TSTP Solution File: SWV486+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV486+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:55:02 EDT 2024
% Result : Theorem 2.20s 0.65s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 219
% Syntax : Number of formulae : 763 ( 37 unt; 0 def)
% Number of atoms : 3184 ( 309 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 4426 (2005 ~;2142 |; 54 &)
% ( 207 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 208 ( 206 usr; 205 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 951 ( 941 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4326,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f71,f76,f81,f86,f91,f95,f99,f103,f107,f111,f115,f119,f129,f137,f141,f153,f157,f162,f174,f183,f194,f203,f213,f227,f239,f247,f254,f259,f273,f278,f295,f299,f317,f322,f343,f347,f351,f355,f382,f394,f419,f423,f427,f431,f484,f503,f507,f549,f576,f605,f614,f634,f651,f657,f674,f680,f697,f703,f716,f720,f764,f784,f789,f819,f849,f937,f945,f950,f956,f961,f966,f1003,f1042,f1052,f1057,f1096,f1100,f1104,f1109,f1113,f1117,f1154,f1155,f1173,f1190,f1199,f1203,f1215,f1230,f1234,f1262,f1265,f1266,f1274,f1279,f1284,f1308,f1320,f1323,f1332,f1336,f1381,f1441,f1461,f1478,f1482,f1486,f1490,f1494,f1584,f1602,f1617,f1652,f1698,f1705,f1711,f1733,f1737,f1741,f1745,f1749,f1754,f1800,f1856,f1904,f1970,f1991,f2009,f2013,f2021,f2030,f2049,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2110,f2114,f2118,f2122,f2126,f2428,f2432,f2436,f2441,f2544,f2548,f2552,f2631,f2635,f2639,f2643,f2751,f2787,f2859,f2863,f2867,f2871,f2875,f2879,f2902,f3139,f3143,f3144,f3254,f3360,f3407,f3411,f3484,f3489,f3493,f3587,f3620,f3661,f3728,f3733,f3803,f3809,f3815,f3821,f3827,f3833,f3840,f3845,f3859,f3861,f3889,f3908,f3912,f3916,f3920,f3928,f3932,f4071,f4076,f4081,f4086,f4216,f4236,f4240,f4244,f4245,f4325]) ).
fof(f4325,plain,
( ~ spl3_1
| ~ spl3_133
| ~ spl3_67
| ~ spl3_102
| spl3_103
| ~ spl3_3
| ~ spl3_22
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f263,f256,f192,f73,f1314,f1310,f816,f2015,f63]) ).
fof(f63,plain,
( spl3_1
<=> int_leq(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f2015,plain,
( spl3_133
<=> int_leq(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_133])]) ).
fof(f816,plain,
( spl3_67
<=> int_leq(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).
fof(f1310,plain,
( spl3_102
<=> int_less(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_102])]) ).
fof(f1314,plain,
( spl3_103
<=> ! [X0] :
( ~ int_leq(X0,sK0)
| real_zero = a(X0,plus(X0,sK2(sK0,sK1)))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_103])]) ).
fof(f73,plain,
( spl3_3
<=> int_leq(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f192,plain,
( spl3_22
<=> ! [X2,X0,X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X0,X2),n)
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f256,plain,
( spl3_31
<=> sK1 = plus(sK0,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f263,plain,
( ! [X0] :
( ~ int_leq(sK1,n)
| ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK2(sK0,sK1))
| real_zero = a(X0,plus(X0,sK2(sK0,sK1)))
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0) )
| ~ spl3_22
| ~ spl3_31 ),
inference(superposition,[],[f193,f258]) ).
fof(f258,plain,
( sK1 = plus(sK0,sK2(sK0,sK1))
| ~ spl3_31 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f193,plain,
( ! [X2,X3,X0] :
( ~ int_leq(plus(X0,X2),n)
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_less(int_zero,X2)
| real_zero = a(X3,plus(X3,X2))
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f4245,plain,
( ~ spl3_96
| spl3_4
| ~ spl3_1
| ~ spl3_31
| ~ spl3_103 ),
inference(avatar_split_clause,[],[f1458,f1314,f256,f63,f78,f1259]) ).
fof(f1259,plain,
( spl3_96
<=> int_leq(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_96])]) ).
fof(f78,plain,
( spl3_4
<=> real_zero = a(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f1458,plain,
( real_zero = a(sK0,sK1)
| ~ int_leq(sK0,sK0)
| ~ spl3_1
| ~ spl3_31
| ~ spl3_103 ),
inference(forward_demodulation,[],[f1450,f258]) ).
fof(f1450,plain,
( real_zero = a(sK0,plus(sK0,sK2(sK0,sK1)))
| ~ int_leq(sK0,sK0)
| ~ spl3_1
| ~ spl3_103 ),
inference(resolution,[],[f1315,f65]) ).
fof(f65,plain,
( int_leq(int_one,sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f1315,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| real_zero = a(X0,plus(X0,sK2(sK0,sK1)))
| ~ int_leq(X0,sK0) )
| ~ spl3_103 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f4244,plain,
( spl3_204
| ~ spl3_69
| ~ spl3_83 ),
inference(avatar_split_clause,[],[f1127,f1102,f934,f4242]) ).
fof(f4242,plain,
( spl3_204
<=> ! [X0] :
( ~ int_leq(sK0,X0)
| int_leq(sK1,plus(sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_204])]) ).
fof(f934,plain,
( spl3_69
<=> int_less(sK2(sK0,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
fof(f1102,plain,
( spl3_83
<=> ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK0,X1)
| ~ int_less(sK2(sK0,sK1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_83])]) ).
fof(f1127,plain,
( ! [X0] :
( ~ int_leq(sK0,X0)
| int_leq(sK1,plus(sK1,X0)) )
| ~ spl3_69
| ~ spl3_83 ),
inference(resolution,[],[f1103,f936]) ).
fof(f936,plain,
( int_less(sK2(sK0,sK1),sK1)
| ~ spl3_69 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f1103,plain,
( ! [X0,X1] :
( ~ int_less(sK2(sK0,sK1),X0)
| ~ int_leq(sK0,X1)
| int_leq(sK1,plus(X0,X1)) )
| ~ spl3_83 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f4240,plain,
( spl3_203
| ~ spl3_40
| ~ spl3_68 ),
inference(avatar_split_clause,[],[f998,f847,f349,f4238]) ).
fof(f4238,plain,
( spl3_203
<=> ! [X0] :
( int_less(int_zero,plus(sK0,X0))
| ~ int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_203])]) ).
fof(f349,plain,
( spl3_40
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| int_leq(X1,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
fof(f847,plain,
( spl3_68
<=> ! [X0] :
( ~ int_leq(sK0,X0)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
fof(f998,plain,
( ! [X0] :
( int_less(int_zero,plus(sK0,X0))
| ~ int_less(int_zero,X0) )
| ~ spl3_40
| ~ spl3_68 ),
inference(resolution,[],[f848,f350]) ).
fof(f350,plain,
( ! [X0,X1] :
( int_leq(X1,plus(X1,X0))
| ~ int_less(int_zero,X0) )
| ~ spl3_40 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f848,plain,
( ! [X0] :
( ~ int_leq(sK0,X0)
| int_less(int_zero,X0) )
| ~ spl3_68 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f4236,plain,
( spl3_202
| ~ spl3_18
| ~ spl3_69 ),
inference(avatar_split_clause,[],[f940,f934,f155,f4234]) ).
fof(f4234,plain,
( spl3_202
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK2(sK0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_202])]) ).
fof(f155,plain,
( spl3_18
<=> ! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f940,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK2(sK0,sK1)) )
| ~ spl3_18
| ~ spl3_69 ),
inference(resolution,[],[f936,f156]) ).
fof(f156,plain,
( ! [X2,X0,X1] :
( ~ int_less(X1,X2)
| int_less(X0,X2)
| ~ int_less(X0,X1) )
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f4216,plain,
( ~ spl3_6
| spl3_201
| ~ spl3_41
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f913,f786,f353,f4213,f88]) ).
fof(f88,plain,
( spl3_6
<=> int_less(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f4213,plain,
( spl3_201
<=> int_less(sK2(int_one,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_201])]) ).
fof(f353,plain,
( spl3_41
<=> ! [X0,X1] :
( int_less(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
fof(f786,plain,
( spl3_66
<=> sK0 = plus(int_one,sK2(int_one,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).
fof(f913,plain,
( int_less(sK2(int_one,sK0),sK0)
| ~ int_less(int_zero,int_one)
| ~ spl3_41
| ~ spl3_66 ),
inference(superposition,[],[f354,f788]) ).
fof(f788,plain,
( sK0 = plus(int_one,sK2(int_one,sK0))
| ~ spl3_66 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f354,plain,
( ! [X0,X1] :
( int_less(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) )
| ~ spl3_41 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f4086,plain,
( spl3_200
| ~ spl3_27
| ~ spl3_114 ),
inference(avatar_split_clause,[],[f1659,f1599,f232,f4083]) ).
fof(f4083,plain,
( spl3_200
<=> sK1 = plus(sK1,sK2(sK1,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_200])]) ).
fof(f232,plain,
( spl3_27
<=> n = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f1599,plain,
( spl3_114
<=> n = plus(sK1,sK2(sK1,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_114])]) ).
fof(f1659,plain,
( sK1 = plus(sK1,sK2(sK1,sK1))
| ~ spl3_27
| ~ spl3_114 ),
inference(superposition,[],[f1601,f234]) ).
fof(f234,plain,
( n = sK1
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f1601,plain,
( n = plus(sK1,sK2(sK1,n))
| ~ spl3_114 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f4081,plain,
( spl3_199
| ~ spl3_13
| ~ spl3_190 ),
inference(avatar_split_clause,[],[f3891,f3886,f117,f4078]) ).
fof(f4078,plain,
( spl3_199
<=> int_leq(sK1,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_199])]) ).
fof(f117,plain,
( spl3_13
<=> ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f3886,plain,
( spl3_190
<=> int_less(sK1,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_190])]) ).
fof(f3891,plain,
( int_leq(sK1,sK2(sK0,sK1))
| ~ spl3_13
| ~ spl3_190 ),
inference(resolution,[],[f3888,f118]) ).
fof(f118,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f3888,plain,
( int_less(sK1,sK2(sK0,sK1))
| ~ spl3_190 ),
inference(avatar_component_clause,[],[f3886]) ).
fof(f4076,plain,
( spl3_198
| ~ spl3_20
| ~ spl3_42 ),
inference(avatar_split_clause,[],[f659,f379,f172,f4073]) ).
fof(f4073,plain,
( spl3_198
<=> sK1 = plus(int_one,sK2(int_one,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_198])]) ).
fof(f172,plain,
( spl3_20
<=> ! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f379,plain,
( spl3_42
<=> int_less(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f659,plain,
( sK1 = plus(int_one,sK2(int_one,sK1))
| ~ spl3_20
| ~ spl3_42 ),
inference(resolution,[],[f381,f173]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| plus(X0,sK2(X0,X1)) = X1 )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f381,plain,
( int_less(int_one,sK1)
| ~ spl3_42 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f4071,plain,
( spl3_197
| ~ spl3_20
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f569,f314,f172,f4068]) ).
fof(f4068,plain,
( spl3_197
<=> sK1 = plus(int_zero,sK2(int_zero,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_197])]) ).
fof(f314,plain,
( spl3_36
<=> int_less(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f569,plain,
( sK1 = plus(int_zero,sK2(int_zero,sK1))
| ~ spl3_20
| ~ spl3_36 ),
inference(resolution,[],[f316,f173]) ).
fof(f316,plain,
( int_less(int_zero,sK1)
| ~ spl3_36 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f3932,plain,
( spl3_196
| ~ spl3_36
| ~ spl3_129 ),
inference(avatar_split_clause,[],[f1958,f1902,f314,f3930]) ).
fof(f3930,plain,
( spl3_196
<=> ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_196])]) ).
fof(f1902,plain,
( spl3_129
<=> ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_leq(X0,int_zero)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_129])]) ).
fof(f1958,plain,
( ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK1) )
| ~ spl3_36
| ~ spl3_129 ),
inference(resolution,[],[f1903,f316]) ).
fof(f1903,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X1)
| ~ int_leq(X0,int_zero)
| int_leq(X0,X1) )
| ~ spl3_129 ),
inference(avatar_component_clause,[],[f1902]) ).
fof(f3928,plain,
( spl3_195
| ~ spl3_19
| ~ spl3_129 ),
inference(avatar_split_clause,[],[f1957,f1902,f159,f3926]) ).
fof(f3926,plain,
( spl3_195
<=> ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_195])]) ).
fof(f159,plain,
( spl3_19
<=> int_less(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f1957,plain,
( ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK0) )
| ~ spl3_19
| ~ spl3_129 ),
inference(resolution,[],[f1903,f161]) ).
fof(f161,plain,
( int_less(int_zero,sK0)
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f3920,plain,
( spl3_194
| ~ spl3_33
| ~ spl3_86
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f1472,f1310,f1115,f276,f3918]) ).
fof(f3918,plain,
( spl3_194
<=> ! [X0] :
( int_leq(X0,sK1)
| ~ int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_194])]) ).
fof(f276,plain,
( spl3_33
<=> ! [X0] : plus(int_zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f1115,plain,
( spl3_86
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X1,sK0)
| ~ int_less(X0,sK2(sK0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_86])]) ).
fof(f1472,plain,
( ! [X0] :
( int_leq(X0,sK1)
| ~ int_leq(X0,sK0) )
| ~ spl3_33
| ~ spl3_86
| ~ spl3_102 ),
inference(forward_demodulation,[],[f1462,f277]) ).
