TSTP Solution File: SWV486+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV486+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n027.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 : Sat Sep 2 13:48:19 EDT 2023
% Result : Theorem 1.00s 0.60s
% Output : Refutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 223
% Syntax : Number of formulae : 763 ( 35 unt; 0 def)
% Number of atoms : 2846 ( 287 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 3788 (1705 ~;1792 |; 60 &)
% ( 211 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 212 ( 210 usr; 209 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 818 (; 808 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3553,plain,
$false,
inference(avatar_sat_refutation,[],[f62,f67,f72,f77,f82,f87,f91,f95,f99,f103,f107,f111,f115,f123,f131,f139,f145,f149,f162,f171,f179,f193,f199,f204,f208,f226,f240,f247,f251,f257,f276,f281,f286,f301,f308,f315,f334,f346,f352,f363,f370,f374,f392,f397,f409,f413,f417,f436,f455,f460,f464,f468,f472,f506,f523,f528,f532,f566,f590,f613,f617,f621,f625,f645,f650,f655,f686,f716,f721,f727,f732,f737,f767,f779,f788,f797,f807,f813,f818,f823,f833,f837,f841,f845,f849,f853,f861,f890,f894,f907,f919,f942,f946,f963,f972,f977,f981,f985,f989,f1038,f1042,f1046,f1051,f1055,f1059,f1063,f1125,f1130,f1151,f1155,f1187,f1191,f1195,f1199,f1203,f1208,f1212,f1216,f1220,f1224,f1374,f1378,f1382,f1446,f1457,f1461,f1524,f1528,f1587,f1588,f1620,f1624,f1628,f1632,f1636,f1640,f1689,f1839,f1883,f1928,f1932,f2002,f2037,f2097,f2221,f2226,f2227,f2280,f2328,f2345,f2349,f2385,f2390,f2394,f2429,f2439,f2443,f2459,f2463,f2502,f2510,f2514,f2518,f2522,f2546,f2601,f2605,f2644,f2656,f2657,f2667,f2696,f2700,f2704,f2708,f2712,f2716,f2717,f2745,f2773,f2788,f2803,f2807,f2815,f2818,f2845,f2925,f2966,f2982,f2986,f2990,f3110,f3192,f3197,f3202,f3207,f3220,f3224,f3272,f3455,f3470,f3491,f3511,f3529,f3533,f3537,f3541,f3548,f3551,f3552]) ).
fof(f3552,plain,
( ~ spl3_1
| ~ spl3_42
| ~ spl3_64
| ~ spl3_78
| spl3_187
| ~ spl3_3
| ~ spl3_33
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2378,f2347,f254,f69,f2809,f773,f610,f343,f59]) ).
fof(f59,plain,
( spl3_1
<=> int_leq(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f343,plain,
( spl3_42
<=> int_leq(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
fof(f610,plain,
( spl3_64
<=> int_leq(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
fof(f773,plain,
( spl3_78
<=> int_less(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_78])]) ).
fof(f2809,plain,
( spl3_187
<=> ! [X13] :
( ~ int_leq(int_one,X13)
| ~ int_leq(X13,sK0)
| real_zero = a(X13,plus(X13,sK2(sK0,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_187])]) ).
fof(f69,plain,
( spl3_3
<=> int_leq(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f254,plain,
( spl3_33
<=> sK1 = plus(sK0,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f2347,plain,
( spl3_154
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,plus(X0,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_154])]) ).
fof(f2378,plain,
( ! [X13] :
( ~ int_leq(sK1,n)
| ~ int_leq(int_one,X13)
| real_zero = a(X13,plus(X13,sK2(sK0,sK1)))
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0) )
| ~ spl3_33
| ~ spl3_154 ),
inference(superposition,[],[f2348,f256]) ).
fof(f256,plain,
( sK1 = plus(sK0,sK2(sK0,sK1))
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f2348,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,plus(X0,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) )
| ~ spl3_154 ),
inference(avatar_component_clause,[],[f2347]) ).
fof(f3551,plain,
( ~ spl3_36
| spl3_208 ),
inference(avatar_contradiction_clause,[],[f3549]) ).
fof(f3549,plain,
( $false
| ~ spl3_36
| spl3_208 ),
inference(resolution,[],[f3547,f285]) ).
fof(f285,plain,
( ! [X0] : int_leq(X0,X0)
| ~ spl3_36 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl3_36
<=> ! [X0] : int_leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f3547,plain,
( ~ int_leq(sK0,sK0)
| spl3_208 ),
inference(avatar_component_clause,[],[f3545]) ).
fof(f3545,plain,
( spl3_208
<=> int_leq(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_208])]) ).
fof(f3548,plain,
( ~ spl3_208
| spl3_4
| ~ spl3_1
| ~ spl3_33
| ~ spl3_187 ),
inference(avatar_split_clause,[],[f2836,f2809,f254,f59,f74,f3545]) ).
fof(f74,plain,
( spl3_4
<=> real_zero = a(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f2836,plain,
( real_zero = a(sK0,sK1)
| ~ int_leq(sK0,sK0)
| ~ spl3_1
| ~ spl3_33
| ~ spl3_187 ),
inference(forward_demodulation,[],[f2821,f256]) ).
fof(f2821,plain,
( ~ int_leq(sK0,sK0)
| real_zero = a(sK0,plus(sK0,sK2(sK0,sK1)))
| ~ spl3_1
| ~ spl3_187 ),
inference(resolution,[],[f2810,f61]) ).
fof(f61,plain,
( int_leq(int_one,sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f2810,plain,
( ! [X13] :
( ~ int_leq(int_one,X13)
| ~ int_leq(X13,sK0)
| real_zero = a(X13,plus(X13,sK2(sK0,sK1))) )
| ~ spl3_187 ),
inference(avatar_component_clause,[],[f2809]) ).
fof(f3541,plain,
( spl3_207
| ~ spl3_89
| ~ spl3_158 ),
inference(avatar_split_clause,[],[f2650,f2416,f835,f3539]) ).
fof(f3539,plain,
( spl3_207
<=> ! [X4] :
( int_leq(plus(X4,int_one),sK1)
| ~ int_less(X4,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_207])]) ).
fof(f835,plain,
( spl3_89
<=> ! [X4,X3] :
( int_leq(plus(X3,X4),sK1)
| ~ int_leq(X4,sK2(sK0,sK1))
| ~ int_less(X3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_89])]) ).
fof(f2416,plain,
( spl3_158
<=> int_leq(int_one,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_158])]) ).
fof(f2650,plain,
( ! [X4] :
( int_leq(plus(X4,int_one),sK1)
| ~ int_less(X4,sK0) )
| ~ spl3_89
| ~ spl3_158 ),
inference(resolution,[],[f2417,f836]) ).
fof(f836,plain,
( ! [X3,X4] :
( ~ int_leq(X4,sK2(sK0,sK1))
| int_leq(plus(X3,X4),sK1)
| ~ int_less(X3,sK0) )
| ~ spl3_89 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f2417,plain,
( int_leq(int_one,sK2(sK0,sK1))
| ~ spl3_158 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f3537,plain,
( spl3_206
| ~ spl3_91
| ~ spl3_158 ),
inference(avatar_split_clause,[],[f2649,f2416,f843,f3535]) ).
fof(f3535,plain,
( spl3_206
<=> ! [X3] :
( int_leq(plus(int_one,X3),sK1)
| ~ int_less(X3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_206])]) ).
fof(f843,plain,
( spl3_91
<=> ! [X11,X12] :
( int_leq(plus(X11,X12),sK1)
| ~ int_leq(X11,sK2(sK0,sK1))
| ~ int_less(X12,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_91])]) ).
fof(f2649,plain,
( ! [X3] :
( int_leq(plus(int_one,X3),sK1)
| ~ int_less(X3,sK0) )
| ~ spl3_91
| ~ spl3_158 ),
inference(resolution,[],[f2417,f844]) ).
fof(f844,plain,
( ! [X11,X12] :
( ~ int_leq(X11,sK2(sK0,sK1))
| int_leq(plus(X11,X12),sK1)
| ~ int_less(X12,sK0) )
| ~ spl3_91 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f3533,plain,
( spl3_205
| ~ spl3_18
| ~ spl3_78 ),
inference(avatar_split_clause,[],[f2234,f773,f147,f3531]) ).
fof(f3531,plain,
( spl3_205
<=> ! [X4] :
( int_less(X4,sK2(sK0,sK1))
| ~ int_less(X4,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_205])]) ).
