TSTP Solution File: SWV487+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV487+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:26:07 EDT 2024
% Result : Theorem 3.92s 0.96s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 246
% Syntax : Number of formulae : 855 ( 37 unt; 0 def)
% Number of atoms : 3507 ( 341 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 4866 (2214 ~;2346 |; 54 &)
% ( 234 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 235 ( 233 usr; 232 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 1020 (1010 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6189,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,f214,f228,f240,f248,f255,f260,f274,f279,f296,f300,f318,f323,f344,f348,f352,f356,f383,f395,f420,f424,f428,f432,f485,f504,f508,f550,f577,f610,f613,f620,f639,f650,f660,f677,f683,f696,f702,f720,f726,f731,f749,f753,f766,f771,f848,f853,f861,f866,f872,f877,f910,f923,f928,f965,f969,f973,f977,f981,f985,f994,f1038,f1039,f1057,f1074,f1083,f1087,f1095,f1245,f1266,f1301,f1319,f1358,f1362,f1371,f1404,f1477,f1481,f1499,f1547,f1581,f1586,f1628,f1660,f1669,f1673,f1699,f1709,f1713,f1717,f1721,f1725,f1729,f1733,f1821,f1828,f1832,f1837,f1841,f1845,f1849,f1914,f1916,f1920,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1973,f1984,f1988,f1992,f1996,f2274,f2278,f2282,f2287,f2497,f2536,f2555,f2583,f2667,f2671,f2675,f2747,f2751,f2755,f2759,f2764,f3005,f3061,f3065,f3168,f3196,f3200,f3204,f3208,f3212,f3216,f3220,f3224,f3311,f3508,f3512,f3516,f3521,f3622,f3667,f3688,f3692,f3770,f3774,f3856,f3889,f3927,f4002,f4006,f4056,f4123,f4127,f4188,f4192,f4247,f4273,f4277,f4327,f4331,f4388,f4389,f4441,f4647,f4703,f4704,f4723,f4755,f4796,f4797,f5011,f5082,f5169,f5212,f5216,f5287,f5339,f5357,f5388,f5425,f5428,f5432,f5436,f5440,f5453,f5580,f5585,f5729,f5734,f5754,f5758,f5763,f5781,f5790,f5811,f5856,f5876,f5885,f5889,f5894,f5897,f6188]) ).
fof(f6188,plain,
( ~ spl3_2
| ~ spl3_27
| spl3_106 ),
inference(avatar_split_clause,[],[f1548,f1544,f233,f68]) ).
fof(f68,plain,
( spl3_2
<=> int_less(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f233,plain,
( spl3_27
<=> n = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f1544,plain,
( spl3_106
<=> int_less(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_106])]) ).
fof(f1548,plain,
( ~ int_less(sK1,sK0)
| ~ spl3_27
| spl3_106 ),
inference(forward_demodulation,[],[f1545,f235]) ).
fof(f235,plain,
( n = sK0
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f1545,plain,
( ~ int_less(sK1,n)
| spl3_106 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f5897,plain,
( ~ spl3_8
| spl3_231 ),
inference(avatar_contradiction_clause,[],[f5895]) ).
fof(f5895,plain,
( $false
| ~ spl3_8
| spl3_231 ),
inference(resolution,[],[f5893,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(f5893,plain,
( ~ int_leq(sK1,sK1)
| spl3_231 ),
inference(avatar_component_clause,[],[f5891]) ).
fof(f5891,plain,
( spl3_231
<=> int_leq(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_231])]) ).
fof(f5894,plain,
( ~ spl3_231
| spl3_4
| ~ spl3_1
| ~ spl3_31
| ~ spl3_115 ),
inference(avatar_split_clause,[],[f3332,f1697,f257,f63,f78,f5891]) ).
fof(f78,plain,
( spl3_4
<=> real_zero = a(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f63,plain,
( spl3_1
<=> int_leq(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f257,plain,
( spl3_31
<=> sK0 = plus(sK1,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f1697,plain,
( spl3_115
<=> ! [X0] :
( ~ int_leq(X0,sK1)
| real_zero = a(plus(X0,sK2(sK1,sK0)),X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_115])]) ).
fof(f3332,plain,
( real_zero = a(sK0,sK1)
| ~ int_leq(sK1,sK1)
| ~ spl3_1
| ~ spl3_31
| ~ spl3_115 ),
inference(forward_demodulation,[],[f3317,f259]) ).
fof(f259,plain,
( sK0 = plus(sK1,sK2(sK1,sK0))
| ~ spl3_31 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f3317,plain,
( real_zero = a(plus(sK1,sK2(sK1,sK0)),sK1)
| ~ int_leq(sK1,sK1)
| ~ spl3_1
| ~ spl3_115 ),
inference(resolution,[],[f1698,f65]) ).
fof(f65,plain,
( int_leq(int_one,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f1698,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| real_zero = a(plus(X0,sK2(sK1,sK0)),X0)
| ~ int_leq(X0,sK1) )
| ~ spl3_115 ),
inference(avatar_component_clause,[],[f1697]) ).
fof(f5889,plain,
( spl3_230
| ~ spl3_82
| ~ spl3_123 ),
inference(avatar_split_clause,[],[f1979,f1811,f967,f5887]) ).
fof(f5887,plain,
( spl3_230
<=> ! [X0] :
( int_leq(plus(X0,int_one),sK0)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_230])]) ).
fof(f967,plain,
( spl3_82
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X1,sK2(sK1,sK0))
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_82])]) ).
fof(f1811,plain,
( spl3_123
<=> int_leq(int_one,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_123])]) ).
fof(f1979,plain,
( ! [X0] :
( int_leq(plus(X0,int_one),sK0)
| ~ int_less(X0,sK1) )
| ~ spl3_82
| ~ spl3_123 ),
inference(resolution,[],[f1812,f968]) ).
fof(f968,plain,
( ! [X0,X1] :
( ~ int_leq(X1,sK2(sK1,sK0))
| int_leq(plus(X0,X1),sK0)
| ~ int_less(X0,sK1) )
| ~ spl3_82 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f1812,plain,
( int_leq(int_one,sK2(sK1,sK0))
| ~ spl3_123 ),
inference(avatar_component_clause,[],[f1811]) ).
fof(f5885,plain,
( spl3_229
| ~ spl3_84
| ~ spl3_123 ),
inference(avatar_split_clause,[],[f1978,f1811,f975,f5883]) ).
fof(f5883,plain,
( spl3_229
<=> ! [X0] :
( int_leq(plus(int_one,X0),sK0)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_229])]) ).
fof(f975,plain,
( spl3_84
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X0,sK2(sK1,sK0))
| ~ int_less(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_84])]) ).
fof(f1978,plain,
( ! [X0] :
( int_leq(plus(int_one,X0),sK0)
| ~ int_less(X0,sK1) )
| ~ spl3_84
| ~ spl3_123 ),
inference(resolution,[],[f1812,f976]) ).
fof(f976,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK2(sK1,sK0))
| int_leq(plus(X0,X1),sK0)
| ~ int_less(X1,sK1) )
| ~ spl3_84 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f5876,plain,
( ~ spl3_114
| ~ spl3_228
| ~ spl3_31
| ~ spl3_122 ),
inference(avatar_split_clause,[],[f1807,f1731,f257,f5873,f1693]) ).
fof(f1693,plain,
( spl3_114
<=> int_less(int_zero,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_114])]) ).
fof(f5873,plain,
( spl3_228
<=> int_less(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_228])]) ).
fof(f1731,plain,
( spl3_122
<=> ! [X0,X1] :
( ~ int_less(plus(X0,X1),X0)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_122])]) ).
fof(f1807,plain,
( ~ int_less(sK0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ spl3_31
| ~ spl3_122 ),
inference(superposition,[],[f1732,f259]) ).
fof(f1732,plain,
( ! [X0,X1] :
( ~ int_less(plus(X0,X1),X0)
| ~ int_less(int_zero,X1) )
| ~ spl3_122 ),
inference(avatar_component_clause,[],[f1731]) ).
fof(f5856,plain,
( ~ spl3_226
| ~ spl3_227
| ~ spl3_105
| ~ spl3_122 ),
inference(avatar_split_clause,[],[f1806,f1731,f1496,f5853,f5849]) ).
fof(f5849,plain,
( spl3_226
<=> int_less(int_zero,sK2(sK0,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_226])]) ).
fof(f5853,plain,
( spl3_227
<=> int_less(n,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_227])]) ).
fof(f1496,plain,
( spl3_105
<=> n = plus(sK0,sK2(sK0,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_105])]) ).
fof(f1806,plain,
( ~ int_less(n,sK0)
| ~ int_less(int_zero,sK2(sK0,n))
| ~ spl3_105
| ~ spl3_122 ),
inference(superposition,[],[f1732,f1498]) ).
fof(f1498,plain,
( n = plus(sK0,sK2(sK0,n))
| ~ spl3_105 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f5811,plain,
( ~ spl3_26
| ~ spl3_15
| spl3_224 ),
inference(avatar_split_clause,[],[f5801,f5783,f135,f225]) ).
fof(f225,plain,
( spl3_26
<=> int_less(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
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(f5783,plain,
( spl3_224
<=> int_less(int_zero,sK2(int_one,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_224])]) ).
fof(f5801,plain,
( ~ int_less(int_one,sK1)
| ~ spl3_15
| spl3_224 ),
inference(resolution,[],[f5785,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(f5785,plain,
( ~ int_less(int_zero,sK2(int_one,sK1))
| spl3_224 ),
inference(avatar_component_clause,[],[f5783]) ).
fof(f5790,plain,
( ~ spl3_224
| ~ spl3_225
| ~ spl3_69
| ~ spl3_122 ),
inference(avatar_split_clause,[],[f1805,f1731,f768,f5787,f5783]) ).
fof(f5787,plain,
( spl3_225
<=> int_less(sK1,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_225])]) ).
fof(f768,plain,
( spl3_69
<=> sK1 = plus(int_one,sK2(int_one,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
fof(f1805,plain,
( ~ int_less(sK1,int_one)
| ~ int_less(int_zero,sK2(int_one,sK1))
| ~ spl3_69
| ~ spl3_122 ),
inference(superposition,[],[f1732,f770]) ).
fof(f770,plain,
( sK1 = plus(int_one,sK2(int_one,sK1))
| ~ spl3_69 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f5781,plain,
( spl3_223
| ~ spl3_67
| ~ spl3_118 ),
inference(avatar_split_clause,[],[f1738,f1715,f751,f5779]) ).
fof(f5779,plain,
( spl3_223
<=> ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_223])]) ).
fof(f751,plain,
( spl3_67
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).
fof(f1715,plain,
( spl3_118
<=> ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_118])]) ).
fof(f1738,plain,
( ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,sK1) )
| ~ spl3_67
| ~ spl3_118 ),
inference(resolution,[],[f1716,f752]) ).
fof(f752,plain,
( ! [X0] :
( ~ int_less(X0,int_one)
| int_less(X0,sK1) )
| ~ spl3_67 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f1716,plain,
( ! [X0] :
( int_less(X0,int_one)
| sK2(int_zero,X0) = X0 )
| ~ spl3_118 ),
inference(avatar_component_clause,[],[f1715]) ).
fof(f5763,plain,
( ~ spl3_36
| spl3_222
| ~ spl3_41
| ~ spl3_105 ),
inference(avatar_split_clause,[],[f1606,f1496,f354,f5760,f315]) ).
fof(f315,plain,
( spl3_36
<=> int_less(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f5760,plain,
( spl3_222
<=> int_less(sK2(sK0,n),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_222])]) ).
fof(f354,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(f1606,plain,
( int_less(sK2(sK0,n),n)
| ~ int_less(int_zero,sK0)
| ~ spl3_41
| ~ spl3_105 ),
inference(superposition,[],[f355,f1498]) ).
fof(f355,plain,
( ! [X0,X1] :
( int_less(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) )
| ~ spl3_41 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f5758,plain,
( spl3_221
| ~ spl3_70
| ~ spl3_83 ),
inference(avatar_split_clause,[],[f1011,f971,f845,f5756]) ).
fof(f5756,plain,
( spl3_221
<=> ! [X0] :
( ~ int_leq(sK1,X0)
| int_leq(sK0,plus(sK0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_221])]) ).
fof(f845,plain,
( spl3_70
<=> int_less(sK2(sK1,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).
fof(f971,plain,
( spl3_83
<=> ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK1,X1)
| ~ int_less(sK2(sK1,sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_83])]) ).
fof(f1011,plain,
( ! [X0] :
( ~ int_leq(sK1,X0)
| int_leq(sK0,plus(sK0,X0)) )
| ~ spl3_70
| ~ spl3_83 ),
inference(resolution,[],[f972,f847]) ).
fof(f847,plain,
( int_less(sK2(sK1,sK0),sK0)
| ~ spl3_70 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f972,plain,
( ! [X0,X1] :
( ~ int_less(sK2(sK1,sK0),X0)
| ~ int_leq(sK1,X1)
| int_leq(sK0,plus(X0,X1)) )
| ~ spl3_83 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f5754,plain,
( spl3_220
| ~ spl3_18
| ~ spl3_70 ),
inference(avatar_split_clause,[],[f856,f845,f155,f5752]) ).
fof(f5752,plain,
( spl3_220
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,sK2(sK1,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_220])]) ).
