f1616,f1620,f1624,f1628,f1632,f1636,f1764,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1846,f1850,f1854,f1858,f1862,f1953,f2020,f2028,f2045,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2082,f2086,f2228,f2243,f2250,f2255,f2264,f2269,f2273,f2277,f2307,f2311,f2315,f2319,f2328,f2336,f2444,f2448,f2461,f2465,f2469,f2473,f2477,f2539,f2543,f2548,f2682,f2686,f2840,f2844,f2882,f2895,f2899,f2925,f2940,f2944,f2972,f2994,f3003,f3022,f3031,f3050,f3054,f3058,f3066,f3070,f3091,f3099]) ).
fof(f3099,plain,
( spl1_37
| ~ spl1_28
| ~ spl1_31
| ~ spl1_32
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(avatar_split_clause,[],[f3098,f3088,f997,f993,f808,f801,f786,f832]) ).
fof(f832,plain,
( spl1_37
<=> ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
fof(f786,plain,
( spl1_28
<=> ! [X0] : number_number_of(int,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f801,plain,
( spl1_31
<=> pls = zero_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f808,plain,
( spl1_32
<=> ! [X0] : pls = times_times(int,pls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f993,plain,
( spl1_66
<=> ! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
fof(f997,plain,
( spl1_67
<=> ! [X0,X1] : plus_plus(int,X1,X0) = plus_plus(int,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
fof(f3088,plain,
( spl1_210
<=> ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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_210])]) ).
fof(f3098,plain,
( ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls)
| ~ spl1_28
| ~ spl1_31
| ~ spl1_32
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3097,f998]) ).
fof(f998,plain,
( ! [X0,X1] : plus_plus(int,X1,X0) = plus_plus(int,X0,X1)
| ~ spl1_67 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f3097,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),pls)
| ~ spl1_28
| ~ spl1_31
| ~ spl1_32
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3096,f809]) ).
fof(f809,plain,
( ! [X0] : pls = times_times(int,pls,X0)
| ~ spl1_32 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f3096,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),times_times(int,pls,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))))
| ~ spl1_28
| ~ spl1_31
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3095,f803]) ).
fof(f803,plain,
( pls = zero_zero(int)
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f3095,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))))
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3094,f787]) ).
fof(f787,plain,
( ! [X0] : number_number_of(int,X0) = X0
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f3094,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))))
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3093,f994]) ).
fof(f994,plain,
( ! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0)
| ~ spl1_66 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f3093,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))))
| ~ spl1_66
| ~ spl1_67
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3092,f998]) ).
fof(f3092,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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_66
| ~ spl1_210 ),
inference(forward_demodulation,[],[f3090,f994]) ).
fof(f3090,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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_210 ),
inference(avatar_component_clause,[],[f3088]) ).
fof(f3091,plain,
spl1_210,
inference(avatar_split_clause,[],[f637,f3088]) ).
fof(f637,plain,
ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),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,[],[f458,f457]) ).
fof(f457,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,[],[f43]) ).
fof(f43,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) ).
fof(f458,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,[],[f42]) ).
fof(f42,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) ).
fof(f3070,plain,
spl1_209,
inference(avatar_split_clause,[],[f491,f3068]) ).
fof(f3068,plain,
( spl1_209
<=> ! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_209])]) ).
fof(f491,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ! [X1,X2] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) ) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X6,X7] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X6,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X7,number_number_of(nat,bit0(bit1(pls))))))
<=> ( zero_zero(X0) != ti(X0,X7)
| zero_zero(X0) != ti(X0,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
fof(f3066,plain,
spl1_208,
inference(avatar_split_clause,[],[f490,f3064]) ).
fof(f3064,plain,
( spl1_208
<=> ! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_208])]) ).
fof(f490,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f3058,plain,
spl1_207,
inference(avatar_split_clause,[],[f487,f3056]) ).
fof(f3056,plain,
( spl1_207
<=> ! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_207])]) ).
fof(f487,plain,
! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X6,X7] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X6,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X7,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) = ti(X0,X7)
& zero_zero(X0) = ti(X0,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
fof(f3054,plain,
spl1_206,
inference(avatar_split_clause,[],[f486,f3052]) ).
fof(f3052,plain,
( spl1_206
<=> ! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_206])]) ).
fof(f486,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f3050,plain,
( ~ spl1_205
| spl1_179
| ~ spl1_64
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1284,f1207,f984,f2333,f3047]) ).
fof(f3047,plain,
( spl1_205
<=> ord_less_eq(int,pls,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_205])]) ).
fof(f2333,plain,
( spl1_179
<=> pls = t ),
introduced(avatar_definition,[new_symbols(naming,[spl1_179])]) ).
fof(f984,plain,
( spl1_64
<=> ord_less_eq(int,t,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
fof(f1207,plain,
( spl1_92
<=> ! [X0,X1] :
( X0 = X1
| ~ ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
fof(f1284,plain,
( pls = t
| ~ ord_less_eq(int,pls,t)
| ~ spl1_64
| ~ spl1_92 ),
inference(resolution,[],[f1208,f986]) ).
fof(f986,plain,
( ord_less_eq(int,t,pls)
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1208,plain,
( ! [X0,X1] :
( ~ ord_less_eq(int,X1,X0)
| X0 = X1
| ~ ord_less_eq(int,X0,X1) )
| ~ spl1_92 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f3031,plain,
( spl1_204
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_203 ),
inference(avatar_split_clause,[],[f3026,f3019,f997,f993,f786,f3028]) ).
fof(f3028,plain,
( spl1_204
<=> plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_204])]) ).
fof(f3019,plain,
( spl1_203
<=> plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_203])]) ).
fof(f3026,plain,
( plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),sK0)
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_203 ),
inference(forward_demodulation,[],[f3025,f998]) ).
fof(f3025,plain,
( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),sK0)
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_203 ),
inference(forward_demodulation,[],[f3024,f787]) ).
fof(f3024,plain,
( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))),sK0)
| ~ spl1_66
| ~ spl1_67
| ~ spl1_203 ),
inference(forward_demodulation,[],[f3023,f994]) ).
fof(f3023,plain,
( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)),sK0)
| ~ spl1_67
| ~ spl1_203 ),
inference(forward_demodulation,[],[f3021,f998]) ).
fof(f3021,plain,
( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sK0)
| ~ spl1_203 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f3022,plain,
spl1_203,
inference(avatar_split_clause,[],[f460,f3019]) ).
fof(f460,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sK0),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f270,f359]) ).
fof(f359,plain,
( ? [X0] : plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),X0)
=> plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),sK0) ),
introduced(choice_axiom,[]) ).
fof(f270,plain,
? [X0] : plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),X0),
inference(ennf_transformation,[],[f162]) ).
fof(f162,plain,
~ ! [X0] : plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) != times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),X0),
inference(rectify,[],[f58]) ).
fof(f58,axiom,
~ ! [X12] : plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) != times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
fof(f3003,plain,
( spl1_202
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_201 ),
inference(avatar_split_clause,[],[f2998,f2991,f997,f993,f786,f3000]) ).
fof(f3000,plain,
( spl1_202
<=> plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_202])]) ).
fof(f2991,plain,
( spl1_201
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_201])]) ).
fof(f2998,plain,
( plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t)
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_201 ),
inference(forward_demodulation,[],[f2997,f787]) ).
fof(f2997,plain,
( plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))),t)
| ~ spl1_66
| ~ spl1_67
| ~ spl1_201 ),
inference(forward_demodulation,[],[f2996,f994]) ).
fof(f2996,plain,
( plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)),t)
| ~ spl1_67
| ~ spl1_201 ),
inference(forward_demodulation,[],[f2995,f998]) ).
fof(f2995,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,number_number_of(nat,bit0(bit1(pls)))))
| ~ spl1_67
| ~ spl1_201 ),
inference(forward_demodulation,[],[f2993,f998]) ).
fof(f2993,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))
| ~ spl1_201 ),
inference(avatar_component_clause,[],[f2991]) ).
fof(f2994,plain,
spl1_201,
inference(avatar_split_clause,[],[f457,f2991]) ).
fof(f2972,plain,
spl1_200,
inference(avatar_split_clause,[],[f516,f2970]) ).
fof(f2970,plain,
( spl1_200
<=> ! [X0,X3,X2,X1] :
( times_times(X0,plus_plus(X0,X1,X2),number_number_of(X0,X3)) = plus_plus(X0,times_times(X0,X1,number_number_of(X0,X3)),times_times(X0,X2,number_number_of(X0,X3)))
| ~ semiring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_200])]) ).
fof(f516,plain,
! [X2,X3,X0,X1] :
( times_times(X0,plus_plus(X0,X1,X2),number_number_of(X0,X3)) = plus_plus(X0,times_times(X0,X1,number_number_of(X0,X3)),times_times(X0,X2,number_number_of(X0,X3)))
| ~ semiring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,plus_plus(X0,X1,X2),number_number_of(X0,X3)) = plus_plus(X0,times_times(X0,X1,number_number_of(X0,X3)),times_times(X0,X2,number_number_of(X0,X3)))
| ~ semiring(X0)
| ~ number(X0) ),
inference(flattening,[],[f312]) ).
fof(f312,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,plus_plus(X0,X1,X2),number_number_of(X0,X3)) = plus_plus(X0,times_times(X0,X1,number_number_of(X0,X3)),times_times(X0,X2,number_number_of(X0,X3)))
| ~ semiring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ( semiring(X0)
& number(X0) )
=> ! [X1,X2,X3] : times_times(X0,plus_plus(X0,X1,X2),number_number_of(X0,X3)) = plus_plus(X0,times_times(X0,X1,number_number_of(X0,X3)),times_times(X0,X2,number_number_of(X0,X3))) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X3] :
( ( semiring(X3)
& number(X3) )
=> ! [X8,X32,X11] : times_times(X3,plus_plus(X3,X8,X32),number_number_of(X3,X11)) = plus_plus(X3,times_times(X3,X8,number_number_of(X3,X11)),times_times(X3,X32,number_number_of(X3,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_left__distrib__number__of) ).
fof(f2944,plain,
spl1_199,
inference(avatar_split_clause,[],[f515,f2942]) ).
fof(f2942,plain,
( spl1_199
<=> ! [X0,X3,X2,X1] :
( times_times(X0,number_number_of(X0,X1),plus_plus(X0,X2,X3)) = plus_plus(X0,times_times(X0,number_number_of(X0,X1),X2),times_times(X0,number_number_of(X0,X1),X3))
| ~ semiring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_199])]) ).
fof(f515,plain,
! [X2,X3,X0,X1] :
( times_times(X0,number_number_of(X0,X1),plus_plus(X0,X2,X3)) = plus_plus(X0,times_times(X0,number_number_of(X0,X1),X2),times_times(X0,number_number_of(X0,X1),X3))
| ~ semiring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,number_number_of(X0,X1),plus_plus(X0,X2,X3)) = plus_plus(X0,times_times(X0,number_number_of(X0,X1),X2),times_times(X0,number_number_of(X0,X1),X3))
| ~ semiring(X0)
| ~ number(X0) ),
inference(flattening,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,number_number_of(X0,X1),plus_plus(X0,X2,X3)) = plus_plus(X0,times_times(X0,number_number_of(X0,X1),X2),times_times(X0,number_number_of(X0,X1),X3))
| ~ semiring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ( semiring(X0)
& number(X0) )
=> ! [X1,X2,X3] : times_times(X0,number_number_of(X0,X1),plus_plus(X0,X2,X3)) = plus_plus(X0,times_times(X0,number_number_of(X0,X1),X2),times_times(X0,number_number_of(X0,X1),X3)) ),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X3] :
( ( semiring(X3)
& number(X3) )
=> ! [X11,X32,X33] : times_times(X3,number_number_of(X3,X11),plus_plus(X3,X32,X33)) = plus_plus(X3,times_times(X3,number_number_of(X3,X11),X32),times_times(X3,number_number_of(X3,X11),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_right__distrib__number__of) ).
fof(f2940,plain,
spl1_198,
inference(avatar_split_clause,[],[f474,f2938]) ).
fof(f2938,plain,
( spl1_198
<=> ! [X2,X0,X1] :
( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_198])]) ).