fof(f147,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(f2234,plain,
( ! [X4] :
( int_less(X4,sK2(sK0,sK1))
| ~ int_less(X4,int_zero) )
| ~ spl3_18
| ~ spl3_78 ),
inference(resolution,[],[f774,f148]) ).
fof(f148,plain,
( ! [X2,X0,X1] :
( ~ int_less(X1,X2)
| int_less(X0,X2)
| ~ int_less(X0,X1) )
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f774,plain,
( int_less(int_zero,sK2(sK0,sK1))
| ~ spl3_78 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f3529,plain,
( spl3_204
| ~ spl3_78
| ~ spl3_113 ),
inference(avatar_split_clause,[],[f2230,f1061,f773,f3527]) ).
fof(f3527,plain,
( spl3_204
<=> ! [X2] :
( ~ int_leq(X2,int_zero)
| int_leq(X2,sK2(sK0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_204])]) ).
fof(f1061,plain,
( spl3_113
<=> ! [X9,X10] :
( int_leq(X9,X10)
| ~ int_leq(X9,int_zero)
| ~ int_less(int_zero,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_113])]) ).
fof(f2230,plain,
( ! [X2] :
( ~ int_leq(X2,int_zero)
| int_leq(X2,sK2(sK0,sK1)) )
| ~ spl3_78
| ~ spl3_113 ),
inference(resolution,[],[f774,f1062]) ).
fof(f1062,plain,
( ! [X10,X9] :
( ~ int_less(int_zero,X10)
| ~ int_leq(X9,int_zero)
| int_leq(X9,X10) )
| ~ spl3_113 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f3511,plain,
( ~ spl3_48
| spl3_203
| ~ spl3_69
| ~ spl3_105 ),
inference(avatar_split_clause,[],[f1027,f983,f647,f3508,f394]) ).
fof(f394,plain,
( spl3_48
<=> int_less(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).
fof(f3508,plain,
( spl3_203
<=> int_less(sK2(sK1,n),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_203])]) ).
fof(f647,plain,
( spl3_69
<=> n = plus(sK1,sK2(sK1,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
fof(f983,plain,
( spl3_105
<=> ! [X2,X1] :
( int_less(X1,plus(X2,X1))
| ~ int_less(int_zero,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_105])]) ).
fof(f1027,plain,
( int_less(sK2(sK1,n),n)
| ~ int_less(int_zero,sK1)
| ~ spl3_69
| ~ spl3_105 ),
inference(superposition,[],[f984,f649]) ).
fof(f649,plain,
( n = plus(sK1,sK2(sK1,n))
| ~ spl3_69 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f984,plain,
( ! [X2,X1] :
( int_less(X1,plus(X2,X1))
| ~ int_less(int_zero,X2) )
| ~ spl3_105 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f3491,plain,
( ~ spl3_6
| spl3_202
| ~ spl3_70
| ~ spl3_105 ),
inference(avatar_split_clause,[],[f1025,f983,f652,f3488,f84]) ).
fof(f84,plain,
( spl3_6
<=> int_less(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f3488,plain,
( spl3_202
<=> int_less(sK2(int_one,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_202])]) ).
fof(f652,plain,
( spl3_70
<=> sK0 = plus(int_one,sK2(int_one,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).
fof(f1025,plain,
( int_less(sK2(int_one,sK0),sK0)
| ~ int_less(int_zero,int_one)
| ~ spl3_70
| ~ spl3_105 ),
inference(superposition,[],[f984,f654]) ).
fof(f654,plain,
( sK0 = plus(int_one,sK2(int_one,sK0))
| ~ spl3_70 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f3470,plain,
( ~ spl3_34
| ~ spl3_156 ),
inference(avatar_contradiction_clause,[],[f3457]) ).
fof(f3457,plain,
( $false
| ~ spl3_34
| ~ spl3_156 ),
inference(resolution,[],[f2389,f275]) ).
fof(f275,plain,
( ! [X0] : ~ int_less(X0,X0)
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f274,plain,
( spl3_34
<=> ! [X0] : ~ int_less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f2389,plain,
( int_less(n,n)
| ~ spl3_156 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f2387,plain,
( spl3_156
<=> int_less(n,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_156])]) ).
fof(f3455,plain,
( spl3_201
| ~ spl3_67
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f990,f970,f623,f3453]) ).
fof(f3453,plain,
( spl3_201
<=> ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_201])]) ).
fof(f623,plain,
( spl3_67
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).
fof(f970,plain,
( spl3_102
<=> ! [X1] :
( sK2(int_zero,X1) = X1
| int_less(X1,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_102])]) ).
fof(f990,plain,
( ! [X0] :
( sK2(int_zero,X0) = X0
| int_less(X0,sK0) )
| ~ spl3_67
| ~ spl3_102 ),
inference(resolution,[],[f971,f624]) ).
fof(f624,plain,
( ! [X0] :
( ~ int_less(X0,int_one)
| int_less(X0,sK0) )
| ~ spl3_67 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f971,plain,
( ! [X1] :
( int_less(X1,int_one)
| sK2(int_zero,X1) = X1 )
| ~ spl3_102 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f3272,plain,
( spl3_200
| spl3_63
| ~ spl3_102 ),
inference(avatar_split_clause,[],[f3209,f970,f587,f3269]) ).
fof(f3269,plain,
( spl3_200
<=> sK1 = sK2(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_200])]) ).
fof(f587,plain,
( spl3_63
<=> int_less(sK1,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).
fof(f3209,plain,
( sK1 = sK2(int_zero,sK1)
| spl3_63
| ~ spl3_102 ),
inference(resolution,[],[f588,f971]) ).
fof(f588,plain,
( ~ int_less(sK1,int_one)
| spl3_63 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f3224,plain,
( spl3_199
| ~ spl3_10
| ~ spl3_152 ),
inference(avatar_split_clause,[],[f2334,f2326,f101,f3222]) ).
fof(f3222,plain,
( spl3_199
<=> ! [X9,X8] :
( ~ int_leq(X8,n)
| real_one = a(X9,X9)
| ~ int_leq(X9,X8)
| int_less(X9,int_one)
| int_less(X8,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_199])]) ).
fof(f101,plain,
( spl3_10
<=> ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f2326,plain,
( spl3_152
<=> ! [X2,X1] :
( ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1)
| int_less(X2,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_152])]) ).
fof(f2334,plain,
( ! [X8,X9] :
( ~ int_leq(X8,n)
| real_one = a(X9,X9)
| ~ int_leq(X9,X8)
| int_less(X9,int_one)
| int_less(X8,int_one) )
| ~ spl3_10
| ~ spl3_152 ),
inference(resolution,[],[f2327,f102]) ).
fof(f102,plain,
( ! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f2327,plain,
( ! [X2,X1] :
( ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1)
| int_less(X2,int_one) )
| ~ spl3_152 ),
inference(avatar_component_clause,[],[f2326]) ).
fof(f3220,plain,
( spl3_198
| ~ spl3_32
| ~ spl3_123 ),
inference(avatar_split_clause,[],[f2203,f1205,f249,f3217]) ).
fof(f3217,plain,
( spl3_198
<=> int_less(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_198])]) ).
fof(f249,plain,
( spl3_32
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f1205,plain,
( spl3_123
<=> int_less(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_123])]) ).
fof(f2203,plain,
( int_less(sK1,sK1)
| ~ spl3_32
| ~ spl3_123 ),
inference(resolution,[],[f1207,f250]) ).
fof(f250,plain,
( ! [X0] :
( ~ int_less(X0,sK0)
| int_less(X0,sK1) )
| ~ spl3_32 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f1207,plain,
( int_less(sK1,sK0)
| ~ spl3_123 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f3207,plain,
( spl3_197
| ~ spl3_19
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f606,f587,f160,f3204]) ).
fof(f3204,plain,
( spl3_197
<=> int_one = plus(sK1,sK2(sK1,int_one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_197])]) ).
fof(f160,plain,
( spl3_19
<=> ! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f606,plain,
( int_one = plus(sK1,sK2(sK1,int_one))
| ~ spl3_19
| ~ spl3_63 ),
inference(resolution,[],[f589,f161]) ).
fof(f161,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| plus(X0,sK2(X0,X1)) = X1 )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f589,plain,
( int_less(sK1,int_one)
| ~ spl3_63 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f3202,plain,
( spl3_196
| ~ spl3_19
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f602,f525,f160,f3199]) ).