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(f856,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,sK2(sK1,sK0)) )
| ~ spl3_18
| ~ spl3_70 ),
inference(resolution,[],[f847,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(f5734,plain,
( ~ spl3_6
| spl3_219
| ~ spl3_41
| ~ spl3_69 ),
inference(avatar_split_clause,[],[f826,f768,f354,f5731,f88]) ).
fof(f88,plain,
( spl3_6
<=> int_less(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f5731,plain,
( spl3_219
<=> int_less(sK2(int_one,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_219])]) ).
fof(f826,plain,
( int_less(sK2(int_one,sK1),sK1)
| ~ int_less(int_zero,int_one)
| ~ spl3_41
| ~ spl3_69 ),
inference(superposition,[],[f355,f770]) ).
fof(f5729,plain,
( spl3_218
| ~ spl3_13
| ~ spl3_200 ),
inference(avatar_split_clause,[],[f4779,f4720,f117,f5726]) ).
fof(f5726,plain,
( spl3_218
<=> int_leq(n,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_218])]) ).
fof(f117,plain,
( spl3_13
<=> ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f4720,plain,
( spl3_200
<=> int_less(n,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_200])]) ).
fof(f4779,plain,
( int_leq(n,sK2(sK1,sK0))
| ~ spl3_13
| ~ spl3_200 ),
inference(resolution,[],[f4722,f118]) ).
fof(f118,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f4722,plain,
( int_less(n,sK2(sK1,sK0))
| ~ spl3_200 ),
inference(avatar_component_clause,[],[f4720]) ).
fof(f5585,plain,
( spl3_217
| ~ spl3_20
| ~ spl3_42 ),
inference(avatar_split_clause,[],[f654,f380,f172,f5582]) ).
fof(f5582,plain,
( spl3_217
<=> sK0 = plus(int_one,sK2(int_one,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_217])]) ).
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(f380,plain,
( spl3_42
<=> int_less(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f654,plain,
( sK0 = plus(int_one,sK2(int_one,sK0))
| ~ spl3_20
| ~ spl3_42 ),
inference(resolution,[],[f382,f173]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| plus(X0,sK2(X0,X1)) = X1 )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f382,plain,
( int_less(int_one,sK0)
| ~ spl3_42 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f5580,plain,
( spl3_216
| ~ spl3_20
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f570,f315,f172,f5577]) ).
fof(f5577,plain,
( spl3_216
<=> sK0 = plus(int_zero,sK2(int_zero,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_216])]) ).
fof(f570,plain,
( sK0 = plus(int_zero,sK2(int_zero,sK0))
| ~ spl3_20
| ~ spl3_36 ),
inference(resolution,[],[f317,f173]) ).
fof(f317,plain,
( int_less(int_zero,sK0)
| ~ spl3_36 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f5453,plain,
( spl3_124
| ~ spl3_13
| ~ spl3_198 ),
inference(avatar_split_clause,[],[f4764,f4438,f117,f1815]) ).
fof(f1815,plain,
( spl3_124
<=> int_leq(sK2(sK1,sK0),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_124])]) ).
fof(f4438,plain,
( spl3_198
<=> int_less(sK2(sK1,sK0),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_198])]) ).
fof(f4764,plain,
( int_leq(sK2(sK1,sK0),n)
| ~ spl3_13
| ~ spl3_198 ),
inference(resolution,[],[f4440,f118]) ).
fof(f4440,plain,
( int_less(sK2(sK1,sK0),n)
| ~ spl3_198 ),
inference(avatar_component_clause,[],[f4438]) ).
fof(f5440,plain,
( spl3_215
| ~ spl3_33
| ~ spl3_86
| ~ spl3_114 ),
inference(avatar_split_clause,[],[f4415,f1693,f983,f277,f5438]) ).
fof(f5438,plain,
( spl3_215
<=> ! [X0] :
( int_leq(X0,sK0)
| ~ int_leq(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_215])]) ).
fof(f277,plain,
( spl3_33
<=> ! [X0] : plus(int_zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f983,plain,
( spl3_86
<=> ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X1,sK1)
| ~ int_less(X0,sK2(sK1,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_86])]) ).
fof(f4415,plain,
( ! [X0] :
( int_leq(X0,sK0)
| ~ int_leq(X0,sK1) )
| ~ spl3_33
| ~ spl3_86
| ~ spl3_114 ),
inference(forward_demodulation,[],[f4390,f278]) ).
fof(f278,plain,
( ! [X0] : plus(int_zero,X0) = X0
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f4390,plain,
( ! [X0] :
( ~ int_leq(X0,sK1)
| int_leq(plus(int_zero,X0),sK0) )
| ~ spl3_86
| ~ spl3_114 ),
inference(resolution,[],[f1694,f984]) ).
fof(f984,plain,
( ! [X0,X1] :
( ~ int_less(X0,sK2(sK1,sK0))
| ~ int_leq(X1,sK1)
| int_leq(plus(X0,X1),sK0) )
| ~ spl3_86 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f1694,plain,
( int_less(int_zero,sK2(sK1,sK0))
| ~ spl3_114 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f5436,plain,
( spl3_214
| ~ spl3_19
| ~ spl3_131 ),
inference(avatar_split_clause,[],[f1900,f1847,f159,f5434]) ).
fof(f5434,plain,
( spl3_214
<=> ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_214])]) ).
fof(f159,plain,
( spl3_19
<=> int_less(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f1847,plain,
( spl3_131
<=> ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_leq(X0,int_zero)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_131])]) ).
fof(f1900,plain,
( ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK1) )
| ~ spl3_19
| ~ spl3_131 ),
inference(resolution,[],[f1848,f161]) ).
fof(f161,plain,
( int_less(int_zero,sK1)
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f1848,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X1)
| ~ int_leq(X0,int_zero)
| int_leq(X0,X1) )
| ~ spl3_131 ),
inference(avatar_component_clause,[],[f1847]) ).
fof(f5432,plain,
( spl3_213
| ~ spl3_36
| ~ spl3_131 ),
inference(avatar_split_clause,[],[f1899,f1847,f315,f5430]) ).
fof(f5430,plain,
( spl3_213
<=> ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_213])]) ).
fof(f1899,plain,
( ! [X0] :
( ~ int_leq(X0,int_zero)
| int_leq(X0,sK0) )
| ~ spl3_36
| ~ spl3_131 ),
inference(resolution,[],[f1848,f317]) ).
fof(f5428,plain,
( ~ spl3_8
| spl3_212 ),
inference(avatar_contradiction_clause,[],[f5426]) ).
fof(f5426,plain,
( $false
| ~ spl3_8
| spl3_212 ),
inference(resolution,[],[f5424,f98]) ).
fof(f5424,plain,
( ~ int_leq(sK0,sK0)
| spl3_212 ),
inference(avatar_component_clause,[],[f5422]) ).
fof(f5422,plain,
( spl3_212
<=> int_leq(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_212])]) ).
fof(f5425,plain,
( ~ spl3_212
| ~ spl3_65
| ~ spl3_24
| ~ spl3_96 ),
inference(avatar_split_clause,[],[f1349,f1295,f211,f728,f5422]) ).
fof(f728,plain,
( spl3_65
<=> int_leq(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
fof(f211,plain,
( spl3_24
<=> int_leq(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f1295,plain,
( spl3_96
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(sK1,X0)
| ~ int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_96])]) ).
fof(f1349,plain,
( ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,sK0)
| ~ spl3_24
| ~ spl3_96 ),
inference(resolution,[],[f1296,f213]) ).
fof(f213,plain,
( int_leq(sK1,sK0)
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1296,plain,
( ! [X0] :
( ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) )
| ~ spl3_96 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f5388,plain,
( spl3_211
| ~ spl3_46
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f5148,f1402,f426,f5386]) ).
fof(f5386,plain,
( spl3_211
<=> ! [X2,X0,X1] :
( ~ int_leq(sK1,X0)
| a(plus(X1,X2),plus(X1,X2)) = lu(plus(X1,X2),plus(X1,X2))
| ~ int_leq(plus(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_zero,X2)
| ~ int_less(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_211])]) ).
fof(f426,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(f1402,plain,
( spl3_102
<=> ! [X0,X1] :
( ~ int_leq(sK1,X1)
| ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_102])]) ).
fof(f5148,plain,
( ! [X2,X0,X1] :
( ~ int_leq(sK1,X0)
| a(plus(X1,X2),plus(X1,X2)) = lu(plus(X1,X2),plus(X1,X2))
| ~ int_leq(plus(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_zero,X2)
| ~ int_less(sK1,X1) )
| ~ spl3_46
| ~ spl3_102 ),
inference(resolution,[],[f1403,f427]) ).
fof(f427,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,[],[f426]) ).
fof(f1403,plain,
( ! [X0,X1] :
( ~ int_leq(sK1,X1)
| ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) )
| ~ spl3_102 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f5357,plain,
( spl3_210
| ~ spl3_40
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f5143,f1402,f350,f5355]) ).
fof(f5355,plain,
( spl3_210
<=> ! [X0,X1] :
( ~ int_leq(sK1,X0)
| a(plus(sK1,X1),plus(sK1,X1)) = lu(plus(sK1,X1),plus(sK1,X1))
| ~ int_leq(plus(sK1,X1),X0)
| ~ int_leq(X0,n)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_210])]) ).
fof(f350,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(f5143,plain,
( ! [X0,X1] :
( ~ int_leq(sK1,X0)
| a(plus(sK1,X1),plus(sK1,X1)) = lu(plus(sK1,X1),plus(sK1,X1))
| ~ int_leq(plus(sK1,X1),X0)
| ~ int_leq(X0,n)
| ~ int_less(int_zero,X1) )
| ~ spl3_40
| ~ spl3_102 ),
inference(resolution,[],[f1403,f351]) ).
fof(f351,plain,
( ! [X0,X1] :
( int_leq(X1,plus(X1,X0))
| ~ int_less(int_zero,X0) )
| ~ spl3_40 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f5339,plain,
( spl3_209
| ~ spl3_12
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f5141,f1402,f113,f5337]) ).
fof(f5337,plain,
( spl3_209
<=> ! [X0,X1] :
( ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n)
| int_less(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_209])]) ).
fof(f113,plain,
( spl3_12
<=> ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f5141,plain,
( ! [X0,X1] :
( ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n)
| int_less(X1,sK1) )
| ~ spl3_12
| ~ spl3_102 ),
inference(resolution,[],[f1403,f114]) ).
fof(f114,plain,
( ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f5287,plain,
( spl3_208
| ~ spl3_25
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f5094,f294,f221,f5214]) ).
fof(f5214,plain,
( spl3_208
<=> ! [X0] :
( int_less(X0,sK1)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_208])]) ).
fof(f221,plain,
( spl3_25
<=> int_one = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f294,plain,
( spl3_34
<=> ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f5094,plain,
( ! [X0] :
( int_less(X0,sK1)
| int_less(int_zero,X0) )
| ~ spl3_25
| ~ spl3_34 ),
inference(superposition,[],[f295,f223]) ).
fof(f223,plain,
( int_one = sK1
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f295,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f5216,plain,
( spl3_208
| ~ spl3_34
| ~ spl3_67 ),
inference(avatar_split_clause,[],[f757,f751,f294,f5214]) ).
fof(f757,plain,
( ! [X0] :
( int_less(X0,sK1)
| int_less(int_zero,X0) )
| ~ spl3_34
| ~ spl3_67 ),
inference(resolution,[],[f752,f295]) ).
fof(f5212,plain,
( spl3_206
| spl3_207
| ~ spl3_24
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f5138,f1402,f211,f5210,f5206]) ).
fof(f5206,plain,
( spl3_206
<=> a(sK0,sK0) = lu(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_206])]) ).
fof(f5210,plain,
( spl3_207
<=> ! [X0] :
( ~ int_leq(sK1,X0)
| ~ int_leq(X0,n)
| ~ int_leq(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_207])]) ).
fof(f5138,plain,
( ! [X0] :
( ~ int_leq(sK1,X0)
| a(sK0,sK0) = lu(sK0,sK0)
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,n) )
| ~ spl3_24
| ~ spl3_102 ),
inference(resolution,[],[f1403,f213]) ).
fof(f5169,plain,
( spl3_205
| ~ spl3_11
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f386,f221,f109,f5167]) ).
fof(f5167,plain,
( spl3_205
<=> ! [X0] :
( ~ int_leq(sK1,X0)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_205])]) ).