fof(f277,plain,
( ! [X0] : plus(int_zero,X0) = X0
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f1462,plain,
( ! [X0] :
( ~ int_leq(X0,sK0)
| int_leq(plus(int_zero,X0),sK1) )
| ~ spl3_86
| ~ spl3_102 ),
inference(resolution,[],[f1311,f1116]) ).
fof(f1116,plain,
( ! [X0,X1] :
( ~ int_less(X0,sK2(sK0,sK1))
| ~ int_leq(X1,sK0)
| int_leq(plus(X0,X1),sK1) )
| ~ spl3_86 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1311,plain,
( int_less(int_zero,sK2(sK0,sK1))
| ~ spl3_102 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f3916,plain,
( spl3_193
| ~ spl3_34
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f775,f718,f293,f3914]) ).
fof(f3914,plain,
( spl3_193
<=> ! [X0] :
( int_less(X0,sK0)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_193])]) ).
fof(f293,plain,
( spl3_34
<=> ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f718,plain,
( spl3_63
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).
fof(f775,plain,
( ! [X0] :
( int_less(X0,sK0)
| int_less(int_zero,X0) )
| ~ spl3_34
| ~ spl3_63 ),
inference(resolution,[],[f719,f294]) ).
fof(f294,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f719,plain,
( ! [X0] :
( ~ int_less(X0,int_one)
| int_less(X0,sK0) )
| ~ spl3_63 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f3912,plain,
( spl3_192
| ~ spl3_18
| ~ spl3_42 ),
inference(avatar_split_clause,[],[f660,f379,f155,f3910]) ).
fof(f3910,plain,
( spl3_192
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_192])]) ).
fof(f660,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_42 ),
inference(resolution,[],[f381,f156]) ).
fof(f3908,plain,
( spl3_191
| ~ spl3_18
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f570,f314,f155,f3906]) ).
fof(f3906,plain,
( spl3_191
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_191])]) ).
fof(f570,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) )
| ~ spl3_18
| ~ spl3_36 ),
inference(resolution,[],[f316,f156]) ).
fof(f3889,plain,
( spl3_190
| ~ spl3_27
| ~ spl3_189 ),
inference(avatar_split_clause,[],[f3860,f3856,f232,f3886]) ).
fof(f3856,plain,
( spl3_189
<=> int_less(n,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_189])]) ).
fof(f3860,plain,
( int_less(sK1,sK2(sK0,sK1))
| ~ spl3_27
| ~ spl3_189 ),
inference(forward_demodulation,[],[f3858,f234]) ).
fof(f3858,plain,
( int_less(n,sK2(sK0,sK1))
| ~ spl3_189 ),
inference(avatar_component_clause,[],[f3856]) ).
fof(f3861,plain,
( ~ spl3_100
| ~ spl3_27
| spl3_135 ),
inference(avatar_split_clause,[],[f2806,f2024,f232,f1281]) ).
fof(f1281,plain,
( spl3_100
<=> int_leq(sK2(sK0,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_100])]) ).
fof(f2024,plain,
( spl3_135
<=> int_leq(sK2(sK0,sK1),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_135])]) ).
fof(f2806,plain,
( ~ int_leq(sK2(sK0,sK1),sK1)
| ~ spl3_27
| spl3_135 ),
inference(superposition,[],[f2026,f234]) ).
fof(f2026,plain,
( ~ int_leq(sK2(sK0,sK1),n)
| spl3_135 ),
inference(avatar_component_clause,[],[f2024]) ).
fof(f3859,plain,
( spl3_189
| ~ spl3_12
| spl3_135 ),
inference(avatar_split_clause,[],[f2045,f2024,f113,f3856]) ).
fof(f113,plain,
( spl3_12
<=> ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f2045,plain,
( int_less(n,sK2(sK0,sK1))
| ~ spl3_12
| spl3_135 ),
inference(resolution,[],[f2026,f114]) ).
fof(f114,plain,
( ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f3845,plain,
( ~ spl3_188
| ~ spl3_27
| spl3_153 ),
inference(avatar_split_clause,[],[f2807,f2438,f232,f3842]) ).
fof(f3842,plain,
( spl3_188
<=> int_less(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_188])]) ).
fof(f2438,plain,
( spl3_153
<=> int_less(n,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_153])]) ).
fof(f2807,plain,
( ~ int_less(sK1,sK0)
| ~ spl3_27
| spl3_153 ),
inference(superposition,[],[f2439,f234]) ).
fof(f2439,plain,
( ~ int_less(n,sK0)
| spl3_153 ),
inference(avatar_component_clause,[],[f2438]) ).
fof(f3840,plain,
( spl3_117
| ~ spl3_10
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f1467,f1310,f105,f1692]) ).
fof(f1692,plain,
( spl3_117
<=> int_leq(int_one,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_117])]) ).
fof(f105,plain,
( spl3_10
<=> ! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f1467,plain,
( int_leq(int_one,sK2(sK0,sK1))
| ~ spl3_10
| ~ spl3_102 ),
inference(resolution,[],[f1311,f106]) ).
fof(f106,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f3833,plain,
( spl3_187
| ~ spl3_47
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f1426,f695,f429,f3831]) ).
fof(f3831,plain,
( spl3_187
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X2,X1))
| ~ int_leq(X1,int_zero)
| ~ int_less(X2,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_187])]) ).
fof(f429,plain,
( spl3_47
<=> ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).
fof(f695,plain,
( spl3_60
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
fof(f1426,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X2,X1))
| ~ int_leq(X1,int_zero)
| ~ int_less(X2,n) )
| ~ spl3_47
| ~ spl3_60 ),
inference(resolution,[],[f696,f430]) ).
fof(f430,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X0) )
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f696,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_60 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f3827,plain,
( spl3_186
| ~ spl3_23
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f462,f429,f201,f3825]) ).
fof(f3825,plain,
( spl3_186
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,n)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_186])]) ).
fof(f201,plain,
( spl3_23
<=> ! [X4,X5,X1] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5)
| ~ int_less(int_zero,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(plus(X1,X4),n)
| ~ int_leq(int_one,plus(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,n)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_23
| ~ spl3_47 ),
inference(resolution,[],[f430,f202]) ).
fof(f202,plain,
( ! [X1,X4,X5] :
( ~ int_leq(plus(X1,X4),n)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5)
| ~ int_less(int_zero,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(int_one,plus(X1,X4)) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f3821,plain,
( spl3_185
| ~ spl3_14
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f1416,f672,f127,f3819]) ).
fof(f3819,plain,
( spl3_185
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(X2,X0)
| int_less(n,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_185])]) ).
fof(f127,plain,
( spl3_14
<=> ! [X0,X1] : plus(X0,X1) = plus(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f672,plain,
( spl3_58
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
fof(f1416,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(X2,X0)
| int_less(n,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_58 ),
inference(superposition,[],[f673,f128]) ).
fof(f128,plain,
( ! [X0,X1] : plus(X0,X1) = plus(X1,X0)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f673,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(X0,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_58 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f3815,plain,
( spl3_184
| ~ spl3_47
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f1400,f649,f429,f3813]) ).
fof(f3813,plain,
( spl3_184
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X2,X1))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,int_zero)
| ~ int_less(X2,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_184])]) ).
fof(f649,plain,
( spl3_56
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).
fof(f1400,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X2,X1))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,int_zero)
| ~ int_less(X2,n) )
| ~ spl3_47
| ~ spl3_56 ),
inference(resolution,[],[f650,f430]) ).
fof(f650,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_56 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f3809,plain,
( spl3_183
| ~ spl3_22
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f463,f429,f192,f3807]) ).
fof(f3807,plain,
( spl3_183
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,n)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| real_zero = a(X2,plus(X2,X0))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_183])]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,n)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| real_zero = a(X2,plus(X2,X0))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) )
| ~ spl3_22
| ~ spl3_47 ),
inference(resolution,[],[f430,f193]) ).
fof(f3803,plain,
( spl3_182
| ~ spl3_14
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f1390,f603,f127,f3801]) ).
fof(f3801,plain,
( spl3_182
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(X2,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| int_less(n,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_182])]) ).
fof(f603,plain,
( spl3_53
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
fof(f1390,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(X2,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| int_less(n,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_53 ),
inference(superposition,[],[f604,f128]) ).
fof(f604,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(X0,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_53 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f3733,plain,
( spl3_181
| ~ spl3_48
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f578,f574,f482,f3731]) ).
fof(f3731,plain,
( spl3_181
<=> ! [X0,X3,X2,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| sK2(plus(X0,X2),plus(X1,X3)) = sK2(int_zero,sK2(plus(X0,X2),plus(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_181])]) ).
fof(f482,plain,
( spl3_48
<=> ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).
fof(f574,plain,
( spl3_52
<=> ! [X0,X3,X2,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X2,X0),plus(X3,X1))
| plus(X2,X0) = plus(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).
fof(f578,plain,
( ! [X2,X3,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| sK2(plus(X0,X2),plus(X1,X3)) = sK2(int_zero,sK2(plus(X0,X2),plus(X1,X3))) )
| ~ spl3_48
| ~ spl3_52 ),
inference(resolution,[],[f575,f483]) ).
fof(f483,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| sK2(X0,X1) = sK2(int_zero,sK2(X0,X1)) )
| ~ spl3_48 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f575,plain,
( ! [X2,X3,X0,X1] :
( int_less(plus(X2,X0),plus(X3,X1))
| ~ int_less(X2,X3)
| ~ int_leq(X0,X1)
| plus(X2,X0) = plus(X3,X1) )
| ~ spl3_52 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f3728,plain,
( spl3_133
| ~ spl3_13
| ~ spl3_128 ),
inference(avatar_split_clause,[],[f2241,f1853,f117,f2015]) ).
fof(f1853,plain,
( spl3_128
<=> int_less(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_128])]) ).
fof(f2241,plain,
( int_leq(sK0,n)
| ~ spl3_13
| ~ spl3_128 ),
inference(resolution,[],[f1855,f118]) ).
fof(f1855,plain,
( int_less(sK0,n)
| ~ spl3_128 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f3661,plain,
( spl3_180
| ~ spl3_20
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f579,f574,f172,f3659]) ).
fof(f3659,plain,
( spl3_180
<=> ! [X0,X3,X2,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| plus(X1,X3) = plus(plus(X0,X2),sK2(plus(X0,X2),plus(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_180])]) ).
fof(f579,plain,
( ! [X2,X3,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| plus(X1,X3) = plus(plus(X0,X2),sK2(plus(X0,X2),plus(X1,X3))) )
| ~ spl3_20
| ~ spl3_52 ),
inference(resolution,[],[f575,f173]) ).
fof(f3620,plain,
( spl3_179
| ~ spl3_18
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f580,f574,f155,f3618]) ).
fof(f3618,plain,
( spl3_179
<=> ! [X4,X0,X3,X2,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| int_less(X4,plus(X1,X3))
| ~ int_less(X4,plus(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_179])]) ).
fof(f580,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ int_less(X0,X1)
| ~ int_leq(X2,X3)
| plus(X0,X2) = plus(X1,X3)
| int_less(X4,plus(X1,X3))
| ~ int_less(X4,plus(X0,X2)) )
| ~ spl3_18
| ~ spl3_52 ),
inference(resolution,[],[f575,f156]) ).
fof(f3587,plain,
( spl3_178
| ~ spl3_45
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f559,f547,f421,f3585]) ).
fof(f3585,plain,
( spl3_178
<=> ! [X2,X0,X1] :
( plus(X0,plus(X1,X2)) = plus(X0,sK2(X0,plus(X0,plus(X1,X2))))
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_178])]) ).
fof(f421,plain,
( spl3_45
<=> ! [X2,X0,X1] :
( int_less(X0,plus(X1,X2))
| ~ int_less(X0,X1)
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
fof(f547,plain,
( spl3_51
<=> ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).
fof(f559,plain,
( ! [X2,X0,X1] :
( plus(X0,plus(X1,X2)) = plus(X0,sK2(X0,plus(X0,plus(X1,X2))))
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X2) )
| ~ spl3_45
| ~ spl3_51 ),
inference(resolution,[],[f548,f422]) ).
fof(f422,plain,
( ! [X2,X0,X1] :
( int_less(X0,plus(X1,X2))
| ~ int_less(X0,X1)
| ~ int_less(int_zero,X2) )
| ~ spl3_45 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f548,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X1)
| plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1))) )
| ~ spl3_51 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f3493,plain,
( spl3_177
| ~ spl3_17
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f527,f505,f151,f3491]) ).
fof(f3491,plain,
( spl3_177
<=> ! [X0,X3,X2,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X2,X0),plus(X1,X3))
| plus(X1,X3) = plus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_177])]) ).
fof(f151,plain,
( spl3_17
<=> ! [X0,X1] :
( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f505,plain,
( spl3_50
<=> ! [X0,X3,X2,X1] :
( int_leq(plus(X2,X3),plus(X1,X0))
| ~ int_leq(X3,X1)
| ~ int_less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).
fof(f527,plain,
( ! [X2,X3,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X2,X0),plus(X1,X3))
| plus(X1,X3) = plus(X2,X0) )
| ~ spl3_17
| ~ spl3_50 ),
inference(resolution,[],[f506,f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( ~ int_leq(X0,X1)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f506,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X2,X3),plus(X1,X0))
| ~ int_leq(X3,X1)
| ~ int_less(X2,X0) )
| ~ spl3_50 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f3489,plain,
( spl3_176
| ~ spl3_17
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f508,f501,f151,f3487]) ).