fof(f3199,plain,
( spl3_196
<=> sK0 = plus(n,sK2(n,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_196])]) ).
fof(f525,plain,
( spl3_60
<=> int_less(n,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
fof(f602,plain,
( sK0 = plus(n,sK2(n,sK0))
| ~ spl3_19
| ~ spl3_60 ),
inference(resolution,[],[f527,f161]) ).
fof(f527,plain,
( int_less(n,sK0)
| ~ spl3_60 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f3197,plain,
( spl3_195
| ~ spl3_19
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f597,f457,f160,f3194]) ).
fof(f3194,plain,
( spl3_195
<=> sK1 = plus(int_one,sK2(int_one,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_195])]) ).
fof(f457,plain,
( spl3_54
<=> int_less(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
fof(f597,plain,
( sK1 = plus(int_one,sK2(int_one,sK1))
| ~ spl3_19
| ~ spl3_54 ),
inference(resolution,[],[f459,f161]) ).
fof(f459,plain,
( int_less(int_one,sK1)
| ~ spl3_54 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f3192,plain,
( spl3_194
| ~ spl3_19
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f593,f394,f160,f3189]) ).
fof(f3189,plain,
( spl3_194
<=> sK1 = plus(int_zero,sK2(int_zero,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_194])]) ).
fof(f593,plain,
( sK1 = plus(int_zero,sK2(int_zero,sK1))
| ~ spl3_19
| ~ spl3_48 ),
inference(resolution,[],[f396,f161]) ).
fof(f396,plain,
( int_less(int_zero,sK1)
| ~ spl3_48 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f3110,plain,
( spl3_42
| ~ spl3_12
| ~ spl3_115 ),
inference(avatar_split_clause,[],[f2189,f1127,f109,f343]) ).
fof(f109,plain,
( spl3_12
<=> ! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f1127,plain,
( spl3_115
<=> int_less(sK0,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_115])]) ).
fof(f2189,plain,
( int_leq(sK0,n)
| ~ spl3_12
| ~ spl3_115 ),
inference(resolution,[],[f1129,f110]) ).
fof(f110,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f1129,plain,
( int_less(sK0,n)
| ~ spl3_115 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f2990,plain,
( spl3_193
| ~ spl3_43
| ~ spl3_78
| ~ spl3_93 ),
inference(avatar_split_clause,[],[f2245,f851,f773,f350,f2988]) ).
fof(f2988,plain,
( spl3_193
<=> ! [X3] :
( int_leq(X3,sK1)
| ~ int_leq(X3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_193])]) ).
fof(f350,plain,
( spl3_43
<=> ! [X0] : plus(int_zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
fof(f851,plain,
( spl3_93
<=> ! [X11,X12] :
( int_leq(plus(X11,X12),sK1)
| ~ int_leq(X12,sK0)
| ~ int_less(X11,sK2(sK0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_93])]) ).
fof(f2245,plain,
( ! [X3] :
( int_leq(X3,sK1)
| ~ int_leq(X3,sK0) )
| ~ spl3_43
| ~ spl3_78
| ~ spl3_93 ),
inference(forward_demodulation,[],[f2232,f351]) ).
fof(f351,plain,
( ! [X0] : plus(int_zero,X0) = X0
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f2232,plain,
( ! [X3] :
( ~ int_leq(X3,sK0)
| int_leq(plus(int_zero,X3),sK1) )
| ~ spl3_78
| ~ spl3_93 ),
inference(resolution,[],[f774,f852]) ).
fof(f852,plain,
( ! [X11,X12] :
( ~ int_less(X11,sK2(sK0,sK1))
| ~ int_leq(X12,sK0)
| int_leq(plus(X11,X12),sK1) )
| ~ spl3_93 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f2986,plain,
( spl3_192
| ~ spl3_48
| ~ spl3_113 ),
inference(avatar_split_clause,[],[f1111,f1061,f394,f2984]) ).
fof(f2984,plain,
( spl3_192
<=> ! [X4] :
( ~ int_leq(X4,int_zero)
| int_leq(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_192])]) ).
fof(f1111,plain,
( ! [X4] :
( ~ int_leq(X4,int_zero)
| int_leq(X4,sK1) )
| ~ spl3_48
| ~ spl3_113 ),
inference(resolution,[],[f1062,f396]) ).
fof(f2982,plain,
( spl3_191
| ~ spl3_14
| ~ spl3_113 ),
inference(avatar_split_clause,[],[f1110,f1061,f120,f2980]) ).
fof(f2980,plain,
( spl3_191
<=> ! [X3] :
( ~ int_leq(X3,int_zero)
| int_leq(X3,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_191])]) ).
fof(f120,plain,
( spl3_14
<=> int_less(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f1110,plain,
( ! [X3] :
( ~ int_leq(X3,int_zero)
| int_leq(X3,sK0) )
| ~ spl3_14
| ~ spl3_113 ),
inference(resolution,[],[f1062,f122]) ).
fof(f122,plain,
( int_less(int_zero,sK0)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f2966,plain,
( spl3_190
| ~ spl3_25
| ~ spl3_183 ),
inference(avatar_split_clause,[],[f2784,f2771,f201,f2963]) ).
fof(f2963,plain,
( spl3_190
<=> int_less(sK0,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_190])]) ).
fof(f201,plain,
( spl3_25
<=> int_leq(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f2771,plain,
( spl3_183
<=> ! [X0] :
( ~ int_leq(X0,sK1)
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_183])]) ).
fof(f2784,plain,
( int_less(sK0,int_one)
| ~ spl3_25
| ~ spl3_183 ),
inference(resolution,[],[f2772,f203]) ).
fof(f203,plain,
( int_leq(sK0,sK1)
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f2772,plain,
( ! [X0] :
( ~ int_leq(X0,sK1)
| int_less(X0,int_one) )
| ~ spl3_183 ),
inference(avatar_component_clause,[],[f2771]) ).
fof(f2925,plain,
( ~ spl3_71
| ~ spl3_29
| spl3_166 ),
inference(avatar_split_clause,[],[f2736,f2496,f233,f683]) ).
fof(f683,plain,
( spl3_71
<=> int_leq(int_zero,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).
fof(f233,plain,
( spl3_29
<=> n = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f2496,plain,
( spl3_166
<=> int_leq(int_zero,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_166])]) ).
fof(f2736,plain,
( ~ int_leq(int_zero,sK1)
| ~ spl3_29
| spl3_166 ),
inference(superposition,[],[f2498,f235]) ).
fof(f235,plain,
( n = sK1
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f2498,plain,
( ~ int_leq(int_zero,n)
| spl3_166 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f2845,plain,
( ~ spl3_64
| ~ spl3_1
| ~ spl3_78
| spl3_189
| ~ spl3_188
| ~ spl3_25
| ~ spl3_29
| ~ spl3_33
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2755,f2343,f254,f233,f201,f2812,f2843,f773,f59,f610]) ).
fof(f2843,plain,
( spl3_189
<=> ! [X13] :
( ~ int_leq(int_one,X13)
| ~ int_leq(X13,sK0)
| real_zero = a(plus(X13,sK2(sK0,sK1)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_189])]) ).
fof(f2812,plain,
( spl3_188
<=> int_leq(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_188])]) ).
fof(f2343,plain,
( spl3_153
<=> ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X0,X2),X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,plus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_153])]) ).
fof(f2755,plain,
( ! [X13] :
( ~ int_leq(sK0,sK1)
| ~ int_leq(sK1,sK1)
| ~ int_leq(int_one,X13)
| real_zero = a(plus(X13,sK2(sK0,sK1)),X13)
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(int_one,sK0)
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1) )
| ~ spl3_29
| ~ spl3_33
| ~ spl3_153 ),
inference(forward_demodulation,[],[f2754,f235]) ).
fof(f2754,plain,
( ! [X13] :
( ~ int_leq(sK1,sK1)
| ~ int_leq(int_one,X13)
| real_zero = a(plus(X13,sK2(sK0,sK1)),X13)
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0)
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1) )
| ~ spl3_29
| ~ spl3_33
| ~ spl3_153 ),
inference(forward_demodulation,[],[f2362,f235]) ).
fof(f2362,plain,
( ! [X13] :
( ~ int_leq(sK1,n)
| ~ int_leq(int_one,X13)
| real_zero = a(plus(X13,sK2(sK0,sK1)),X13)
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0)
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1) )
| ~ spl3_33
| ~ spl3_153 ),
inference(superposition,[],[f2344,f256]) ).