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(f386,plain,
( ! [X0] :
( ~ int_leq(sK1,X0)
| int_less(int_zero,X0) )
| ~ spl3_11
| ~ spl3_25 ),
inference(superposition,[],[f110,f223]) ).
fof(f110,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f5082,plain,
( spl3_204
| ~ spl3_18
| ~ spl3_42 ),
inference(avatar_split_clause,[],[f655,f380,f155,f5080]) ).
fof(f5080,plain,
( spl3_204
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_204])]) ).
fof(f655,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_42 ),
inference(resolution,[],[f382,f156]) ).
fof(f5011,plain,
( spl3_203
| ~ spl3_47
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f732,f724,f430,f5009]) ).
fof(f5009,plain,
( spl3_203
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_203])]) ).
fof(f430,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(f724,plain,
( spl3_64
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK0) )
| ~ spl3_47
| ~ spl3_64 ),
inference(resolution,[],[f725,f431]) ).
fof(f431,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,[],[f430]) ).
fof(f725,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_64 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f4797,plain,
( spl3_124
| ~ spl3_13
| ~ spl3_198 ),
inference(avatar_split_clause,[],[f4764,f4438,f117,f1815]) ).
fof(f4796,plain,
( spl3_202
| ~ spl3_18
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f571,f315,f155,f4794]) ).
fof(f4794,plain,
( spl3_202
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_202])]) ).
fof(f571,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_zero) )
| ~ spl3_18
| ~ spl3_36 ),
inference(resolution,[],[f317,f156]) ).
fof(f4755,plain,
( ~ spl3_123
| ~ spl3_124
| ~ spl3_65
| ~ spl3_30
| spl3_201
| ~ spl3_3
| ~ spl3_31
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f1256,f718,f257,f73,f4753,f252,f728,f1815,f1811]) ).
fof(f252,plain,
( spl3_30
<=> int_leq(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f4753,plain,
( spl3_201
<=> ! [X0] :
( ~ int_leq(X0,sK2(sK1,sK0))
| a(X0,plus(X0,sK1)) = lu(X0,plus(X0,sK1))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_201])]) ).
fof(f73,plain,
( spl3_3
<=> int_leq(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f718,plain,
( spl3_63
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(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_63])]) ).
fof(f1256,plain,
( ! [X0] :
( ~ int_leq(sK0,n)
| ~ int_leq(X0,sK2(sK1,sK0))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,sK1)
| a(X0,plus(X0,sK1)) = lu(X0,plus(X0,sK1))
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK2(sK1,sK0),n)
| ~ int_leq(int_one,sK2(sK1,sK0)) )
| ~ spl3_31
| ~ spl3_63 ),
inference(superposition,[],[f719,f259]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_63 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f4723,plain,
( spl3_200
| ~ spl3_12
| spl3_124 ),
inference(avatar_split_clause,[],[f1824,f1815,f113,f4720]) ).
fof(f1824,plain,
( int_less(n,sK2(sK1,sK0))
| ~ spl3_12
| spl3_124 ),
inference(resolution,[],[f1817,f114]) ).
fof(f1817,plain,
( ~ int_leq(sK2(sK1,sK0),n)
| spl3_124 ),
inference(avatar_component_clause,[],[f1815]) ).
fof(f4704,plain,
( spl3_28
| ~ spl3_12
| spl3_175 ),
inference(avatar_split_clause,[],[f4296,f3518,f113,f237]) ).
fof(f237,plain,
( spl3_28
<=> int_less(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f3518,plain,
( spl3_175
<=> int_leq(n,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_175])]) ).
fof(f4296,plain,
( int_less(sK0,n)
| ~ spl3_12
| spl3_175 ),
inference(resolution,[],[f3519,f114]) ).
fof(f3519,plain,
( ~ int_leq(n,sK0)
| spl3_175 ),
inference(avatar_component_clause,[],[f3518]) ).
fof(f4703,plain,
( spl3_199
| ~ spl3_14
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f4583,f700,f127,f4645]) ).
fof(f4645,plain,
( spl3_199
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| int_less(sK0,plus(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_199])]) ).
fof(f127,plain,
( spl3_14
<=> ! [X0,X1] : plus(X0,X1) = plus(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f700,plain,
( spl3_62
<=> ! [X2,X0,X1] :
( int_less(sK0,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).
fof(f4583,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| int_less(sK0,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_14
| ~ spl3_62 ),
inference(superposition,[],[f701,f128]) ).
fof(f128,plain,
( ! [X0,X1] : plus(X0,X1) = plus(X1,X0)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f701,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(X0,plus(X0,X2))
| int_less(sK0,plus(X1,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_62 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f4647,plain,
( spl3_199
| ~ spl3_12
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f1162,f724,f113,f4645]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(int_one,X0)
| int_less(sK0,plus(X2,X0)) )
| ~ spl3_12
| ~ spl3_64 ),
inference(resolution,[],[f725,f114]) ).
fof(f4441,plain,
( spl3_198
| ~ spl3_70
| ~ spl3_95 ),
inference(avatar_split_clause,[],[f1314,f1264,f845,f4438]) ).
fof(f1264,plain,
( spl3_95
<=> ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_95])]) ).
fof(f1314,plain,
( int_less(sK2(sK1,sK0),n)
| ~ spl3_70
| ~ spl3_95 ),
inference(resolution,[],[f1265,f847]) ).
fof(f1265,plain,
( ! [X0] :
( ~ int_less(X0,sK0)
| int_less(X0,n) )
| ~ spl3_95 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f4389,plain,
( spl3_114
| ~ spl3_12
| spl3_78 ),
inference(avatar_split_clause,[],[f924,f917,f113,f1693]) ).
fof(f917,plain,
( spl3_78
<=> int_leq(sK2(sK1,sK0),int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_78])]) ).
fof(f924,plain,
( int_less(int_zero,sK2(sK1,sK0))
| ~ spl3_12
| spl3_78 ),
inference(resolution,[],[f919,f114]) ).
fof(f919,plain,
( ~ int_leq(sK2(sK1,sK0),int_zero)
| spl3_78 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f4388,plain,
( spl3_197
| ~ spl3_13
| ~ spl3_70 ),
inference(avatar_split_clause,[],[f857,f845,f117,f4385]) ).
fof(f4385,plain,
( spl3_197
<=> int_leq(sK2(sK1,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_197])]) ).
fof(f857,plain,
( int_leq(sK2(sK1,sK0),sK0)
| ~ spl3_13
| ~ spl3_70 ),
inference(resolution,[],[f847,f118]) ).
fof(f4331,plain,
( spl3_196
| ~ spl3_47
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f1246,f718,f430,f4329]) ).
fof(f4329,plain,
( spl3_196
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(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_196])]) ).
fof(f1246,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(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_63 ),
inference(resolution,[],[f719,f431]) ).
fof(f4327,plain,
( spl3_195
| ~ spl3_23
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f463,f430,f201,f4325]) ).
fof(f4325,plain,
( spl3_195
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,int_zero)
| ~ int_less(X1,n)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X0)
| a(X2,plus(X2,X0)) = lu(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_195])]) ).
fof(f201,plain,
( spl3_23
<=> ! [X2,X0,X3] :
( a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_leq(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_23])]) ).
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_leq(int_zero,X0)
| a(X2,plus(X2,X0)) = lu(X2,plus(X2,X0))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) )
| ~ spl3_23
| ~ spl3_47 ),
inference(resolution,[],[f431,f202]) ).
fof(f202,plain,
( ! [X2,X3,X0] :
( ~ int_leq(plus(X0,X2),n)
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_leq(int_zero,X2)
| a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f4277,plain,
( spl3_194
| ~ spl3_14
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f1226,f694,f127,f4275]) ).
fof(f4275,plain,
( spl3_194
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(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_194])]) ).
fof(f694,plain,
( spl3_61
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(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_61])]) ).
fof(f1226,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(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_61 ),
inference(superposition,[],[f695,f128]) ).
fof(f695,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(X0,plus(X0,X2))
| ~ int_leq(X0,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_61 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f4273,plain,
( spl3_193
| ~ spl3_12
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f1224,f694,f113,f4271]) ).
fof(f4271,plain,
( spl3_193
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X1)
| a(X0,plus(X0,X1)) = lu(X0,plus(X0,X1))
| ~ int_leq(X0,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| int_less(n,plus(X2,X1))
| int_less(plus(X2,X1),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_193])]) ).
fof(f1224,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X1)
| a(X0,plus(X0,X1)) = lu(X0,plus(X0,X1))
| ~ int_leq(X0,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| int_less(n,plus(X2,X1))
| int_less(plus(X2,X1),int_one) )
| ~ spl3_12
| ~ spl3_61 ),
inference(resolution,[],[f695,f114]) ).
fof(f4247,plain,
( spl3_192
| ~ spl3_46
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f1235,f694,f426,f4245]) ).
fof(f4245,plain,
( spl3_192
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X1)
| a(X0,plus(X0,X1)) = lu(X0,plus(X0,X1))
| ~ int_leq(X0,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| int_less(n,plus(X2,X1))
| ~ int_less(int_one,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_192])]) ).
fof(f1235,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X1)
| a(X0,plus(X0,X1)) = lu(X0,plus(X0,X1))
| ~ int_leq(X0,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| int_less(n,plus(X2,X1))
| ~ int_less(int_one,X2) )
| ~ spl3_46
| ~ spl3_61 ),
inference(duplicate_literal_removal,[],[f1223]) ).
fof(f1223,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X1)
| a(X0,plus(X0,X1)) = lu(X0,plus(X0,X1))
| ~ int_leq(X0,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| int_less(n,plus(X2,X1))
| ~ int_leq(int_zero,X1)
| ~ int_less(int_one,X2) )
| ~ spl3_46
| ~ spl3_61 ),
inference(resolution,[],[f695,f427]) ).
fof(f4192,plain,
( spl3_191
| ~ spl3_47
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f1210,f675,f430,f4190]) ).
fof(f4190,plain,
( spl3_191
<=> ! [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)
| real_zero = a(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_191])]) ).
fof(f675,plain,
( spl3_59
<=> ! [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)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
fof(f1210,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)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X2,X1))
| ~ int_leq(X1,int_zero)
| ~ int_less(X2,n) )
| ~ spl3_47
| ~ spl3_59 ),
inference(resolution,[],[f676,f431]) ).
fof(f676,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)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_59 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f4188,plain,
( spl3_190
| ~ spl3_22
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f464,f430,f192,f4186]) ).
fof(f4186,plain,
( spl3_190
<=> ! [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)
| real_zero = a(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_190])]) ).
fof(f192,plain,
( spl3_22
<=> ! [X4,X5,X1] :
( real_zero = a(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_22])]) ).
fof(f464,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)
| real_zero = a(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_22
| ~ spl3_47 ),
inference(resolution,[],[f431,f193]) ).
fof(f193,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)
| real_zero = a(plus(X5,X4),X5)
| ~ int_leq(int_one,plus(X1,X4)) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f4127,plain,
( spl3_189
| ~ spl3_14
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f1196,f648,f127,f4125]) ).
fof(f4125,plain,
( spl3_189
<=> ! [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)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(X2,X0)
| int_less(n,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_189])]) ).
fof(f648,plain,
( spl3_57
<=> ! [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)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).
fof(f1196,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)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(X2,X0)
| int_less(n,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_57 ),
inference(superposition,[],[f649,f128]) ).
fof(f649,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)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(X0,X1)
| int_less(n,plus(X1,X2)) )
| ~ spl3_57 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f4123,plain,
( spl3_188
| ~ spl3_46
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f1189,f608,f426,f4121]) ).
fof(f4121,plain,
( spl3_188
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| a(plus(X1,X2),plus(X1,X2)) = lu(plus(X1,X2),plus(X1,X2))
| ~ int_leq(plus(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_188])]) ).
fof(f608,plain,
( spl3_54
<=> ! [X0,X1] :
( a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
fof(f1189,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| a(plus(X1,X2),plus(X1,X2)) = lu(plus(X1,X2),plus(X1,X2))
| ~ int_leq(plus(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X1) )
| ~ spl3_46
| ~ spl3_54 ),
inference(resolution,[],[f609,f427]) ).
fof(f609,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) )
| ~ spl3_54 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f4056,plain,
( spl3_187
| ~ spl3_48
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f579,f575,f483,f4054]) ).
fof(f4054,plain,
( spl3_187
<=> ! [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_187])]) ).
fof(f483,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(f575,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(f579,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,[],[f576,f484]) ).
fof(f484,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| sK2(X0,X1) = sK2(int_zero,sK2(X0,X1)) )
| ~ spl3_48 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f576,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,[],[f575]) ).
fof(f4006,plain,
( spl3_186
| ~ spl3_40
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f1188,f608,f350,f4004]) ).
fof(f4004,plain,
( spl3_186
<=> ! [X0,X1] :
( ~ int_leq(int_one,X0)
| a(plus(int_one,X1),plus(int_one,X1)) = lu(plus(int_one,X1),plus(int_one,X1))
| ~ int_leq(plus(int_one,X1),X0)
| ~ int_leq(X0,n)
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_186])]) ).
fof(f1188,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X0)
| a(plus(int_one,X1),plus(int_one,X1)) = lu(plus(int_one,X1),plus(int_one,X1))
| ~ int_leq(plus(int_one,X1),X0)
| ~ int_leq(X0,n)
| ~ int_less(int_zero,X1) )
| ~ spl3_40
| ~ spl3_54 ),
inference(resolution,[],[f609,f351]) ).
fof(f4002,plain,
( spl3_185
| ~ spl3_38
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f1183,f608,f342,f4000]) ).
fof(f4000,plain,
( spl3_185
<=> ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| a(sK2(X1,X2),sK2(X1,X2)) = lu(sK2(X1,X2),sK2(X1,X2))
| ~ int_leq(sK2(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_185])]) ).
fof(f342,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(f1183,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,X0)
| a(sK2(X1,X2),sK2(X1,X2)) = lu(sK2(X1,X2),sK2(X1,X2))
| ~ int_leq(sK2(X1,X2),X0)
| ~ int_leq(X0,n)
| ~ int_less(X1,X2) )
| ~ spl3_38
| ~ spl3_54 ),
inference(resolution,[],[f609,f343]) ).
fof(f343,plain,
( ! [X0,X1] :
( int_leq(int_one,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f3927,plain,
( spl3_184
| ~ spl3_20
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f580,f575,f172,f3925]) ).
fof(f3925,plain,
( spl3_184
<=> ! [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_184])]) ).
fof(f580,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,[],[f576,f173]) ).
fof(f3889,plain,
( spl3_183
| ~ spl3_18
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f581,f575,f155,f3887]) ).
fof(f3887,plain,
( spl3_183
<=> ! [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_183])]) ).
fof(f581,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,[],[f576,f156]) ).
fof(f3856,plain,
( spl3_182
| ~ spl3_45
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f560,f548,f422,f3854]) ).
fof(f3854,plain,
( spl3_182
<=> ! [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_182])]) ).
fof(f422,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(f548,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(f560,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,[],[f549,f423]) ).
fof(f423,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,[],[f422]) ).
fof(f549,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X1)
| plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1))) )
| ~ spl3_51 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f3774,plain,
( spl3_181
| ~ spl3_17
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f528,f506,f151,f3772]) ).
fof(f3772,plain,
( spl3_181
<=> ! [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_181])]) ).