fof(f474,plain,
! [X2,X0,X1] :
( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0)) ) )
| ~ linord581940658strict(X0) ),
inference(flattening,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0)) ) )
| ~ linord581940658strict(X0) ),
inference(nnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0] :
( ! [X1,X2] :
( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2] :
( ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( linord581940658strict(X0)
=> ! [X6,X7] :
( ord_less_eq(X0,plus_plus(X0,times_times(X0,X6,X6),times_times(X0,X7,X7)),zero_zero(X0))
<=> ( zero_zero(X0) = ti(X0,X7)
& zero_zero(X0) = ti(X0,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_sum__squares__le__zero__iff) ).
fof(f2925,plain,
spl1_197,
inference(avatar_split_clause,[],[f471,f2923]) ).
fof(f2923,plain,
( spl1_197
<=> ! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_197])]) ).
fof(f471,plain,
! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)) ) )
| ~ linord581940658strict(X0) ),
inference(flattening,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)) ) )
| ~ linord581940658strict(X0) ),
inference(nnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X0] :
( linord581940658strict(X0)
=> ! [X6,X7] :
( zero_zero(X0) = plus_plus(X0,times_times(X0,X6,X6),times_times(X0,X7,X7))
<=> ( zero_zero(X0) = ti(X0,X7)
& zero_zero(X0) = ti(X0,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__squares__eq__zero__iff) ).
fof(f2899,plain,
spl1_196,
inference(avatar_split_clause,[],[f493,f2897]) ).
fof(f2897,plain,
( spl1_196
<=> ! [X2,X0,X1] :
( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_196])]) ).
fof(f493,plain,
! [X2,X0,X1] :
( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ! [X1,X2] :
( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(flattening,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ! [X1,X2] :
( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( number_semiring(X0)
=> ! [X1,X2] :
( ord_less_eq(int,pls,X2)
=> ( ord_less_eq(int,pls,X1)
=> plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) ) ) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X0] :
( number_semiring(X0)
=> ! [X27,X11] :
( ord_less_eq(int,pls,X11)
=> ( ord_less_eq(int,pls,X27)
=> plus_plus(X0,number_number_of(X0,X11),number_number_of(X0,X27)) = number_number_of(X0,plus_plus(int,X11,X27)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__add__number__of) ).
fof(f2895,plain,
spl1_195,
inference(avatar_split_clause,[],[f492,f2893]) ).
fof(f2893,plain,
( spl1_195
<=> ! [X2,X0,X1] :
( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_195])]) ).
fof(f492,plain,
! [X2,X0,X1] :
( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ! [X1,X2] :
( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(flattening,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ! [X1,X2] :
( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ ord_less_eq(int,pls,X2) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( number_semiring(X0)
=> ! [X1,X2] :
( ord_less_eq(int,pls,X2)
=> ( ord_less_eq(int,pls,X1)
=> times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) ) ) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( number_semiring(X0)
=> ! [X27,X11] :
( ord_less_eq(int,pls,X11)
=> ( ord_less_eq(int,pls,X27)
=> times_times(X0,number_number_of(X0,X11),number_number_of(X0,X27)) = number_number_of(X0,times_times(int,X11,X27)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_semiring__mult__number__of) ).
fof(f2882,plain,
spl1_194,
inference(avatar_split_clause,[],[f485,f2880]) ).
fof(f2880,plain,
( spl1_194
<=> ! [X2,X0,X1] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_194])]) ).
fof(f485,plain,
! [X2,X0,X1] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ! [X1,X2] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X4,X5] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X5,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
fof(f2844,plain,
spl1_193,
inference(avatar_split_clause,[],[f547,f2842]) ).
fof(f2842,plain,
( spl1_193
<=> ! [X0,X1] :
( 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_193])]) ).
fof(f547,plain,
! [X0,X1] :
( 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,[],[f314]) ).
fof(f314,plain,
! [X0,X1] :
( ( ( ( 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,[],[f212]) ).
fof(f212,plain,
! [X0,X1] :
( ( ~ 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,[],[f124]) ).
fof(f124,axiom,
! [X27,X11] :
( ( ~ ord_less(int,X11,pls)
=> ( ( ~ ord_less(int,X27,pls)
=> plus_plus(nat,number_number_of(nat,X11),number_number_of(nat,X27)) = number_number_of(nat,plus_plus(int,X11,X27)) )
& ( ord_less(int,X27,pls)
=> number_number_of(nat,X11) = plus_plus(nat,number_number_of(nat,X11),number_number_of(nat,X27)) ) ) )
& ( ord_less(int,X11,pls)
=> number_number_of(nat,X27) = plus_plus(nat,number_number_of(nat,X11),number_number_of(nat,X27)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__nat__number__of) ).
fof(f2840,plain,
spl1_192,
inference(avatar_split_clause,[],[f481,f2838]) ).
fof(f2838,plain,
( spl1_192
<=> ! [X0,X3,X2,X1] :
( times_times(X0,number_number_of(X0,X1),times_times(X0,number_number_of(X0,X2),X3)) = times_times(X0,number_number_of(X0,times_times(int,X1,X2)),X3)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_192])]) ).
fof(f481,plain,
! [X2,X3,X0,X1] :
( times_times(X0,number_number_of(X0,X1),times_times(X0,number_number_of(X0,X2),X3)) = times_times(X0,number_number_of(X0,times_times(int,X1,X2)),X3)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,number_number_of(X0,X1),times_times(X0,number_number_of(X0,X2),X3)) = times_times(X0,number_number_of(X0,times_times(int,X1,X2)),X3)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2,X3] : times_times(X0,number_number_of(X0,X1),times_times(X0,number_number_of(X0,X2),X3)) = times_times(X0,number_number_of(X0,times_times(int,X1,X2)),X3) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( number_ring(X0)
=> ! [X11,X10,X14] : times_times(X0,number_number_of(X0,X11),times_times(X0,number_number_of(X0,X10),X14)) = times_times(X0,number_number_of(X0,times_times(int,X11,X10)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult__number__of__left) ).
fof(f2686,plain,
spl1_191,
inference(avatar_split_clause,[],[f473,f2684]) ).
fof(f2684,plain,
( spl1_191
<=> ! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_191])]) ).
fof(f473,plain,
! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f2682,plain,
spl1_190,
inference(avatar_split_clause,[],[f472,f2680]) ).
fof(f2680,plain,
( spl1_190
<=> ! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_190])]) ).
fof(f472,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| ~ ord_less_eq(X0,plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)),zero_zero(X0))
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f2548,plain,
( spl1_189
| ~ spl1_32
| ~ spl1_174 ),
inference(avatar_split_clause,[],[f2377,f2309,f808,f2545]) ).
fof(f2545,plain,
( spl1_189
<=> pls = plus_plus(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_189])]) ).
fof(f2309,plain,
( spl1_174
<=> ! [X2,X0,X1] : 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_174])]) ).
fof(f2377,plain,
( pls = plus_plus(int,pls,pls)
| ~ spl1_32
| ~ spl1_174 ),
inference(forward_demodulation,[],[f2376,f809]) ).
fof(f2376,plain,
( ! [X0,X1] : times_times(int,pls,plus_plus(int,X0,X1)) = plus_plus(int,pls,pls)
| ~ spl1_32
| ~ spl1_174 ),
inference(forward_demodulation,[],[f2353,f809]) ).
fof(f2353,plain,
( ! [X0,X1] : times_times(int,pls,plus_plus(int,X0,X1)) = plus_plus(int,pls,times_times(int,pls,X1))
| ~ spl1_32
| ~ spl1_174 ),
inference(superposition,[],[f2310,f809]) ).
fof(f2310,plain,
( ! [X2,X0,X1] : times_times(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,times_times(int,X0,X1),times_times(int,X0,X2))
| ~ spl1_174 ),
inference(avatar_component_clause,[],[f2309]) ).
fof(f2543,plain,
spl1_188,
inference(avatar_split_clause,[],[f470,f2541]) ).
fof(f2541,plain,
( spl1_188
<=> ! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_188])]) ).
fof(f470,plain,
! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f2539,plain,
spl1_187,
inference(avatar_split_clause,[],[f469,f2537]) ).
fof(f2537,plain,
( spl1_187
<=> ! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_187])]) ).
fof(f469,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f2477,plain,
spl1_186,
inference(avatar_split_clause,[],[f546,f2475]) ).
fof(f2475,plain,
( spl1_186
<=> ! [X0,X1] :
( 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_186])]) ).
fof(f546,plain,
! [X0,X1] :
( 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,[],[f314]) ).
fof(f2473,plain,
spl1_185,
inference(avatar_split_clause,[],[f514,f2471]) ).
fof(f2471,plain,
( spl1_185
<=> ! [X2,X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linorder(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_185])]) ).
fof(f514,plain,
! [X2,X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linorder(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
& ( ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(nnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] :
( ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(flattening,[],[f308]) ).
fof(f308,plain,
! [X0] :
( ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ( linorder(X0)
& number(X0) )
=> ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ( linorder(X0)
& number(X0) )
=> ! [X26,X25] :
( ord_less_eq(X0,number_number_of(X0,X26),number_number_of(X0,X25))
<=> ~ ord_less(X0,number_number_of(X0,X25),number_number_of(X0,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
fof(f2469,plain,
spl1_184,
inference(avatar_split_clause,[],[f513,f2467]) ).
fof(f2467,plain,
( spl1_184
<=> ! [X2,X0,X1] :
( ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_184])]) ).
fof(f513,plain,
! [X2,X0,X1] :
( ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f2465,plain,
spl1_183,
inference(avatar_split_clause,[],[f484,f2463]) ).
fof(f2463,plain,
( spl1_183
<=> ! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_183])]) ).
fof(f484,plain,
! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X1) = zero_zero(X0) )
& ( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X0,X1) != zero_zero(X0) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X0,X1) != zero_zero(X0) ) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X9] :
( ord_less(X0,zero_zero(X0),power_power(X0,X9,number_number_of(nat,bit0(bit1(pls)))))
<=> zero_zero(X0) != ti(X0,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
fof(f2461,plain,
spl1_182,
inference(avatar_split_clause,[],[f483,f2459]) ).
fof(f2459,plain,
( spl1_182
<=> ! [X0,X1] :
( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_182])]) ).
fof(f483,plain,
! [X0,X1] :
( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f2448,plain,
spl1_181,
inference(avatar_split_clause,[],[f468,f2446]) ).
fof(f2446,plain,
( spl1_181
<=> ! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_181])]) ).
fof(f468,plain,
! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ti(X0,X1) != zero_zero(X0) )
& ( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ ring_11004092258visors(X0) ),
inference(nnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
<=> ti(X0,X1) = zero_zero(X0) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
<=> ti(X0,X1) = zero_zero(X0) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X9] :
( zero_zero(X0) = power_power(X0,X9,number_number_of(nat,bit0(bit1(pls))))
<=> zero_zero(X0) = ti(X0,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__eq__power2) ).
fof(f2444,plain,
spl1_180,
inference(avatar_split_clause,[],[f467,f2442]) ).
fof(f2442,plain,
( spl1_180
<=> ! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_180])]) ).
fof(f467,plain,
! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f2336,plain,
( ~ spl1_179
| ~ spl1_31
| spl1_177 ),
inference(avatar_split_clause,[],[f2329,f2321,f801,f2333]) ).
fof(f2321,plain,
( spl1_177
<=> t = zero_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_177])]) ).
fof(f2329,plain,
( pls != t
| ~ spl1_31
| spl1_177 ),
inference(superposition,[],[f2323,f803]) ).
fof(f2323,plain,
( t != zero_zero(int)
| spl1_177 ),
inference(avatar_component_clause,[],[f2321]) ).
fof(f2328,plain,
( ~ spl1_177
| spl1_178 ),
inference(avatar_split_clause,[],[f638,f2325,f2321]) ).
fof(f2325,plain,
( spl1_178
<=> t = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_178])]) ).
fof(f638,plain,
( t = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))
| t != zero_zero(int) ),
inference(inner_rewriting,[],[f459]) ).
fof(f459,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,[],[f269]) ).
fof(f269,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,[],[f44]) ).
fof(f44,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) ).
fof(f2319,plain,
spl1_176,
inference(avatar_split_clause,[],[f632,f2317]) ).
fof(f2317,plain,
( spl1_176
<=> ! [X0,X3,X2,X1] :
( 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_176])]) ).
fof(f632,plain,
! [X2,X3,X0,X1] :
( 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,[],[f358]) ).