fof(f2344,plain,
( ! [X2,X0,X1] :
( ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X0,X2),X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,X1)
| ~ int_leq(int_one,plus(X1,X2)) )
| ~ spl3_153 ),
inference(avatar_component_clause,[],[f2343]) ).
fof(f2818,plain,
( ~ spl3_36
| spl3_188 ),
inference(avatar_contradiction_clause,[],[f2816]) ).
fof(f2816,plain,
( $false
| ~ spl3_36
| spl3_188 ),
inference(resolution,[],[f2814,f285]) ).
fof(f2814,plain,
( ~ int_leq(sK1,sK1)
| spl3_188 ),
inference(avatar_component_clause,[],[f2812]) ).
fof(f2815,plain,
( ~ spl3_1
| ~ spl3_64
| ~ spl3_78
| spl3_187
| ~ spl3_188
| ~ spl3_25
| ~ spl3_29
| ~ spl3_33
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2751,f2347,f254,f233,f201,f2812,f2809,f773,f610,f59]) ).
fof(f2751,plain,
( ! [X13] :
( ~ int_leq(sK0,sK1)
| ~ int_leq(sK1,sK1)
| ~ int_leq(int_one,X13)
| real_zero = a(X13,plus(X13,sK2(sK0,sK1)))
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK0) )
| ~ spl3_29
| ~ spl3_33
| ~ spl3_154 ),
inference(forward_demodulation,[],[f2750,f235]) ).
fof(f2750,plain,
( ! [X13] :
( ~ int_leq(sK1,sK1)
| ~ int_leq(int_one,X13)
| real_zero = a(X13,plus(X13,sK2(sK0,sK1)))
| ~ int_less(int_zero,sK2(sK0,sK1))
| ~ int_leq(X13,sK0)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0) )
| ~ spl3_29
| ~ spl3_33
| ~ spl3_154 ),
inference(forward_demodulation,[],[f2378,f235]) ).
fof(f2807,plain,
( spl3_186
| ~ spl3_29
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2734,f2347,f233,f2805]) ).
fof(f2805,plain,
( spl3_186
<=> ! [X9,X11,X10] :
( ~ int_leq(plus(X9,X10),sK1)
| ~ int_leq(int_one,X11)
| real_zero = a(X11,plus(X11,X10))
| ~ int_less(int_zero,X10)
| ~ int_leq(X11,X9)
| ~ int_leq(int_one,plus(X9,X10))
| ~ int_leq(X9,sK1)
| ~ int_leq(int_one,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_186])]) ).
fof(f2734,plain,
( ! [X10,X11,X9] :
( ~ int_leq(plus(X9,X10),sK1)
| ~ int_leq(int_one,X11)
| real_zero = a(X11,plus(X11,X10))
| ~ int_less(int_zero,X10)
| ~ int_leq(X11,X9)
| ~ int_leq(int_one,plus(X9,X10))
| ~ int_leq(X9,sK1)
| ~ int_leq(int_one,X9) )
| ~ spl3_29
| ~ spl3_154 ),
inference(superposition,[],[f2348,f235]) ).
fof(f2803,plain,
( spl3_185
| ~ spl3_29
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2733,f2343,f233,f2801]) ).
fof(f2801,plain,
( spl3_185
<=> ! [X6,X7,X8] :
( ~ int_leq(plus(X6,X7),sK1)
| ~ int_leq(int_one,X8)
| real_zero = a(plus(X8,X7),X8)
| ~ int_less(int_zero,X7)
| ~ int_leq(X6,sK1)
| ~ int_leq(int_one,X6)
| ~ int_leq(X8,X6)
| ~ int_leq(int_one,plus(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_185])]) ).
fof(f2733,plain,
( ! [X8,X6,X7] :
( ~ int_leq(plus(X6,X7),sK1)
| ~ int_leq(int_one,X8)
| real_zero = a(plus(X8,X7),X8)
| ~ int_less(int_zero,X7)
| ~ int_leq(X6,sK1)
| ~ int_leq(int_one,X6)
| ~ int_leq(X8,X6)
| ~ int_leq(int_one,plus(X6,X7)) )
| ~ spl3_29
| ~ spl3_153 ),
inference(superposition,[],[f2344,f235]) ).
fof(f2788,plain,
( spl3_184
| ~ spl3_25
| ~ spl3_1
| ~ spl3_29
| ~ spl3_152 ),
inference(avatar_split_clause,[],[f2758,f2326,f233,f59,f201,f2786]) ).
fof(f2786,plain,
( spl3_184
<=> ! [X2] :
( real_one = a(X2,X2)
| int_less(X2,int_one)
| ~ int_leq(X2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_184])]) ).
fof(f2758,plain,
( ! [X2] :
( ~ int_leq(sK0,sK1)
| real_one = a(X2,X2)
| ~ int_leq(X2,sK0)
| int_less(X2,int_one) )
| ~ spl3_1
| ~ spl3_29
| ~ spl3_152 ),
inference(forward_demodulation,[],[f2330,f235]) ).
fof(f2330,plain,
( ! [X2] :
( ~ int_leq(sK0,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,sK0)
| int_less(X2,int_one) )
| ~ spl3_1
| ~ spl3_152 ),
inference(resolution,[],[f2327,f61]) ).
fof(f2773,plain,
( spl3_183
| ~ spl3_29
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f2720,f361,f233,f2771]) ).
fof(f361,plain,
( spl3_44
<=> ! [X0] :
( ~ int_leq(X0,n)
| int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
fof(f2720,plain,
( ! [X0] :
( ~ int_leq(X0,sK1)
| int_less(X0,int_one) )
| ~ spl3_29
| ~ spl3_44 ),
inference(superposition,[],[f362,f235]) ).
fof(f362,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| int_less(X0,int_one) )
| ~ spl3_44 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f2745,plain,
( ~ spl3_25
| ~ spl3_29
| spl3_42 ),
inference(avatar_split_clause,[],[f2719,f343,f233,f201]) ).
fof(f2719,plain,
( ~ int_leq(sK0,sK1)
| ~ spl3_29
| spl3_42 ),
inference(superposition,[],[f345,f235]) ).
fof(f345,plain,
( ~ int_leq(sK0,n)
| spl3_42 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f2717,plain,
( spl3_166
| ~ spl3_12
| ~ spl3_103 ),
inference(avatar_split_clause,[],[f2159,f974,f109,f2496]) ).
fof(f974,plain,
( spl3_103
<=> int_less(int_zero,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_103])]) ).
fof(f2159,plain,
( int_leq(int_zero,n)
| ~ spl3_12
| ~ spl3_103 ),
inference(resolution,[],[f976,f110]) ).
fof(f976,plain,
( int_less(int_zero,n)
| ~ spl3_103 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f2716,plain,
( spl3_182
| ~ spl3_67
| ~ spl3_98 ),
inference(avatar_split_clause,[],[f920,f917,f623,f2714]) ).
fof(f2714,plain,
( spl3_182
<=> ! [X0] :
( int_less(n,X0)
| int_less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_182])]) ).
fof(f917,plain,
( spl3_98
<=> ! [X0] :
( int_less(X0,int_one)
| int_less(n,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_98])]) ).
fof(f920,plain,
( ! [X0] :
( int_less(n,X0)
| int_less(X0,sK0) )
| ~ spl3_67
| ~ spl3_98 ),
inference(resolution,[],[f918,f624]) ).
fof(f918,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(n,X0) )
| ~ spl3_98 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f2712,plain,
( spl3_181
| ~ spl3_45
| ~ spl3_67 ),
inference(avatar_split_clause,[],[f635,f623,f368,f2710]) ).
fof(f2710,plain,
( spl3_181
<=> ! [X0] :
( int_less(X0,sK0)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_181])]) ).
fof(f368,plain,
( spl3_45
<=> ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
fof(f635,plain,
( ! [X0] :
( int_less(X0,sK0)
| int_less(int_zero,X0) )
| ~ spl3_45
| ~ spl3_67 ),
inference(resolution,[],[f624,f369]) ).
fof(f369,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_45 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f2708,plain,
( spl3_180
| ~ spl3_18
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f607,f587,f147,f2706]) ).
fof(f2706,plain,
( spl3_180
<=> ! [X0] :
( int_less(X0,int_one)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_180])]) ).