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(f506,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(f528,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,[],[f507,f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( ~ int_leq(X0,X1)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f507,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,[],[f506]) ).
fof(f3770,plain,
( spl3_180
| ~ spl3_17
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f509,f502,f151,f3768]) ).
fof(f3768,plain,
( spl3_180
<=> ! [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_180])]) ).
fof(f502,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(f509,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,[],[f503,f152]) ).
fof(f503,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,[],[f502]) ).
fof(f3692,plain,
( spl3_179
| ~ spl3_44
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f492,f483,f418,f3690]) ).
fof(f3690,plain,
( spl3_179
<=> ! [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_179])]) ).
fof(f418,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(f492,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,[],[f484,f419]) ).
fof(f419,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,[],[f418]) ).
fof(f3688,plain,
( spl3_178
| ~ spl3_45
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f491,f483,f422,f3686]) ).
fof(f3686,plain,
( spl3_178
<=> ! [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_178])]) ).
fof(f491,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,[],[f484,f423]) ).
fof(f3667,plain,
( spl3_177
| ~ spl3_12
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f1186,f608,f113,f3665]) ).
fof(f3665,plain,
( spl3_177
<=> ! [X0,X1] :
( ~ int_leq(int_one,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n)
| int_less(X1,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_177])]) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n)
| int_less(X1,int_one) )
| ~ spl3_12
| ~ spl3_54 ),
inference(resolution,[],[f609,f114]) ).
fof(f3622,plain,
( spl3_176
| ~ spl3_15
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f554,f548,f135,f3620]) ).
fof(f3620,plain,
( spl3_176
<=> ! [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_176])]) ).
fof(f554,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,[],[f549,f136]) ).
fof(f3521,plain,
( spl3_175
| ~ spl3_77
| ~ spl3_128 ),
inference(avatar_split_clause,[],[f2093,f1834,f908,f3518]) ).
fof(f908,plain,
( spl3_77
<=> ! [X0] :
( int_leq(X0,sK0)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_77])]) ).
fof(f1834,plain,
( spl3_128
<=> int_less(n,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_128])]) ).
fof(f2093,plain,
( int_leq(n,sK0)
| ~ spl3_77
| ~ spl3_128 ),
inference(resolution,[],[f1836,f909]) ).
fof(f909,plain,
( ! [X0] :
( ~ int_less(X0,sK1)
| int_leq(X0,sK0) )
| ~ spl3_77 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f1836,plain,
( int_less(n,sK1)
| ~ spl3_128 ),
inference(avatar_component_clause,[],[f1834]) ).
fof(f3516,plain,
( spl3_174
| ~ spl3_43
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f555,f548,f393,f3514]) ).
fof(f3514,plain,
( spl3_174
<=> ! [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_174])]) ).
fof(f393,plain,
( spl3_43
<=> ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f555,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,[],[f549,f394]) ).
fof(f394,plain,
( ! [X0,X1] :
( int_less(X1,X0)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f3512,plain,
( spl3_173
| ~ spl3_20
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f440,f422,f172,f3510]) ).
fof(f3510,plain,
( spl3_173
<=> ! [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_173])]) ).
fof(f440,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,[],[f423,f173]) ).
fof(f3508,plain,
( spl3_172
| ~ spl3_20
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f435,f418,f172,f3506]) ).
fof(f3506,plain,
( spl3_172
<=> ! [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_172])]) ).
fof(f435,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,[],[f419,f173]) ).
fof(f3311,plain,
( spl3_113
| ~ spl3_13
| ~ spl3_106 ),
inference(avatar_split_clause,[],[f1737,f1544,f117,f1689]) ).
fof(f1689,plain,
( spl3_113
<=> int_leq(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_113])]) ).
fof(f1737,plain,
( int_leq(sK1,n)
| ~ spl3_13
| ~ spl3_106 ),
inference(resolution,[],[f1546,f118]) ).
fof(f1546,plain,
( int_less(sK1,n)
| ~ spl3_106 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f3224,plain,
( spl3_171
| ~ spl3_33
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f593,f575,f277,f3222]) ).
fof(f3222,plain,
( spl3_171
<=> ! [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_171])]) ).
fof(f593,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,[],[f576,f278]) ).
fof(f3220,plain,
( spl3_170
| ~ spl3_33
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f587,f575,f277,f3218]) ).
fof(f3218,plain,
( spl3_170
<=> ! [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_170])]) ).
fof(f587,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,[],[f576,f278]) ).
fof(f3216,plain,
( spl3_169
| ~ spl3_15
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f496,f483,f135,f3214]) ).
fof(f3214,plain,
( spl3_169
<=> ! [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_169])]) ).
fof(f496,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,[],[f484,f136]) ).
fof(f3212,plain,
( spl3_168
| ~ spl3_41
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f490,f483,f354,f3210]) ).
fof(f3210,plain,
( spl3_168
<=> ! [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_168])]) ).
fof(f490,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,[],[f484,f355]) ).
fof(f3208,plain,
( spl3_167
| ~ spl3_16
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f489,f483,f139,f3206]) ).
fof(f3206,plain,
( spl3_167
<=> ! [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_167])]) ).
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(f489,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,[],[f484,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(f3204,plain,
( spl3_166
| ~ spl3_17
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f465,f430,f151,f3202]) ).
fof(f3202,plain,
( spl3_166
<=> ! [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_166])]) ).
fof(f465,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,[],[f431,f152]) ).
fof(f3200,plain,
( spl3_165
| ~ spl3_17
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f452,f426,f151,f3198]) ).
fof(f3198,plain,
( spl3_165
<=> ! [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_165])]) ).
fof(f452,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,[],[f427,f152]) ).
fof(f3196,plain,
( spl3_149
| ~ spl3_13
| ~ spl3_101 ),
inference(avatar_split_clause,[],[f1687,f1368,f117,f2284]) ).
fof(f2284,plain,
( spl3_149
<=> int_leq(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_149])]) ).
fof(f1368,plain,
( spl3_101
<=> int_less(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_101])]) ).
fof(f1687,plain,
( int_leq(int_one,n)
| ~ spl3_13
| ~ spl3_101 ),
inference(resolution,[],[f1370,f118]) ).
fof(f1370,plain,
( int_less(int_one,n)
| ~ spl3_101 ),
inference(avatar_component_clause,[],[f1368]) ).
fof(f3168,plain,
( spl3_164
| ~ spl3_43
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f486,f483,f393,f3166]) ).
fof(f3166,plain,
( spl3_164
<=> ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_164])]) ).
fof(f486,plain,
( ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 )
| ~ spl3_43
| ~ spl3_48 ),
inference(resolution,[],[f484,f394]) ).
fof(f3065,plain,
( spl3_163
| ~ spl3_14
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f736,f724,f127,f3063]) ).
fof(f3063,plain,
( spl3_163
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X1,sK0)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X0)
| a(X2,plus(X2,X0)) = lu(X2,plus(X2,X0))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_163])]) ).
fof(f736,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X1,sK0)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X0)
| a(X2,plus(X2,X0)) = lu(X2,plus(X2,X0))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X1) )
| ~ spl3_14
| ~ spl3_64 ),
inference(superposition,[],[f725,f128]) ).
fof(f3061,plain,
( spl3_162
| ~ spl3_12
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f705,f700,f113,f3059]) ).
fof(f3059,plain,
( spl3_162
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| int_less(sK0,plus(X0,X2))
| ~ int_leq(int_one,X0)
| int_less(plus(X0,X2),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_162])]) ).
fof(f705,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| int_less(sK0,plus(X0,X2))
| ~ int_leq(int_one,X0)
| int_less(plus(X0,X2),int_one) )
| ~ spl3_12
| ~ spl3_62 ),
inference(resolution,[],[f701,f114]) ).
fof(f3005,plain,
( spl3_161
| ~ spl3_47
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f684,f681,f430,f3003]) ).
fof(f3003,plain,
( spl3_161
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_161])]) ).
fof(f681,plain,
( spl3_60
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| ~ int_leq(X0,int_zero)
| ~ int_less(X2,sK0) )
| ~ spl3_47
| ~ spl3_60 ),
inference(resolution,[],[f682,f431]) ).
fof(f682,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_60 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f2764,plain,
( spl3_160
| ~ spl3_13
| ~ spl3_98 ),
inference(avatar_split_clause,[],[f1455,f1316,f117,f2761]) ).
fof(f2761,plain,
( spl3_160
<=> int_leq(int_zero,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_160])]) ).
fof(f1316,plain,
( spl3_98
<=> int_less(int_zero,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_98])]) ).
fof(f1455,plain,
( int_leq(int_zero,n)
| ~ spl3_13
| ~ spl3_98 ),
inference(resolution,[],[f1318,f118]) ).
fof(f1318,plain,
( int_less(int_zero,n)
| ~ spl3_98 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f2759,plain,
( spl3_159
| ~ spl3_34
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f551,f548,f294,f2757]) ).
fof(f2757,plain,
( spl3_159
<=> ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_159])]) ).
fof(f551,plain,
( ! [X0,X1] :
( plus(X0,X1) = plus(X0,sK2(X0,plus(X0,X1)))
| int_less(X1,int_one) )
| ~ spl3_34
| ~ spl3_51 ),
inference(resolution,[],[f549,f295]) ).
fof(f2755,plain,
( spl3_158
| ~ spl3_18
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f441,f422,f155,f2753]) ).
fof(f2753,plain,
( spl3_158
<=> ! [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_158])]) ).
fof(f441,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,[],[f423,f156]) ).
fof(f2751,plain,
( spl3_157
| ~ spl3_18
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f436,f418,f155,f2749]) ).
fof(f2749,plain,
( spl3_157
<=> ! [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_157])]) ).
fof(f436,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,[],[f419,f156]) ).
fof(f2747,plain,
( spl3_156
| ~ spl3_20
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f369,f354,f172,f2745]) ).
fof(f2745,plain,
( spl3_156
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X0,X1) = plus(X1,sK2(X1,plus(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_156])]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X0,X1) = plus(X1,sK2(X1,plus(X0,X1))) )
| ~ spl3_20
| ~ spl3_41 ),
inference(resolution,[],[f355,f173]) ).
fof(f2675,plain,
( spl3_155
| ~ spl3_14
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f517,f502,f127,f2673]) ).
fof(f2673,plain,
( spl3_155
<=> ! [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_155])]) ).
fof(f517,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,[],[f503,f128]) ).
fof(f2671,plain,
( spl3_154
| ~ spl3_20
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f398,f393,f172,f2669]) ).
fof(f2669,plain,
( spl3_154
<=> ! [X0,X1] :
( int_less(X1,X0)
| X0 = X1
| plus(X0,sK2(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_154])]) ).
fof(f398,plain,
( ! [X0,X1] :
( int_less(X1,X0)
| X0 = X1
| plus(X0,sK2(X0,X1)) = X1 )
| ~ spl3_20
| ~ spl3_43 ),
inference(resolution,[],[f394,f173]) ).
fof(f2667,plain,
( spl3_153
| ~ spl3_17
| ~ spl3_38 ),
inference(avatar_split_clause,[],[f358,f342,f151,f2665]) ).
fof(f2665,plain,
( spl3_153
<=> ! [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_153])]) ).
fof(f358,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,[],[f343,f152]) ).
fof(f2583,plain,
( spl3_152
| ~ spl3_46
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f713,f700,f426,f2581]) ).
fof(f2581,plain,
( spl3_152
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| int_less(sK0,plus(X0,X2))
| ~ int_leq(int_one,X0)
| ~ int_less(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_152])]) ).
fof(f713,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| int_less(sK0,plus(X0,X2))
| ~ int_leq(int_one,X0)
| ~ int_less(int_one,X0) )
| ~ spl3_46
| ~ spl3_62 ),
inference(duplicate_literal_removal,[],[f704]) ).
fof(f704,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,X2)
| a(X1,plus(X1,X2)) = lu(X1,plus(X1,X2))
| int_less(sK0,plus(X0,X2))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X0) )
| ~ spl3_46
| ~ spl3_62 ),
inference(resolution,[],[f701,f427]) ).
fof(f2555,plain,
( spl3_151
| ~ spl3_14
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f2385,f658,f127,f2534]) ).
fof(f2534,plain,
( spl3_151
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| int_less(sK0,plus(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_151])]) ).
fof(f658,plain,
( spl3_58
<=> ! [X2,X0,X1] :
( int_less(sK0,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
fof(f2385,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| int_less(sK0,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_58 ),
inference(superposition,[],[f659,f128]) ).
fof(f659,plain,
( ! [X2,X0,X1] :
( ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X0,X2),X0)
| int_less(sK0,plus(X1,X2)) )
| ~ spl3_58 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f2536,plain,
( spl3_151
| ~ spl3_12
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f1131,f681,f113,f2534]) ).
fof(f1131,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| ~ int_leq(int_one,plus(X2,X0))
| int_less(sK0,plus(X2,X0)) )
| ~ spl3_12
| ~ spl3_60 ),
inference(resolution,[],[f682,f114]) ).
fof(f2497,plain,
( spl3_150
| ~ spl3_46
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f645,f637,f426,f2495]) ).
fof(f2495,plain,
( spl3_150
<=> ! [X2,X0,X1] :
( a(plus(X0,X1),plus(X0,X1)) = lu(plus(X0,X1),plus(X0,X1))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,sK0)
| ~ int_leq(plus(X0,X1),X2)
| ~ int_leq(int_zero,X1)
| ~ int_less(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_150])]) ).
fof(f637,plain,
( spl3_56
<=> ! [X0,X1] :
( ~ int_leq(X0,sK0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).
fof(f645,plain,
( ! [X2,X0,X1] :
( a(plus(X0,X1),plus(X0,X1)) = lu(plus(X0,X1),plus(X0,X1))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,sK0)
| ~ int_leq(plus(X0,X1),X2)
| ~ int_leq(int_zero,X1)
| ~ int_less(int_one,X0) )
| ~ spl3_46
| ~ spl3_56 ),
inference(resolution,[],[f638,f427]) ).
fof(f638,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X1)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0) )
| ~ spl3_56 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f2287,plain,
( spl3_149
| ~ spl3_10
| ~ spl3_98 ),
inference(avatar_split_clause,[],[f1451,f1316,f105,f2284]) ).