fof(f358,plain,
! [X0,X1,X2,X3] :
( 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,[],[f357]) ).
fof(f357,plain,
! [X0,X1,X2,X3] :
( 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,[],[f268]) ).
fof(f268,plain,
! [X0,X1,X2,X3] :
( 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,[],[f96]) ).
fof(f96,axiom,
! [X28,X14,X29,X10] :
( ord_less(int,X29,X10)
=> ( ord_less_eq(int,X28,X14)
=> ord_less(int,plus_plus(int,X29,X28),plus_plus(int,X10,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zadd__zless__mono) ).
fof(f2315,plain,
spl1_175,
inference(avatar_split_clause,[],[f598,f2313]) ).
fof(f2313,plain,
( spl1_175
<=> ! [X2,X0,X1] : 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_175])]) ).
fof(f598,plain,
! [X2,X0,X1] : 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,[],[f242]) ).
fof(f242,plain,
! [X0,X1,X2] : times_times(int,plus_plus(int,X0,X1),X2) = plus_plus(int,times_times(int,X0,X2),times_times(int,X1,X2)),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X17,X18,X10] : times_times(int,plus_plus(int,X17,X18),X10) = plus_plus(int,times_times(int,X17,X10),times_times(int,X18,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zadd__zmult__distrib) ).
fof(f2311,plain,
spl1_174,
inference(avatar_split_clause,[],[f597,f2309]) ).
fof(f597,plain,
! [X2,X0,X1] : 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,[],[f241]) ).
fof(f241,plain,
! [X0,X1,X2] : times_times(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,times_times(int,X0,X1),times_times(int,X0,X2)),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X10,X17,X18] : times_times(int,X10,plus_plus(int,X17,X18)) = plus_plus(int,times_times(int,X10,X17),times_times(int,X10,X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zadd__zmult__distrib2) ).
fof(f2307,plain,
spl1_173,
inference(avatar_split_clause,[],[f596,f2305]) ).
fof(f2305,plain,
( spl1_173
<=> ! [X2,X0,X1] : 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_173])]) ).
fof(f596,plain,
! [X2,X0,X1] : 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,[],[f240]) ).
fof(f240,plain,
! [X0,X1,X2] : power_power(int,X0,plus_plus(nat,X1,X2)) = times_times(int,power_power(int,X0,X1),power_power(int,X0,X2)),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X4,X5,X14] : power_power(int,X4,plus_plus(nat,X5,X14)) = times_times(int,power_power(int,X4,X5),power_power(int,X4,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zpower__zadd__distrib) ).
fof(f2277,plain,
spl1_172,
inference(avatar_split_clause,[],[f479,f2275]) ).
fof(f2275,plain,
( spl1_172
<=> ! [X2,X0,X1] :
( number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_172])]) ).
fof(f479,plain,
! [X2,X0,X1] :
( number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ! [X1,X2] : number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2] : number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( number_ring(X0)
=> ! [X11,X10] : number_number_of(X0,times_times(int,X11,X10)) = times_times(X0,number_number_of(X0,X11),number_number_of(X0,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_number__of__mult) ).
fof(f2273,plain,
spl1_171,
inference(avatar_split_clause,[],[f478,f2271]) ).
fof(f2271,plain,
( spl1_171
<=> ! [X0,X1] :
( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls)))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_171])]) ).
fof(f478,plain,
! [X0,X1] :
( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls)))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ! [X1] : plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls)))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f173]) ).
fof(f173,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( number_ring(X0)
=> ! [X11] : plus_plus(X0,number_number_of(X0,X11),one_one(X0)) = number_number_of(X0,plus_plus(int,X11,bit1(pls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__special_I3_J) ).
fof(f2269,plain,
spl1_170,
inference(avatar_split_clause,[],[f477,f2267]) ).
fof(f2267,plain,
( spl1_170
<=> ! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_170])]) ).
fof(f477,plain,
! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ! [X1] : plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( number_ring(X0)
=> ! [X10] : plus_plus(X0,one_one(X0),number_number_of(X0,X10)) = number_number_of(X0,plus_plus(int,bit1(pls),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__special_I2_J) ).
fof(f2264,plain,
( spl1_169
| ~ spl1_28
| ~ spl1_31
| ~ spl1_66
| ~ spl1_67
| ~ spl1_168 ),
inference(avatar_split_clause,[],[f2259,f2252,f997,f993,f801,f786,f2261]) ).
fof(f2261,plain,
( spl1_169
<=> ord_less(int,pls,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_169])]) ).
fof(f2252,plain,
( spl1_168
<=> 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_168])]) ).
fof(f2259,plain,
( ord_less(int,pls,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))
| ~ spl1_28
| ~ spl1_31
| ~ spl1_66
| ~ spl1_67
| ~ spl1_168 ),
inference(forward_demodulation,[],[f2258,f803]) ).
fof(f2258,plain,
( ord_less(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_168 ),
inference(forward_demodulation,[],[f2257,f787]) ).
fof(f2257,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_66
| ~ spl1_67
| ~ spl1_168 ),
inference(forward_demodulation,[],[f2256,f994]) ).
fof(f2256,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_67
| ~ spl1_168 ),
inference(forward_demodulation,[],[f2254,f998]) ).
fof(f2254,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_168 ),
inference(avatar_component_clause,[],[f2252]) ).
fof(f2255,plain,
spl1_168,
inference(avatar_split_clause,[],[f456,f2252]) ).
fof(f456,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,[],[f46]) ).
fof(f46,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) ).
fof(f2250,plain,
( spl1_167
| ~ spl1_67
| ~ spl1_166 ),
inference(avatar_split_clause,[],[f2245,f2240,f997,f2247]) ).
fof(f2247,plain,
( spl1_167
<=> twoSqu33214720sum2sq(plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_167])]) ).
fof(f2240,plain,
( spl1_166
<=> twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
fof(f2245,plain,
( twoSqu33214720sum2sq(plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))))
| ~ spl1_67
| ~ spl1_166 ),
inference(forward_demodulation,[],[f2244,f998]) ).
fof(f2244,plain,
( twoSqu33214720sum2sq(plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)))
| ~ spl1_166 ),
inference(forward_demodulation,[],[f2242,f457]) ).
fof(f2242,plain,
( twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ~ spl1_166 ),
inference(avatar_component_clause,[],[f2240]) ).
fof(f2243,plain,
spl1_166,
inference(avatar_split_clause,[],[f455,f2240]) ).
fof(f455,plain,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
twoSqu33214720sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_qf1pt) ).
fof(f2228,plain,
( spl1_165
| ~ spl1_11
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f1004,f939,f702,f2225]) ).
fof(f2225,plain,
( spl1_165
<=> zero_zero(nat) = ti(nat,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
fof(f702,plain,
( spl1_11
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f939,plain,
( spl1_53
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
fof(f1004,plain,
( zero_zero(nat) = ti(nat,zero_zero(nat))
| ~ spl1_11
| ~ spl1_53 ),
inference(resolution,[],[f940,f704]) ).
fof(f704,plain,
( semiring_1(nat)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f940,plain,
( ! [X0] :
( ~ semiring_1(X0)
| zero_zero(X0) = ti(X0,zero_zero(X0)) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f939]) ).
fof(f2086,plain,
spl1_164,
inference(avatar_split_clause,[],[f588,f2084]) ).
fof(f2084,plain,
( spl1_164
<=> ! [X0,X1] :
( 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_164])]) ).
fof(f588,plain,
! [X0,X1] :
( 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,[],[f407]) ).
fof(f407,plain,
! [X0,X1] :
( ( 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,[],[f406]) ).
fof(f406,plain,
! [X0,X1] :
( ( 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,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( 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,[],[f234]) ).
fof(f234,plain,
! [X0,X1] :
( 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,[],[f116]) ).
fof(f116,axiom,
! [X26,X31] :
( ord_less(nat,number_number_of(nat,X26),number_number_of(nat,X31))
<=> ( ord_less(int,X26,X31)
& ( ord_less(int,X26,X31)
=> ord_less(int,pls,X31) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__nat__number__of) ).
fof(f2082,plain,
( spl1_163
| ~ spl1_11
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f1002,f935,f702,f2079]) ).
fof(f2079,plain,
( spl1_163
<=> one_one(nat) = ti(nat,one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
fof(f935,plain,
( spl1_52
<=> ! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
fof(f1002,plain,
( one_one(nat) = ti(nat,one_one(nat))
| ~ spl1_11
| ~ spl1_52 ),
inference(resolution,[],[f936,f704]) ).
fof(f936,plain,
( ! [X0] :
( ~ semiring_1(X0)
| one_one(X0) = ti(X0,one_one(X0)) )
| ~ spl1_52 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f2077,plain,
spl1_162,
inference(avatar_split_clause,[],[f585,f2075]) ).
fof(f2075,plain,
( spl1_162
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
fof(f585,plain,
! [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(cnf_transformation,[],[f407]) ).
fof(f2073,plain,
spl1_161,
inference(avatar_split_clause,[],[f545,f2071]) ).
fof(f2071,plain,
( spl1_161
<=> ! [X0,X1] :
( 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_161])]) ).
fof(f545,plain,
! [X0,X1] :
( 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,[],[f314]) ).
fof(f2069,plain,
spl1_160,
inference(avatar_split_clause,[],[f512,f2067]) ).
fof(f2067,plain,
( spl1_160
<=> ! [X2,X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(int,X1,X2)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
fof(f512,plain,
! [X2,X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(int,X1,X2)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(int,X1,X2) )
& ( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0] :
( ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less_eq(int,X1,X2) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less_eq(int,X1,X2) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1,X2] :
( ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less_eq(int,X1,X2) ) ),
inference(rectify,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X6,X7] :
( ord_less_eq(X0,number_number_of(X0,X6),number_number_of(X0,X7))
<=> ord_less_eq(int,X6,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__number__of) ).
fof(f2065,plain,
spl1_159,
inference(avatar_split_clause,[],[f511,f2063]) ).
fof(f2063,plain,
( spl1_159
<=> ! [X2,X0,X1] :
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_159])]) ).
fof(f511,plain,
! [X2,X0,X1] :
( ord_less_eq(int,X1,X2)
| ~ ord_less_eq(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f2061,plain,
spl1_158,
inference(avatar_split_clause,[],[f508,f2059]) ).
fof(f2059,plain,
( spl1_158
<=> ! [X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
fof(f508,plain,
! [X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0] :
( ! [X1] :
( ( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less_eq(int,X1,bit1(pls)) )
& ( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less_eq(int,X1,bit1(pls)) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X6] :
( ord_less_eq(X0,number_number_of(X0,X6),one_one(X0))
<=> ord_less_eq(int,X6,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__special_I4_J) ).
fof(f2057,plain,
spl1_157,
inference(avatar_split_clause,[],[f507,f2055]) ).
fof(f2055,plain,
( spl1_157
<=> ! [X0,X1] :
( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
fof(f507,plain,
! [X0,X1] :
( ord_less_eq(int,X1,bit1(pls))
| ~ ord_less_eq(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f2053,plain,
spl1_156,
inference(avatar_split_clause,[],[f504,f2051]) ).
fof(f2051,plain,
( spl1_156
<=> ! [X0,X1] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
fof(f504,plain,
! [X0,X1] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1) )
& ( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) ) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X7] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X7))
<=> ord_less_eq(int,bit1(pls),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__special_I2_J) ).
fof(f2049,plain,
spl1_155,
inference(avatar_split_clause,[],[f503,f2047]) ).
fof(f2047,plain,
( spl1_155
<=> ! [X0,X1] :
( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
fof(f503,plain,
! [X0,X1] :
( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f2045,plain,
spl1_154,
inference(avatar_split_clause,[],[f476,f2043]) ).
fof(f2043,plain,
( spl1_154
<=> ! [X2,X0,X1] :
( ord_less_eq(X0,zero_zero(X0),plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)))
| ~ linordered_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
fof(f476,plain,
! [X2,X0,X1] :
( ord_less_eq(X0,zero_zero(X0),plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)))
| ~ linordered_ring(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0] :
( ! [X1,X2] : ord_less_eq(X0,zero_zero(X0),plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2)))
| ~ linordered_ring(X0) ),
inference(ennf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0] :
( linordered_ring(X0)
=> ! [X1,X2] : ord_less_eq(X0,zero_zero(X0),plus_plus(X0,times_times(X0,X1,X1),times_times(X0,X2,X2))) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( linordered_ring(X0)
=> ! [X4,X5] : ord_less_eq(X0,zero_zero(X0),plus_plus(X0,times_times(X0,X4,X4),times_times(X0,X5,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_sum__squares__ge__zero) ).