fof(f3487,plain,
( spl3_176
<=> ! [X0,X3,X2,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X0,X2),plus(X3,X1))
| plus(X0,X2) = plus(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_176])]) ).
fof(f501,plain,
( spl3_49
<=> ! [X0,X3,X2,X1] :
( int_leq(plus(X1,X0),plus(X2,X3))
| ~ int_leq(X1,X3)
| ~ int_less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).
fof(f508,plain,
( ! [X2,X3,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X0,X2),plus(X3,X1))
| plus(X0,X2) = plus(X3,X1) )
| ~ spl3_17
| ~ spl3_49 ),
inference(resolution,[],[f502,f152]) ).
fof(f502,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X1,X0),plus(X2,X3))
| ~ int_leq(X1,X3)
| ~ int_less(X0,X2) )
| ~ spl3_49 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f3484,plain,
( spl3_162
| ~ spl3_13
| ~ spl3_126 ),
inference(avatar_split_clause,[],[f2106,f1751,f117,f2784]) ).
fof(f2784,plain,
( spl3_162
<=> int_leq(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_162])]) ).
fof(f1751,plain,
( spl3_126
<=> int_less(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_126])]) ).
fof(f2106,plain,
( int_leq(int_one,n)
| ~ spl3_13
| ~ spl3_126 ),
inference(resolution,[],[f1753,f118]) ).
fof(f1753,plain,
( int_less(int_one,n)
| ~ spl3_126 ),
inference(avatar_component_clause,[],[f1751]) ).
fof(f3411,plain,
( spl3_175
| ~ spl3_44
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f491,f482,f417,f3409]) ).
fof(f3409,plain,
( spl3_175
<=> ! [X2,X0,X1] :
( sK2(X0,sK2(X1,X2)) = sK2(int_zero,sK2(X0,sK2(X1,X2)))
| ~ int_less(X0,int_zero)
| ~ int_less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_175])]) ).
fof(f417,plain,
( spl3_44
<=> ! [X2,X0,X1] :
( int_less(X0,sK2(X1,X2))
| ~ int_less(X0,int_zero)
| ~ int_less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
fof(f491,plain,
( ! [X2,X0,X1] :
( sK2(X0,sK2(X1,X2)) = sK2(int_zero,sK2(X0,sK2(X1,X2)))
| ~ int_less(X0,int_zero)
| ~ int_less(X1,X2) )
| ~ spl3_44
| ~ spl3_48 ),
inference(resolution,[],[f483,f418]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( int_less(X0,sK2(X1,X2))
| ~ int_less(X0,int_zero)
| ~ int_less(X1,X2) )
| ~ spl3_44 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f3407,plain,
( spl3_174
| ~ spl3_45
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f490,f482,f421,f3405]) ).
fof(f3405,plain,
( spl3_174
<=> ! [X2,X0,X1] :
( sK2(X0,plus(X1,X2)) = sK2(int_zero,sK2(X0,plus(X1,X2)))
| ~ int_less(X0,X1)
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_174])]) ).
fof(f490,plain,
( ! [X2,X0,X1] :
( sK2(X0,plus(X1,X2)) = sK2(int_zero,sK2(X0,plus(X1,X2)))
| ~ int_less(X0,X1)
| ~ int_less(int_zero,X2) )
| ~ spl3_45
| ~ spl3_48 ),
inference(resolution,[],[f483,f422]) ).
fof(f3360,plain,
( spl3_173
| ~ spl3_15
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f553,f547,f135,f3358]) ).
fof(f3358,plain,
( spl3_173
<=> ! [X2,X0,X1] :
( plus(X0,sK2(X1,X2)) = plus(X0,sK2(X0,plus(X0,sK2(X1,X2))))
| ~ int_less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_173])]) ).
fof(f135,plain,
( spl3_15
<=> ! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f553,plain,
( ! [X2,X0,X1] :
( plus(X0,sK2(X1,X2)) = plus(X0,sK2(X0,plus(X0,sK2(X1,X2))))
| ~ int_less(X1,X2) )
| ~ spl3_15
| ~ spl3_51 ),
inference(resolution,[],[f548,f136]) ).
fof(f136,plain,
( ! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f3254,plain,
( spl3_172
| ~ spl3_43
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f554,f547,f392,f3252]) ).
fof(f3252,plain,
( spl3_172
<=> ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_zero)
| int_zero = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_172])]) ).
fof(f392,plain,
( spl3_43
<=> ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f554,plain,
( ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_zero)
| int_zero = X1 )
| ~ spl3_43
| ~ spl3_51 ),
inference(resolution,[],[f548,f393]) ).
fof(f393,plain,
( ! [X0,X1] :
( int_less(X1,X0)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f3144,plain,
( ~ spl3_36
| ~ spl3_27
| spl3_119 ),
inference(avatar_split_clause,[],[f1707,f1702,f232,f314]) ).
fof(f1702,plain,
( spl3_119
<=> int_less(int_zero,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_119])]) ).
fof(f1707,plain,
( ~ int_less(int_zero,sK1)
| ~ spl3_27
| spl3_119 ),
inference(forward_demodulation,[],[f1703,f234]) ).
fof(f1703,plain,
( ~ int_less(int_zero,n)
| spl3_119 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f3143,plain,
( spl3_171
| ~ spl3_20
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f439,f421,f172,f3141]) ).
fof(f3141,plain,
( spl3_171
<=> ! [X2,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| plus(X1,X2) = plus(X0,sK2(X0,plus(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_171])]) ).
fof(f439,plain,
( ! [X2,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| plus(X1,X2) = plus(X0,sK2(X0,plus(X1,X2))) )
| ~ spl3_20
| ~ spl3_45 ),
inference(resolution,[],[f422,f173]) ).
fof(f3139,plain,
( spl3_170
| ~ spl3_20
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f434,f417,f172,f3137]) ).
fof(f3137,plain,
( spl3_170
<=> ! [X2,X0,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| sK2(X1,X2) = plus(X0,sK2(X0,sK2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_170])]) ).
fof(f434,plain,
( ! [X2,X0,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| sK2(X1,X2) = plus(X0,sK2(X0,sK2(X1,X2))) )
| ~ spl3_20
| ~ spl3_44 ),
inference(resolution,[],[f418,f173]) ).
fof(f2902,plain,
( spl3_169
| ~ spl3_33
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f592,f574,f276,f2900]) ).
fof(f2900,plain,
( spl3_169
<=> ! [X2,X0,X1] :
( int_less(plus(X1,X2),X0)
| ~ int_less(X1,int_zero)
| ~ int_leq(X2,X0)
| plus(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_169])]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( int_less(plus(X1,X2),X0)
| ~ int_less(X1,int_zero)
| ~ int_leq(X2,X0)
| plus(X1,X2) = X0 )
| ~ spl3_33
| ~ spl3_52 ),
inference(superposition,[],[f575,f277]) ).
fof(f2879,plain,
( spl3_168
| ~ spl3_33
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f586,f574,f276,f2877]) ).
fof(f2877,plain,
( spl3_168
<=> ! [X2,X0,X1] :
( int_less(X0,plus(X1,X2))
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,X2)
| plus(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_168])]) ).
fof(f586,plain,
( ! [X2,X0,X1] :
( int_less(X0,plus(X1,X2))
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,X2)
| plus(X1,X2) = X0 )
| ~ spl3_33
| ~ spl3_52 ),
inference(superposition,[],[f575,f277]) ).
fof(f2875,plain,
( spl3_167
| ~ spl3_15
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f495,f482,f135,f2873]) ).
fof(f2873,plain,
( spl3_167
<=> ! [X0,X1] :
( sK2(int_zero,sK2(X0,X1)) = sK2(int_zero,sK2(int_zero,sK2(X0,X1)))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_167])]) ).
fof(f495,plain,
( ! [X0,X1] :
( sK2(int_zero,sK2(X0,X1)) = sK2(int_zero,sK2(int_zero,sK2(X0,X1)))
| ~ int_less(X0,X1) )
| ~ spl3_15
| ~ spl3_48 ),
inference(resolution,[],[f483,f136]) ).
fof(f2871,plain,
( spl3_166
| ~ spl3_41
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f489,f482,f353,f2869]) ).
fof(f2869,plain,
( spl3_166
<=> ! [X0,X1] :
( sK2(X0,plus(X1,X0)) = sK2(int_zero,sK2(X0,plus(X1,X0)))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_166])]) ).
fof(f489,plain,
( ! [X0,X1] :
( sK2(X0,plus(X1,X0)) = sK2(int_zero,sK2(X0,plus(X1,X0)))
| ~ int_less(int_zero,X1) )
| ~ spl3_41
| ~ spl3_48 ),
inference(resolution,[],[f483,f354]) ).
fof(f2867,plain,
( spl3_165
| ~ spl3_16
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f488,f482,f139,f2865]) ).
fof(f2865,plain,
( spl3_165
<=> ! [X0,X1] :
( sK2(X0,plus(X0,X1)) = sK2(int_zero,sK2(X0,plus(X0,X1)))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_165])]) ).
fof(f139,plain,
( spl3_16
<=> ! [X2,X0] :
( int_less(X0,plus(X0,X2))
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f488,plain,
( ! [X0,X1] :
( sK2(X0,plus(X0,X1)) = sK2(int_zero,sK2(X0,plus(X0,X1)))
| ~ int_less(int_zero,X1) )
| ~ spl3_16
| ~ spl3_48 ),
inference(resolution,[],[f483,f140]) ).
fof(f140,plain,
( ! [X2,X0] :
( int_less(X0,plus(X0,X2))
| ~ int_less(int_zero,X2) )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f2863,plain,
( spl3_164
| ~ spl3_17
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f464,f429,f151,f2861]) ).
fof(f2861,plain,
( spl3_164
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,X2)
| int_less(plus(X1,X0),X2)
| plus(X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_164])]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,X2)
| int_less(plus(X1,X0),X2)
| plus(X1,X0) = X2 )
| ~ spl3_17
| ~ spl3_47 ),
inference(resolution,[],[f430,f152]) ).
fof(f2859,plain,
( spl3_163
| ~ spl3_17
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f451,f425,f151,f2857]) ).
fof(f2857,plain,
( spl3_163
<=> ! [X2,X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(X1,X2)
| int_less(X1,plus(X2,X0))
| plus(X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_163])]) ).
fof(f425,plain,
( spl3_46
<=> ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).
fof(f451,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(X1,X2)
| int_less(X1,plus(X2,X0))
| plus(X2,X0) = X1 )
| ~ spl3_17
| ~ spl3_46 ),
inference(resolution,[],[f426,f152]) ).
fof(f426,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(X0,X1) )
| ~ spl3_46 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f2787,plain,
( spl3_162
| ~ spl3_10
| ~ spl3_119 ),
inference(avatar_split_clause,[],[f2031,f1702,f105,f2784]) ).
fof(f2031,plain,
( int_leq(int_one,n)
| ~ spl3_10
| ~ spl3_119 ),
inference(resolution,[],[f1704,f106]) ).
fof(f1704,plain,
( int_less(int_zero,n)
| ~ spl3_119 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f2751,plain,
( spl3_161
| ~ spl3_43
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f485,f482,f392,f2749]) ).
fof(f2749,plain,
( spl3_161
<=> ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_161])]) ).
fof(f485,plain,
( ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 )
| ~ spl3_43
| ~ spl3_48 ),
inference(resolution,[],[f483,f393]) ).
fof(f2643,plain,
( spl3_160
| ~ spl3_34
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f550,f547,f293,f2641]) ).
fof(f2641,plain,
( spl3_160
<=> ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_160])]) ).
fof(f550,plain,
( ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_one) )
| ~ spl3_34
| ~ spl3_51 ),
inference(resolution,[],[f548,f294]) ).
fof(f2639,plain,
( spl3_159
| ~ spl3_18
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f440,f421,f155,f2637]) ).
fof(f2637,plain,
( spl3_159
<=> ! [X0,X3,X2,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| int_less(X3,plus(X1,X2))
| ~ int_less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_159])]) ).
fof(f440,plain,
( ! [X2,X3,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| int_less(X3,plus(X1,X2))
| ~ int_less(X3,X0) )
| ~ spl3_18
| ~ spl3_45 ),
inference(resolution,[],[f422,f156]) ).
fof(f2635,plain,
( spl3_158
| ~ spl3_18
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f435,f417,f155,f2633]) ).
fof(f2633,plain,
( spl3_158
<=> ! [X0,X3,X2,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| int_less(X3,sK2(X1,X2))
| ~ int_less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_158])]) ).
fof(f435,plain,
( ! [X2,X3,X0,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| int_less(X3,sK2(X1,X2))
| ~ int_less(X3,X0) )
| ~ spl3_18
| ~ spl3_44 ),
inference(resolution,[],[f418,f156]) ).
fof(f2631,plain,
( spl3_157
| ~ spl3_20
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f368,f353,f172,f2629]) ).
fof(f2629,plain,
( spl3_157
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X0,X1) = plus(X1,sK2(X1,plus(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_157])]) ).
fof(f368,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X0,X1) = plus(X1,sK2(X1,plus(X0,X1))) )
| ~ spl3_20
| ~ spl3_41 ),
inference(resolution,[],[f354,f173]) ).
fof(f2552,plain,
( spl3_156
| ~ spl3_14
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f516,f501,f127,f2550]) ).
fof(f2550,plain,
( spl3_156
<=> ! [X0,X3,X2,X1] :
( int_leq(plus(X2,X3),plus(X1,X0))
| ~ int_leq(X2,X1)
| ~ int_less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_156])]) ).
fof(f516,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X2,X3),plus(X1,X0))
| ~ int_leq(X2,X1)
| ~ int_less(X3,X0) )
| ~ spl3_14
| ~ spl3_49 ),
inference(superposition,[],[f502,f128]) ).