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(f1451,plain,
( int_leq(int_one,n)
| ~ spl3_10
| ~ spl3_98 ),
inference(resolution,[],[f1318,f106]) ).
fof(f106,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f2282,plain,
( spl3_148
| ~ spl3_34
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f493,f483,f294,f2280]) ).
fof(f2280,plain,
( spl3_148
<=> ! [X0] :
( sK2(int_zero,X0) = sK2(int_zero,sK2(int_zero,X0))
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_148])]) ).
fof(f493,plain,
( ! [X0] :
( sK2(int_zero,X0) = sK2(int_zero,sK2(int_zero,X0))
| int_less(X0,int_one) )
| ~ spl3_34
| ~ spl3_48 ),
inference(resolution,[],[f484,f295]) ).
fof(f2278,plain,
( spl3_147
| ~ spl3_34
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f488,f483,f294,f2276]) ).
fof(f2276,plain,
( spl3_147
<=> ! [X0] :
( sK2(X0,int_one) = sK2(int_zero,sK2(X0,int_one))
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_147])]) ).
fof(f488,plain,
( ! [X0] :
( sK2(X0,int_one) = sK2(int_zero,sK2(X0,int_one))
| int_less(int_zero,X0) )
| ~ spl3_34
| ~ spl3_48 ),
inference(resolution,[],[f484,f295]) ).
fof(f2274,plain,
( spl3_146
| ~ spl3_18
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f399,f393,f155,f2272]) ).
fof(f2272,plain,
( spl3_146
<=> ! [X2,X0,X1] :
( int_less(X1,X0)
| X0 = X1
| int_less(X2,X1)
| ~ int_less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_146])]) ).
fof(f399,plain,
( ! [X2,X0,X1] :
( int_less(X1,X0)
| X0 = X1
| int_less(X2,X1)
| ~ int_less(X2,X0) )
| ~ spl3_18
| ~ spl3_43 ),
inference(resolution,[],[f394,f156]) ).
fof(f1996,plain,
( spl3_145
| ~ spl3_6
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f552,f548,f88,f1994]) ).
fof(f1994,plain,
( spl3_145
<=> ! [X0] : plus(X0,int_one) = plus(X0,sK2(X0,plus(X0,int_one))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_145])]) ).
fof(f552,plain,
( ! [X0] : plus(X0,int_one) = plus(X0,sK2(X0,plus(X0,int_one)))
| ~ spl3_6
| ~ spl3_51 ),
inference(resolution,[],[f549,f90]) ).
fof(f90,plain,
( int_less(int_zero,int_one)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f1992,plain,
( spl3_144
| ~ spl3_33
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f533,f506,f277,f1990]) ).
fof(f1990,plain,
( spl3_144
<=> ! [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_144])]) ).
fof(f533,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,[],[f507,f278]) ).
fof(f1988,plain,
( spl3_143
| ~ spl3_33
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f520,f502,f277,f1986]) ).
fof(f1986,plain,
( spl3_143
<=> ! [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_143])]) ).
fof(f520,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,[],[f503,f278]) ).
fof(f1984,plain,
( spl3_142
| ~ spl3_14
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f467,f430,f127,f1982]) ).
fof(f1982,plain,
( spl3_142
<=> ! [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_142])]) ).
fof(f467,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,[],[f431,f128]) ).
fof(f1973,plain,
( ~ spl3_2
| ~ spl3_38
| spl3_123 ),
inference(avatar_split_clause,[],[f1822,f1811,f342,f68]) ).
fof(f1822,plain,
( ~ int_less(sK1,sK0)
| ~ spl3_38
| spl3_123 ),
inference(resolution,[],[f1813,f343]) ).
fof(f1813,plain,
( ~ int_leq(int_one,sK2(sK1,sK0))
| spl3_123 ),
inference(avatar_component_clause,[],[f1811]) ).
fof(f1972,plain,
( spl3_141
| ~ spl3_14
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f454,f426,f127,f1970]) ).
fof(f1970,plain,
( spl3_141
<=> ! [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_141])]) ).
fof(f454,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,[],[f427,f128]) ).
fof(f1968,plain,
( spl3_140
| ~ spl3_11
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f451,f426,f109,f1966]) ).
fof(f1966,plain,
( spl3_140
<=> ! [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_140])]) ).
fof(f451,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,[],[f427,f110]) ).
fof(f1964,plain,
( spl3_139
| ~ spl3_13
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f442,f422,f117,f1962]) ).
fof(f1962,plain,
( spl3_139
<=> ! [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_139])]) ).
fof(f442,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,[],[f423,f118]) ).
fof(f1960,plain,
( spl3_138
| ~ spl3_10
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f439,f422,f105,f1958]) ).
fof(f1958,plain,
( spl3_138
<=> ! [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_138])]) ).
fof(f439,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,[],[f423,f106]) ).
fof(f1956,plain,
( spl3_137
| ~ spl3_13
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f437,f418,f117,f1954]) ).
fof(f1954,plain,
( spl3_137
<=> ! [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_137])]) ).
fof(f437,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,[],[f419,f118]) ).
fof(f1952,plain,
( spl3_136
| ~ spl3_18
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f370,f354,f155,f1950]) ).
fof(f1950,plain,
( spl3_136
<=> ! [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_136])]) ).
fof(f370,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,[],[f355,f156]) ).
fof(f1948,plain,
( spl3_135
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f286,f277,f181,f1946]) ).
fof(f1946,plain,
( spl3_135
<=> ! [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_135])]) ).
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(f286,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,f278]) ).
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(f1944,plain,
( spl3_134
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f285,f277,f181,f1942]) ).
fof(f1942,plain,
( spl3_134
<=> ! [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_134])]) ).
fof(f285,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,f278]) ).
fof(f1920,plain,
( spl3_133
| ~ spl3_20
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f303,f294,f172,f1918]) ).
fof(f1918,plain,
( spl3_133
<=> ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_133])]) ).
fof(f303,plain,
( ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) )
| ~ spl3_20
| ~ spl3_34 ),
inference(resolution,[],[f295,f173]) ).
fof(f1916,plain,
( ~ spl3_2
| ~ spl3_15
| spl3_114 ),
inference(avatar_split_clause,[],[f1701,f1693,f135,f68]) ).
fof(f1701,plain,
( ~ int_less(sK1,sK0)
| ~ spl3_15
| spl3_114 ),
inference(resolution,[],[f1695,f136]) ).
fof(f1695,plain,
( ~ int_less(int_zero,sK2(sK1,sK0))
| spl3_114 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f1914,plain,
( ~ spl3_1
| ~ spl3_113
| ~ spl3_65
| ~ spl3_76
| spl3_132
| ~ spl3_3
| ~ spl3_23
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f265,f257,f201,f73,f1912,f904,f728,f1689,f63]) ).
fof(f904,plain,
( spl3_76
<=> int_leq(int_zero,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_76])]) ).
fof(f1912,plain,
( spl3_132
<=> ! [X0] :
( ~ int_leq(X0,sK1)
| a(X0,plus(X0,sK2(sK1,sK0))) = lu(X0,plus(X0,sK2(sK1,sK0)))
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_132])]) ).
fof(f265,plain,
( ! [X0] :
( ~ int_leq(sK0,n)
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,sK2(sK1,sK0))
| a(X0,plus(X0,sK2(sK1,sK0))) = lu(X0,plus(X0,sK2(sK1,sK0)))
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1) )
| ~ spl3_23
| ~ spl3_31 ),
inference(superposition,[],[f202,f259]) ).
fof(f1849,plain,
( spl3_131
| ~ spl3_33
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f470,f430,f277,f1847]) ).
fof(f470,plain,
( ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_leq(X0,int_zero)
| ~ int_less(int_zero,X1) )
| ~ spl3_33
| ~ spl3_47 ),
inference(superposition,[],[f431,f278]) ).
fof(f1845,plain,
( spl3_130
| ~ spl3_33
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f457,f426,f277,f1843]) ).
fof(f1843,plain,
( spl3_130
<=> ! [X0,X1] :
( int_leq(X1,X0)
| ~ int_leq(int_zero,X0)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_130])]) ).
fof(f457,plain,
( ! [X0,X1] :
( int_leq(X1,X0)
| ~ int_leq(int_zero,X0)
| ~ int_less(X1,int_zero) )
| ~ spl3_33
| ~ spl3_46 ),
inference(superposition,[],[f427,f278]) ).
fof(f1841,plain,
( spl3_129
| ~ spl3_10
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f406,f393,f105,f1839]) ).
fof(f1839,plain,
( spl3_129
<=> ! [X0] :
( int_less(X0,int_zero)
| int_zero = X0
| int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_129])]) ).
fof(f406,plain,
( ! [X0] :
( int_less(X0,int_zero)
| int_zero = X0
| int_leq(int_one,X0) )
| ~ spl3_10
| ~ spl3_43 ),
inference(resolution,[],[f394,f106]) ).
fof(f1837,plain,
( spl3_128
| ~ spl3_12
| spl3_113 ),
inference(avatar_split_clause,[],[f1700,f1689,f113,f1834]) ).
fof(f1700,plain,
( int_less(n,sK1)
| ~ spl3_12
| spl3_113 ),
inference(resolution,[],[f1691,f114]) ).
fof(f1691,plain,
( ~ int_leq(sK1,n)
| spl3_113 ),
inference(avatar_component_clause,[],[f1689]) ).
fof(f1832,plain,
( spl3_127
| ~ spl3_18
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f309,f294,f155,f1830]) ).
fof(f1830,plain,
( spl3_127
<=> ! [X0,X1] :
( int_less(X0,int_one)
| int_less(X1,X0)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_127])]) ).
fof(f309,plain,
( ! [X0,X1] :
( int_less(X0,int_one)
| int_less(X1,X0)
| ~ int_less(X1,int_zero) )
| ~ spl3_18
| ~ spl3_34 ),
inference(resolution,[],[f295,f156]) ).
fof(f1828,plain,
( spl3_126
| ~ spl3_18
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f304,f294,f155,f1826]) ).
fof(f1826,plain,
( spl3_126
<=> ! [X0,X1] :
( int_less(int_zero,X0)
| int_less(X1,int_one)
| ~ int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_126])]) ).
fof(f304,plain,
( ! [X0,X1] :
( int_less(int_zero,X0)
| int_less(X1,int_one)
| ~ int_less(X1,X0) )
| ~ spl3_18
| ~ spl3_34 ),
inference(resolution,[],[f295,f156]) ).
fof(f1821,plain,
( ~ spl3_65
| ~ spl3_123
| ~ spl3_124
| ~ spl3_19
| spl3_125
| ~ spl3_3
| ~ spl3_31
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f1220,f675,f257,f73,f1819,f159,f1815,f1811,f728]) ).
fof(f1819,plain,
( spl3_125
<=> ! [X0] :
( ~ int_leq(X0,sK2(sK1,sK0))
| real_zero = a(plus(X0,sK1),X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_125])]) ).
fof(f1220,plain,
( ! [X0] :
( ~ int_leq(sK0,n)
| ~ int_leq(X0,sK2(sK1,sK0))
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK2(sK1,sK0),n)
| ~ int_leq(int_one,sK2(sK1,sK0))
| real_zero = a(plus(X0,sK1),X0)
| ~ int_leq(int_one,sK0) )
| ~ spl3_31
| ~ spl3_59 ),
inference(superposition,[],[f676,f259]) ).
fof(f1733,plain,
( spl3_122
| ~ spl3_7
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f438,f422,f93,f1731]) ).
fof(f93,plain,
( spl3_7
<=> ! [X1] : ~ int_less(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f438,plain,
( ! [X0,X1] :
( ~ int_less(plus(X0,X1),X0)
| ~ int_less(int_zero,X1) )
| ~ spl3_7
| ~ spl3_45 ),
inference(resolution,[],[f423,f94]) ).
fof(f94,plain,
( ! [X1] : ~ int_less(X1,X1)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f1729,plain,
( spl3_121
| ~ spl3_7
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f433,f418,f93,f1727]) ).
fof(f1727,plain,
( spl3_121
<=> ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_121])]) ).
fof(f433,plain,
( ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) )
| ~ spl3_7
| ~ spl3_44 ),
inference(resolution,[],[f419,f94]) ).