fof(f2028,plain,
( spl1_153
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_152 ),
inference(avatar_split_clause,[],[f2023,f2017,f997,f993,f786,f2025]) ).
fof(f2025,plain,
( spl1_153
<=> ord_less(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
fof(f2017,plain,
( spl1_152
<=> 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_152])]) ).
fof(f2023,plain,
( ord_less(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_152 ),
inference(forward_demodulation,[],[f2022,f787]) ).
fof(f2022,plain,
( ord_less(int,t,plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))))
| ~ spl1_66
| ~ spl1_67
| ~ spl1_152 ),
inference(forward_demodulation,[],[f2021,f994]) ).
fof(f2021,plain,
( ord_less(int,t,plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)))
| ~ spl1_67
| ~ spl1_152 ),
inference(forward_demodulation,[],[f2019,f998]) ).
fof(f2019,plain,
( ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ spl1_152 ),
inference(avatar_component_clause,[],[f2017]) ).
fof(f2020,plain,
spl1_152,
inference(avatar_split_clause,[],[f454,f2017]) ).
fof(f454,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,[],[f57]) ).
fof(f57,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_17_t__l__p) ).
fof(f1953,plain,
( spl1_151
| ~ spl1_64
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1145,f1088,f984,f1950]) ).
fof(f1950,plain,
( spl1_151
<=> zero_zero(nat) = number_number_of(nat,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
fof(f1088,plain,
( spl1_74
<=> ! [X0] :
( zero_zero(nat) = number_number_of(nat,X0)
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
fof(f1145,plain,
( zero_zero(nat) = number_number_of(nat,t)
| ~ spl1_64
| ~ spl1_74 ),
inference(resolution,[],[f1089,f986]) ).
fof(f1089,plain,
( ! [X0] :
( ~ ord_less_eq(int,X0,pls)
| zero_zero(nat) = number_number_of(nat,X0) )
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f1862,plain,
spl1_150,
inference(avatar_split_clause,[],[f631,f1860]) ).
fof(f1860,plain,
( spl1_150
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
fof(f631,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f355]) ).
fof(f355,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> plus_plus(X3,ti(X3,X1),X2) = plus_plus(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
fof(f1858,plain,
spl1_149,
inference(avatar_split_clause,[],[f630,f1856]) ).
fof(f1856,plain,
( spl1_149
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
fof(f630,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f353]) ).
fof(f353,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> times_times(X3,ti(X3,X1),X2) = times_times(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
fof(f1854,plain,
spl1_148,
inference(avatar_split_clause,[],[f629,f1852]) ).
fof(f1852,plain,
( spl1_148
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
fof(f629,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f351]) ).
fof(f351,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> plus_plus(X3,X1,X2) = plus_plus(X3,X1,ti(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
fof(f1850,plain,
spl1_147,
inference(avatar_split_clause,[],[f628,f1848]) ).
fof(f1848,plain,
( spl1_147
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
fof(f628,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f349]) ).
fof(f349,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> plus_plus(X3,X1,X2) = ti(X3,plus_plus(X3,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(f1846,plain,
spl1_146,
inference(avatar_split_clause,[],[f627,f1844]) ).
fof(f1844,plain,
( spl1_146
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
fof(f627,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> times_times(X3,X1,X2) = times_times(X3,X1,ti(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
fof(f1826,plain,
spl1_145,
inference(avatar_split_clause,[],[f626,f1824]) ).
fof(f1824,plain,
( spl1_145
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
fof(f626,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(flattening,[],[f345]) ).
fof(f345,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0,X1,X2] :
( ( semiring(X2)
& number(X2) )
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X2,X3] :
( ( semiring(X3)
& number(X3) )
=> times_times(X3,X1,X2) = ti(X3,times_times(X3,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
fof(f1822,plain,
spl1_144,
inference(avatar_split_clause,[],[f595,f1820]) ).
fof(f1820,plain,
( spl1_144
<=> ! [X2,X0,X1] : 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_144])]) ).
fof(f595,plain,
! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X17,X18,X19] : plus_plus(int,plus_plus(int,X17,X18),X19) = plus_plus(int,X17,plus_plus(int,X18,X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__assoc) ).
fof(f1818,plain,
spl1_143,
inference(avatar_split_clause,[],[f594,f1816]) ).
fof(f1816,plain,
( spl1_143
<=> ! [X2,X0,X1] : 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_143])]) ).
fof(f594,plain,
! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X4,X5,X14] : plus_plus(int,X4,plus_plus(int,X5,X14)) = plus_plus(int,X5,plus_plus(int,X4,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__left__commute) ).
fof(f1814,plain,
spl1_142,
inference(avatar_split_clause,[],[f593,f1812]) ).
fof(f1812,plain,
( spl1_142
<=> ! [X2,X0,X1] : 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_142])]) ).
fof(f593,plain,
! [X2,X0,X1] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0,X1,X2] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X17,X18,X19] : times_times(int,times_times(int,X17,X18),X19) = times_times(int,X17,times_times(int,X18,X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zmult__assoc) ).
fof(f1810,plain,
spl1_141,
inference(avatar_split_clause,[],[f510,f1808]) ).
fof(f1808,plain,
( spl1_141
<=> ! [X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
fof(f510,plain,
! [X0,X1] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ! [X1] :
( ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls) )
& ( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) ) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X6] :
( ord_less_eq(X0,number_number_of(X0,X6),zero_zero(X0))
<=> ord_less_eq(int,X6,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__special_I3_J) ).
fof(f1806,plain,
spl1_140,
inference(avatar_split_clause,[],[f509,f1804]) ).
fof(f1804,plain,
( spl1_140
<=> ! [X0,X1] :
( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
fof(f509,plain,
! [X0,X1] :
( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f1802,plain,
spl1_139,
inference(avatar_split_clause,[],[f506,f1800]) ).
fof(f1800,plain,
( spl1_139
<=> ! [X0,X1] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
fof(f506,plain,
! [X0,X1] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,pls,X1) )
& ( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ! [X1] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,pls,X1) ) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X7] :
( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X7))
<=> ord_less_eq(int,pls,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__special_I1_J) ).
fof(f1798,plain,
spl1_138,
inference(avatar_split_clause,[],[f505,f1796]) ).
fof(f1796,plain,
( spl1_138
<=> ! [X0,X1] :
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
fof(f505,plain,
! [X0,X1] :
( ord_less_eq(int,pls,X1)
| ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f1764,plain,
( spl1_137
| ~ spl1_88
| ~ spl1_127 ),
inference(avatar_split_clause,[],[f1649,f1598,f1191,f1761]) ).
fof(f1761,plain,
( spl1_137
<=> pls = bit0(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
fof(f1191,plain,
( spl1_88
<=> ! [X0,X1] : times_times(int,bit0(X0),X1) = bit0(times_times(int,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
fof(f1598,plain,
( spl1_127
<=> ! [X0] : pls = times_times(int,X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
fof(f1649,plain,
( pls = bit0(pls)
| ~ spl1_88
| ~ spl1_127 ),
inference(forward_demodulation,[],[f1646,f1599]) ).
fof(f1599,plain,
( ! [X0] : pls = times_times(int,X0,pls)
| ~ spl1_127 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f1646,plain,
( ! [X0] : bit0(pls) = times_times(int,bit0(X0),pls)
| ~ spl1_88
| ~ spl1_127 ),
inference(superposition,[],[f1192,f1599]) ).
fof(f1192,plain,
( ! [X0,X1] : times_times(int,bit0(X0),X1) = bit0(times_times(int,X0,X1))
| ~ spl1_88 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1636,plain,
spl1_136,
inference(avatar_split_clause,[],[f625,f1634]) ).
fof(f1634,plain,
( spl1_136
<=> ! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
fof(f625,plain,
! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f417]) ).
fof(f417,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1) ) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(nnf_transformation,[],[f344]) ).
fof(f344,plain,
! [X0,X1,X2] :
( ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(flattening,[],[f343]) ).
fof(f343,plain,
! [X0,X1,X2] :
( ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ( linorder(X2)
& number(X2) )
=> ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X1,X2,X0] :
( ( linorder(X0)
& number(X0) )
=> ( ord_less(X0,ti(X0,X1),X2)
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg1) ).
fof(f1632,plain,
spl1_135,
inference(avatar_split_clause,[],[f624,f1630]) ).
fof(f1630,plain,
( spl1_135
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
fof(f624,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f417]) ).
fof(f1628,plain,
spl1_134,
inference(avatar_split_clause,[],[f623,f1626]) ).
fof(f1626,plain,
( spl1_134
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
fof(f623,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f416]) ).
fof(f416,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1)) ) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(nnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0,X1,X2] :
( ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(flattening,[],[f341]) ).
fof(f341,plain,
! [X0,X1,X2] :
( ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ( linorder(X2)
& number(X2) )
=> ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1,X2,X0] :
( ( linorder(X0)
& number(X0) )
=> ( ord_less(X0,X1,ti(X0,X2))
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg2) ).
fof(f1624,plain,
spl1_133,
inference(avatar_split_clause,[],[f622,f1622]) ).
fof(f1622,plain,
( spl1_133
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
fof(f622,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f416]) ).
fof(f1620,plain,
spl1_132,
inference(avatar_split_clause,[],[f621,f1618]) ).
fof(f1618,plain,
( spl1_132
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
fof(f621,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f415]) ).
fof(f415,plain,
! [X0,X1,X2] :
( ( ( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1) )
& ( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1) ) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(nnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,ti(X2,X0),X1)
<=> ord_less_eq(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(flattening,[],[f339]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,ti(X2,X0),X1)
<=> ord_less_eq(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ( linorder(X2)
& number(X2) )
=> ( ord_less_eq(X2,ti(X2,X0),X1)
<=> ord_less_eq(X2,X0,X1) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X1,X2,X0] :
( ( linorder(X0)
& number(X0) )
=> ( ord_less_eq(X0,ti(X0,X1),X2)
<=> ord_less_eq(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg1) ).
fof(f1616,plain,
spl1_131,
inference(avatar_split_clause,[],[f620,f1614]) ).
fof(f1614,plain,
( spl1_131
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
fof(f620,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f415]) ).
fof(f1612,plain,
spl1_130,
inference(avatar_split_clause,[],[f619,f1610]) ).
fof(f1610,plain,
( spl1_130
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
fof(f619,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1)
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f414]) ).
fof(f414,plain,
! [X0,X1,X2] :
( ( ( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1) )
& ( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1)) ) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(nnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,X0,ti(X2,X1))
<=> ord_less_eq(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(flattening,[],[f337]) ).
fof(f337,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,X0,ti(X2,X1))
<=> ord_less_eq(X2,X0,X1) )
| ~ linorder(X2)
| ~ number(X2) ),
inference(ennf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ( linorder(X2)
& number(X2) )
=> ( ord_less_eq(X2,X0,ti(X2,X1))
<=> ord_less_eq(X2,X0,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X1,X2,X0] :
( ( linorder(X0)
& number(X0) )
=> ( ord_less_eq(X0,X1,ti(X0,X2))
<=> ord_less_eq(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg2) ).
fof(f1608,plain,
spl1_129,
inference(avatar_split_clause,[],[f618,f1606]) ).
fof(f1606,plain,
( spl1_129
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1))
| ~ linorder(X2)
| ~ number(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
fof(f618,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1))
| ~ linorder(X2)
| ~ number(X2) ),
inference(cnf_transformation,[],[f414]) ).
fof(f1604,plain,
spl1_128,
inference(avatar_split_clause,[],[f616,f1602]) ).
fof(f1602,plain,
( spl1_128
<=> ! [X2,X0,X1] :
( 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_128])]) ).
fof(f616,plain,
! [X2,X0,X1] :
( ord_less_eq(int,plus_plus(int,X0,X1),plus_plus(int,X0,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0,X1,X2] :
( ord_less_eq(int,plus_plus(int,X0,X1),plus_plus(int,X0,X2))
| ~ ord_less_eq(int,X1,X2) ),
inference(ennf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ord_less_eq(int,X1,X2)
=> ord_less_eq(int,plus_plus(int,X0,X1),plus_plus(int,X0,X2)) ),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X13,X20,X21] :
( ord_less_eq(int,X20,X21)
=> ord_less_eq(int,plus_plus(int,X13,X20),plus_plus(int,X13,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zadd__left__mono) ).