fof(f607,plain,
( ! [X0] :
( int_less(X0,int_one)
| ~ int_less(X0,sK1) )
| ~ spl3_18
| ~ spl3_63 ),
inference(resolution,[],[f589,f148]) ).
fof(f2704,plain,
( spl3_179
| ~ spl3_18
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f603,f525,f147,f2702]) ).
fof(f2702,plain,
( spl3_179
<=> ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_179])]) ).
fof(f603,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,n) )
| ~ spl3_18
| ~ spl3_60 ),
inference(resolution,[],[f527,f148]) ).
fof(f2700,plain,
( spl3_178
| ~ spl3_18
| ~ spl3_54 ),
inference(avatar_split_clause,[],[f598,f457,f147,f2698]) ).
fof(f2698,plain,
( spl3_178
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_178])]) ).
fof(f598,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_54 ),
inference(resolution,[],[f459,f148]) ).
fof(f2696,plain,
( spl3_177
| ~ spl3_18
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f594,f394,f147,f2694]) ).
fof(f2694,plain,
( spl3_177
<=> ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_177])]) ).
fof(f594,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,int_zero) )
| ~ spl3_18
| ~ spl3_48 ),
inference(resolution,[],[f396,f148]) ).
fof(f2667,plain,
( spl3_176
| ~ spl3_85
| ~ spl3_36
| ~ spl3_152 ),
inference(avatar_split_clause,[],[f2333,f2326,f284,f810,f2665]) ).
fof(f2665,plain,
( spl3_176
<=> ! [X7] :
( real_one = a(X7,X7)
| int_less(X7,int_one)
| ~ int_leq(X7,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_176])]) ).
fof(f810,plain,
( spl3_85
<=> int_leq(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_85])]) ).
fof(f2333,plain,
( ! [X7] :
( ~ int_leq(int_one,n)
| real_one = a(X7,X7)
| ~ int_leq(X7,int_one)
| int_less(X7,int_one) )
| ~ spl3_36
| ~ spl3_152 ),
inference(resolution,[],[f2327,f285]) ).
fof(f2657,plain,
( spl3_85
| ~ spl3_8
| ~ spl3_103 ),
inference(avatar_split_clause,[],[f2158,f974,f93,f810]) ).
fof(f93,plain,
( spl3_8
<=> ! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f2158,plain,
( int_leq(int_one,n)
| ~ spl3_8
| ~ spl3_103 ),
inference(resolution,[],[f976,f94]) ).
fof(f94,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f2656,plain,
( spl3_175
| ~ spl3_10
| spl3_159 ),
inference(avatar_split_clause,[],[f2434,f2420,f101,f2653]) ).
fof(f2653,plain,
( spl3_175
<=> int_less(n,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_175])]) ).
fof(f2420,plain,
( spl3_159
<=> int_leq(sK2(sK0,sK1),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_159])]) ).
fof(f2434,plain,
( int_less(n,sK2(sK0,sK1))
| ~ spl3_10
| spl3_159 ),
inference(resolution,[],[f2422,f102]) ).
fof(f2422,plain,
( ~ int_leq(sK2(sK0,sK1),n)
| spl3_159 ),
inference(avatar_component_clause,[],[f2420]) ).
fof(f2644,plain,
( spl3_158
| ~ spl3_8
| ~ spl3_78 ),
inference(avatar_split_clause,[],[f2231,f773,f93,f2416]) ).
fof(f2231,plain,
( int_leq(int_one,sK2(sK0,sK1))
| ~ spl3_8
| ~ spl3_78 ),
inference(resolution,[],[f774,f94]) ).
fof(f2605,plain,
( spl3_174
| ~ spl3_57
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2369,f2347,f470,f2603]) ).
fof(f2603,plain,
( spl3_174
<=> ! [X9,X11,X10] :
( ~ int_leq(int_one,X9)
| real_zero = a(X9,plus(X9,X10))
| ~ int_less(int_zero,X10)
| ~ int_leq(X9,X11)
| ~ int_leq(int_one,plus(X11,X10))
| ~ int_leq(X11,n)
| ~ int_leq(int_one,X11)
| ~ int_leq(X10,int_zero)
| ~ int_less(X11,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_174])]) ).
fof(f470,plain,
( spl3_57
<=> ! [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_57])]) ).
fof(f2369,plain,
( ! [X10,X11,X9] :
( ~ int_leq(int_one,X9)
| real_zero = a(X9,plus(X9,X10))
| ~ int_less(int_zero,X10)
| ~ int_leq(X9,X11)
| ~ int_leq(int_one,plus(X11,X10))
| ~ int_leq(X11,n)
| ~ int_leq(int_one,X11)
| ~ int_leq(X10,int_zero)
| ~ int_less(X11,n) )
| ~ spl3_57
| ~ spl3_154 ),
inference(resolution,[],[f2348,f471]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X0) )
| ~ spl3_57 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f2601,plain,
( spl3_173
| ~ spl3_57
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2353,f2343,f470,f2599]) ).
fof(f2599,plain,
( spl3_173
<=> ! [X9,X11,X10] :
( ~ int_leq(int_one,X9)
| real_zero = a(plus(X9,X10),X9)
| ~ int_less(int_zero,X10)
| ~ int_leq(X11,n)
| ~ int_leq(int_one,X11)
| ~ int_leq(X9,X11)
| ~ int_leq(int_one,plus(X11,X10))
| ~ int_leq(X10,int_zero)
| ~ int_less(X11,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_173])]) ).
fof(f2353,plain,
( ! [X10,X11,X9] :
( ~ int_leq(int_one,X9)
| real_zero = a(plus(X9,X10),X9)
| ~ int_less(int_zero,X10)
| ~ int_leq(X11,n)
| ~ int_leq(int_one,X11)
| ~ int_leq(X9,X11)
| ~ int_leq(int_one,plus(X11,X10))
| ~ int_leq(X10,int_zero)
| ~ int_less(X11,n) )
| ~ spl3_57
| ~ spl3_153 ),
inference(resolution,[],[f2344,f471]) ).
fof(f2546,plain,
( spl3_172
| ~ spl3_12
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f1453,f764,f109,f2543]) ).
fof(f2543,plain,
( spl3_172
<=> int_leq(n,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_172])]) ).
fof(f764,plain,
( spl3_77
<=> int_less(n,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_77])]) ).
fof(f1453,plain,
( int_leq(n,sK1)
| ~ spl3_12
| ~ spl3_77 ),
inference(resolution,[],[f766,f110]) ).
fof(f766,plain,
( int_less(n,sK1)
| ~ spl3_77 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f2522,plain,
( spl3_171
| ~ spl3_15
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2372,f2347,f129,f2520]) ).
fof(f2520,plain,
( spl3_171
<=> ! [X2,X4,X3] :
( ~ int_leq(plus(X3,X2),n)
| ~ int_leq(int_one,X4)
| real_zero = a(X4,plus(X4,X3))
| ~ int_less(int_zero,X3)
| ~ int_leq(X4,X2)
| ~ int_leq(int_one,plus(X3,X2))
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_171])]) ).
fof(f129,plain,
( spl3_15
<=> ! [X0,X1] : plus(X0,X1) = plus(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f2372,plain,
( ! [X2,X3,X4] :
( ~ int_leq(plus(X3,X2),n)
| ~ int_leq(int_one,X4)
| real_zero = a(X4,plus(X4,X3))
| ~ int_less(int_zero,X3)
| ~ int_leq(X4,X2)
| ~ int_leq(int_one,plus(X3,X2))
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2) )
| ~ spl3_15
| ~ spl3_154 ),
inference(superposition,[],[f2348,f130]) ).
fof(f130,plain,
( ! [X0,X1] : plus(X0,X1) = plus(X1,X0)
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f2518,plain,
( spl3_170
| ~ spl3_10
| ~ spl3_154 ),
inference(avatar_split_clause,[],[f2370,f2347,f101,f2516]) ).
fof(f2516,plain,
( spl3_170
<=> ! [X13,X12,X14] :
( ~ int_leq(int_one,X12)
| real_zero = a(X12,plus(X12,X13))
| ~ int_less(int_zero,X13)
| ~ int_leq(X12,X14)
| ~ int_leq(int_one,plus(X14,X13))
| ~ int_leq(X14,n)
| ~ int_leq(int_one,X14)
| int_less(n,plus(X14,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_170])]) ).