fof(f1725,plain,
( spl3_120
| ~ spl3_14
| ~ spl3_40 ),
inference(avatar_split_clause,[],[f363,f350,f127,f1723]) ).
fof(f1723,plain,
( spl3_120
<=> ! [X0,X1] :
( int_leq(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_120])]) ).
fof(f363,plain,
( ! [X0,X1] :
( int_leq(X0,plus(X1,X0))
| ~ int_less(int_zero,X1) )
| ~ spl3_14
| ~ spl3_40 ),
inference(superposition,[],[f351,f128]) ).
fof(f1721,plain,
( spl3_119
| ~ spl3_11
| ~ spl3_40 ),
inference(avatar_split_clause,[],[f360,f350,f109,f1719]) ).
fof(f1719,plain,
( spl3_119
<=> ! [X0] :
( ~ int_less(int_zero,X0)
| int_less(int_zero,plus(int_one,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_119])]) ).
fof(f360,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| int_less(int_zero,plus(int_one,X0)) )
| ~ spl3_11
| ~ spl3_40 ),
inference(resolution,[],[f351,f110]) ).
fof(f1717,plain,
( spl3_118
| ~ spl3_20
| ~ spl3_33
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f312,f294,f277,f172,f1715]) ).
fof(f312,plain,
( ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,int_one) )
| ~ spl3_20
| ~ spl3_33
| ~ spl3_34 ),
inference(forward_demodulation,[],[f308,f278]) ).
fof(f308,plain,
( ! [X0] :
( int_less(X0,int_one)
| plus(int_zero,sK2(int_zero,X0)) = X0 )
| ~ spl3_20
| ~ spl3_34 ),
inference(resolution,[],[f295,f173]) ).
fof(f1713,plain,
( spl3_117
| ~ spl3_14
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f688,f681,f127,f1711]) ).
fof(f1711,plain,
( spl3_117
<=> ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X1,sK0)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_117])]) ).
fof(f688,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X1,sK0)
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X2,X0),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_60 ),
inference(superposition,[],[f682,f128]) ).
fof(f1709,plain,
( spl3_116
| ~ spl3_12
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f663,f658,f113,f1707]) ).
fof(f1707,plain,
( spl3_116
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| int_less(sK0,plus(X0,X2))
| int_less(plus(X0,X2),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_116])]) ).
fof(f663,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X1,X2),X1)
| int_less(sK0,plus(X0,X2))
| int_less(plus(X0,X2),int_one) )
| ~ spl3_12
| ~ spl3_58 ),
inference(resolution,[],[f659,f114]) ).
fof(f1699,plain,
( ~ spl3_65
| ~ spl3_1
| ~ spl3_113
| ~ spl3_114
| spl3_115
| ~ spl3_3
| ~ spl3_22
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f264,f257,f192,f73,f1697,f1693,f1689,f63,f728]) ).
fof(f264,plain,
( ! [X0] :
( ~ int_leq(sK0,n)
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK1)
| real_zero = a(plus(X0,sK2(sK1,sK0)),X0)
| ~ int_leq(int_one,sK0) )
| ~ spl3_22
| ~ spl3_31 ),
inference(superposition,[],[f193,f259]) ).
fof(f1673,plain,
( ~ spl3_53
| spl3_112
| ~ spl3_9
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f1156,f700,f101,f1671,f604]) ).
fof(f604,plain,
( spl3_53
<=> int_leq(int_zero,int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
fof(f1671,plain,
( spl3_112
<=> ! [X0,X1] :
( a(X1,X1) = lu(X1,X1)
| int_less(sK0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_112])]) ).
fof(f101,plain,
( spl3_9
<=> ! [X0] : plus(X0,int_zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f1156,plain,
( ! [X0,X1] :
( a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| int_less(sK0,X0) )
| ~ spl3_9
| ~ spl3_62 ),
inference(forward_demodulation,[],[f1154,f102]) ).
fof(f102,plain,
( ! [X0] : plus(X0,int_zero) = X0
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| int_less(sK0,X0) )
| ~ spl3_9
| ~ spl3_62 ),
inference(duplicate_literal_removal,[],[f1145]) ).
fof(f1145,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| int_less(sK0,X0)
| ~ int_leq(int_one,X0) )
| ~ spl3_9
| ~ spl3_62 ),
inference(superposition,[],[f701,f102]) ).
fof(f1669,plain,
( ~ spl3_53
| spl3_56
| ~ spl3_9
| ~ spl3_33
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f741,f724,f277,f101,f637,f604]) ).
fof(f741,plain,
( ! [X0,X1] :
( a(X1,X1) = lu(X1,X1)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| ~ int_leq(int_one,X0) )
| ~ spl3_9
| ~ spl3_33
| ~ spl3_64 ),
inference(forward_demodulation,[],[f740,f102]) ).
fof(f740,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| ~ int_leq(int_one,X0) )
| ~ spl3_33
| ~ spl3_64 ),
inference(duplicate_literal_removal,[],[f738]) ).
fof(f738,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(X0,sK0)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,X0) )
| ~ spl3_33
| ~ spl3_64 ),
inference(superposition,[],[f725,f278]) ).
fof(f1660,plain,
( spl3_111
| ~ spl3_40
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f644,f637,f350,f1658]) ).
fof(f1658,plain,
( spl3_111
<=> ! [X0,X1] :
( a(plus(int_one,X0),plus(int_one,X0)) = lu(plus(int_one,X0),plus(int_one,X0))
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,sK0)
| ~ int_leq(plus(int_one,X0),X1)
| ~ int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_111])]) ).
fof(f644,plain,
( ! [X0,X1] :
( a(plus(int_one,X0),plus(int_one,X0)) = lu(plus(int_one,X0),plus(int_one,X0))
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,sK0)
| ~ int_leq(plus(int_one,X0),X1)
| ~ int_less(int_zero,X0) )
| ~ spl3_40
| ~ spl3_56 ),
inference(resolution,[],[f638,f351]) ).
fof(f1628,plain,
( spl3_110
| ~ spl3_28
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f1108,f483,f237,f1625]) ).
fof(f1625,plain,
( spl3_110
<=> sK2(sK0,n) = sK2(int_zero,sK2(sK0,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_110])]) ).
fof(f1108,plain,
( sK2(sK0,n) = sK2(int_zero,sK2(sK0,n))
| ~ spl3_28
| ~ spl3_48 ),
inference(resolution,[],[f239,f484]) ).
fof(f239,plain,
( int_less(sK0,n)
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f1586,plain,
( spl3_109
| ~ spl3_38
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f641,f637,f342,f1584]) ).
fof(f1584,plain,
( spl3_109
<=> ! [X2,X0,X1] :
( a(sK2(X0,X1),sK2(X0,X1)) = lu(sK2(X0,X1),sK2(X0,X1))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,sK0)
| ~ int_leq(sK2(X0,X1),X2)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_109])]) ).
fof(f641,plain,
( ! [X2,X0,X1] :
( a(sK2(X0,X1),sK2(X0,X1)) = lu(sK2(X0,X1),sK2(X0,X1))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,sK0)
| ~ int_leq(sK2(X0,X1),X2)
| ~ int_less(X0,X1) )
| ~ spl3_38
| ~ spl3_56 ),
inference(resolution,[],[f638,f343]) ).
fof(f1581,plain,
( ~ spl3_107
| ~ spl3_71
| spl3_108
| ~ spl3_33
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f668,f658,f277,f1579,f850,f1575]) ).
fof(f1575,plain,
( spl3_107
<=> int_leq(int_one,int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_107])]) ).
fof(f850,plain,
( spl3_71
<=> int_leq(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).
fof(f1579,plain,
( spl3_108
<=> ! [X0,X1] :
( ~ int_leq(int_one,X0)
| int_less(sK0,X0)
| real_zero = a(plus(X1,X0),X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(X1,int_zero)
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_108])]) ).
fof(f668,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,sK0)
| ~ int_leq(X1,int_zero)
| ~ int_leq(int_one,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,int_zero)
| real_zero = a(plus(X1,X0),X1)
| int_less(sK0,X0) )
| ~ spl3_33
| ~ spl3_58 ),
inference(superposition,[],[f659,f278]) ).
fof(f1547,plain,
( spl3_106
| ~ spl3_2
| ~ spl3_95 ),
inference(avatar_split_clause,[],[f1312,f1264,f68,f1544]) ).
fof(f1312,plain,
( int_less(sK1,n)
| ~ spl3_2
| ~ spl3_95 ),
inference(resolution,[],[f1265,f70]) ).
fof(f70,plain,
( int_less(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f1499,plain,
( spl3_105
| ~ spl3_20
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f1109,f237,f172,f1496]) ).
fof(f1109,plain,
( n = plus(sK0,sK2(sK0,n))
| ~ spl3_20
| ~ spl3_28 ),
inference(resolution,[],[f239,f173]) ).
fof(f1481,plain,
( ~ spl3_8
| spl3_103 ),
inference(avatar_contradiction_clause,[],[f1479]) ).
fof(f1479,plain,
( $false
| ~ spl3_8
| spl3_103 ),
inference(resolution,[],[f1473,f98]) ).
fof(f1473,plain,
( ~ int_leq(int_one,int_one)
| spl3_103 ),
inference(avatar_component_clause,[],[f1471]) ).
fof(f1471,plain,
( spl3_103
<=> int_leq(int_one,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_103])]) ).
fof(f1477,plain,
( ~ spl3_103
| spl3_104
| ~ spl3_65
| ~ spl3_40
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f671,f658,f350,f728,f1475,f1471]) ).
fof(f1475,plain,
( spl3_104
<=> ! [X0,X1] :
( ~ int_leq(X0,int_one)
| int_less(sK0,plus(int_one,X1))
| real_zero = a(plus(X0,X1),X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_104])]) ).
fof(f671,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK0)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,int_one)
| real_zero = a(plus(X0,X1),X0)
| int_less(sK0,plus(int_one,X1)) )
| ~ spl3_40
| ~ spl3_58 ),
inference(duplicate_literal_removal,[],[f661]) ).
fof(f661,plain,
( ! [X0,X1] :
( ~ int_leq(int_one,sK0)
| ~ int_leq(X0,int_one)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,int_one)
| real_zero = a(plus(X0,X1),X0)
| int_less(sK0,plus(int_one,X1))
| ~ int_less(int_zero,X1) )
| ~ spl3_40
| ~ spl3_58 ),
inference(resolution,[],[f659,f351]) ).
fof(f1404,plain,
( spl3_102
| ~ spl3_25
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f615,f608,f221,f1402]) ).
fof(f615,plain,
( ! [X0,X1] :
( ~ int_leq(sK1,X1)
| ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) )
| ~ spl3_25
| ~ spl3_54 ),
inference(forward_demodulation,[],[f614,f223]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X0)
| ~ int_leq(X0,n) )
| ~ spl3_25
| ~ spl3_54 ),
inference(forward_demodulation,[],[f609,f223]) ).
fof(f1371,plain,
( spl3_101
| ~ spl3_42
| ~ spl3_95 ),
inference(avatar_split_clause,[],[f1311,f1264,f380,f1368]) ).
fof(f1311,plain,
( int_less(int_one,n)
| ~ spl3_42
| ~ spl3_95 ),
inference(resolution,[],[f1265,f382]) ).
fof(f1362,plain,
( spl3_100
| ~ spl3_12
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f643,f637,f113,f1360]) ).
fof(f1360,plain,
( spl3_100
<=> ! [X0,X1] :
( a(X0,X0) = lu(X0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_100])]) ).
fof(f643,plain,
( ! [X0,X1] :
( a(X0,X0) = lu(X0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| int_less(X0,int_one) )
| ~ spl3_12
| ~ spl3_56 ),
inference(resolution,[],[f638,f114]) ).
fof(f1358,plain,
( spl3_97
| spl3_99
| ~ spl3_1
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f1182,f608,f63,f1356,f1298]) ).
fof(f1298,plain,
( spl3_97
<=> a(sK1,sK1) = lu(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_97])]) ).
fof(f1356,plain,
( spl3_99
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_99])]) ).
fof(f1182,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| a(sK1,sK1) = lu(sK1,sK1)
| ~ int_leq(sK1,X0)
| ~ int_leq(X0,n) )
| ~ spl3_1
| ~ spl3_54 ),
inference(resolution,[],[f609,f65]) ).
fof(f1319,plain,
( spl3_98
| ~ spl3_36
| ~ spl3_95 ),
inference(avatar_split_clause,[],[f1309,f1264,f315,f1316]) ).
fof(f1309,plain,
( int_less(int_zero,n)
| ~ spl3_36
| ~ spl3_95 ),
inference(resolution,[],[f1265,f317]) ).
fof(f1301,plain,
( spl3_96
| spl3_97
| ~ spl3_1
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f640,f637,f63,f1298,f1295]) ).
fof(f640,plain,
( ! [X0] :
( a(sK1,sK1) = lu(sK1,sK1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(sK1,X0) )
| ~ spl3_1
| ~ spl3_56 ),
inference(resolution,[],[f638,f65]) ).
fof(f1266,plain,
( spl3_95
| ~ spl3_18
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f1110,f237,f155,f1264]) ).
fof(f1110,plain,
( ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK0) )
| ~ spl3_18
| ~ spl3_28 ),
inference(resolution,[],[f239,f156]) ).
fof(f1245,plain,
( spl3_94
| ~ spl3_33
| ~ spl3_68 ),
inference(avatar_split_clause,[],[f772,f763,f277,f1242]) ).
fof(f1242,plain,
( spl3_94
<=> sK1 = sK2(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_94])]) ).