fof(f2548,plain,
( spl3_155
| ~ spl3_20
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f397,f392,f172,f2546]) ).
fof(f2546,plain,
( spl3_155
<=> ! [X0,X1] :
( int_less(X1,X0)
| X0 = X1
| plus(X0,sK2(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_155])]) ).
fof(f397,plain,
( ! [X0,X1] :
( int_less(X1,X0)
| X0 = X1
| plus(X0,sK2(X0,X1)) = X1 )
| ~ spl3_20
| ~ spl3_43 ),
inference(resolution,[],[f393,f173]) ).
fof(f2544,plain,
( spl3_154
| ~ spl3_17
| ~ spl3_38 ),
inference(avatar_split_clause,[],[f357,f341,f151,f2542]) ).
fof(f2542,plain,
( spl3_154
<=> ! [X0,X1] :
( ~ int_less(X0,X1)
| int_less(int_one,sK2(X0,X1))
| int_one = sK2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_154])]) ).
fof(f341,plain,
( spl3_38
<=> ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_one,sK2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f357,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_less(int_one,sK2(X0,X1))
| int_one = sK2(X0,X1) )
| ~ spl3_17
| ~ spl3_38 ),
inference(resolution,[],[f342,f152]) ).
fof(f342,plain,
( ! [X0,X1] :
( int_leq(int_one,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f2441,plain,
( spl3_153
| ~ spl3_12
| spl3_133 ),
inference(avatar_split_clause,[],[f2022,f2015,f113,f2438]) ).
fof(f2022,plain,
( int_less(n,sK0)
| ~ spl3_12
| spl3_133 ),
inference(resolution,[],[f2017,f114]) ).
fof(f2017,plain,
( ~ int_leq(sK0,n)
| spl3_133 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f2436,plain,
( spl3_152
| ~ spl3_34
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f492,f482,f293,f2434]) ).
fof(f2434,plain,
( spl3_152
<=> ! [X0] :
( sK2(int_zero,X0) = sK2(int_zero,sK2(int_zero,X0))
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_152])]) ).
fof(f492,plain,
( ! [X0] :
( sK2(int_zero,X0) = sK2(int_zero,sK2(int_zero,X0))
| int_less(X0,int_one) )
| ~ spl3_34
| ~ spl3_48 ),
inference(resolution,[],[f483,f294]) ).
fof(f2432,plain,
( spl3_151
| ~ spl3_34
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f487,f482,f293,f2430]) ).
fof(f2430,plain,
( spl3_151
<=> ! [X0] :
( sK2(X0,int_one) = sK2(int_zero,sK2(X0,int_one))
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_151])]) ).
fof(f487,plain,
( ! [X0] :
( sK2(X0,int_one) = sK2(int_zero,sK2(X0,int_one))
| int_less(int_zero,X0) )
| ~ spl3_34
| ~ spl3_48 ),
inference(resolution,[],[f483,f294]) ).
fof(f2428,plain,
( spl3_150
| ~ spl3_18
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f398,f392,f155,f2426]) ).
fof(f2426,plain,
( spl3_150
<=> ! [X2,X0,X1] :
( int_less(X1,X0)
| X0 = X1
| int_less(X2,X1)
| ~ int_less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_150])]) ).
fof(f398,plain,
( ! [X2,X0,X1] :
( int_less(X1,X0)
| X0 = X1
| int_less(X2,X1)
| ~ int_less(X2,X0) )
| ~ spl3_18
| ~ spl3_43 ),
inference(resolution,[],[f393,f156]) ).
fof(f2126,plain,
( spl3_149
| ~ spl3_6
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f551,f547,f88,f2124]) ).
fof(f2124,plain,
( spl3_149
<=> ! [X0] : plus(X0,int_one) = plus(X0,sK2(X0,plus(X0,int_one))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_149])]) ).
fof(f551,plain,
( ! [X0] : plus(X0,int_one) = plus(X0,sK2(X0,plus(X0,int_one)))
| ~ spl3_6
| ~ spl3_51 ),
inference(resolution,[],[f548,f90]) ).
fof(f90,plain,
( int_less(int_zero,int_one)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f2122,plain,
( spl3_148
| ~ spl3_33
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f532,f505,f276,f2120]) ).
fof(f2120,plain,
( spl3_148
<=> ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_148])]) ).
fof(f532,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2) )
| ~ spl3_33
| ~ spl3_50 ),
inference(superposition,[],[f506,f277]) ).
fof(f2118,plain,
( spl3_147
| ~ spl3_33
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f519,f501,f276,f2116]) ).
fof(f2116,plain,
( spl3_147
<=> ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X1,X0)
| ~ int_less(X2,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_147])]) ).
fof(f519,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X1,X0)
| ~ int_less(X2,int_zero) )
| ~ spl3_33
| ~ spl3_49 ),
inference(superposition,[],[f502,f277]) ).
fof(f2114,plain,
( spl3_146
| ~ spl3_14
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f466,f429,f127,f2112]) ).
fof(f2112,plain,
( spl3_146
<=> ! [X2,X0,X1] :
( int_leq(plus(X1,X0),X2)
| ~ int_leq(X1,int_zero)
| ~ int_less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_146])]) ).
fof(f466,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X0),X2)
| ~ int_leq(X1,int_zero)
| ~ int_less(X0,X2) )
| ~ spl3_14
| ~ spl3_47 ),
inference(superposition,[],[f430,f128]) ).
fof(f2110,plain,
( spl3_145
| ~ spl3_14
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f453,f425,f127,f2108]) ).
fof(f2108,plain,
( spl3_145
<=> ! [X2,X0,X1] :
( int_leq(X2,plus(X1,X0))
| ~ int_leq(int_zero,X1)
| ~ int_less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_145])]) ).
fof(f453,plain,
( ! [X2,X0,X1] :
( int_leq(X2,plus(X1,X0))
| ~ int_leq(int_zero,X1)
| ~ int_less(X2,X0) )
| ~ spl3_14
| ~ spl3_46 ),
inference(superposition,[],[f426,f128]) ).
fof(f2100,plain,
( spl3_144
| ~ spl3_11
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f450,f425,f109,f2098]) ).
fof(f2098,plain,
( spl3_144
<=> ! [X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(int_one,X1)
| int_less(int_zero,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_144])]) ).
fof(f109,plain,
( spl3_11
<=> ! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(int_one,X1)
| int_less(int_zero,plus(X1,X0)) )
| ~ spl3_11
| ~ spl3_46 ),
inference(resolution,[],[f426,f110]) ).
fof(f110,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f2096,plain,
( spl3_143
| ~ spl3_13
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f441,f421,f117,f2094]) ).
fof(f2094,plain,
( spl3_143
<=> ! [X2,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| int_leq(X0,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_143])]) ).
fof(f441,plain,
( ! [X2,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(int_zero,X2)
| int_leq(X0,plus(X1,X2)) )
| ~ spl3_13
| ~ spl3_45 ),
inference(resolution,[],[f422,f118]) ).
fof(f2092,plain,
( spl3_142
| ~ spl3_10
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f438,f421,f105,f2090]) ).
fof(f2090,plain,
( spl3_142
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| ~ int_less(int_zero,X1)
| int_leq(int_one,plus(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_142])]) ).
fof(f438,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| ~ int_less(int_zero,X1)
| int_leq(int_one,plus(X0,X1)) )
| ~ spl3_10
| ~ spl3_45 ),
inference(resolution,[],[f422,f106]) ).
fof(f2088,plain,
( spl3_141
| ~ spl3_13
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f436,f417,f117,f2086]) ).
fof(f2086,plain,
( spl3_141
<=> ! [X2,X0,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| int_leq(X0,sK2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_141])]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( ~ int_less(X0,int_zero)
| ~ int_less(X1,X2)
| int_leq(X0,sK2(X1,X2)) )
| ~ spl3_13
| ~ spl3_44 ),
inference(resolution,[],[f418,f118]) ).
fof(f2084,plain,
( spl3_140
| ~ spl3_18
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f369,f353,f155,f2082]) ).
fof(f2082,plain,
( spl3_140
<=> ! [X2,X0,X1] :
( ~ int_less(int_zero,X0)
| int_less(X1,plus(X0,X2))
| ~ int_less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_140])]) ).
fof(f369,plain,
( ! [X2,X0,X1] :
( ~ int_less(int_zero,X0)
| int_less(X1,plus(X0,X2))
| ~ int_less(X1,X2) )
| ~ spl3_18
| ~ spl3_41 ),
inference(resolution,[],[f354,f156]) ).
fof(f2080,plain,
( spl3_139
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f285,f276,f181,f2078]) ).
fof(f2078,plain,
( spl3_139
<=> ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,X0)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_139])]) ).
fof(f181,plain,
( spl3_21
<=> ! [X0,X3,X2,X1] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_leq(X2,X3)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f285,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,X0)
| ~ int_less(X1,int_zero) )
| ~ spl3_21
| ~ spl3_33 ),
inference(superposition,[],[f182,f277]) ).
fof(f182,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_leq(X2,X3)
| ~ int_less(X0,X1) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f2076,plain,
( spl3_138
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f284,f276,f181,f2074]) ).
fof(f2074,plain,
( spl3_138
<=> ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(X0,X2)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_138])]) ).
fof(f284,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(X0,X2)
| ~ int_less(int_zero,X1) )
| ~ spl3_21
| ~ spl3_33 ),
inference(superposition,[],[f182,f277]) ).
fof(f2049,plain,
( spl3_137
| ~ spl3_20
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f302,f293,f172,f2047]) ).
fof(f2047,plain,
( spl3_137
<=> ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_137])]) ).
fof(f302,plain,
( ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) )
| ~ spl3_20
| ~ spl3_34 ),
inference(resolution,[],[f294,f173]) ).
fof(f2030,plain,
( ~ spl3_67
| ~ spl3_117
| ~ spl3_135
| ~ spl3_19
| spl3_136
| ~ spl3_3
| ~ spl3_31
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f1436,f695,f256,f73,f2028,f159,f2024,f1692,f816]) ).
fof(f2028,plain,
( spl3_136
<=> ! [X0] :
( ~ int_leq(X0,sK2(sK0,sK1))
| a(plus(X0,sK0),X0) = qr(plus(X0,sK0),X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_136])]) ).
fof(f1436,plain,
( ! [X0] :
( ~ int_leq(sK1,n)
| ~ int_leq(X0,sK2(sK0,sK1))
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK2(sK0,sK1),n)
| ~ int_leq(int_one,sK2(sK0,sK1))
| a(plus(X0,sK0),X0) = qr(plus(X0,sK0),X0)
| ~ int_leq(int_one,sK1) )
| ~ spl3_31
| ~ spl3_60 ),
inference(superposition,[],[f696,f258]) ).
fof(f2021,plain,
( ~ spl3_67
| ~ spl3_1
| ~ spl3_133
| ~ spl3_102
| spl3_134
| ~ spl3_3
| ~ spl3_23
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f264,f256,f201,f73,f2019,f1310,f2015,f63,f816]) ).
fof(f2019,plain,
( spl3_134
<=> ! [X0] :
( ~ int_leq(X0,sK0)
| a(plus(X0,sK2(sK0,sK1)),X0) = qr(plus(X0,sK2(sK0,sK1)),X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_134])]) ).
fof(f264,plain,
( ! [X0] :
( ~ int_leq(sK1,n)
| ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0)
| a(plus(X0,sK2(sK0,sK1)),X0) = qr(plus(X0,sK2(sK0,sK1)),X0)
| ~ int_leq(int_one,sK1) )
| ~ spl3_23
| ~ spl3_31 ),
inference(superposition,[],[f202,f258]) ).
fof(f2013,plain,
( spl3_132
| ~ spl3_47
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f704,f701,f429,f2011]) ).
fof(f2011,plain,
( spl3_132
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_132])]) ).
fof(f701,plain,
( spl3_61
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).
fof(f704,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK1) )
| ~ spl3_47
| ~ spl3_61 ),
inference(resolution,[],[f702,f430]) ).
fof(f702,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X0,sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_61 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f2009,plain,
( spl3_131
| ~ spl3_46
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f682,f678,f425,f2007]) ).
fof(f2007,plain,
( spl3_131
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_131])]) ).
fof(f678,plain,
( spl3_59
<=> ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
fof(f682,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X0) )
| ~ spl3_46
| ~ spl3_59 ),
inference(resolution,[],[f679,f426]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| int_less(sK1,plus(X1,X2)) )
| ~ spl3_59 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f1991,plain,
( spl3_130
| ~ spl3_23
| ~ spl3_27
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f624,f429,f232,f201,f1989]) ).
fof(f1989,plain,
( spl3_130
<=> ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_less(X1,sK1)
| ~ int_leq(X0,int_zero)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_130])]) ).
fof(f624,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_less(X1,sK1)
| ~ int_leq(X0,int_zero)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_23
| ~ spl3_27
| ~ spl3_47 ),
inference(forward_demodulation,[],[f471,f234]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( ~ int_less(X1,sK1)
| ~ int_leq(X0,int_zero)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_23
| ~ spl3_27
| ~ spl3_47 ),
inference(forward_demodulation,[],[f462,f234]) ).
fof(f1970,plain,
( ~ spl3_2
| ~ spl3_38
| spl3_117 ),
inference(avatar_split_clause,[],[f1699,f1692,f341,f68]) ).
fof(f68,plain,
( spl3_2
<=> int_less(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f1699,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_38
| spl3_117 ),
inference(resolution,[],[f1694,f342]) ).