fof(f1600,plain,
( spl1_127
| ~ spl1_32
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f1043,f993,f808,f1598]) ).
fof(f1043,plain,
( ! [X0] : pls = times_times(int,X0,pls)
| ~ spl1_32
| ~ spl1_66 ),
inference(superposition,[],[f994,f809]) ).
fof(f1596,plain,
spl1_126,
inference(avatar_split_clause,[],[f501,f1594]) ).
fof(f1594,plain,
( spl1_126
<=> ! [X2,X0,X1] :
( X1 = X2
| number_number_of(X0,X1) != number_number_of(X0,X2)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
fof(f501,plain,
! [X2,X0,X1] :
( X1 = X2
| number_number_of(X0,X1) != number_number_of(X0,X2)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1,X2] :
( ( number_number_of(X0,X1) = number_number_of(X0,X2)
| X1 != X2 )
& ( X1 = X2
| number_number_of(X0,X1) != number_number_of(X0,X2) ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 ) ),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X0] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X6,X7] :
( number_number_of(X0,X6) = number_number_of(X0,X7)
<=> X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_eq__number__of) ).
fof(f1592,plain,
spl1_125,
inference(avatar_split_clause,[],[f497,f1590]) ).
fof(f1590,plain,
( spl1_125
<=> ! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
fof(f497,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( semiring_1(X0)
=> zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_zero__power2) ).
fof(f1588,plain,
spl1_124,
inference(avatar_split_clause,[],[f496,f1586]) ).
fof(f1586,plain,
( spl1_124
<=> ! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
fof(f496,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( semiring_1(X0)
=> one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
fof(f1584,plain,
spl1_123,
inference(avatar_split_clause,[],[f482,f1582]) ).
fof(f1582,plain,
( spl1_123
<=> ! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X8] : ~ ord_less(X0,power_power(X0,X8,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
fof(f1580,plain,
( spl1_122
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_121 ),
inference(avatar_split_clause,[],[f1575,f1569,f997,f993,f786,f1577]) ).
fof(f1577,plain,
( spl1_122
<=> zprime(plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
fof(f1569,plain,
( spl1_121
<=> zprime(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])]) ).
fof(f1575,plain,
( zprime(plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))
| ~ spl1_28
| ~ spl1_66
| ~ spl1_67
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1574,f787]) ).
fof(f1574,plain,
( zprime(plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))))
| ~ spl1_66
| ~ spl1_67
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1573,f994]) ).
fof(f1573,plain,
( zprime(plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)))
| ~ spl1_67
| ~ spl1_121 ),
inference(forward_demodulation,[],[f1571,f998]) ).
fof(f1571,plain,
( zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ spl1_121 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f1572,plain,
spl1_121,
inference(avatar_split_clause,[],[f453,f1569]) ).
fof(f453,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
zprime(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_p) ).
fof(f1552,plain,
spl1_120,
inference(avatar_split_clause,[],[f615,f1550]) ).
fof(f1550,plain,
( spl1_120
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
fof(f615,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_1(X2) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_1(X2) ),
inference(ennf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( semiring_1(X2)
=> power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X1,X2,X0] :
( semiring_1(X0)
=> power_power(X0,ti(X0,X1),X2) = power_power(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
fof(f1548,plain,
spl1_119,
inference(avatar_split_clause,[],[f614,f1546]) ).
fof(f1546,plain,
( spl1_119
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
fof(f614,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_1(X2) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_1(X2) ),
inference(ennf_transformation,[],[f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( semiring_1(X2)
=> power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1)) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X1,X2,X0] :
( semiring_1(X0)
=> power_power(X0,X1,X2) = ti(X0,power_power(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
fof(f1544,plain,
spl1_118,
inference(avatar_split_clause,[],[f613,f1542]) ).
fof(f1542,plain,
( spl1_118
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
fof(f613,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_1(X2) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_1(X2) ),
inference(ennf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0,X1,X2] :
( semiring_1(X2)
=> power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1)) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X1,X2,X0] :
( semiring_1(X0)
=> power_power(X0,X1,X2) = power_power(X0,X1,ti(nat,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg2) ).
fof(f1540,plain,
spl1_117,
inference(avatar_split_clause,[],[f604,f1538]) ).
fof(f1538,plain,
( spl1_117
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
fof(f604,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> plus_plus(X0,ti(X0,X1),X2) = plus_plus(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
fof(f1536,plain,
( spl1_116
| ~ spl1_48
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1321,f1242,f907,f1533]) ).
fof(f1533,plain,
( spl1_116
<=> ord_less_eq(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
fof(f907,plain,
( spl1_48
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
fof(f1242,plain,
( spl1_94
<=> ord_less(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
fof(f1321,plain,
( ord_less_eq(int,pls,one_one(int))
| ~ spl1_48
| ~ spl1_94 ),
inference(resolution,[],[f1244,f908]) ).
fof(f908,plain,
( ! [X0,X1] :
( ~ ord_less(int,X0,X1)
| ord_less_eq(int,X0,X1) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1244,plain,
( ord_less(int,pls,one_one(int))
| ~ spl1_94 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f1531,plain,
spl1_115,
inference(avatar_split_clause,[],[f603,f1529]) ).
fof(f1529,plain,
( spl1_115
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
fof(f603,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> times_times(X0,ti(X0,X1),X2) = times_times(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
fof(f1527,plain,
spl1_114,
inference(avatar_split_clause,[],[f602,f1525]) ).
fof(f1525,plain,
( spl1_114
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
fof(f602,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> plus_plus(X0,X1,X2) = plus_plus(X0,X1,ti(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
fof(f1523,plain,
spl1_113,
inference(avatar_split_clause,[],[f601,f1521]) ).
fof(f1521,plain,
( spl1_113
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
fof(f601,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> plus_plus(X0,X1,X2) = ti(X0,plus_plus(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(f1519,plain,
spl1_112,
inference(avatar_split_clause,[],[f600,f1517]) ).
fof(f1517,plain,
( spl1_112
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
fof(f600,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> times_times(X0,X1,X2) = times_times(X0,X1,ti(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
fof(f1515,plain,
spl1_111,
inference(avatar_split_clause,[],[f599,f1513]) ).
fof(f1513,plain,
( spl1_111
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
fof(f599,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> times_times(X0,X1,X2) = ti(X0,times_times(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
fof(f1365,plain,
( spl1_110
| ~ spl1_16
| ~ spl1_28
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1267,f1199,f786,f727,f1363]) ).
fof(f1363,plain,
( spl1_110
<=> ! [X0] : ti(int,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
fof(f727,plain,
( spl1_16
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f1199,plain,
( spl1_90
<=> ! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
fof(f1267,plain,
( ! [X0] : ti(int,X0) = X0
| ~ spl1_16
| ~ spl1_28
| ~ spl1_90 ),
inference(forward_demodulation,[],[f1266,f787]) ).
fof(f1266,plain,
( ! [X0] : number_number_of(int,X0) = ti(int,number_number_of(int,X0))
| ~ spl1_16
| ~ spl1_90 ),
inference(resolution,[],[f1200,f729]) ).
fof(f729,plain,
( number(int)
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f1200,plain,
( ! [X0,X1] :
( ~ number(X1)
| number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0)) )
| ~ spl1_90 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1361,plain,
spl1_109,
inference(avatar_split_clause,[],[f617,f1359]) ).
fof(f1359,plain,
( spl1_109
<=> ! [X2,X0,X1] :
( 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_109])]) ).
fof(f617,plain,
! [X2,X0,X1] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X2,X0)
| ~ ord_less_eq(int,X1,X2) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0,X1,X2] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X2,X0)
| ~ ord_less_eq(int,X1,X2) ),
inference(flattening,[],[f335]) ).
fof(f335,plain,
! [X0,X1,X2] :
( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X2,X0)
| ~ ord_less_eq(int,X1,X2) ),
inference(ennf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ord_less_eq(int,X1,X2)
=> ( ord_less_eq(int,X2,X0)
=> ord_less_eq(int,X1,X0) ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X13,X20,X21] :
( ord_less_eq(int,X20,X21)
=> ( ord_less_eq(int,X21,X13)
=> ord_less_eq(int,X20,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zle__trans) ).
fof(f1357,plain,
spl1_108,
inference(avatar_split_clause,[],[f612,f1355]) ).
fof(f1355,plain,
( spl1_108
<=> ! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
fof(f612,plain,
! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f413]) ).
fof(f413,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1) ) )
| ~ linordered_idom(X2) ),
inference(nnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0,X1,X2] :
( ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) )
| ~ linordered_idom(X2) ),
inference(ennf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0,X1,X2] :
( linordered_idom(X2)
=> ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X1,X2,X0] :
( linordered_idom(X0)
=> ( ord_less(X0,ti(X0,X1),X2)
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
fof(f1353,plain,
spl1_107,
inference(avatar_split_clause,[],[f611,f1351]) ).
fof(f1351,plain,
( spl1_107
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
fof(f611,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f413]) ).
fof(f1349,plain,
spl1_106,
inference(avatar_split_clause,[],[f610,f1347]) ).
fof(f1347,plain,
( spl1_106
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
fof(f610,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1)) ) )
| ~ linordered_idom(X2) ),
inference(nnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0,X1,X2] :
( ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) )
| ~ linordered_idom(X2) ),
inference(ennf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( linordered_idom(X2)
=> ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X1,X2,X0] :
( linordered_idom(X0)
=> ( ord_less(X0,X1,ti(X0,X2))
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg2) ).
fof(f1345,plain,
spl1_105,
inference(avatar_split_clause,[],[f609,f1343]) ).
fof(f1343,plain,
( spl1_105
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
fof(f609,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f1341,plain,
spl1_104,
inference(avatar_split_clause,[],[f608,f1339]) ).
fof(f1339,plain,
( spl1_104
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1)
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
fof(f608,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1)
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f411]) ).
fof(f411,plain,
! [X0,X1,X2] :
( ( ( ord_less_eq(X2,ti(X2,X0),X1)
| ~ ord_less_eq(X2,X0,X1) )
& ( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1) ) )
| ~ linordered_ring(X2) ),
inference(nnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,ti(X2,X0),X1)
<=> ord_less_eq(X2,X0,X1) )
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> ( ord_less_eq(X2,ti(X2,X0),X1)
<=> ord_less_eq(X2,X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> ( ord_less_eq(X0,ti(X0,X1),X2)
<=> ord_less_eq(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg1) ).
fof(f1337,plain,
spl1_103,
inference(avatar_split_clause,[],[f607,f1335]) ).
fof(f1335,plain,
( spl1_103
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
fof(f607,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,ti(X2,X0),X1)
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f411]) ).
fof(f1333,plain,
spl1_102,
inference(avatar_split_clause,[],[f606,f1331]) ).
fof(f1331,plain,
( spl1_102
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1)
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).
fof(f606,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1)
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ( ( ord_less_eq(X2,X0,ti(X2,X1))
| ~ ord_less_eq(X2,X0,X1) )
& ( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1)) ) )
| ~ linordered_ring(X2) ),
inference(nnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0,X1,X2] :
( ( ord_less_eq(X2,X0,ti(X2,X1))
<=> ord_less_eq(X2,X0,X1) )
| ~ linordered_ring(X2) ),
inference(ennf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0,X1,X2] :
( linordered_ring(X2)
=> ( ord_less_eq(X2,X0,ti(X2,X1))
<=> ord_less_eq(X2,X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X1,X2,X0] :
( linordered_ring(X0)
=> ( ord_less_eq(X0,X1,ti(X0,X2))
<=> ord_less_eq(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg2) ).
fof(f1329,plain,
spl1_101,
inference(avatar_split_clause,[],[f605,f1327]) ).
fof(f1327,plain,
( spl1_101
<=> ! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
fof(f605,plain,
! [X2,X0,X1] :
( ord_less_eq(X2,X0,X1)
| ~ ord_less_eq(X2,X0,ti(X2,X1))
| ~ linordered_ring(X2) ),
inference(cnf_transformation,[],[f410]) ).