fof(f763,plain,
( spl3_68
<=> sK1 = plus(int_zero,sK2(int_zero,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
fof(f772,plain,
( sK1 = sK2(int_zero,sK1)
| ~ spl3_33
| ~ spl3_68 ),
inference(superposition,[],[f765,f278]) ).
fof(f765,plain,
( sK1 = plus(int_zero,sK2(int_zero,sK1))
| ~ spl3_68 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f1095,plain,
( ~ spl3_24
| ~ spl3_1
| ~ spl3_87 ),
inference(avatar_split_clause,[],[f995,f988,f63,f211]) ).
fof(f988,plain,
( spl3_87
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_87])]) ).
fof(f995,plain,
( ~ int_leq(sK1,sK0)
| ~ spl3_1
| ~ spl3_87 ),
inference(resolution,[],[f989,f65]) ).
fof(f989,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) )
| ~ spl3_87 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1087,plain,
( spl3_93
| ~ spl3_13
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f310,f294,f117,f1085]) ).
fof(f1085,plain,
( spl3_93
<=> ! [X0] :
( int_less(X0,int_one)
| int_leq(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_93])]) ).
fof(f310,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_leq(int_zero,X0) )
| ~ spl3_13
| ~ spl3_34 ),
inference(resolution,[],[f295,f118]) ).
fof(f1083,plain,
( spl3_92
| ~ spl3_13
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f305,f294,f117,f1081]) ).
fof(f1081,plain,
( spl3_92
<=> ! [X0] :
( int_less(int_zero,X0)
| int_leq(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_92])]) ).
fof(f305,plain,
( ! [X0] :
( int_less(int_zero,X0)
| int_leq(X0,int_one) )
| ~ spl3_13
| ~ spl3_34 ),
inference(resolution,[],[f295,f118]) ).
fof(f1074,plain,
( spl3_91
| ~ spl3_33
| ~ spl3_37 ),
inference(avatar_split_clause,[],[f324,f320,f277,f1071]) ).
fof(f1071,plain,
( spl3_91
<=> int_one = sK2(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_91])]) ).
fof(f320,plain,
( spl3_37
<=> int_one = plus(int_zero,sK2(int_zero,int_one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f324,plain,
( int_one = sK2(int_zero,int_one)
| ~ spl3_33
| ~ spl3_37 ),
inference(superposition,[],[f322,f278]) ).
fof(f322,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_37 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f1057,plain,
( spl3_90
| ~ spl3_31
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f592,f575,f257,f1055]) ).
fof(f1055,plain,
( spl3_90
<=> ! [X0,X1] :
( int_less(plus(X0,X1),sK0)
| ~ int_less(X0,sK1)
| ~ int_leq(X1,sK2(sK1,sK0))
| plus(X0,X1) = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_90])]) ).
fof(f592,plain,
( ! [X0,X1] :
( int_less(plus(X0,X1),sK0)
| ~ int_less(X0,sK1)
| ~ int_leq(X1,sK2(sK1,sK0))
| plus(X0,X1) = sK0 )
| ~ spl3_31
| ~ spl3_52 ),
inference(superposition,[],[f576,f259]) ).
fof(f1039,plain,
( ~ spl3_2
| ~ spl3_39
| spl3_76 ),
inference(avatar_split_clause,[],[f911,f904,f346,f68]) ).
fof(f346,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(f911,plain,
( ~ int_less(sK1,sK0)
| ~ spl3_39
| spl3_76 ),
inference(resolution,[],[f906,f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( int_leq(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_39 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f906,plain,
( ~ int_leq(int_zero,sK2(sK1,sK0))
| spl3_76 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f1038,plain,
( spl3_89
| ~ spl3_31
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f586,f575,f257,f1036]) ).
fof(f1036,plain,
( spl3_89
<=> ! [X0,X1] :
( int_less(sK0,plus(X0,X1))
| ~ int_less(sK1,X0)
| ~ int_leq(sK2(sK1,sK0),X1)
| plus(X0,X1) = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_89])]) ).
fof(f586,plain,
( ! [X0,X1] :
( int_less(sK0,plus(X0,X1))
| ~ int_less(sK1,X0)
| ~ int_leq(sK2(sK1,sK0),X1)
| plus(X0,X1) = sK0 )
| ~ spl3_31
| ~ spl3_52 ),
inference(superposition,[],[f576,f259]) ).
fof(f994,plain,
( spl3_87
| spl3_88
| ~ spl3_8
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f646,f637,f97,f991,f988]) ).
fof(f991,plain,
( spl3_88
<=> a(int_one,int_one) = lu(int_one,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_88])]) ).
fof(f646,plain,
( ! [X0] :
( a(int_one,int_one) = lu(int_one,int_one)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) )
| ~ spl3_8
| ~ spl3_56 ),
inference(duplicate_literal_removal,[],[f642]) ).
fof(f642,plain,
( ! [X0] :
( a(int_one,int_one) = lu(int_one,int_one)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0) )
| ~ spl3_8
| ~ spl3_56 ),
inference(resolution,[],[f638,f98]) ).
fof(f985,plain,
( spl3_86
| ~ spl3_31
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f538,f506,f257,f983]) ).
fof(f538,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X1,sK1)
| ~ int_less(X0,sK2(sK1,sK0)) )
| ~ spl3_31
| ~ spl3_50 ),
inference(superposition,[],[f507,f259]) ).
fof(f981,plain,
( spl3_85
| ~ spl3_31
| ~ spl3_50 ),
inference(avatar_split_clause,[],[f532,f506,f257,f979]) ).
fof(f979,plain,
( spl3_85
<=> ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK2(sK1,sK0),X0)
| ~ int_less(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_85])]) ).
fof(f532,plain,
( ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK2(sK1,sK0),X0)
| ~ int_less(sK1,X1) )
| ~ spl3_31
| ~ spl3_50 ),
inference(superposition,[],[f507,f259]) ).
fof(f977,plain,
( spl3_84
| ~ spl3_31
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f519,f502,f257,f975]) ).
fof(f519,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X0,sK2(sK1,sK0))
| ~ int_less(X1,sK1) )
| ~ spl3_31
| ~ spl3_49 ),
inference(superposition,[],[f503,f259]) ).
fof(f973,plain,
( spl3_83
| ~ spl3_31
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f513,f502,f257,f971]) ).
fof(f513,plain,
( ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK1,X1)
| ~ int_less(sK2(sK1,sK0),X0) )
| ~ spl3_31
| ~ spl3_49 ),
inference(superposition,[],[f503,f259]) ).
fof(f969,plain,
( spl3_82
| ~ spl3_21
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f263,f257,f181,f967]) ).
fof(f263,plain,
( ! [X0,X1] :
( int_leq(plus(X0,X1),sK0)
| ~ int_leq(X1,sK2(sK1,sK0))
| ~ int_less(X0,sK1) )
| ~ spl3_21
| ~ spl3_31 ),
inference(superposition,[],[f182,f259]) ).
fof(f965,plain,
( spl3_81
| ~ spl3_21
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f262,f257,f181,f963]) ).
fof(f963,plain,
( spl3_81
<=> ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK2(sK1,sK0),X1)
| ~ int_less(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_81])]) ).
fof(f262,plain,
( ! [X0,X1] :
( int_leq(sK0,plus(X0,X1))
| ~ int_leq(sK2(sK1,sK0),X1)
| ~ int_less(sK1,X0) )
| ~ spl3_21
| ~ spl3_31 ),
inference(superposition,[],[f182,f259]) ).
fof(f928,plain,
( spl3_80
| ~ spl3_19
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f553,f548,f159,f926]) ).
fof(f926,plain,
( spl3_80
<=> ! [X0] : plus(X0,sK1) = plus(X0,sK2(X0,plus(X0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_80])]) ).
fof(f553,plain,
( ! [X0] : plus(X0,sK1) = plus(X0,sK2(X0,plus(X0,sK1)))
| ~ spl3_19
| ~ spl3_51 ),
inference(resolution,[],[f549,f161]) ).
fof(f923,plain,
( ~ spl3_78
| spl3_79
| ~ spl3_31
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f469,f430,f257,f921,f917]) ).
fof(f921,plain,
( spl3_79
<=> ! [X0] :
( int_leq(sK0,X0)
| ~ int_less(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_79])]) ).
fof(f469,plain,
( ! [X0] :
( int_leq(sK0,X0)
| ~ int_leq(sK2(sK1,sK0),int_zero)
| ~ int_less(sK1,X0) )
| ~ spl3_31
| ~ spl3_47 ),
inference(superposition,[],[f431,f259]) ).
fof(f910,plain,
( ~ spl3_76
| spl3_77
| ~ spl3_31
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f456,f426,f257,f908,f904]) ).
fof(f456,plain,
( ! [X0] :
( int_leq(X0,sK0)
| ~ int_leq(int_zero,sK2(sK1,sK0))
| ~ int_less(X0,sK1) )
| ~ spl3_31
| ~ spl3_46 ),
inference(superposition,[],[f427,f259]) ).
fof(f877,plain,
( spl3_75
| ~ spl3_26
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f632,f483,f225,f874]) ).
fof(f874,plain,
( spl3_75
<=> sK2(int_one,sK1) = sK2(int_zero,sK2(int_one,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_75])]) ).
fof(f632,plain,
( sK2(int_one,sK1) = sK2(int_zero,sK2(int_one,sK1))
| ~ spl3_26
| ~ spl3_48 ),
inference(resolution,[],[f227,f484]) ).
fof(f227,plain,
( int_less(int_one,sK1)
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f872,plain,
( spl3_74
| ~ spl3_2
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f497,f483,f68,f869]) ).
fof(f869,plain,
( spl3_74
<=> sK2(sK1,sK0) = sK2(int_zero,sK2(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_74])]) ).
fof(f497,plain,
( sK2(sK1,sK0) = sK2(int_zero,sK2(sK1,sK0))
| ~ spl3_2
| ~ spl3_48 ),
inference(resolution,[],[f484,f70]) ).
fof(f866,plain,
( spl3_73
| ~ spl3_19
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f495,f483,f159,f863]) ).
fof(f863,plain,
( spl3_73
<=> sK2(int_zero,sK1) = sK2(int_zero,sK2(int_zero,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_73])]) ).
fof(f495,plain,
( sK2(int_zero,sK1) = sK2(int_zero,sK2(int_zero,sK1))
| ~ spl3_19
| ~ spl3_48 ),
inference(resolution,[],[f484,f161]) ).
fof(f861,plain,
( spl3_72
| ~ spl3_29
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f403,f393,f246,f859]) ).
fof(f859,plain,
( spl3_72
<=> ! [X0] :
( int_less(sK1,X0)
| sK1 = X0
| int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).
fof(f246,plain,
( spl3_29
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f403,plain,
( ! [X0] :
( int_less(sK1,X0)
| sK1 = X0
| int_less(X0,sK0) )
| ~ spl3_29
| ~ spl3_43 ),
inference(resolution,[],[f394,f247]) ).
fof(f247,plain,
( ! [X0] :
( ~ int_less(X0,sK1)
| int_less(X0,sK0) )
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f853,plain,
( spl3_71
| ~ spl3_13
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f572,f315,f117,f850]) ).
fof(f572,plain,
( int_leq(int_zero,sK0)
| ~ spl3_13
| ~ spl3_36 ),
inference(resolution,[],[f317,f118]) ).
fof(f848,plain,
( ~ spl3_19
| spl3_70
| ~ spl3_31
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f375,f354,f257,f845,f159]) ).
fof(f375,plain,
( int_less(sK2(sK1,sK0),sK0)
| ~ int_less(int_zero,sK1)
| ~ spl3_31
| ~ spl3_41 ),
inference(superposition,[],[f355,f259]) ).
fof(f771,plain,
( spl3_69
| ~ spl3_20
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f229,f225,f172,f768]) ).
fof(f229,plain,
( sK1 = plus(int_one,sK2(int_one,sK1))
| ~ spl3_20
| ~ spl3_26 ),
inference(resolution,[],[f227,f173]) ).
fof(f766,plain,
( spl3_68
| ~ spl3_19
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f216,f172,f159,f763]) ).
fof(f216,plain,
( sK1 = plus(int_zero,sK2(int_zero,sK1))
| ~ spl3_19
| ~ spl3_20 ),
inference(resolution,[],[f161,f173]) ).
fof(f753,plain,
( spl3_67
| ~ spl3_18
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f230,f225,f155,f751]) ).
fof(f230,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_26 ),
inference(resolution,[],[f227,f156]) ).
fof(f749,plain,
( spl3_66
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f217,f159,f155,f747]) ).
fof(f747,plain,
( spl3_66
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).
fof(f217,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) )
| ~ spl3_18
| ~ spl3_19 ),
inference(resolution,[],[f161,f156]) ).
fof(f731,plain,
( spl3_65
| ~ spl3_10
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f568,f315,f105,f728]) ).
fof(f568,plain,
( int_leq(int_one,sK0)
| ~ spl3_10
| ~ spl3_36 ),
inference(resolution,[],[f317,f106]) ).
fof(f726,plain,
( spl3_64
| ~ spl3_27
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f722,f718,f233,f724]) ).
fof(f722,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(int_one,X0) )
| ~ spl3_27
| ~ spl3_63 ),
inference(forward_demodulation,[],[f721,f235]) ).
fof(f721,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_27
| ~ spl3_63 ),
inference(forward_demodulation,[],[f719,f235]) ).
fof(f720,plain,
( spl3_63
| ~ spl3_14
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f206,f201,f127,f718]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_zero,X1)
| a(X2,plus(X2,X1)) = lu(X2,plus(X2,X1))
| ~ int_leq(int_one,plus(X1,X0))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_14
| ~ spl3_23 ),
inference(superposition,[],[f202,f128]) ).
fof(f702,plain,
( spl3_62
| ~ spl3_27
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f698,f694,f233,f700]) ).
fof(f698,plain,
( ! [X2,X0,X1] :
( int_less(sK0,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(X0,plus(X0,X2))
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(int_one,X1) )
| ~ spl3_27
| ~ spl3_61 ),
inference(forward_demodulation,[],[f697,f235]) ).
fof(f697,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(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_61 ),
inference(forward_demodulation,[],[f695,f235]) ).
fof(f696,plain,
( spl3_61
| ~ spl3_12
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f204,f201,f113,f694]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_zero,X2)
| a(X0,plus(X0,X2)) = lu(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_23 ),
inference(resolution,[],[f202,f114]) ).
fof(f683,plain,
( spl3_60
| ~ spl3_27
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f679,f675,f233,f681]) ).
fof(f679,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_27
| ~ spl3_59 ),
inference(forward_demodulation,[],[f678,f235]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X0),sK0)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_27
| ~ spl3_59 ),
inference(forward_demodulation,[],[f676,f235]) ).
fof(f677,plain,
( spl3_59
| ~ spl3_14
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f197,f192,f127,f675]) ).