fof(f1694,plain,
( ~ int_leq(int_one,sK2(sK0,sK1))
| spl3_117 ),
inference(avatar_component_clause,[],[f1692]) ).
fof(f1904,plain,
( spl3_129
| ~ spl3_33
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f469,f429,f276,f1902]) ).
fof(f469,plain,
( ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_leq(X0,int_zero)
| ~ int_less(int_zero,X1) )
| ~ spl3_33
| ~ spl3_47 ),
inference(superposition,[],[f430,f277]) ).
fof(f1856,plain,
( spl3_128
| ~ spl3_2
| ~ spl3_107 ),
inference(avatar_split_clause,[],[f1595,f1439,f68,f1853]) ).
fof(f1439,plain,
( spl3_107
<=> ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_107])]) ).
fof(f1595,plain,
( int_less(sK0,n)
| ~ spl3_2
| ~ spl3_107 ),
inference(resolution,[],[f1440,f70]) ).
fof(f70,plain,
( int_less(sK0,sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f1440,plain,
( ! [X0] :
( ~ int_less(X0,sK1)
| int_less(X0,n) )
| ~ spl3_107 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1800,plain,
( spl3_127
| ~ spl3_14
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f708,f701,f127,f1798]) ).
fof(f1798,plain,
( spl3_127
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X1,sK1)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_127])]) ).
fof(f708,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X1,sK1)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| a(plus(X2,X0),X2) = qr(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_61 ),
inference(superposition,[],[f702,f128]) ).
fof(f1754,plain,
( spl3_126
| ~ spl3_42
| ~ spl3_107 ),
inference(avatar_split_clause,[],[f1594,f1439,f379,f1751]) ).
fof(f1594,plain,
( int_less(int_one,n)
| ~ spl3_42
| ~ spl3_107 ),
inference(resolution,[],[f1440,f381]) ).
fof(f1749,plain,
( spl3_125
| ~ spl3_33
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f456,f425,f276,f1747]) ).
fof(f1747,plain,
( spl3_125
<=> ! [X0,X1] :
( int_leq(X1,X0)
| ~ int_leq(int_zero,X0)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_125])]) ).
fof(f456,plain,
( ! [X0,X1] :
( int_leq(X1,X0)
| ~ int_leq(int_zero,X0)
| ~ int_less(X1,int_zero) )
| ~ spl3_33
| ~ spl3_46 ),
inference(superposition,[],[f426,f277]) ).
fof(f1745,plain,
( spl3_124
| ~ spl3_10
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f405,f392,f105,f1743]) ).
fof(f1743,plain,
( spl3_124
<=> ! [X0] :
( int_less(X0,int_zero)
| int_zero = X0
| int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_124])]) ).
fof(f405,plain,
( ! [X0] :
( int_less(X0,int_zero)
| int_zero = X0
| int_leq(int_one,X0) )
| ~ spl3_10
| ~ spl3_43 ),
inference(resolution,[],[f393,f106]) ).
fof(f1741,plain,
( spl3_123
| ~ spl3_18
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f308,f293,f155,f1739]) ).
fof(f1739,plain,
( spl3_123
<=> ! [X0,X1] :
( int_less(X0,int_one)
| int_less(X1,X0)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_123])]) ).
fof(f308,plain,
( ! [X0,X1] :
( int_less(X0,int_one)
| int_less(X1,X0)
| ~ int_less(X1,int_zero) )
| ~ spl3_18
| ~ spl3_34 ),
inference(resolution,[],[f294,f156]) ).
fof(f1737,plain,
( spl3_122
| ~ spl3_18
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f303,f293,f155,f1735]) ).
fof(f1735,plain,
( spl3_122
<=> ! [X0,X1] :
( int_less(int_zero,X0)
| int_less(X1,int_one)
| ~ int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_122])]) ).
fof(f303,plain,
( ! [X0,X1] :
( int_less(int_zero,X0)
| int_less(X1,int_one)
| ~ int_less(X1,X0) )
| ~ spl3_18
| ~ spl3_34 ),
inference(resolution,[],[f294,f156]) ).
fof(f1733,plain,
( spl3_121
| ~ spl3_12
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f705,f701,f113,f1731]) ).
fof(f1731,plain,
( spl3_121
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| int_less(sK1,plus(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_121])]) ).
fof(f705,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| int_less(sK1,plus(X2,X0)) )
| ~ spl3_12
| ~ spl3_61 ),
inference(resolution,[],[f702,f114]) ).
fof(f1711,plain,
( spl3_120
| ~ spl3_12
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f683,f678,f113,f1709]) ).
fof(f1709,plain,
( spl3_120
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| int_less(sK1,plus(X0,X2))
| int_less(plus(X0,X2),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_120])]) ).
fof(f683,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| a(plus(X1,X2),X1) = qr(plus(X1,X2),X1)
| int_less(sK1,plus(X0,X2))
| int_less(plus(X0,X2),int_one) )
| ~ spl3_12
| ~ spl3_59 ),
inference(resolution,[],[f679,f114]) ).
fof(f1705,plain,
( spl3_119
| ~ spl3_36
| ~ spl3_107 ),
inference(avatar_split_clause,[],[f1592,f1439,f314,f1702]) ).
fof(f1592,plain,
( int_less(int_zero,n)
| ~ spl3_36
| ~ spl3_107 ),
inference(resolution,[],[f1440,f316]) ).
fof(f1698,plain,
( ~ spl3_117
| ~ spl3_67
| ~ spl3_19
| spl3_118
| ~ spl3_100
| ~ spl3_104
| ~ spl3_31
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f667,f655,f256,f1317,f1281,f1696,f159,f816,f1692]) ).
fof(f1696,plain,
( spl3_118
<=> ! [X0] :
( ~ int_leq(X0,sK2(sK0,sK1))
| real_zero = a(X0,plus(X0,sK0))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_118])]) ).
fof(f1317,plain,
( spl3_104
<=> int_leq(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_104])]) ).
fof(f655,plain,
( spl3_57
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).
fof(f667,plain,
( ! [X0] :
( ~ int_leq(sK1,sK1)
| ~ int_leq(sK2(sK0,sK1),sK1)
| ~ int_leq(X0,sK2(sK0,sK1))
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK0)
| real_zero = a(X0,plus(X0,sK0))
| ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK2(sK0,sK1)) )
| ~ spl3_31
| ~ spl3_57 ),
inference(superposition,[],[f656,f258]) ).
fof(f656,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X0,sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_57 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f1652,plain,
( spl3_116
| ~ spl3_28
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f1382,f482,f236,f1649]) ).
fof(f1649,plain,
( spl3_116
<=> sK2(sK1,n) = sK2(int_zero,sK2(sK1,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_116])]) ).
fof(f236,plain,
( spl3_28
<=> int_less(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f1382,plain,
( sK2(sK1,n) = sK2(int_zero,sK2(sK1,n))
| ~ spl3_28
| ~ spl3_48 ),
inference(resolution,[],[f238,f483]) ).
fof(f238,plain,
( int_less(sK1,n)
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f1617,plain,
( spl3_115
| ~ spl3_47
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f662,f655,f429,f1615]) ).
fof(f1615,plain,
( spl3_115
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_115])]) ).
fof(f662,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK1) )
| ~ spl3_47
| ~ spl3_57 ),
inference(resolution,[],[f656,f430]) ).
fof(f1602,plain,
( spl3_114
| ~ spl3_20
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f1383,f236,f172,f1599]) ).
fof(f1383,plain,
( n = plus(sK1,sK2(sK1,n))
| ~ spl3_20
| ~ spl3_28 ),
inference(resolution,[],[f238,f173]) ).
fof(f1584,plain,
( spl3_113
| ~ spl3_46
| ~ spl3_55 ),
inference(avatar_split_clause,[],[f636,f632,f425,f1582]) ).
fof(f1582,plain,
( spl3_113
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_113])]) ).
fof(f632,plain,
( spl3_55
<=> ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
fof(f636,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X0) )
| ~ spl3_46
| ~ spl3_55 ),
inference(resolution,[],[f633,f426]) ).
fof(f633,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| int_less(sK1,plus(X1,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_55 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f1494,plain,
( spl3_112
| ~ spl3_7
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f437,f421,f93,f1492]) ).
fof(f1492,plain,
( spl3_112
<=> ! [X0,X1] :
( ~ int_less(plus(X0,X1),X0)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_112])]) ).
fof(f93,plain,
( spl3_7
<=> ! [X1] : ~ int_less(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f437,plain,
( ! [X0,X1] :
( ~ int_less(plus(X0,X1),X0)
| ~ int_less(int_zero,X1) )
| ~ spl3_7
| ~ spl3_45 ),
inference(resolution,[],[f422,f94]) ).
fof(f94,plain,
( ! [X1] : ~ int_less(X1,X1)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f1490,plain,
( spl3_111
| ~ spl3_7
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f432,f417,f93,f1488]) ).
fof(f1488,plain,
( spl3_111
<=> ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_111])]) ).
fof(f432,plain,
( ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) )
| ~ spl3_7
| ~ spl3_44 ),
inference(resolution,[],[f418,f94]) ).
fof(f1486,plain,
( spl3_110
| ~ spl3_14
| ~ spl3_40 ),
inference(avatar_split_clause,[],[f362,f349,f127,f1484]) ).
fof(f1484,plain,
( spl3_110
<=> ! [X0,X1] :
( int_leq(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_110])]) ).
fof(f362,plain,
( ! [X0,X1] :
( int_leq(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) )
| ~ spl3_14
| ~ spl3_40 ),
inference(superposition,[],[f350,f128]) ).
fof(f1482,plain,
( spl3_109
| ~ spl3_11
| ~ spl3_40 ),
inference(avatar_split_clause,[],[f359,f349,f109,f1480]) ).
fof(f1480,plain,
( spl3_109
<=> ! [X0] :
( ~ int_less(int_zero,X0)
| int_less(int_zero,plus(int_one,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_109])]) ).
fof(f359,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| int_less(int_zero,plus(int_one,X0)) )
| ~ spl3_11
| ~ spl3_40 ),
inference(resolution,[],[f350,f110]) ).
fof(f1478,plain,
( spl3_108
| ~ spl3_20
| ~ spl3_33
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f311,f293,f276,f172,f1476]) ).
fof(f1476,plain,
( spl3_108
<=> ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_108])]) ).
fof(f311,plain,
( ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,int_one) )
| ~ spl3_20
| ~ spl3_33
| ~ spl3_34 ),
inference(forward_demodulation,[],[f307,f277]) ).
fof(f307,plain,
( ! [X0] :
( int_less(X0,int_one)
| plus(int_zero,sK2(int_zero,X0)) = X0 )
| ~ spl3_20
| ~ spl3_34 ),
inference(resolution,[],[f294,f173]) ).
fof(f1461,plain,
( spl3_102
| ~ spl3_12
| spl3_78 ),
inference(avatar_split_clause,[],[f1053,f1046,f113,f1310]) ).
fof(f1046,plain,
( spl3_78
<=> int_leq(sK2(sK0,sK1),int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_78])]) ).
fof(f1053,plain,
( int_less(int_zero,sK2(sK0,sK1))
| ~ spl3_12
| spl3_78 ),
inference(resolution,[],[f1048,f114]) ).
fof(f1048,plain,
( ~ int_leq(sK2(sK0,sK1),int_zero)
| spl3_78 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1441,plain,
( spl3_107
| ~ spl3_18
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f1384,f236,f155,f1439]) ).
fof(f1384,plain,
( ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK1) )
| ~ spl3_18
| ~ spl3_28 ),
inference(resolution,[],[f238,f156]) ).
fof(f1381,plain,
( ~ spl3_2
| ~ spl3_15
| spl3_102 ),
inference(avatar_split_clause,[],[f1324,f1310,f135,f68]) ).
fof(f1324,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_15
| spl3_102 ),
inference(resolution,[],[f1312,f136]) ).
fof(f1312,plain,
( ~ int_less(int_zero,sK2(sK0,sK1))
| spl3_102 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f1336,plain,
( spl3_106
| ~ spl3_14
| ~ spl3_55 ),
inference(avatar_split_clause,[],[f639,f632,f127,f1334]) ).
fof(f1334,plain,
( spl3_106
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| int_less(sK1,plus(X1,X0))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_106])]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| int_less(sK1,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_14
| ~ spl3_55 ),
inference(superposition,[],[f633,f128]) ).
fof(f1332,plain,
( spl3_105
| ~ spl3_12
| ~ spl3_55 ),
inference(avatar_split_clause,[],[f637,f632,f113,f1330]) ).
fof(f1330,plain,
( spl3_105
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_one,X0)
| int_less(plus(X0,X2),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_105])]) ).
fof(f637,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X1,plus(X1,X2))
| int_less(sK1,plus(X0,X2))
| ~ int_leq(int_one,X0)
| int_less(plus(X0,X2),int_one) )
| ~ spl3_12
| ~ spl3_55 ),
inference(resolution,[],[f633,f114]) ).
fof(f1323,plain,
( ~ spl3_8
| spl3_104 ),
inference(avatar_contradiction_clause,[],[f1321]) ).
fof(f1321,plain,
( $false
| ~ spl3_8
| spl3_104 ),
inference(resolution,[],[f1319,f98]) ).
fof(f98,plain,
( ! [X1] : int_leq(X1,X1)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f97,plain,
( spl3_8
<=> ! [X1] : int_leq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f1319,plain,
( ~ int_leq(sK1,sK1)
| spl3_104 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f1320,plain,
( ~ spl3_1
| ~ spl3_67
| ~ spl3_102
| spl3_103
| ~ spl3_104
| ~ spl3_24
| ~ spl3_22
| ~ spl3_27
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f266,f256,f232,f192,f210,f1317,f1314,f1310,f816,f63]) ).