fof(f2370,plain,
( ! [X14,X12,X13] :
( ~ int_leq(int_one,X12)
| real_zero = a(X12,plus(X12,X13))
| ~ int_less(int_zero,X13)
| ~ int_leq(X12,X14)
| ~ int_leq(int_one,plus(X14,X13))
| ~ int_leq(X14,n)
| ~ int_leq(int_one,X14)
| int_less(n,plus(X14,X13)) )
| ~ spl3_10
| ~ spl3_154 ),
inference(resolution,[],[f2348,f102]) ).
fof(f2514,plain,
( spl3_169
| ~ spl3_15
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2356,f2343,f129,f2512]) ).
fof(f2512,plain,
( spl3_169
<=> ! [X2,X4,X3] :
( ~ int_leq(plus(X3,X2),n)
| ~ int_leq(int_one,X4)
| real_zero = a(plus(X4,X3),X4)
| ~ int_less(int_zero,X3)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X4,X2)
| ~ int_leq(int_one,plus(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_169])]) ).
fof(f2356,plain,
( ! [X2,X3,X4] :
( ~ int_leq(plus(X3,X2),n)
| ~ int_leq(int_one,X4)
| real_zero = a(plus(X4,X3),X4)
| ~ int_less(int_zero,X3)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X4,X2)
| ~ int_leq(int_one,plus(X3,X2)) )
| ~ spl3_15
| ~ spl3_153 ),
inference(superposition,[],[f2344,f130]) ).
fof(f2510,plain,
( spl3_168
| ~ spl3_10
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2354,f2343,f101,f2508]) ).
fof(f2508,plain,
( spl3_168
<=> ! [X13,X12,X14] :
( ~ int_leq(int_one,X12)
| real_zero = a(plus(X12,X13),X12)
| ~ int_less(int_zero,X13)
| ~ int_leq(X14,n)
| ~ int_leq(int_one,X14)
| ~ int_leq(X12,X14)
| ~ int_leq(int_one,plus(X14,X13))
| int_less(n,plus(X14,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_168])]) ).
fof(f2354,plain,
( ! [X14,X12,X13] :
( ~ int_leq(int_one,X12)
| real_zero = a(plus(X12,X13),X12)
| ~ int_less(int_zero,X13)
| ~ int_leq(X14,n)
| ~ int_leq(int_one,X14)
| ~ int_leq(X12,X14)
| ~ int_leq(int_one,plus(X14,X13))
| int_less(n,plus(X14,X13)) )
| ~ spl3_10
| ~ spl3_153 ),
inference(resolution,[],[f2344,f102]) ).
fof(f2502,plain,
( ~ spl3_165
| ~ spl3_166
| spl3_167
| ~ spl3_43
| ~ spl3_153 ),
inference(avatar_split_clause,[],[f2358,f2343,f350,f2500,f2496,f2492]) ).
fof(f2492,plain,
( spl3_165
<=> int_leq(int_one,int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_165])]) ).
fof(f2500,plain,
( spl3_167
<=> ! [X9,X8] :
( ~ int_leq(X8,n)
| ~ int_leq(int_one,X8)
| ~ int_leq(X9,int_zero)
| ~ int_less(int_zero,X8)
| real_zero = a(plus(X9,X8),X9)
| ~ int_leq(int_one,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_167])]) ).
fof(f2358,plain,
( ! [X8,X9] :
( ~ int_leq(X8,n)
| ~ int_leq(int_one,X9)
| real_zero = a(plus(X9,X8),X9)
| ~ int_less(int_zero,X8)
| ~ int_leq(int_zero,n)
| ~ int_leq(int_one,int_zero)
| ~ int_leq(X9,int_zero)
| ~ int_leq(int_one,X8) )
| ~ spl3_43
| ~ spl3_153 ),
inference(superposition,[],[f2344,f351]) ).
fof(f2463,plain,
( spl3_164
| ~ spl3_23
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f2292,f466,f191,f2461]) ).
fof(f2461,plain,
( spl3_164
<=> ! [X22,X20,X21] :
( ~ int_leq(int_one,X20)
| ~ int_leq(X20,n)
| real_one = a(plus(X21,X22),plus(X21,X22))
| ~ int_leq(plus(X21,X22),X20)
| ~ int_leq(int_zero,X22)
| ~ int_less(int_one,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_164])]) ).
fof(f191,plain,
( spl3_23
<=> ! [X4,X1] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f466,plain,
( spl3_56
<=> ! [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_56])]) ).
fof(f2292,plain,
( ! [X21,X22,X20] :
( ~ int_leq(int_one,X20)
| ~ int_leq(X20,n)
| real_one = a(plus(X21,X22),plus(X21,X22))
| ~ int_leq(plus(X21,X22),X20)
| ~ int_leq(int_zero,X22)
| ~ int_less(int_one,X21) )
| ~ spl3_23
| ~ spl3_56 ),
inference(resolution,[],[f192,f467]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(X0,X1) )
| ~ spl3_56 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f192,plain,
( ! [X1,X4] :
( ~ int_leq(int_one,X4)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| real_one = a(X4,X4)
| ~ int_leq(X4,X1) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f2459,plain,
( ~ spl3_2
| ~ spl3_49
| spl3_158 ),
inference(avatar_split_clause,[],[f2430,f2416,f407,f64]) ).
fof(f64,plain,
( spl3_2
<=> int_less(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f407,plain,
( spl3_49
<=> ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_one,sK2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).
fof(f2430,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_49
| spl3_158 ),
inference(resolution,[],[f2418,f408]) ).
fof(f408,plain,
( ! [X0,X1] :
( int_leq(int_one,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_49 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f2418,plain,
( ~ int_leq(int_one,sK2(sK0,sK1))
| spl3_158 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f2443,plain,
( spl3_163
| ~ spl3_23
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f2285,f407,f191,f2441]) ).
fof(f2441,plain,
( spl3_163
<=> ! [X6,X4,X5] :
( ~ int_leq(int_one,X4)
| ~ int_leq(X4,n)
| real_one = a(sK2(X5,X6),sK2(X5,X6))
| ~ int_leq(sK2(X5,X6),X4)
| ~ int_less(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_163])]) ).
fof(f2285,plain,
( ! [X6,X4,X5] :
( ~ int_leq(int_one,X4)
| ~ int_leq(X4,n)
| real_one = a(sK2(X5,X6),sK2(X5,X6))
| ~ int_leq(sK2(X5,X6),X4)
| ~ int_less(X5,X6) )
| ~ spl3_23
| ~ spl3_49 ),
inference(resolution,[],[f192,f408]) ).
fof(f2439,plain,
( spl3_162
| spl3_22
| ~ spl3_23
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f316,f284,f191,f188,f2436]) ).
fof(f2436,plain,
( spl3_162
<=> real_one = a(int_one,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_162])]) ).
fof(f188,plain,
( spl3_22
<=> ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f316,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| real_one = a(int_one,int_one) )
| ~ spl3_23
| ~ spl3_36 ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f287,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| real_one = a(int_one,int_one)
| ~ int_leq(int_one,X0) )
| ~ spl3_23
| ~ spl3_36 ),
inference(resolution,[],[f285,f192]) ).
fof(f2429,plain,
( ~ spl3_158
| ~ spl3_159
| ~ spl3_14
| spl3_160
| spl3_161
| ~ spl3_33
| ~ spl3_155 ),
inference(avatar_split_clause,[],[f2402,f2383,f254,f2427,f2424,f120,f2420,f2416]) ).
fof(f2424,plain,
( spl3_160
<=> ! [X21] :
( ~ int_leq(X21,sK2(sK0,sK1))
| real_zero = a(plus(X21,sK0),X21)
| ~ int_leq(int_one,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_160])]) ).
fof(f2427,plain,
( spl3_161
<=> ! [X20] :
( sK1 != X20
| ~ int_leq(int_one,X20)
| ~ int_leq(X20,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_161])]) ).
fof(f2383,plain,
( spl3_155
<=> ! [X5,X4,X6,X3] :
( plus(X4,X3) != X5
| ~ int_leq(X6,X3)
| ~ int_leq(int_one,X6)
| real_zero = a(plus(X6,X4),X6)
| ~ int_less(int_zero,X4)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3)
| ~ int_leq(X5,n)
| ~ int_leq(int_one,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_155])]) ).