fof(f1325,plain,
spl1_100,
inference(avatar_split_clause,[],[f590,f1323]) ).
fof(f1323,plain,
( spl1_100
<=> ! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
fof(f590,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( ( 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,[],[f235]) ).
fof(f235,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
<=> ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X25,X24] :
( ord_less(int,X25,plus_plus(int,X24,one_one(int)))
<=> ord_less_eq(int,X25,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zle__add1__eq__le) ).
fof(f1320,plain,
spl1_99,
inference(avatar_split_clause,[],[f589,f1318]) ).
fof(f1318,plain,
( spl1_99
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
fof(f589,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ),
inference(cnf_transformation,[],[f408]) ).
fof(f1316,plain,
spl1_98,
inference(avatar_split_clause,[],[f586,f1314]) ).
fof(f1314,plain,
( spl1_98
<=> ! [X0,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_98])]) ).
fof(f586,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(nat,number_number_of(nat,X0),number_number_of(nat,X1)) ),
inference(cnf_transformation,[],[f407]) ).
fof(f1312,plain,
spl1_97,
inference(avatar_split_clause,[],[f583,f1310]) ).
fof(f1310,plain,
( spl1_97
<=> ! [X0,X1] :
( 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])]) ).
fof(f583,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1] :
( ( 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,[],[f233]) ).
fof(f233,plain,
! [X0,X1] :
( ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1)
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X25,X24] :
( ord_less_eq(int,plus_plus(int,X25,one_one(int)),X24)
<=> ord_less(int,X25,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add1__zle__eq) ).
fof(f1308,plain,
spl1_96,
inference(avatar_split_clause,[],[f553,f1306]) ).
fof(f1306,plain,
( spl1_96
<=> ! [X0,X1] :
( ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1)
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
fof(f553,plain,
! [X0,X1] :
( ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1)
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1)
| ~ ord_less(int,X0,X1) ),
inference(ennf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
=> ord_less_eq(int,plus_plus(int,X0,one_one(int)),X1) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X10,X14] :
( ord_less(int,X10,X14)
=> ord_less_eq(int,plus_plus(int,X10,one_one(int)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zless__imp__add1__zle) ).
fof(f1304,plain,
spl1_95,
inference(avatar_split_clause,[],[f452,f1301]) ).
fof(f1301,plain,
( spl1_95
<=> number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
fof(f452,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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_61_nat__1__add__1) ).
fof(f1245,plain,
( spl1_94
| ~ spl1_19
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f1069,f1066,f743,f1242]) ).
fof(f743,plain,
( spl1_19
<=> ! [X0] : ord_less_eq(int,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f1066,plain,
( spl1_70
<=> ! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less_eq(int,one_one(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
fof(f1069,plain,
( ord_less(int,pls,one_one(int))
| ~ spl1_19
| ~ spl1_70 ),
inference(resolution,[],[f1067,f744]) ).
fof(f744,plain,
( ! [X0] : ord_less_eq(int,X0,X0)
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f1067,plain,
( ! [X0] :
( ~ ord_less_eq(int,one_one(int),X0)
| ord_less(int,pls,X0) )
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f1213,plain,
spl1_93,
inference(avatar_split_clause,[],[f556,f1211]) ).
fof(f1211,plain,
( spl1_93
<=> ! [X0,X1] :
( ord_less(int,X0,X1)
| X0 = X1
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).
fof(f556,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| X0 = X1
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0,X1] :
( ( 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,[],[f390]) ).
fof(f390,plain,
! [X0,X1] :
( ( 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,[],[f219]) ).
fof(f219,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
<=> ( X0 != X1
& ord_less_eq(int,X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X24,X25] :
( ord_less(int,X24,X25)
<=> ( X24 != X25
& ord_less_eq(int,X24,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
fof(f1209,plain,
spl1_92,
inference(avatar_split_clause,[],[f552,f1207]) ).
fof(f552,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X0,X1) ),
inference(flattening,[],[f317]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,X0,X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
=> ( ord_less_eq(int,X1,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X14,X10] :
( ord_less_eq(int,X14,X10)
=> ( ord_less_eq(int,X10,X14)
=> X10 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zle__antisym) ).
fof(f1205,plain,
spl1_91,
inference(avatar_split_clause,[],[f551,f1203]) ).
fof(f1203,plain,
( spl1_91
<=> ! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
fof(f551,plain,
! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ),
inference(ennf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,X0) = number_number_of(X1,ti(int,X0)) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X1,X0] :
( number(X0)
=> number_number_of(X0,ti(int,X1)) = number_number_of(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
fof(f1201,plain,
spl1_90,
inference(avatar_split_clause,[],[f550,f1199]) ).
fof(f550,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(ennf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0)) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X1,X0] :
( number(X0)
=> number_number_of(X0,X1) = ti(X0,number_number_of(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(f1197,plain,
spl1_89,
inference(avatar_split_clause,[],[f549,f1195]) ).
fof(f1195,plain,
( spl1_89
<=> ! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
fof(f549,plain,
! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X4,X5] :
( ord_less(int,X5,X4)
| X4 = X5
| ord_less(int,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_zless__linear) ).
fof(f1193,plain,
spl1_88,
inference(avatar_split_clause,[],[f542,f1191]) ).
fof(f542,plain,
! [X0,X1] : times_times(int,bit0(X0),X1) = bit0(times_times(int,X0,X1)),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0,X1] : times_times(int,bit0(X0),X1) = bit0(times_times(int,X0,X1)),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X13,X30] : times_times(int,bit0(X13),X30) = bit0(times_times(int,X13,X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__Bit0) ).
fof(f1189,plain,
spl1_87,
inference(avatar_split_clause,[],[f538,f1187]) ).
fof(f1187,plain,
( spl1_87
<=> ! [X0] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
fof(f538,plain,
! [X0] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0] :
( ( 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,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X26] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X26))
<=> ord_less(int,pls,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__0__number__of) ).
fof(f1185,plain,
spl1_86,
inference(avatar_split_clause,[],[f537,f1183]) ).
fof(f1183,plain,
( spl1_86
<=> ! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
fof(f537,plain,
! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f389]) ).
fof(f1135,plain,
spl1_85,
inference(avatar_split_clause,[],[f578,f1133]) ).
fof(f1133,plain,
( spl1_85
<=> ! [X0,X1] :
( ord_less(int,bit0(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
fof(f578,plain,
! [X0,X1] :
( ord_less(int,bit0(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f402]) ).
fof(f402,plain,
! [X0,X1] :
( ( 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,[],[f230]) ).
fof(f230,plain,
! [X0,X1] :
( ord_less(int,bit0(X0),bit1(X1))
<=> ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X15,X16] :
( ord_less(int,bit0(X15),bit1(X16))
<=> ord_less_eq(int,X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I15_J) ).
fof(f1131,plain,
spl1_84,
inference(avatar_split_clause,[],[f577,f1129]) ).
fof(f1129,plain,
( spl1_84
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,bit0(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).
fof(f577,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,bit0(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f402]) ).
fof(f1127,plain,
spl1_83,
inference(avatar_split_clause,[],[f574,f1125]) ).
fof(f1125,plain,
( spl1_83
<=> ! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit0(X1))
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).
fof(f574,plain,
! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit0(X1))
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f400]) ).
fof(f400,plain,
! [X0,X1] :
( ( 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,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit0(X1))
<=> ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X15,X16] :
( ord_less_eq(int,bit0(X15),bit0(X16))
<=> ord_less_eq(int,X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I31_J) ).
fof(f1123,plain,
spl1_82,
inference(avatar_split_clause,[],[f573,f1121]) ).
fof(f1121,plain,
( spl1_82
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit0(X0),bit0(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
fof(f573,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit0(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f400]) ).
fof(f1119,plain,
spl1_81,
inference(avatar_split_clause,[],[f570,f1117]) ).
fof(f1117,plain,
( spl1_81
<=> ! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
fof(f570,plain,
! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( ( 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,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( ord_less_eq(int,bit0(X0),bit1(X1))
<=> ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X15,X16] :
( ord_less_eq(int,bit0(X15),bit1(X16))
<=> ord_less_eq(int,X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I32_J) ).
fof(f1115,plain,
spl1_80,
inference(avatar_split_clause,[],[f569,f1113]) ).
fof(f1113,plain,
( spl1_80
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit0(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
fof(f569,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit0(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f398]) ).
fof(f1111,plain,
spl1_79,
inference(avatar_split_clause,[],[f566,f1109]) ).
fof(f1109,plain,
( spl1_79
<=> ! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit0(X1))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
fof(f566,plain,
! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit0(X1))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f396]) ).
fof(f396,plain,
! [X0,X1] :
( ( 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,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit0(X1))
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X22,X23] :
( ord_less_eq(int,bit1(X22),bit0(X23))
<=> ord_less(int,X22,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__eq__int__code_I15_J) ).
fof(f1107,plain,
( ~ spl1_78
| spl1_23
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f1081,f1078,f761,f1104]) ).
fof(f1104,plain,
( spl1_78
<=> ord_less(int,pls,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
fof(f761,plain,
( spl1_23
<=> ord_less_eq(int,one_one(int),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f1078,plain,
( spl1_72
<=> ! [X0] :
( ~ ord_less(int,pls,X0)
| ord_less_eq(int,one_one(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
fof(f1081,plain,
( ~ ord_less(int,pls,t)
| spl1_23
| ~ spl1_72 ),
inference(resolution,[],[f1079,f763]) ).
fof(f763,plain,
( ~ ord_less_eq(int,one_one(int),t)
| spl1_23 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f1079,plain,
( ! [X0] :
( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,pls,X0) )
| ~ spl1_72 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1102,plain,
spl1_77,
inference(avatar_split_clause,[],[f565,f1100]) ).
fof(f1100,plain,
( spl1_77
<=> ! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,bit1(X0),bit0(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
fof(f565,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less_eq(int,bit1(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1098,plain,
spl1_76,
inference(avatar_split_clause,[],[f562,f1096]) ).
fof(f1096,plain,
( spl1_76
<=> ! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_76])]) ).
fof(f562,plain,
! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit1(X1))
| ~ ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f394]) ).
fof(f394,plain,
! [X0,X1] :
( ( 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,[],[f222]) ).
fof(f222,plain,
! [X0,X1] :
( ord_less_eq(int,bit1(X0),bit1(X1))
<=> ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X15,X16] :
( ord_less_eq(int,bit1(X15),bit1(X16))
<=> ord_less_eq(int,X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I34_J) ).
fof(f1094,plain,
spl1_75,
inference(avatar_split_clause,[],[f561,f1092]) ).
fof(f1092,plain,
( spl1_75
<=> ! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit1(X0),bit1(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
fof(f561,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less_eq(int,bit1(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f394]) ).
fof(f1090,plain,
spl1_74,
inference(avatar_split_clause,[],[f534,f1088]) ).
fof(f534,plain,
! [X0] :
( zero_zero(nat) = number_number_of(nat,X0)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f387]) ).
fof(f387,plain,
! [X0] :
( ( 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,[],[f203]) ).
fof(f203,plain,
! [X0] :
( zero_zero(nat) = number_number_of(nat,X0)
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X26] :
( number_number_of(nat,X26) = zero_zero(nat)
<=> ord_less_eq(int,X26,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_eq__number__of__0) ).
fof(f1086,plain,
spl1_73,
inference(avatar_split_clause,[],[f533,f1084]) ).
fof(f1084,plain,
( spl1_73
<=> ! [X0] :
( ord_less_eq(int,X0,pls)
| zero_zero(nat) != number_number_of(nat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
fof(f533,plain,
! [X0] :
( ord_less_eq(int,X0,pls)
| zero_zero(nat) != number_number_of(nat,X0) ),
inference(cnf_transformation,[],[f387]) ).
fof(f1080,plain,
( spl1_72
| ~ spl1_31
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f1076,f1073,f801,f1078]) ).
fof(f1073,plain,
( spl1_71
<=> ! [X0] :
( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
fof(f1076,plain,
( ! [X0] :
( ~ ord_less(int,pls,X0)
| ord_less_eq(int,one_one(int),X0) )
| ~ spl1_31
| ~ spl1_71 ),
inference(forward_demodulation,[],[f1074,f803]) ).
fof(f1074,plain,
( ! [X0] :
( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) )
| ~ spl1_71 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1075,plain,
spl1_71,
inference(avatar_split_clause,[],[f526,f1073]) ).