fof(f210,plain,
( spl3_24
<=> int_leq(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f266,plain,
( ! [X0] :
( ~ int_leq(sK0,sK1)
| ~ int_leq(sK1,sK1)
| ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK2(sK0,sK1))
| real_zero = a(X0,plus(X0,sK2(sK0,sK1)))
| ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK0) )
| ~ spl3_22
| ~ spl3_27
| ~ spl3_31 ),
inference(forward_demodulation,[],[f265,f234]) ).
fof(f265,plain,
( ! [X0] :
( ~ int_leq(sK1,sK1)
| ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK2(sK0,sK1))
| real_zero = a(X0,plus(X0,sK2(sK0,sK1)))
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0) )
| ~ spl3_22
| ~ spl3_27
| ~ spl3_31 ),
inference(forward_demodulation,[],[f263,f234]) ).
fof(f1308,plain,
( spl3_101
| ~ spl3_22
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f241,f232,f192,f1306]) ).
fof(f1306,plain,
( spl3_101
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X0,X1),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_101])]) ).
fof(f241,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X0,X1),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0) )
| ~ spl3_22
| ~ spl3_27 ),
inference(superposition,[],[f193,f234]) ).
fof(f1284,plain,
( spl3_100
| ~ spl3_13
| ~ spl3_69 ),
inference(avatar_split_clause,[],[f941,f934,f117,f1281]) ).
fof(f941,plain,
( int_leq(sK2(sK0,sK1),sK1)
| ~ spl3_13
| ~ spl3_69 ),
inference(resolution,[],[f936,f118]) ).
fof(f1279,plain,
( ~ spl3_93
| spl3_99
| ~ spl3_67
| ~ spl3_40
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f691,f678,f349,f816,f1277,f1224]) ).
fof(f1224,plain,
( spl3_93
<=> int_leq(int_one,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_93])]) ).
fof(f1277,plain,
( spl3_99
<=> ! [X0,X1] :
( ~ int_leq(X0,int_one)
| int_less(sK1,plus(int_one,X1))
| a(plus(X0,X1),X0) = qr(plus(X0,X1),X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_99])]) ).
fof(f691,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK1)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,int_one)
| a(plus(X0,X1),X0) = qr(plus(X0,X1),X0)
| int_less(sK1,plus(int_one,X1)) )
| ~ spl3_40
| ~ spl3_59 ),
inference(duplicate_literal_removal,[],[f681]) ).
fof(f681,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK1)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,int_one)
| a(plus(X0,X1),X0) = qr(plus(X0,X1),X0)
| int_less(sK1,plus(int_one,X1))
| ~ int_less(int_zero,X1) )
| ~ spl3_40
| ~ spl3_59 ),
inference(resolution,[],[f679,f350]) ).
fof(f1274,plain,
( ~ spl3_97
| spl3_98
| ~ spl3_72
| ~ spl3_22
| ~ spl3_27
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f289,f276,f232,f192,f953,f1272,f1268]) ).
fof(f1268,plain,
( spl3_97
<=> int_leq(int_one,int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_97])]) ).
fof(f1272,plain,
( spl3_98
<=> ! [X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X0)
| ~ int_leq(X1,int_zero)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_98])]) ).
fof(f953,plain,
( spl3_72
<=> int_leq(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).
fof(f289,plain,
( ! [X0,X1] :
( ~ int_leq(int_zero,sK1)
| ~ int_leq(X0,sK1)
| ~ int_leq(X1,int_zero)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,int_zero) )
| ~ spl3_22
| ~ spl3_27
| ~ spl3_33 ),
inference(forward_demodulation,[],[f288,f234]) ).
fof(f288,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(X1,int_zero)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,n)
| ~ int_leq(int_one,int_zero) )
| ~ spl3_22
| ~ spl3_27
| ~ spl3_33 ),
inference(forward_demodulation,[],[f286,f234]) ).
fof(f286,plain,
( ! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(X1,int_zero)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,n)
| ~ int_leq(int_one,int_zero) )
| ~ spl3_22
| ~ spl3_33 ),
inference(superposition,[],[f193,f277]) ).
fof(f1266,plain,
( ~ spl3_1
| spl3_95
| ~ spl3_24
| ~ spl3_40
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f831,f762,f349,f210,f1256,f63]) ).
fof(f1256,plain,
( spl3_95
<=> ! [X0,X1] :
( int_less(sK1,plus(sK0,X0))
| ~ int_less(int_zero,X0)
| ~ int_leq(sK0,X1)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_95])]) ).
fof(f762,plain,
( spl3_64
<=> ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
fof(f831,plain,
( ! [X0,X1] :
( ~ int_leq(sK0,sK1)
| int_less(sK1,plus(sK0,X0))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK0)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,sK0) )
| ~ spl3_40
| ~ spl3_64 ),
inference(duplicate_literal_removal,[],[f821]) ).
fof(f821,plain,
( ! [X0,X1] :
( ~ int_leq(sK0,sK1)
| int_less(sK1,plus(sK0,X0))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK0)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_leq(int_one,sK0)
| ~ int_less(int_zero,X0) )
| ~ spl3_40
| ~ spl3_64 ),
inference(resolution,[],[f763,f350]) ).
fof(f763,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(X1,sK1)
| int_less(sK1,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_64 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1265,plain,
( ~ spl3_8
| spl3_96 ),
inference(avatar_contradiction_clause,[],[f1263]) ).
fof(f1263,plain,
( $false
| ~ spl3_8
| spl3_96 ),
inference(resolution,[],[f1261,f98]) ).
fof(f1261,plain,
( ~ int_leq(sK0,sK0)
| spl3_96 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1262,plain,
( spl3_95
| ~ spl3_24
| ~ spl3_96
| ~ spl3_40
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f754,f612,f349,f1259,f210,f1256]) ).
fof(f612,plain,
( spl3_54
<=> ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
fof(f754,plain,
( ! [X0,X1] :
( ~ int_leq(sK0,sK0)
| ~ int_leq(sK0,sK1)
| int_less(sK1,plus(sK0,X0))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK0)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0)) )
| ~ spl3_40
| ~ spl3_54 ),
inference(duplicate_literal_removal,[],[f743]) ).
fof(f743,plain,
( ! [X0,X1] :
( ~ int_leq(sK0,sK0)
| ~ int_leq(sK0,sK1)
| int_less(sK1,plus(sK0,X0))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK0)
| ~ int_less(int_zero,X0)
| real_zero = a(X1,plus(X1,X0))
| ~ int_less(int_zero,X0) )
| ~ spl3_40
| ~ spl3_54 ),
inference(resolution,[],[f613,f350]) ).
fof(f613,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK1)
| int_less(sK1,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2)) )
| ~ spl3_54 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f1234,plain,
( ~ spl3_8
| spl3_93 ),
inference(avatar_contradiction_clause,[],[f1232]) ).
fof(f1232,plain,
( $false
| ~ spl3_8
| spl3_93 ),
inference(resolution,[],[f1226,f98]) ).
fof(f1226,plain,
( ~ int_leq(int_one,int_one)
| spl3_93 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f1230,plain,
( ~ spl3_93
| spl3_94
| ~ spl3_67
| ~ spl3_40
| ~ spl3_55 ),
inference(avatar_split_clause,[],[f645,f632,f349,f816,f1228,f1224]) ).
fof(f1228,plain,
( spl3_94
<=> ! [X0,X1] :
( ~ int_leq(X0,int_one)
| int_less(sK1,plus(int_one,X1))
| real_zero = a(X0,plus(X0,X1))
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_94])]) ).
fof(f645,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK1)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| real_zero = a(X0,plus(X0,X1))
| int_less(sK1,plus(int_one,X1))
| ~ int_leq(int_one,int_one) )
| ~ spl3_40
| ~ spl3_55 ),
inference(duplicate_literal_removal,[],[f635]) ).
fof(f635,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK1)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| real_zero = a(X0,plus(X0,X1))
| int_less(sK1,plus(int_one,X1))
| ~ int_leq(int_one,int_one)
| ~ int_less(int_zero,X1) )
| ~ spl3_40
| ~ spl3_55 ),
inference(resolution,[],[f633,f350]) ).
fof(f1215,plain,
( spl3_92
| ~ spl3_33
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f857,f781,f276,f1212]) ).
fof(f1212,plain,
( spl3_92
<=> sK0 = sK2(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_92])]) ).
fof(f781,plain,
( spl3_65
<=> sK0 = plus(int_zero,sK2(int_zero,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
fof(f857,plain,
( sK0 = sK2(int_zero,sK0)
| ~ spl3_33
| ~ spl3_65 ),
inference(superposition,[],[f783,f277]) ).
fof(f783,plain,
( sK0 = plus(int_zero,sK2(int_zero,sK0))
| ~ spl3_65 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f1203,plain,
( spl3_91
| ~ spl3_13
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f309,f293,f117,f1201]) ).
fof(f1201,plain,
( spl3_91
<=> ! [X0] :
( int_less(X0,int_one)
| int_leq(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_91])]) ).
fof(f309,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_leq(int_zero,X0) )
| ~ spl3_13
| ~ spl3_34 ),
inference(resolution,[],[f294,f118]) ).
fof(f1199,plain,
( spl3_90
| ~ spl3_13
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f304,f293,f117,f1197]) ).
fof(f1197,plain,
( spl3_90
<=> ! [X0] :
( int_less(int_zero,X0)
| int_leq(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_90])]) ).
fof(f304,plain,
( ! [X0] :
( int_less(int_zero,X0)
| int_leq(X0,int_one) )
| ~ spl3_13
| ~ spl3_34 ),
inference(resolution,[],[f294,f118]) ).
fof(f1190,plain,
( spl3_89
| ~ spl3_33
| ~ spl3_37 ),
inference(avatar_split_clause,[],[f323,f319,f276,f1187]) ).
fof(f1187,plain,
( spl3_89
<=> int_one = sK2(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_89])]) ).
fof(f319,plain,
( spl3_37
<=> int_one = plus(int_zero,sK2(int_zero,int_one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f323,plain,
( int_one = sK2(int_zero,int_one)
| ~ spl3_33
| ~ spl3_37 ),
inference(superposition,[],[f321,f277]) ).
fof(f321,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_37 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1173,plain,
( spl3_88
| ~ spl3_31
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f591,f574,f256,f1171]) ).
fof(f1171,plain,
( spl3_88
<=> ! [X0,X1] :
( int_less(plus(X0,X1),sK1)
| ~ int_less(X0,sK0)
| ~ int_leq(X1,sK2(sK0,sK1))
| plus(X0,X1) = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_88])]) ).
fof(f591,plain,
( ! [X0,X1] :
( int_less(plus(X0,X1),sK1)
| ~ int_less(X0,sK0)
| ~ int_leq(X1,sK2(sK0,sK1))
| plus(X0,X1) = sK1 )
| ~ spl3_31
| ~ spl3_52 ),
inference(superposition,[],[f575,f258]) ).
fof(f1155,plain,
( ~ spl3_2
| ~ spl3_39
| spl3_76 ),
inference(avatar_split_clause,[],[f1043,f1036,f345,f68]) ).
fof(f345,plain,
( spl3_39
<=> ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_zero,sK2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
fof(f1036,plain,
( spl3_76
<=> int_leq(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_76])]) ).
fof(f1043,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_39
| spl3_76 ),
inference(resolution,[],[f1038,f346]) ).
fof(f346,plain,
( ! [X0,X1] :
( int_leq(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_39 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f1038,plain,
( ~ int_leq(int_zero,sK2(sK0,sK1))
| spl3_76 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1154,plain,
( spl3_87
| ~ spl3_31
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f585,f574,f256,f1152]) ).
fof(f1152,plain,
( spl3_87
<=> ! [X0,X1] :
( int_less(sK1,plus(X0,X1))
| ~ int_less(sK0,X0)
| ~ int_leq(sK2(sK0,sK1),X1)
| plus(X0,X1) = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_87])]) ).
fof(f585,plain,
( ! [X0,X1] :
( int_less(sK1,plus(X0,X1))
| ~ int_less(sK0,X0)
| ~ int_leq(sK2(sK0,sK1),X1)
| plus(X0,X1) = sK1 )
| ~ spl3_31
| ~ spl3_52 ),
inference(superposition,[],[f575,f258]) ).
fof(f1117,plain,
( spl3_86
| ~ spl3_31
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f537,f505,f256,f1115]) ).
fof(f537,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X1,sK0)
| ~ int_less(X0,sK2(sK0,sK1)) )
| ~ spl3_31
| ~ spl3_50 ),
inference(superposition,[],[f506,f258]) ).
fof(f1113,plain,
( spl3_85
| ~ spl3_31
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f531,f505,f256,f1111]) ).
fof(f1111,plain,
( spl3_85
<=> ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK2(sK0,sK1),X0)
| ~ int_less(sK0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_85])]) ).
fof(f531,plain,
( ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK2(sK0,sK1),X0)
| ~ int_less(sK0,X1) )
| ~ spl3_31
| ~ spl3_50 ),
inference(superposition,[],[f506,f258]) ).
fof(f1109,plain,
( spl3_84
| ~ spl3_31
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f518,f501,f256,f1107]) ).
fof(f1107,plain,
( spl3_84
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X0,sK2(sK0,sK1))
| ~ int_less(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_84])]) ).
fof(f518,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X0,sK2(sK0,sK1))
| ~ int_less(X1,sK0) )
| ~ spl3_31
| ~ spl3_49 ),
inference(superposition,[],[f502,f258]) ).