fof(f2402,plain,
( ! [X21,X20] :
( sK1 != X20
| ~ int_leq(X21,sK2(sK0,sK1))
| ~ int_leq(int_one,X21)
| real_zero = a(plus(X21,sK0),X21)
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK2(sK0,sK1),n)
| ~ int_leq(int_one,sK2(sK0,sK1))
| ~ int_leq(X20,n)
| ~ int_leq(int_one,X20) )
| ~ spl3_33
| ~ spl3_155 ),
inference(superposition,[],[f2384,f256]) ).
fof(f2384,plain,
( ! [X3,X6,X4,X5] :
( plus(X4,X3) != X5
| ~ int_leq(X6,X3)
| ~ int_leq(int_one,X6)
| real_zero = a(plus(X6,X4),X6)
| ~ int_less(int_zero,X4)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3)
| ~ int_leq(X5,n)
| ~ int_leq(int_one,X5) )
| ~ spl3_155 ),
inference(avatar_component_clause,[],[f2383]) ).
fof(f2394,plain,
( spl3_157
| ~ spl3_15
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f214,f206,f129,f2392]) ).
fof(f2392,plain,
( spl3_157
<=> ! [X5,X4,X6,X3] :
( plus(X4,X3) != X5
| ~ int_leq(X6,X3)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X4))
| ~ int_less(int_zero,X4)
| ~ int_leq(X5,n)
| ~ int_leq(int_one,X5)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_157])]) ).
fof(f206,plain,
( spl3_26
<=> ! [X0,X3,X2,X1] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f214,plain,
( ! [X3,X6,X4,X5] :
( plus(X4,X3) != X5
| ~ int_leq(X6,X3)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X4))
| ~ int_less(int_zero,X4)
| ~ int_leq(X5,n)
| ~ int_leq(int_one,X5)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3) )
| ~ spl3_15
| ~ spl3_26 ),
inference(superposition,[],[f207,f130]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( plus(X0,X2) != X1
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| real_zero = a(X3,plus(X3,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f2390,plain,
( spl3_156
| ~ spl3_66
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f1447,f764,f619,f2387]) ).
fof(f619,plain,
( spl3_66
<=> ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).
fof(f1447,plain,
( int_less(n,n)
| ~ spl3_66
| ~ spl3_77 ),
inference(resolution,[],[f766,f620]) ).
fof(f620,plain,
( ! [X0] :
( ~ int_less(X0,sK1)
| int_less(X0,n) )
| ~ spl3_66 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f2385,plain,
( spl3_155
| ~ spl3_15
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f210,f197,f129,f2383]) ).
fof(f197,plain,
( spl3_24
<=> ! [X5,X0,X6,X1] :
( real_zero = a(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6)
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f210,plain,
( ! [X3,X6,X4,X5] :
( plus(X4,X3) != X5
| ~ int_leq(X6,X3)
| ~ int_leq(int_one,X6)
| real_zero = a(plus(X6,X4),X6)
| ~ int_less(int_zero,X4)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X3)
| ~ int_leq(X5,n)
| ~ int_leq(int_one,X5) )
| ~ spl3_15
| ~ spl3_24 ),
inference(superposition,[],[f198,f130]) ).
fof(f198,plain,
( ! [X0,X1,X6,X5] :
( plus(X1,X5) != X0
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6)
| real_zero = a(plus(X6,X5),X6)
| ~ int_less(int_zero,X5)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f2349,plain,
( spl3_154
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f216,f206,f2347]) ).
fof(f216,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,plus(X0,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) )
| ~ spl3_26 ),
inference(equality_resolution,[],[f207]) ).
fof(f2345,plain,
( spl3_153
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f212,f197,f2343]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( ~ int_leq(X0,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(plus(X0,X2),X0)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,plus(X1,X2)) )
| ~ spl3_24 ),
inference(equality_resolution,[],[f198]) ).
fof(f2328,plain,
( spl3_152
| ~ spl3_10
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f195,f191,f101,f2326]) ).
fof(f195,plain,
( ! [X2,X1] :
( ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1)
| int_less(X2,int_one) )
| ~ spl3_10
| ~ spl3_23 ),
inference(resolution,[],[f192,f102]) ).
fof(f2280,plain,
( ~ spl3_3
| ~ spl3_22
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f908,f610,f188,f69]) ).
fof(f908,plain,
( ~ int_leq(sK1,n)
| ~ spl3_22
| ~ spl3_64 ),
inference(resolution,[],[f612,f189]) ).
fof(f189,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f612,plain,
( int_leq(int_one,sK1)
| ~ spl3_64 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f2227,plain,
( spl3_78
| ~ spl3_10
| spl3_83 ),
inference(avatar_split_clause,[],[f808,f801,f101,f773]) ).
fof(f801,plain,
( spl3_83
<=> int_leq(sK2(sK0,sK1),int_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_83])]) ).
fof(f808,plain,
( int_less(int_zero,sK2(sK0,sK1))
| ~ spl3_10
| spl3_83 ),
inference(resolution,[],[f803,f102]) ).
fof(f803,plain,
( ~ int_leq(sK2(sK0,sK1),int_zero)
| spl3_83 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f2226,plain,
( spl3_151
| ~ spl3_80 ),
inference(avatar_split_clause,[],[f789,f786,f2223]) ).
fof(f2223,plain,
( spl3_151
<=> int_less(sK2(sK0,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_151])]) ).
fof(f786,plain,
( spl3_80
<=> ! [X8] :
( sK1 != X8
| int_less(sK2(sK0,sK1),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_80])]) ).
fof(f789,plain,
( int_less(sK2(sK0,sK1),sK1)
| ~ spl3_80 ),
inference(equality_resolution,[],[f787]) ).
fof(f787,plain,
( ! [X8] :
( sK1 != X8
| int_less(sK2(sK0,sK1),X8) )
| ~ spl3_80 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f2221,plain,
( spl3_150
| ~ spl3_43
| ~ spl3_68 ),
inference(avatar_split_clause,[],[f656,f642,f350,f2218]) ).
fof(f2218,plain,
( spl3_150
<=> sK0 = sK2(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_150])]) ).
fof(f642,plain,
( spl3_68
<=> sK0 = plus(int_zero,sK2(int_zero,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
fof(f656,plain,
( sK0 = sK2(int_zero,sK0)
| ~ spl3_43
| ~ spl3_68 ),
inference(superposition,[],[f644,f351]) ).
fof(f644,plain,
( sK0 = plus(int_zero,sK2(int_zero,sK0))
| ~ spl3_68 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f2097,plain,
( spl3_149
| ~ spl3_58
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f568,f564,f504,f2095]) ).
fof(f2095,plain,
( spl3_149
<=> ! [X3,X4,X5,X2] :
( ~ int_less(X2,X3)
| ~ int_leq(X4,X5)
| plus(X3,X5) = plus(X2,X4)
| sK2(plus(X2,X4),plus(X3,X5)) = sK2(int_zero,sK2(plus(X2,X4),plus(X3,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_149])]) ).
fof(f504,plain,
( spl3_58
<=> ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
fof(f564,plain,
( spl3_62
<=> ! [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_62])]) ).
fof(f568,plain,
( ! [X2,X3,X4,X5] :
( ~ int_less(X2,X3)
| ~ int_leq(X4,X5)
| plus(X3,X5) = plus(X2,X4)
| sK2(plus(X2,X4),plus(X3,X5)) = sK2(int_zero,sK2(plus(X2,X4),plus(X3,X5))) )
| ~ spl3_58
| ~ spl3_62 ),
inference(resolution,[],[f565,f505]) ).
fof(f505,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| sK2(X0,X1) = sK2(int_zero,sK2(X0,X1)) )
| ~ spl3_58 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f565,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_62 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f2037,plain,
( spl3_148
| ~ spl3_19
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f569,f564,f160,f2035]) ).
fof(f2035,plain,
( spl3_148
<=> ! [X9,X7,X6,X8] :
( ~ int_less(X6,X7)
| ~ int_leq(X8,X9)
| plus(X6,X8) = plus(X7,X9)
| plus(X7,X9) = plus(plus(X6,X8),sK2(plus(X6,X8),plus(X7,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_148])]) ).
fof(f569,plain,
( ! [X8,X6,X9,X7] :
( ~ int_less(X6,X7)
| ~ int_leq(X8,X9)
| plus(X6,X8) = plus(X7,X9)
| plus(X7,X9) = plus(plus(X6,X8),sK2(plus(X6,X8),plus(X7,X9))) )
| ~ spl3_19
| ~ spl3_62 ),
inference(resolution,[],[f565,f161]) ).