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)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X2,X1),X2)
| ~ int_leq(int_one,plus(X1,X0)) )
| ~ spl3_14
| ~ spl3_22 ),
inference(superposition,[],[f193,f128]) ).
fof(f660,plain,
( spl3_58
| ~ spl3_27
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f652,f648,f233,f658]) ).
fof(f652,plain,
( ! [X2,X0,X1] :
( int_less(sK0,plus(X1,X2))
| ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2)) )
| ~ spl3_27
| ~ spl3_57 ),
inference(forward_demodulation,[],[f651,f235]) ).
fof(f651,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X1,sK0)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,X1)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) )
| ~ spl3_27
| ~ spl3_57 ),
inference(forward_demodulation,[],[f649,f235]) ).
fof(f650,plain,
( spl3_57
| ~ spl3_12
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f195,f192,f113,f648]) ).
fof(f195,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)
| real_zero = a(plus(X0,X2),X0)
| ~ int_leq(int_one,plus(X1,X2))
| int_less(n,plus(X1,X2)) )
| ~ spl3_12
| ~ spl3_22 ),
inference(resolution,[],[f193,f114]) ).
fof(f639,plain,
( spl3_56
| ~ spl3_27
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f621,f608,f233,f637]) ).
fof(f621,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X0) )
| ~ spl3_27
| ~ spl3_54 ),
inference(forward_demodulation,[],[f609,f235]) ).
fof(f620,plain,
( spl3_55
| ~ spl3_25
| ~ spl3_27
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f616,f608,f233,f221,f618]) ).
fof(f618,plain,
( spl3_55
<=> ! [X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(sK1,X1)
| ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
fof(f616,plain,
( ! [X0,X1] :
( ~ int_leq(X0,sK0)
| ~ int_leq(sK1,X1)
| ~ int_leq(sK1,X0)
| a(X1,X1) = lu(X1,X1)
| ~ int_leq(X1,X0) )
| ~ spl3_25
| ~ spl3_27
| ~ spl3_54 ),
inference(forward_demodulation,[],[f615,f235]) ).
fof(f613,plain,
( ~ spl3_8
| spl3_53 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f611,plain,
( $false
| ~ spl3_8
| spl3_53 ),
inference(resolution,[],[f606,f98]) ).
fof(f606,plain,
( ~ int_leq(int_zero,int_zero)
| spl3_53 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f610,plain,
( ~ spl3_53
| spl3_54
| ~ spl3_9
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f209,f201,f101,f608,f604]) ).
fof(f209,plain,
( ! [X0,X1] :
( a(X1,X1) = lu(X1,X1)
| ~ int_leq(X0,n)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| ~ int_leq(int_one,X0) )
| ~ spl3_9
| ~ spl3_23 ),
inference(forward_demodulation,[],[f208,f102]) ).
fof(f208,plain,
( ! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| ~ int_leq(int_one,X0) )
| ~ spl3_9
| ~ spl3_23 ),
inference(duplicate_literal_removal,[],[f205]) ).
fof(f205,plain,
( ! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_zero,int_zero)
| a(X1,plus(X1,int_zero)) = lu(X1,plus(X1,int_zero))
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_9
| ~ spl3_23 ),
inference(superposition,[],[f202,f102]) ).
fof(f577,plain,
( spl3_52
| ~ spl3_17
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f184,f181,f151,f575]) ).
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(f550,plain,
( spl3_51
| ~ spl3_16
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f178,f172,f139,f548]) ).
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(f508,plain,
( spl3_50
| ~ spl3_14
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f189,f181,f127,f506]) ).
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(f504,plain,
( spl3_49
| ~ spl3_14
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f186,f181,f127,f502]) ).
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(f485,plain,
( spl3_48
| ~ spl3_9
| ~ spl3_14
| ~ spl3_15
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f179,f172,f135,f127,f101,f483]) ).
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(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(f432,plain,
( spl3_47
| ~ spl3_9
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f188,f181,f101,f430]) ).
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(f428,plain,
( spl3_46
| ~ spl3_9
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f185,f181,f101,f426]) ).
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(f424,plain,
( spl3_45
| ~ spl3_16
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f170,f155,f139,f422]) ).
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(f420,plain,
( spl3_44
| ~ spl3_15
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f169,f155,f135,f418]) ).
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(f395,plain,
( spl3_43
| ~ spl3_12
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f166,f151,f113,f393]) ).
fof(f166,plain,
( ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) )
| ~ spl3_12
| ~ spl3_17 ),
inference(resolution,[],[f152,f114]) ).
fof(f383,plain,
( spl3_42
| ~ spl3_26
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f250,f246,f225,f380]) ).
fof(f250,plain,
( int_less(int_one,sK0)
| ~ spl3_26
| ~ spl3_29 ),
inference(resolution,[],[f247,f227]) ).
fof(f356,plain,
( spl3_41
| ~ spl3_14
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f147,f139,f127,f354]) ).
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(f352,plain,
( spl3_40
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f145,f139,f117,f350]) ).
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(f348,plain,
( spl3_39
| ~ spl3_13
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f143,f135,f117,f346]) ).
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(f344,plain,
( spl3_38
| ~ spl3_10
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f142,f135,f105,f342]) ).
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(f323,plain,
( spl3_37
| ~ spl3_6
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f176,f172,f88,f320]) ).
fof(f176,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_6
| ~ spl3_20 ),
inference(resolution,[],[f173,f90]) ).
fof(f318,plain,
( spl3_36
| ~ spl3_19
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f249,f246,f159,f315]) ).
fof(f249,plain,
( int_less(int_zero,sK0)
| ~ spl3_19
| ~ spl3_29 ),
inference(resolution,[],[f247,f161]) ).
fof(f300,plain,
( spl3_35
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f168,f155,f88,f298]) ).
fof(f298,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(f296,plain,
( spl3_34
| ~ spl3_11
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f123,f113,f109,f294]) ).
fof(f123,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_11
| ~ spl3_12 ),
inference(resolution,[],[f114,f110]) ).
fof(f279,plain,
( spl3_33
| ~ spl3_9
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f130,f127,f101,f277]) ).
fof(f274,plain,
( spl3_32
| ~ spl3_6
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f125,f117,f88,f271]) ).
fof(f271,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(f260,plain,
( spl3_31
| ~ spl3_2
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f175,f172,f68,f257]) ).
fof(f175,plain,
( sK0 = plus(sK1,sK2(sK1,sK0))
| ~ spl3_2
| ~ spl3_20 ),
inference(resolution,[],[f173,f70]) ).
fof(f255,plain,
( spl3_30
| ~ spl3_13
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f218,f159,f117,f252]) ).
fof(f218,plain,
( int_leq(int_zero,sK1)
| ~ spl3_13
| ~ spl3_19 ),
inference(resolution,[],[f161,f118]) ).
fof(f248,plain,
( spl3_29
| ~ spl3_2
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f167,f155,f68,f246]) ).
fof(f167,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,sK1) )
| ~ spl3_2
| ~ spl3_18 ),
inference(resolution,[],[f156,f70]) ).
fof(f240,plain,
( spl3_27
| spl3_28
| ~ spl3_3
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f164,f151,f73,f237,f233]) ).
fof(f164,plain,
( int_less(sK0,n)
| n = sK0
| ~ spl3_3
| ~ spl3_17 ),
inference(resolution,[],[f152,f75]) ).
fof(f75,plain,
( int_leq(sK0,n)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f228,plain,
( spl3_25
| spl3_26
| ~ spl3_1
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f163,f151,f63,f225,f221]) ).
fof(f163,plain,
( int_less(int_one,sK1)
| int_one = sK1
| ~ spl3_1
| ~ spl3_17 ),
inference(resolution,[],[f152,f65]) ).
fof(f214,plain,
( spl3_24
| ~ spl3_2
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f124,f117,f68,f211]) ).
fof(f124,plain,
( int_leq(sK1,sK0)
| ~ spl3_2
| ~ spl3_13 ),
inference(resolution,[],[f118,f70]) ).
fof(f203,plain,
spl3_23,
inference(avatar_split_clause,[],[f57,f201]) ).
fof(f57,plain,
! [X2,X3,X0] :
( a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_leq(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] :
( a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_leq(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(f20,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_leq(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( real_zero = a(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] :
( a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_leq(int_zero,X2) )
& ! [X4] :
( ! [X5] :
( real_zero = a(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_leq(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X2)) = lu(X3,plus(X3,X2)) ) )
& ! [X4] :
( ( plus(X1,X4) = X0
& int_less(int_zero,X4) )
=> ! [X5] :
( ( int_leq(X5,X1)
& int_leq(int_one,X5) )
=> real_zero = a(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_leq(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X0)
& int_leq(int_one,X2) )
=> a(X2,plus(X2,X7)) = lu(X2,plus(X2,X7)) ) )
& ! [X7] :
( ( plus(X1,X7) = X0
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> real_zero = a(plus(X2,X7),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qiu) ).
fof(f194,plain,
spl3_22,
inference(avatar_split_clause,[],[f58,f192]) ).
fof(f58,plain,
! [X1,X4,X5] :
( real_zero = a(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] :
( real_zero = a(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(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,sK1)
| ~ 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(sK0,n)
& int_less(sK1,sK0)
& int_leq(int_one,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f26]) ).
fof(f26,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X0,n)
& int_less(X1,X0)
& int_leq(int_one,X1) )
=> ( real_zero != a(sK0,sK1)
& int_leq(sK0,n)
& int_less(sK1,sK0)
& int_leq(int_one,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X0,n)
& int_less(X1,X0)
& int_leq(int_one,X1) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X0,n)
& int_less(X1,X0)
& int_leq(int_one,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X0,n)
& int_less(X1,X0)
& int_leq(int_one,X1) )
=> real_zero = a(X0,X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X0,n)
& int_less(X1,X0)
& int_leq(int_one,X1) )
=> real_zero = a(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ut) ).
fof(f76,plain,
spl3_3,
inference(avatar_split_clause,[],[f37,f73]) ).
fof(f37,plain,
int_leq(sK0,n),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
spl3_2,
inference(avatar_split_clause,[],[f36,f68]) ).
fof(f36,plain,
int_less(sK1,sK0),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
spl3_1,
inference(avatar_split_clause,[],[f35,f63]) ).
fof(f35,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWV487+1 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.18/0.38 % Computer : n007.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Sun May 19 07:34:23 EDT 2024
% 0.18/0.39 % CPUTime :
% 0.18/0.39 % (1059)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.40 % (1065)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)
% 0.18/0.41 % (1061)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.41 % (1063)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.41 TRYING [1]
% 0.18/0.41 TRYING [2]
% 0.18/0.41 % (1062)WARNING: value z3 for option sas not known
% 0.18/0.41 TRYING [3]
% 0.18/0.41 % (1064)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)
% 0.18/0.41 % (1062)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)
% 0.18/0.41 TRYING [4]
% 0.25/0.42 % (1060)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.25/0.42 TRYING [5]
% 0.25/0.42 % (1066)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)
% 0.25/0.43 TRYING [1]
% 0.25/0.43 TRYING [2]
% 0.25/0.44 TRYING [6]
% 0.25/0.45 TRYING [3]
% 0.25/0.48 TRYING [7]
% 0.25/0.49 TRYING [4]
% 0.25/0.53 TRYING [5]
% 0.25/0.53 TRYING [8]
% 1.43/0.62 TRYING [9]
% 1.43/0.64 TRYING [6]
% 3.17/0.85 TRYING [10]
% 3.52/0.94 % (1064)First to succeed.
% 3.92/0.95 % (1064)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1059"
% 3.92/0.96 % (1064)Refutation found. Thanks to Tanya!
% 3.92/0.96 % SZS status Theorem for theBenchmark
% 3.92/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/0.96 % (1064)------------------------------
% 3.92/0.96 % (1064)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.92/0.96 % (1064)Termination reason: Refutation
% 3.92/0.96
% 3.92/0.96 % (1064)Memory used [KB]: 4027
% 3.92/0.96 % (1064)Time elapsed: 0.544 s
% 3.92/0.96 % (1064)Instructions burned: 1404 (million)
% 3.92/0.96 % (1059)Success in time 0.552 s
%------------------------------------------------------------------------------