fof(f526,plain,
! [X0] :
( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0] :
( ( 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,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ord_less_eq(int,one_one(int),X0)
<=> ord_less(int,zero_zero(int),X0) ),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X24] :
( ord_less_eq(int,one_one(int),X24)
<=> ord_less(int,zero_zero(int),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
fof(f1068,plain,
( spl1_70
| ~ spl1_31
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f1059,f1056,f801,f1066]) ).
fof(f1056,plain,
( spl1_68
<=> ! [X0] :
( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
fof(f1059,plain,
( ! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less_eq(int,one_one(int),X0) )
| ~ spl1_31
| ~ spl1_68 ),
inference(forward_demodulation,[],[f1057,f803]) ).
fof(f1057,plain,
( ! [X0] :
( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) )
| ~ spl1_68 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1064,plain,
( spl1_69
| spl1_23
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f918,f898,f761,f1061]) ).
fof(f1061,plain,
( spl1_69
<=> ord_less_eq(int,t,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
fof(f898,plain,
( spl1_46
<=> ! [X0,X1] :
( ord_less_eq(int,X1,X0)
| ord_less_eq(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
fof(f918,plain,
( ord_less_eq(int,t,one_one(int))
| spl1_23
| ~ spl1_46 ),
inference(resolution,[],[f899,f763]) ).
fof(f899,plain,
( ! [X0,X1] :
( ord_less_eq(int,X1,X0)
| ord_less_eq(int,X0,X1) )
| ~ spl1_46 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1058,plain,
spl1_68,
inference(avatar_split_clause,[],[f525,f1056]) ).
fof(f525,plain,
! [X0] :
( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f999,plain,
spl1_67,
inference(avatar_split_clause,[],[f541,f997]) ).
fof(f541,plain,
! [X0,X1] : plus_plus(int,X1,X0) = plus_plus(int,X0,X1),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] : plus_plus(int,X1,X0) = plus_plus(int,X0,X1),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X14,X10] : plus_plus(int,X10,X14) = plus_plus(int,X14,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
fof(f995,plain,
spl1_66,
inference(avatar_split_clause,[],[f540,f993]) ).
fof(f540,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X14,X10] : times_times(int,X14,X10) = times_times(int,X10,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(f991,plain,
spl1_65,
inference(avatar_split_clause,[],[f539,f989]) ).
fof(f989,plain,
( spl1_65
<=> ! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
fof(f539,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X34,X35] : ti(X34,X35) = ti(X34,ti(X34,X35)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
fof(f987,plain,
( spl1_64
| ~ spl1_27
| ~ spl1_31
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f923,f907,f801,f781,f984]) ).
fof(f781,plain,
( spl1_27
<=> ord_less(int,t,zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f923,plain,
( ord_less_eq(int,t,pls)
| ~ spl1_27
| ~ spl1_31
| ~ spl1_48 ),
inference(forward_demodulation,[],[f922,f803]) ).
fof(f922,plain,
( ord_less_eq(int,t,zero_zero(int))
| ~ spl1_27
| ~ spl1_48 ),
inference(resolution,[],[f908,f783]) ).
fof(f783,plain,
( ord_less(int,t,zero_zero(int))
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f982,plain,
spl1_63,
inference(avatar_split_clause,[],[f532,f980]) ).
fof(f980,plain,
( spl1_63
<=> ! [X0] :
( ord_less(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
fof(f532,plain,
! [X0] :
( ord_less(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f386,plain,
! [X0] :
( ( 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,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ord_less(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X15] :
( ord_less(int,pls,bit1(X15))
<=> ord_less_eq(int,pls,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I5_J) ).
fof(f978,plain,
spl1_62,
inference(avatar_split_clause,[],[f531,f976]) ).
fof(f976,plain,
( spl1_62
<=> ! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less(int,pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
fof(f531,plain,
! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f386]) ).
fof(f974,plain,
spl1_61,
inference(avatar_split_clause,[],[f530,f972]) ).
fof(f972,plain,
( spl1_61
<=> ! [X0] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
fof(f530,plain,
! [X0] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f385]) ).
fof(f385,plain,
! [X0] :
( ( 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,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X15] :
( ord_less_eq(int,bit0(X15),pls)
<=> ord_less_eq(int,X15,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I27_J) ).
fof(f970,plain,
spl1_60,
inference(avatar_split_clause,[],[f529,f968]) ).
fof(f968,plain,
( spl1_60
<=> ! [X0] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
fof(f529,plain,
! [X0] :
( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f385]) ).
fof(f966,plain,
spl1_59,
inference(avatar_split_clause,[],[f528,f964]) ).
fof(f964,plain,
( spl1_59
<=> ! [X0] :
( ord_less_eq(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
fof(f528,plain,
! [X0] :
( ord_less_eq(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f384]) ).
fof(f384,plain,
! [X0] :
( ( 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,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ord_less_eq(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X15] :
( ord_less_eq(int,bit1(X15),pls)
<=> ord_less(int,X15,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I29_J) ).
fof(f962,plain,
spl1_58,
inference(avatar_split_clause,[],[f527,f960]) ).
fof(f960,plain,
( spl1_58
<=> ! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
fof(f527,plain,
! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less_eq(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f384]) ).
fof(f958,plain,
spl1_57,
inference(avatar_split_clause,[],[f524,f956]) ).
fof(f956,plain,
( spl1_57
<=> ! [X0] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
fof(f524,plain,
! [X0] :
( ord_less_eq(int,pls,bit0(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X0] :
( ( 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,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ord_less_eq(int,pls,bit0(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X15] :
( ord_less_eq(int,pls,bit0(X15))
<=> ord_less_eq(int,pls,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I21_J) ).
fof(f954,plain,
spl1_56,
inference(avatar_split_clause,[],[f523,f952]) ).
fof(f952,plain,
( spl1_56
<=> ! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
fof(f523,plain,
! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f382]) ).
fof(f950,plain,
spl1_55,
inference(avatar_split_clause,[],[f522,f948]) ).
fof(f948,plain,
( spl1_55
<=> ! [X0] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
fof(f522,plain,
! [X0] :
( ord_less_eq(int,pls,bit1(X0))
| ~ ord_less_eq(int,pls,X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0] :
( ( 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,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ord_less_eq(int,pls,bit1(X0))
<=> ord_less_eq(int,pls,X0) ),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X15] :
( ord_less_eq(int,pls,bit1(X15))
<=> ord_less_eq(int,pls,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I22_J) ).
fof(f946,plain,
spl1_54,
inference(avatar_split_clause,[],[f521,f944]) ).
fof(f944,plain,
( spl1_54
<=> ! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
fof(f521,plain,
! [X0] :
( ord_less_eq(int,pls,X0)
| ~ ord_less_eq(int,pls,bit1(X0)) ),
inference(cnf_transformation,[],[f381]) ).
fof(f941,plain,
spl1_53,
inference(avatar_split_clause,[],[f495,f939]) ).
fof(f495,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( semiring_1(X0)
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
fof(f937,plain,
spl1_52,
inference(avatar_split_clause,[],[f494,f935]) ).
fof(f494,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( semiring_1(X0)
=> one_one(X0) = ti(X0,one_one(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
fof(f933,plain,
spl1_51,
inference(avatar_split_clause,[],[f475,f931]) ).
fof(f931,plain,
( spl1_51
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linordered_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
fof(f475,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linordered_ring(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linordered_ring(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( linordered_ring(X0)
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_res) ).
fof(f917,plain,
spl1_50,
inference(avatar_split_clause,[],[f559,f915]) ).
fof(f915,plain,
( spl1_50
<=> ! [X0,X1] :
( X0 = X1
| bit0(X1) != bit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
fof(f559,plain,
! [X0,X1] :
( X0 = X1
| bit0(X1) != bit0(X0) ),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0,X1] :
( ( bit0(X1) = bit0(X0)
| X0 != X1 )
& ( X0 = X1
| bit0(X1) != bit0(X0) ) ),
inference(nnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0,X1] :
( bit0(X1) = bit0(X0)
<=> X0 = X1 ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X15,X16] :
( bit0(X15) = bit0(X16)
<=> X15 = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_rel__simps_I48_J) ).
fof(f913,plain,
spl1_49,
inference(avatar_split_clause,[],[f557,f911]) ).
fof(f911,plain,
( spl1_49
<=> ! [X0,X1] :
( X0 = X1
| bit1(X1) != bit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
fof(f557,plain,
! [X0,X1] :
( X0 = X1
| bit1(X1) != bit1(X0) ),
inference(cnf_transformation,[],[f392]) ).
fof(f392,plain,
! [X0,X1] :
( ( bit1(X1) = bit1(X0)
| X0 != X1 )
& ( X0 = X1
| bit1(X1) != bit1(X0) ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1] :
( bit1(X1) = bit1(X0)
<=> X0 = X1 ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X15,X16] :
( bit1(X15) = bit1(X16)
<=> X15 = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rel__simps_I51_J) ).
fof(f909,plain,
spl1_48,
inference(avatar_split_clause,[],[f554,f907]) ).
fof(f554,plain,
! [X0,X1] :
( ord_less_eq(int,X0,X1)
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f905,plain,
( spl1_47
| ~ spl1_27
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f805,f801,f781,f902]) ).
fof(f902,plain,
( spl1_47
<=> ord_less(int,t,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
fof(f805,plain,
( ord_less(int,t,pls)
| ~ spl1_27
| ~ spl1_31 ),
inference(superposition,[],[f783,f803]) ).
fof(f900,plain,
spl1_46,
inference(avatar_split_clause,[],[f548,f898]) ).
fof(f548,plain,
! [X0,X1] :
( ord_less_eq(int,X1,X0)
| ord_less_eq(int,X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ord_less_eq(int,X1,X0)
| ord_less_eq(int,X0,X1) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X14,X10] :
( ord_less_eq(int,X10,X14)
| ord_less_eq(int,X14,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zle__linear) ).
fof(f892,plain,
spl1_45,
inference(avatar_split_clause,[],[f466,f890]) ).
fof(f890,plain,
( spl1_45
<=> ! [X0] : times_times(int,one_one(int),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
fof(f466,plain,
! [X0] : times_times(int,one_one(int),X0) = X0,
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0] : times_times(int,one_one(int),X0) = X0,
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X14] : times_times(int,one_one(int),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmult__1) ).
fof(f888,plain,
spl1_44,
inference(avatar_split_clause,[],[f465,f886]) ).
fof(f886,plain,
( spl1_44
<=> ! [X0] : times_times(int,X0,one_one(int)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
fof(f465,plain,
! [X0] : times_times(int,X0,one_one(int)) = X0,
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0] : times_times(int,X0,one_one(int)) = X0,
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X14] : times_times(int,X14,one_one(int)) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
fof(f884,plain,
spl1_43,
inference(avatar_split_clause,[],[f464,f882]) ).
fof(f882,plain,
( spl1_43
<=> ! [X0] : undefined(X0) = ti(X0,undefined(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
fof(f464,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(f880,plain,
spl1_42,
inference(avatar_split_clause,[],[f450,f877]) ).
fof(f877,plain,
( spl1_42
<=> one_one(nat) = number_number_of(nat,bit1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
fof(f450,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(cnf_transformation,[],[f119]) ).
fof(f119,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
fof(f865,plain,
spl1_41,
inference(avatar_split_clause,[],[f424,f863]) ).
fof(f863,plain,
( spl1_41
<=> ! [X0] : bit0(X0) = bit0(ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
fof(f424,plain,
! [X0] : bit0(X0) = bit0(ti(int,X0)),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] : bit0(X0) = bit0(ti(int,X0)),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(f861,plain,
spl1_40,
inference(avatar_split_clause,[],[f423,f859]) ).
fof(f859,plain,
( spl1_40
<=> ! [X0] : bit1(X0) = bit1(ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
fof(f423,plain,
! [X0] : bit1(X0) = bit1(ti(int,X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] : bit1(X0) = bit1(ti(int,X0)),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X1] : bit1(ti(int,X1)) = bit1(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
fof(f857,plain,
spl1_39,
inference(avatar_split_clause,[],[f422,f855]) ).
fof(f855,plain,
( spl1_39
<=> ! [X0] : bit0(X0) = ti(int,bit0(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
fof(f422,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X1] : bit0(X1) = ti(int,bit0(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
fof(f853,plain,
spl1_38,
inference(avatar_split_clause,[],[f421,f851]) ).