fof(f1104,plain,
( spl3_83
| ~ spl3_31
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f512,f501,f256,f1102]) ).
fof(f512,plain,
( ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK0,X1)
| ~ int_less(sK2(sK0,sK1),X0) )
| ~ spl3_31
| ~ spl3_49 ),
inference(superposition,[],[f502,f258]) ).
fof(f1100,plain,
( spl3_82
| ~ spl3_21
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f262,f256,f181,f1098]) ).
fof(f1098,plain,
( spl3_82
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X1,sK2(sK0,sK1))
| ~ int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_82])]) ).
fof(f262,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK1)
| ~ int_leq(X1,sK2(sK0,sK1))
| ~ int_less(X0,sK0) )
| ~ spl3_21
| ~ spl3_31 ),
inference(superposition,[],[f182,f258]) ).
fof(f1096,plain,
( spl3_81
| ~ spl3_21
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f261,f256,f181,f1094]) ).
fof(f1094,plain,
( spl3_81
<=> ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK2(sK0,sK1),X1)
| ~ int_less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_81])]) ).
fof(f261,plain,
( ! [X0,X1] :
( int_leq(sK1,plus(X0,X1))
| ~ int_leq(sK2(sK0,sK1),X1)
| ~ int_less(sK0,X0) )
| ~ spl3_21
| ~ spl3_31 ),
inference(superposition,[],[f182,f258]) ).
fof(f1057,plain,
( spl3_80
| ~ spl3_19
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f552,f547,f159,f1055]) ).
fof(f1055,plain,
( spl3_80
<=> ! [X0] : plus(X0,sK0) = plus(X0,sK2(X0,plus(X0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_80])]) ).
fof(f552,plain,
( ! [X0] : plus(X0,sK0) = plus(X0,sK2(X0,plus(X0,sK0)))
| ~ spl3_19
| ~ spl3_51 ),
inference(resolution,[],[f548,f161]) ).
fof(f1052,plain,
( ~ spl3_78
| spl3_79
| ~ spl3_31
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f468,f429,f256,f1050,f1046]) ).
fof(f1050,plain,
( spl3_79
<=> ! [X0] :
( int_leq(sK1,X0)
| ~ int_less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_79])]) ).
fof(f468,plain,
( ! [X0] :
( int_leq(sK1,X0)
| ~ int_leq(sK2(sK0,sK1),int_zero)
| ~ int_less(sK0,X0) )
| ~ spl3_31
| ~ spl3_47 ),
inference(superposition,[],[f430,f258]) ).
fof(f1042,plain,
( ~ spl3_76
| spl3_77
| ~ spl3_31
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f455,f425,f256,f1040,f1036]) ).
fof(f1040,plain,
( spl3_77
<=> ! [X0] :
( int_leq(X0,sK1)
| ~ int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_77])]) ).
fof(f455,plain,
( ! [X0] :
( int_leq(X0,sK1)
| ~ int_leq(int_zero,sK2(sK0,sK1))
| ~ int_less(X0,sK0) )
| ~ spl3_31
| ~ spl3_46 ),
inference(superposition,[],[f426,f258]) ).
fof(f1003,plain,
( spl3_75
| ~ spl3_25
| ~ spl3_38 ),
inference(avatar_split_clause,[],[f389,f341,f220,f1001]) ).
fof(f1001,plain,
( spl3_75
<=> ! [X0,X1] :
( int_leq(sK0,sK2(X0,X1))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_75])]) ).
fof(f220,plain,
( spl3_25
<=> int_one = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f389,plain,
( ! [X0,X1] :
( int_leq(sK0,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_25
| ~ spl3_38 ),
inference(superposition,[],[f342,f222]) ).
fof(f222,plain,
( int_one = sK0
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f966,plain,
( spl3_74
| ~ spl3_26
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f627,f482,f224,f963]) ).
fof(f963,plain,
( spl3_74
<=> sK2(int_one,sK0) = sK2(int_zero,sK2(int_one,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_74])]) ).
fof(f224,plain,
( spl3_26
<=> int_less(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f627,plain,
( sK2(int_one,sK0) = sK2(int_zero,sK2(int_one,sK0))
| ~ spl3_26
| ~ spl3_48 ),
inference(resolution,[],[f226,f483]) ).
fof(f226,plain,
( int_less(int_one,sK0)
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f961,plain,
( spl3_73
| ~ spl3_2
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f496,f482,f68,f958]) ).
fof(f958,plain,
( spl3_73
<=> sK2(sK0,sK1) = sK2(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_73])]) ).
fof(f496,plain,
( sK2(sK0,sK1) = sK2(int_zero,sK2(sK0,sK1))
| ~ spl3_2
| ~ spl3_48 ),
inference(resolution,[],[f483,f70]) ).
fof(f956,plain,
( spl3_72
| ~ spl3_13
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f571,f314,f117,f953]) ).
fof(f571,plain,
( int_leq(int_zero,sK1)
| ~ spl3_13
| ~ spl3_36 ),
inference(resolution,[],[f316,f118]) ).
fof(f950,plain,
( spl3_71
| ~ spl3_19
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f494,f482,f159,f947]) ).
fof(f947,plain,
( spl3_71
<=> sK2(int_zero,sK0) = sK2(int_zero,sK2(int_zero,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).
fof(f494,plain,
( sK2(int_zero,sK0) = sK2(int_zero,sK2(int_zero,sK0))
| ~ spl3_19
| ~ spl3_48 ),
inference(resolution,[],[f483,f161]) ).
fof(f945,plain,
( spl3_70
| ~ spl3_29
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f402,f392,f245,f943]) ).
fof(f943,plain,
( spl3_70
<=> ! [X0] :
( int_less(sK0,X0)
| sK0 = X0
| int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).
fof(f245,plain,
( spl3_29
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f402,plain,
( ! [X0] :
( int_less(sK0,X0)
| sK0 = X0
| int_less(X0,sK1) )
| ~ spl3_29
| ~ spl3_43 ),
inference(resolution,[],[f393,f246]) ).
fof(f246,plain,
( ! [X0] :
( ~ int_less(X0,sK0)
| int_less(X0,sK1) )
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f937,plain,
( ~ spl3_19
| spl3_69
| ~ spl3_31
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f374,f353,f256,f934,f159]) ).
fof(f374,plain,
( int_less(sK2(sK0,sK1),sK1)
| ~ int_less(int_zero,sK0)
| ~ spl3_31
| ~ spl3_41 ),
inference(superposition,[],[f354,f258]) ).
fof(f849,plain,
( spl3_68
| ~ spl3_11
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f385,f220,f109,f847]) ).
fof(f385,plain,
( ! [X0] :
( ~ int_leq(sK0,X0)
| int_less(int_zero,X0) )
| ~ spl3_11
| ~ spl3_25 ),
inference(superposition,[],[f110,f222]) ).
fof(f819,plain,
( spl3_67
| ~ spl3_10
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f567,f314,f105,f816]) ).
fof(f567,plain,
( int_leq(int_one,sK1)
| ~ spl3_10
| ~ spl3_36 ),
inference(resolution,[],[f316,f106]) ).
fof(f789,plain,
( spl3_66
| ~ spl3_20
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f228,f224,f172,f786]) ).
fof(f228,plain,
( sK0 = plus(int_one,sK2(int_one,sK0))
| ~ spl3_20
| ~ spl3_26 ),
inference(resolution,[],[f226,f173]) ).
fof(f784,plain,
( spl3_65
| ~ spl3_19
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f215,f172,f159,f781]) ).
fof(f215,plain,
( sK0 = plus(int_zero,sK2(int_zero,sK0))
| ~ spl3_19
| ~ spl3_20 ),
inference(resolution,[],[f161,f173]) ).
fof(f764,plain,
( spl3_64
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f725,f603,f232,f220,f762]) ).
fof(f725,plain,
( ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f724,f234]) ).
fof(f724,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f607,f234]) ).
fof(f607,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_25
| ~ spl3_53 ),
inference(forward_demodulation,[],[f606,f222]) ).
fof(f606,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_25
| ~ spl3_53 ),
inference(forward_demodulation,[],[f604,f222]) ).
fof(f720,plain,
( spl3_63
| ~ spl3_18
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f229,f224,f155,f718]) ).
fof(f229,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_26 ),
inference(resolution,[],[f226,f156]) ).
fof(f716,plain,
( spl3_62
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f216,f159,f155,f714]) ).
fof(f714,plain,
( spl3_62
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).
fof(f216,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_zero) )
| ~ spl3_18
| ~ spl3_19 ),
inference(resolution,[],[f161,f156]) ).
fof(f703,plain,
( spl3_61
| ~ spl3_27
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f699,f695,f232,f701]) ).
fof(f699,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_27
| ~ spl3_60 ),
inference(forward_demodulation,[],[f698,f234]) ).
fof(f698,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_27
| ~ spl3_60 ),
inference(forward_demodulation,[],[f696,f234]) ).
fof(f697,plain,
( spl3_60
| ~ spl3_14
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f206,f201,f127,f695]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| a(plus(X2,X1),X2) = qr(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_23 ),
inference(superposition,[],[f202,f128]) ).
fof(f680,plain,
( spl3_59
| ~ spl3_27
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f676,f672,f232,f678]) ).
fof(f676,plain,
( ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2)) )
| ~ spl3_27
| ~ spl3_58 ),
inference(forward_demodulation,[],[f675,f234]) ).
fof(f675,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) )
| ~ spl3_27
| ~ spl3_58 ),
inference(forward_demodulation,[],[f673,f234]) ).
fof(f674,plain,
( spl3_58
| ~ spl3_12
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f204,f201,f113,f672]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| a(plus(X0,X2),X0) = qr(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) )
| ~ spl3_12
| ~ spl3_23 ),
inference(resolution,[],[f202,f114]) ).
fof(f657,plain,
( spl3_57
| ~ spl3_27
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f653,f649,f232,f655]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK1)
| ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_27
| ~ spl3_56 ),
inference(forward_demodulation,[],[f652,f234]) ).
fof(f652,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK1)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_27
| ~ spl3_56 ),
inference(forward_demodulation,[],[f650,f234]) ).
fof(f651,plain,
( spl3_56
| ~ spl3_14
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f197,f192,f127,f649]) ).
fof(f197,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| real_zero = a(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_14
| ~ spl3_22 ),
inference(superposition,[],[f193,f128]) ).
fof(f634,plain,
( spl3_55
| ~ spl3_27
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f616,f603,f232,f632]) ).
fof(f616,plain,
( ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f615,f234]) ).
fof(f615,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f604,f234]) ).
fof(f614,plain,
( spl3_54
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f610,f603,f232,f220,f612]) ).
fof(f610,plain,
( ! [X2,X0,X1] :
( int_less(sK1,plus(X1,X2))
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2)) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f609,f234]) ).
fof(f609,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK0,X1)
| ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| int_less(n,plus(X1,X2)) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f608,f222]) ).
fof(f608,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK1)
| ~ int_leq(sK0,plus(X1,X2))
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_53 ),
inference(forward_demodulation,[],[f607,f234]) ).
fof(f605,plain,
( spl3_53
| ~ spl3_12
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f195,f192,f113,f603]) ).
fof(f195,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| real_zero = a(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_12
| ~ spl3_22 ),
inference(resolution,[],[f193,f114]) ).
fof(f576,plain,
( spl3_52
| ~ spl3_17
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f184,f181,f151,f574]) ).
fof(f184,plain,
( ! [X2,X3,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_less(X2,X3)
| int_less(plus(X2,X0),plus(X3,X1))
| plus(X2,X0) = plus(X3,X1) )
| ~ spl3_17
| ~ spl3_21 ),
inference(resolution,[],[f182,f152]) ).
fof(f549,plain,
( spl3_51
| ~ spl3_16
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f178,f172,f139,f547]) ).
fof(f178,plain,
( ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| ~ int_less(int_zero,X1) )
| ~ spl3_16
| ~ spl3_20 ),
inference(resolution,[],[f173,f140]) ).
fof(f507,plain,
( spl3_50
| ~ spl3_14
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f189,f181,f127,f505]) ).
fof(f189,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X2,X3),plus(X1,X0))
| ~ int_leq(X3,X1)
| ~ int_less(X2,X0) )
| ~ spl3_14
| ~ spl3_21 ),
inference(superposition,[],[f182,f128]) ).
fof(f503,plain,
( spl3_49
| ~ spl3_14
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f186,f181,f127,f501]) ).
fof(f186,plain,
( ! [X2,X3,X0,X1] :
( int_leq(plus(X1,X0),plus(X2,X3))
| ~ int_leq(X1,X3)
| ~ int_less(X0,X2) )
| ~ spl3_14
| ~ spl3_21 ),
inference(superposition,[],[f182,f128]) ).
fof(f484,plain,
( spl3_48
| ~ spl3_9
| ~ spl3_14
| ~ spl3_15
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f179,f172,f135,f127,f101,f482]) ).
fof(f101,plain,
( spl3_9
<=> ! [X0] : plus(X0,int_zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f179,plain,
( ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_9
| ~ spl3_14
| ~ spl3_15
| ~ spl3_20 ),
inference(forward_demodulation,[],[f177,f130]) ).
fof(f130,plain,
( ! [X0] : plus(int_zero,X0) = X0
| ~ spl3_9
| ~ spl3_14 ),
inference(superposition,[],[f128,f102]) ).
fof(f102,plain,
( ! [X0] : plus(X0,int_zero) = X0
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f177,plain,
( ! [X0,X1] :
( sK2(X0,X1) = plus(int_zero,sK2(int_zero,sK2(X0,X1)))
| ~ int_less(X0,X1) )
| ~ spl3_15
| ~ spl3_20 ),
inference(resolution,[],[f173,f136]) ).
fof(f431,plain,
( spl3_47
| ~ spl3_9
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f188,f181,f101,f429]) ).
fof(f188,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X0) )
| ~ spl3_9
| ~ spl3_21 ),
inference(superposition,[],[f182,f102]) ).
fof(f427,plain,
( spl3_46
| ~ spl3_9
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f185,f181,f101,f425]) ).
fof(f185,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(X0,X1) )
| ~ spl3_9
| ~ spl3_21 ),
inference(superposition,[],[f182,f102]) ).
fof(f423,plain,
( spl3_45
| ~ spl3_16
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f170,f155,f139,f421]) ).
fof(f170,plain,
( ! [X2,X0,X1] :
( int_less(X0,plus(X1,X2))
| ~ int_less(X0,X1)
| ~ int_less(int_zero,X2) )
| ~ spl3_16
| ~ spl3_18 ),
inference(resolution,[],[f156,f140]) ).
fof(f419,plain,
( spl3_44
| ~ spl3_15
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f169,f155,f135,f417]) ).
fof(f169,plain,
( ! [X2,X0,X1] :
( int_less(X0,sK2(X1,X2))
| ~ int_less(X0,int_zero)
| ~ int_less(X1,X2) )
| ~ spl3_15
| ~ spl3_18 ),
inference(resolution,[],[f156,f136]) ).
fof(f394,plain,
( spl3_43
| ~ spl3_12
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f166,f151,f113,f392]) ).
fof(f166,plain,
( ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) )
| ~ spl3_12
| ~ spl3_17 ),
inference(resolution,[],[f152,f114]) ).
fof(f382,plain,
( spl3_42
| ~ spl3_26
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f249,f245,f224,f379]) ).
fof(f249,plain,
( int_less(int_one,sK1)
| ~ spl3_26
| ~ spl3_29 ),
inference(resolution,[],[f246,f226]) ).
fof(f355,plain,
( spl3_41
| ~ spl3_14
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f147,f139,f127,f353]) ).
fof(f147,plain,
( ! [X0,X1] :
( int_less(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) )
| ~ spl3_14
| ~ spl3_16 ),
inference(superposition,[],[f140,f128]) ).
fof(f351,plain,
( spl3_40
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f145,f139,f117,f349]) ).
fof(f145,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| int_leq(X1,plus(X1,X0)) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f140,f118]) ).
fof(f347,plain,
( spl3_39
| ~ spl3_13
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f143,f135,f117,f345]) ).
fof(f143,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_zero,sK2(X0,X1)) )
| ~ spl3_13
| ~ spl3_15 ),
inference(resolution,[],[f136,f118]) ).
fof(f343,plain,
( spl3_38
| ~ spl3_10
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f142,f135,f105,f341]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_one,sK2(X0,X1)) )
| ~ spl3_10
| ~ spl3_15 ),
inference(resolution,[],[f136,f106]) ).
fof(f322,plain,
( spl3_37
| ~ spl3_6
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f176,f172,f88,f319]) ).
fof(f176,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_6
| ~ spl3_20 ),
inference(resolution,[],[f173,f90]) ).
fof(f317,plain,
( spl3_36
| ~ spl3_19
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f248,f245,f159,f314]) ).
fof(f248,plain,
( int_less(int_zero,sK1)
| ~ spl3_19
| ~ spl3_29 ),
inference(resolution,[],[f246,f161]) ).
fof(f299,plain,
( spl3_35
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f168,f155,f88,f297]) ).
fof(f297,plain,
( spl3_35
<=> ! [X0] :
( int_less(X0,int_one)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f168,plain,
( ! [X0] :
( int_less(X0,int_one)
| ~ int_less(X0,int_zero) )
| ~ spl3_6
| ~ spl3_18 ),
inference(resolution,[],[f156,f90]) ).
fof(f295,plain,
( spl3_34
| ~ spl3_11
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f123,f113,f109,f293]) ).
fof(f123,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_11
| ~ spl3_12 ),
inference(resolution,[],[f114,f110]) ).
fof(f278,plain,
( spl3_33
| ~ spl3_9
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f130,f127,f101,f276]) ).
fof(f273,plain,
( spl3_32
| ~ spl3_6
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f125,f117,f88,f270]) ).
fof(f270,plain,
( spl3_32
<=> int_leq(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f125,plain,
( int_leq(int_zero,int_one)
| ~ spl3_6
| ~ spl3_13 ),
inference(resolution,[],[f118,f90]) ).
fof(f259,plain,
( spl3_31
| ~ spl3_2
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f175,f172,f68,f256]) ).
fof(f175,plain,
( sK1 = plus(sK0,sK2(sK0,sK1))
| ~ spl3_2
| ~ spl3_20 ),
inference(resolution,[],[f173,f70]) ).
fof(f254,plain,
( spl3_30
| ~ spl3_13
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f217,f159,f117,f251]) ).
fof(f251,plain,
( spl3_30
<=> int_leq(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f217,plain,
( int_leq(int_zero,sK0)
| ~ spl3_13
| ~ spl3_19 ),
inference(resolution,[],[f161,f118]) ).
fof(f247,plain,
( spl3_29
| ~ spl3_2
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f167,f155,f68,f245]) ).
fof(f167,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK0) )
| ~ spl3_2
| ~ spl3_18 ),
inference(resolution,[],[f156,f70]) ).
fof(f239,plain,
( spl3_27
| spl3_28
| ~ spl3_3
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f164,f151,f73,f236,f232]) ).
fof(f164,plain,
( int_less(sK1,n)
| n = sK1
| ~ spl3_3
| ~ spl3_17 ),
inference(resolution,[],[f152,f75]) ).
fof(f75,plain,
( int_leq(sK1,n)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f227,plain,
( spl3_25
| spl3_26
| ~ spl3_1
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f163,f151,f63,f224,f220]) ).
fof(f163,plain,
( int_less(int_one,sK0)
| int_one = sK0
| ~ spl3_1
| ~ spl3_17 ),
inference(resolution,[],[f152,f65]) ).
fof(f213,plain,
( spl3_24
| ~ spl3_2
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f124,f117,f68,f210]) ).
fof(f124,plain,
( int_leq(sK0,sK1)
| ~ spl3_2
| ~ spl3_13 ),
inference(resolution,[],[f118,f70]) ).
fof(f203,plain,
spl3_23,
inference(avatar_split_clause,[],[f58,f201]) ).
fof(f58,plain,
! [X1,X4,X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5)
| ~ int_less(int_zero,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(plus(X1,X4),n)
| ~ int_leq(int_one,plus(X1,X4)) ),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X4,X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5)
| plus(X1,X4) != X0
| ~ int_less(int_zero,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5) )
| plus(X1,X4) != X0
| ~ int_less(int_zero,X4) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( a(plus(X5,X4),X5) = qr(plus(X5,X4),X5)
| ~ int_leq(X5,X1)
| ~ int_leq(int_one,X5) )
| plus(X1,X4) != X0
| ~ int_less(int_zero,X4) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( plus(X0,X2) = X1
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> real_zero = a(X3,plus(X3,X2)) ) )
& ! [X4] :
( ( plus(X1,X4) = X0
& int_less(int_zero,X4) )
=> ! [X5] :
( ( int_leq(X5,X1)
& int_leq(int_one,X5) )
=> a(plus(X5,X4),X5) = qr(plus(X5,X4),X5) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X7] :
( ( plus(X0,X7) = X1
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X0)
& int_leq(int_one,X2) )
=> real_zero = a(X2,plus(X2,X7)) ) )
& ! [X7] :
( ( plus(X1,X7) = X0
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> a(plus(X2,X7),X2) = qr(plus(X2,X7),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qih) ).
fof(f194,plain,
spl3_22,
inference(avatar_split_clause,[],[f57,f192]) ).
fof(f57,plain,
! [X2,X3,X0] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X0,X2),n)
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f183,plain,
spl3_21,
inference(avatar_split_clause,[],[f56,f181]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_leq(X2,X3)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_leq(X2,X3)
| ~ int_less(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_leq(X2,X3)
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( int_leq(X2,X3)
& int_less(X0,X1) )
=> int_leq(plus(X0,X2),plus(X1,X3)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X3,X4,X5,X6] :
( ( int_leq(X5,X6)
& int_less(X3,X4) )
=> int_leq(plus(X3,X5),plus(X4,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
fof(f174,plain,
spl3_20,
inference(avatar_split_clause,[],[f49,f172]) ).
fof(f49,plain,
! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ( int_less(int_zero,sK2(X0,X1))
& plus(X0,sK2(X0,X1)) = X1 )
| ~ int_less(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
=> ( int_less(int_zero,sK2(X0,X1))
& plus(X0,sK2(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
| ~ int_less(X0,X1) ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 )
| ~ int_less(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(f162,plain,
( spl3_19
| ~ spl3_1
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f121,f109,f63,f159]) ).
fof(f121,plain,
( int_less(int_zero,sK0)
| ~ spl3_1
| ~ spl3_11 ),
inference(resolution,[],[f110,f65]) ).
fof(f157,plain,
spl3_18,
inference(avatar_split_clause,[],[f55,f155]) ).
fof(f55,plain,
! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( int_less(X1,X2)
& int_less(X0,X1) )
=> int_less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
fof(f153,plain,
spl3_17,
inference(avatar_split_clause,[],[f52,f151]) ).
fof(f52,plain,
! [X0,X1] :
( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( X0 = X1
| int_less(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
fof(f141,plain,
spl3_16,
inference(avatar_split_clause,[],[f60,f139]) ).
fof(f60,plain,
! [X2,X0] :
( int_less(X0,plus(X0,X2))
| ~ int_less(int_zero,X2) ),
inference(equality_resolution,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( int_less(X0,X1)
| ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f137,plain,
spl3_15,
inference(avatar_split_clause,[],[f50,f135]) ).
fof(f50,plain,
! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f129,plain,
spl3_14,
inference(avatar_split_clause,[],[f46,f127]) ).
fof(f46,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
fof(f119,plain,
spl3_13,
inference(avatar_split_clause,[],[f53,f117]) ).
fof(f53,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f115,plain,
spl3_12,
inference(avatar_split_clause,[],[f47,f113]) ).
fof(f47,plain,
! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
fof(f111,plain,
spl3_11,
inference(avatar_split_clause,[],[f45,f109]) ).
fof(f45,plain,
! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) )
& ( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(f107,plain,
spl3_10,
inference(avatar_split_clause,[],[f44,f105]) ).
fof(f44,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f103,plain,
spl3_9,
inference(avatar_split_clause,[],[f43,f101]) ).
fof(f43,plain,
! [X0] : plus(X0,int_zero) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : plus(X0,int_zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
fof(f99,plain,
spl3_8,
inference(avatar_split_clause,[],[f61,f97]) ).
fof(f61,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f95,plain,
spl3_7,
inference(avatar_split_clause,[],[f59,f93]) ).
fof(f59,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( int_less(X0,X1)
=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(f91,plain,
spl3_6,
inference(avatar_split_clause,[],[f42,f88]) ).
fof(f42,plain,
int_less(int_zero,int_one),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
int_less(int_zero,int_one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
fof(f86,plain,
~ spl3_5,
inference(avatar_split_clause,[],[f41,f83]) ).
fof(f83,plain,
( spl3_5
<=> real_zero = real_one ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f41,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
fof(f81,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f38,f78]) ).
fof(f38,plain,
real_zero != a(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( real_zero != a(sK0,sK1)
& int_leq(sK1,n)
& int_less(sK0,sK1)
& int_leq(int_one,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f26]) ).
fof(f26,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> ( real_zero != a(sK0,sK1)
& int_leq(sK1,n)
& int_less(sK0,sK1)
& int_leq(int_one,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt) ).
fof(f76,plain,
spl3_3,
inference(avatar_split_clause,[],[f37,f73]) ).
fof(f37,plain,
int_leq(sK1,n),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
spl3_2,
inference(avatar_split_clause,[],[f36,f68]) ).
fof(f36,plain,
int_less(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
spl3_1,
inference(avatar_split_clause,[],[f35,f63]) ).
fof(f35,plain,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV486+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 04:43:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (11143)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (11146)WARNING: value z3 for option sas not known
% 0.12/0.35 % (11144)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (11148)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)
% 0.12/0.35 % (11147)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (11145)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (11149)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)
% 0.12/0.35 % (11146)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)
% 0.12/0.35 % (11150)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)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [3]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [4]
% 0.12/0.36 TRYING [3]
% 0.12/0.37 TRYING [5]
% 0.12/0.38 TRYING [4]
% 0.12/0.39 TRYING [6]
% 0.17/0.42 TRYING [5]
% 0.17/0.43 TRYING [7]
% 0.17/0.51 TRYING [8]
% 0.17/0.52 TRYING [6]
% 2.20/0.64 % (11148)First to succeed.
% 2.20/0.65 % (11148)Refutation found. Thanks to Tanya!
% 2.20/0.65 % SZS status Theorem for theBenchmark
% 2.20/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.66 % (11148)------------------------------
% 2.20/0.66 % (11148)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.20/0.66 % (11148)Termination reason: Refutation
% 2.20/0.66
% 2.20/0.66 % (11148)Memory used [KB]: 2987
% 2.20/0.66 % (11148)Time elapsed: 0.307 s
% 2.20/0.66 % (11148)Instructions burned: 604 (million)
% 2.20/0.66 % (11148)------------------------------
% 2.20/0.66 % (11148)------------------------------
% 2.20/0.66 % (11143)Success in time 0.323 s
%------------------------------------------------------------------------------