fof(f851,plain,
( spl1_38
<=> ! [X0] : bit1(X0) = ti(int,bit1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
fof(f421,plain,
! [X0] : bit1(X0) = ti(int,bit1(X0)),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] : bit1(X0) = ti(int,bit1(X0)),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X1] : bit1(X1) = ti(int,bit1(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
fof(f835,plain,
( ~ spl1_37
| spl1_18
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f806,f801,f738,f832]) ).
fof(f738,plain,
( spl1_18
<=> ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f806,plain,
( ~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls)
| spl1_18
| ~ spl1_31 ),
inference(superposition,[],[f740,f803]) ).
fof(f740,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_18 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f826,plain,
spl1_36,
inference(avatar_split_clause,[],[f520,f824]) ).
fof(f824,plain,
( spl1_36
<=> ! [X0] :
( twoSqu33214720sum2sq(ti(int,X0))
| ~ twoSqu33214720sum2sq(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
fof(f520,plain,
! [X0] :
( twoSqu33214720sum2sq(ti(int,X0))
| ~ twoSqu33214720sum2sq(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ( twoSqu33214720sum2sq(ti(int,X0))
| ~ twoSqu33214720sum2sq(X0) )
& ( twoSqu33214720sum2sq(X0)
| ~ twoSqu33214720sum2sq(ti(int,X0)) ) ),
inference(nnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( twoSqu33214720sum2sq(ti(int,X0))
<=> twoSqu33214720sum2sq(X0) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X1] :
( twoSqu33214720sum2sq(ti(int,X1))
<=> twoSqu33214720sum2sq(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) ).
fof(f822,plain,
spl1_35,
inference(avatar_split_clause,[],[f519,f820]) ).
fof(f820,plain,
( spl1_35
<=> ! [X0] :
( twoSqu33214720sum2sq(X0)
| ~ twoSqu33214720sum2sq(ti(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
fof(f519,plain,
! [X0] :
( twoSqu33214720sum2sq(X0)
| ~ twoSqu33214720sum2sq(ti(int,X0)) ),
inference(cnf_transformation,[],[f380]) ).
fof(f818,plain,
spl1_34,
inference(avatar_split_clause,[],[f518,f816]) ).
fof(f816,plain,
( spl1_34
<=> ! [X0] :
( zprime(ti(int,X0))
| ~ zprime(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
fof(f518,plain,
! [X0] :
( zprime(ti(int,X0))
| ~ zprime(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0] :
( ( zprime(ti(int,X0))
| ~ zprime(X0) )
& ( zprime(X0)
| ~ zprime(ti(int,X0)) ) ),
inference(nnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] :
( zprime(ti(int,X0))
<=> zprime(X0) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X1] :
( zprime(ti(int,X1))
<=> zprime(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
fof(f814,plain,
spl1_33,
inference(avatar_split_clause,[],[f517,f812]) ).
fof(f812,plain,
( spl1_33
<=> ! [X0] :
( zprime(X0)
| ~ zprime(ti(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f517,plain,
! [X0] :
( zprime(X0)
| ~ zprime(ti(int,X0)) ),
inference(cnf_transformation,[],[f379]) ).
fof(f810,plain,
spl1_32,
inference(avatar_split_clause,[],[f463,f808]) ).
fof(f463,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X10] : pls = times_times(int,pls,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(f804,plain,
( spl1_31
| ~ spl1_28
| ~ spl1_30 ),
inference(avatar_split_clause,[],[f799,f795,f786,f801]) ).
fof(f795,plain,
( spl1_30
<=> zero_zero(int) = number_number_of(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f799,plain,
( pls = zero_zero(int)
| ~ spl1_28
| ~ spl1_30 ),
inference(forward_demodulation,[],[f797,f787]) ).
fof(f797,plain,
( zero_zero(int) = number_number_of(int,pls)
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f798,plain,
spl1_30,
inference(avatar_split_clause,[],[f449,f795]) ).
fof(f449,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f137]) ).
fof(f137,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
fof(f793,plain,
spl1_29,
inference(avatar_split_clause,[],[f447,f790]) ).
fof(f790,plain,
( spl1_29
<=> zero_zero(nat) = number_number_of(nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f447,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(cnf_transformation,[],[f97]) ).
fof(f97,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__number__of__Pls) ).
fof(f788,plain,
spl1_28,
inference(avatar_split_clause,[],[f462,f786]) ).
fof(f462,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X13] : number_number_of(int,X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(f784,plain,
spl1_27,
inference(avatar_split_clause,[],[f446,f781]) ).
fof(f446,plain,
ord_less(int,t,zero_zero(int)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
ord_less(int,t,zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
fof(f779,plain,
spl1_26,
inference(avatar_split_clause,[],[f445,f776]) ).
fof(f776,plain,
( spl1_26
<=> ord_less(int,t,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f445,plain,
ord_less(int,t,one_one(int)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
ord_less(int,t,one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
fof(f774,plain,
spl1_25,
inference(avatar_split_clause,[],[f444,f771]) ).
fof(f771,plain,
( spl1_25
<=> m = ti(int,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f444,plain,
m = ti(int,m),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
m = ti(int,m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m_res) ).
fof(f769,plain,
spl1_24,
inference(avatar_split_clause,[],[f443,f766]) ).
fof(f766,plain,
( spl1_24
<=> t = ti(int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f443,plain,
t = ti(int,t),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
t = ti(int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
fof(f764,plain,
~ spl1_23,
inference(avatar_split_clause,[],[f442,f761]) ).
fof(f442,plain,
~ ord_less_eq(int,one_one(int),t),
inference(cnf_transformation,[],[f45]) ).
fof(f45,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) ).
fof(f759,plain,
spl1_22,
inference(avatar_split_clause,[],[f420,f756]) ).
fof(f756,plain,
( spl1_22
<=> pls = ti(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f420,plain,
pls = ti(int,pls),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
pls = ti(int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
fof(f754,plain,
spl1_21,
inference(avatar_split_clause,[],[f419,f751]) ).
fof(f751,plain,
( spl1_21
<=> s = ti(int,s) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f419,plain,
s = ti(int,s),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
s = ti(int,s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_s_____res) ).
fof(f749,plain,
spl1_20,
inference(avatar_split_clause,[],[f634,f747]) ).
fof(f747,plain,
( spl1_20
<=> ! [X1] : ~ ord_less(int,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f634,plain,
! [X1] : ~ ord_less(int,X1,X1),
inference(equality_resolution,[],[f555]) ).
fof(f555,plain,
! [X0,X1] :
( X0 != X1
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f745,plain,
spl1_19,
inference(avatar_split_clause,[],[f461,f743]) ).
fof(f461,plain,
! [X0] : ord_less_eq(int,X0,X0),
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0] : ord_less_eq(int,X0,X0),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X10] : ord_less_eq(int,X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zle__refl) ).
fof(f741,plain,
( ~ spl1_18
| spl1_17 ),
inference(avatar_split_clause,[],[f736,f732,f738]) ).
fof(f732,plain,
( spl1_17
<=> 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_17])]) ).
fof(f736,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_17 ),
inference(forward_demodulation,[],[f734,f541]) ).
fof(f734,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_17 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f735,plain,
~ spl1_17,
inference(avatar_split_clause,[],[f418,f732]) ).
fof(f418,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,[],[f157]) ).
fof(f157,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,[],[f156]) ).
fof(f156,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,[],[f155]) ).
fof(f155,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) ).
fof(f730,plain,
spl1_16,
inference(avatar_split_clause,[],[f440,f727]) ).
fof(f440,plain,
number(int),
inference(cnf_transformation,[],[f148]) ).
fof(f148,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
fof(f725,plain,
spl1_15,
inference(avatar_split_clause,[],[f439,f722]) ).
fof(f722,plain,
( spl1_15
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f439,plain,
number(nat),
inference(cnf_transformation,[],[f153]) ).
fof(f153,axiom,
number(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
fof(f720,plain,
spl1_14,
inference(avatar_split_clause,[],[f438,f717]) ).
fof(f717,plain,
( spl1_14
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f438,plain,
semiring(int),
inference(cnf_transformation,[],[f147]) ).
fof(f147,axiom,
semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
fof(f715,plain,
spl1_13,
inference(avatar_split_clause,[],[f437,f712]) ).
fof(f712,plain,
( spl1_13
<=> semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f437,plain,
semiring(nat),
inference(cnf_transformation,[],[f152]) ).
fof(f152,axiom,
semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
fof(f710,plain,
spl1_12,
inference(avatar_split_clause,[],[f436,f707]) ).
fof(f707,plain,
( spl1_12
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f436,plain,
semiring_1(int),
inference(cnf_transformation,[],[f144]) ).
fof(f144,axiom,
semiring_1(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
fof(f705,plain,
spl1_11,
inference(avatar_split_clause,[],[f435,f702]) ).
fof(f435,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f151]) ).
fof(f151,axiom,
semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(f700,plain,
spl1_10,
inference(avatar_split_clause,[],[f434,f697]) ).
fof(f697,plain,
( spl1_10
<=> linorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f434,plain,
linorder(int),
inference(cnf_transformation,[],[f143]) ).
fof(f143,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(f695,plain,
spl1_9,
inference(avatar_split_clause,[],[f433,f692]) ).
fof(f692,plain,
( spl1_9
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f433,plain,
linorder(nat),
inference(cnf_transformation,[],[f150]) ).
fof(f150,axiom,
linorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(f690,plain,
spl1_8,
inference(avatar_split_clause,[],[f432,f687]) ).
fof(f687,plain,
( spl1_8
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f432,plain,
number_semiring(int),
inference(cnf_transformation,[],[f142]) ).
fof(f142,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
fof(f685,plain,
spl1_7,
inference(avatar_split_clause,[],[f431,f682]) ).
fof(f682,plain,
( spl1_7
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f431,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f149]) ).
fof(f149,axiom,
number_semiring(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(f680,plain,
spl1_6,
inference(avatar_split_clause,[],[f430,f677]) ).
fof(f677,plain,
( spl1_6
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f430,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f141]) ).
fof(f141,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(f675,plain,
spl1_5,
inference(avatar_split_clause,[],[f429,f672]) ).
fof(f672,plain,
( spl1_5
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f429,plain,
number_ring(int),
inference(cnf_transformation,[],[f146]) ).
fof(f146,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(f670,plain,
spl1_4,
inference(avatar_split_clause,[],[f428,f667]) ).
fof(f667,plain,
( spl1_4
<=> linordered_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f428,plain,
linordered_ring(int),
inference(cnf_transformation,[],[f140]) ).
fof(f140,axiom,
linordered_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
fof(f665,plain,
spl1_3,
inference(avatar_split_clause,[],[f427,f662]) ).
fof(f662,plain,
( spl1_3
<=> linord581940658strict(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f427,plain,
linord581940658strict(int),
inference(cnf_transformation,[],[f139]) ).
fof(f139,axiom,
linord581940658strict(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
fof(f660,plain,
spl1_2,
inference(avatar_split_clause,[],[f426,f657]) ).
fof(f657,plain,
( spl1_2
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f426,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f138]) ).
fof(f138,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(f655,plain,
spl1_1,
inference(avatar_split_clause,[],[f425,f652]) ).
fof(f652,plain,
( spl1_1
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f425,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f145]) ).
fof(f145,axiom,
ring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM924+5 : TPTP v8.2.0. Released v5.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 06:00:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (27709)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (27719)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37 % (27716)WARNING: value z3 for option sas not known
% 0.13/0.37 % (27714)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (27717)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (27716)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (27718)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37 % (27715)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (27720)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)
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.45 % (27718)First to succeed.
% 0.20/0.46 TRYING [3]
% 0.20/0.47 % (27718)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27709"
% 0.20/0.47 % (27718)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (27718)------------------------------
% 0.20/0.48 % (27718)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.48 % (27718)Termination reason: Refutation
% 0.20/0.48
% 0.20/0.48 % (27718)Memory used [KB]: 2166
% 0.20/0.48 % (27718)Time elapsed: 0.098 s
% 0.20/0.48 % (27718)Instructions burned: 149 (million)
% 0.20/0.48 % (27709)Success in time 0.116 s
%------------------------------------------------------------------------------