fof(f2002,plain,
( spl3_147
| ~ spl3_18
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f570,f564,f147,f2000]) ).
fof(f2000,plain,
( spl3_147
<=> ! [X10,X11,X13,X14,X12] :
( ~ int_less(X10,X11)
| ~ int_leq(X12,X13)
| plus(X10,X12) = plus(X11,X13)
| int_less(X14,plus(X11,X13))
| ~ int_less(X14,plus(X10,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_147])]) ).
fof(f570,plain,
( ! [X10,X11,X14,X12,X13] :
( ~ int_less(X10,X11)
| ~ int_leq(X12,X13)
| plus(X10,X12) = plus(X11,X13)
| int_less(X14,plus(X11,X13))
| ~ int_less(X14,plus(X10,X12)) )
| ~ spl3_18
| ~ spl3_62 ),
inference(resolution,[],[f565,f148]) ).
fof(f1932,plain,
( spl3_146
| ~ spl3_17
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f548,f530,f143,f1930]) ).
fof(f1930,plain,
( spl3_146
<=> ! [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_146])]) ).
fof(f143,plain,
( spl3_17
<=> ! [X0,X1] :
( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f530,plain,
( spl3_61
<=> ! [X5,X4,X6,X3] :
( int_leq(plus(X5,X6),plus(X4,X3))
| ~ int_leq(X6,X4)
| ~ int_less(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).
fof(f548,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_61 ),
inference(resolution,[],[f531,f144]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ int_leq(X0,X1)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f531,plain,
( ! [X3,X6,X4,X5] :
( int_leq(plus(X5,X6),plus(X4,X3))
| ~ int_leq(X6,X4)
| ~ int_less(X5,X3) )
| ~ spl3_61 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f1928,plain,
( spl3_145
| ~ spl3_17
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f533,f521,f143,f1926]) ).
fof(f1926,plain,
( spl3_145
<=> ! [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_145])]) ).
fof(f521,plain,
( spl3_59
<=> ! [X5,X4,X6,X3] :
( int_leq(plus(X4,X3),plus(X5,X6))
| ~ int_leq(X4,X6)
| ~ int_less(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
fof(f533,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_59 ),
inference(resolution,[],[f522,f144]) ).
fof(f522,plain,
( ! [X3,X6,X4,X5] :
( int_leq(plus(X4,X3),plus(X5,X6))
| ~ int_leq(X4,X6)
| ~ int_less(X3,X5) )
| ~ spl3_59 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f1883,plain,
( spl3_144
| ~ spl3_53
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f511,f504,f453,f1881]) ).
fof(f1881,plain,
( spl3_144
<=> ! [X9,X8,X7] :
( sK2(X7,sK2(X8,X9)) = sK2(int_zero,sK2(X7,sK2(X8,X9)))
| ~ int_less(X7,int_zero)
| ~ int_less(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_144])]) ).
fof(f453,plain,
( spl3_53
<=> ! [X4,X2,X3] :
( int_less(X2,sK2(X3,X4))
| ~ int_less(X2,int_zero)
| ~ int_less(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
fof(f511,plain,
( ! [X8,X9,X7] :
( sK2(X7,sK2(X8,X9)) = sK2(int_zero,sK2(X7,sK2(X8,X9)))
| ~ int_less(X7,int_zero)
| ~ int_less(X8,X9) )
| ~ spl3_53
| ~ spl3_58 ),
inference(resolution,[],[f505,f454]) ).
fof(f454,plain,
( ! [X2,X3,X4] :
( int_less(X2,sK2(X3,X4))
| ~ int_less(X2,int_zero)
| ~ int_less(X3,X4) )
| ~ spl3_53 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f1839,plain,
( spl3_143
| ~ spl3_19
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f474,f453,f160,f1837]) ).
fof(f1837,plain,
( spl3_143
<=> ! [X2,X3,X4] :
( ~ int_less(X2,int_zero)
| ~ int_less(X3,X4)
| sK2(X3,X4) = plus(X2,sK2(X2,sK2(X3,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_143])]) ).
fof(f474,plain,
( ! [X2,X3,X4] :
( ~ int_less(X2,int_zero)
| ~ int_less(X3,X4)
| sK2(X3,X4) = plus(X2,sK2(X2,sK2(X3,X4))) )
| ~ spl3_19
| ~ spl3_53 ),
inference(resolution,[],[f454,f161]) ).
fof(f1689,plain,
( ~ spl3_2
| ~ spl3_50
| spl3_81 ),
inference(avatar_split_clause,[],[f798,f791,f411,f64]) ).
fof(f411,plain,
( spl3_50
<=> ! [X2,X3] :
( ~ int_less(X2,X3)
| int_leq(int_zero,sK2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).
fof(f791,plain,
( spl3_81
<=> int_leq(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_81])]) ).
fof(f798,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_50
| spl3_81 ),
inference(resolution,[],[f793,f412]) ).
fof(f412,plain,
( ! [X2,X3] :
( int_leq(int_zero,sK2(X2,X3))
| ~ int_less(X2,X3) )
| ~ spl3_50 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f793,plain,
( ~ int_leq(int_zero,sK2(sK0,sK1))
| spl3_81 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f1640,plain,
( spl3_142
| ~ spl3_43
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f582,f564,f350,f1638]) ).
fof(f1638,plain,
( spl3_142
<=> ! [X13,X14,X15] :
( int_less(plus(X14,X15),X13)
| ~ int_less(X14,int_zero)
| ~ int_leq(X15,X13)
| plus(X14,X15) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_142])]) ).
fof(f582,plain,
( ! [X14,X15,X13] :
( int_less(plus(X14,X15),X13)
| ~ int_less(X14,int_zero)
| ~ int_leq(X15,X13)
| plus(X14,X15) = X13 )
| ~ spl3_43
| ~ spl3_62 ),
inference(superposition,[],[f565,f351]) ).
fof(f1636,plain,
( spl3_141
| ~ spl3_43
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f576,f564,f350,f1634]) ).
fof(f1634,plain,
( spl3_141
<=> ! [X13,X14,X15] :
( int_less(X13,plus(X14,X15))
| ~ int_less(int_zero,X14)
| ~ int_leq(X13,X15)
| plus(X14,X15) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_141])]) ).
fof(f576,plain,
( ! [X14,X15,X13] :
( int_less(X13,plus(X14,X15))
| ~ int_less(int_zero,X14)
| ~ int_leq(X13,X15)
| plus(X14,X15) = X13 )
| ~ spl3_43
| ~ spl3_62 ),
inference(superposition,[],[f565,f351]) ).
fof(f1632,plain,
( spl3_140
| ~ spl3_16
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f515,f504,f137,f1630]) ).
fof(f1630,plain,
( spl3_140
<=> ! [X11,X12] :
( sK2(int_zero,sK2(X11,X12)) = sK2(int_zero,sK2(int_zero,sK2(X11,X12)))
| ~ int_less(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_140])]) ).
fof(f137,plain,
( spl3_16
<=> ! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f515,plain,
( ! [X11,X12] :
( sK2(int_zero,sK2(X11,X12)) = sK2(int_zero,sK2(int_zero,sK2(X11,X12)))
| ~ int_less(X11,X12) )
| ~ spl3_16
| ~ spl3_58 ),
inference(resolution,[],[f505,f138]) ).
fof(f138,plain,
( ! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f1628,plain,
( spl3_139
| ~ spl3_51
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f510,f504,f415,f1626]) ).
fof(f1626,plain,
( spl3_139
<=> ! [X6,X5] :
( sK2(X5,plus(X5,X6)) = sK2(int_zero,sK2(X5,plus(X5,X6)))
| ~ int_less(int_zero,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_139])]) ).
fof(f415,plain,
( spl3_51
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| int_less(X1,plus(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).
fof(f510,plain,
( ! [X6,X5] :
( sK2(X5,plus(X5,X6)) = sK2(int_zero,sK2(X5,plus(X5,X6)))
| ~ int_less(int_zero,X6) )
| ~ spl3_51
| ~ spl3_58 ),
inference(resolution,[],[f505,f416]) ).
fof(f416,plain,
( ! [X0,X1] :
( int_less(X1,plus(X1,X0))
| ~ int_less(int_zero,X0) )
| ~ spl3_51 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f1624,plain,
( spl3_138
| ~ spl3_17
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f495,f470,f143,f1622]) ).
fof(f1622,plain,
( spl3_138
<=> ! [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_138])]) ).
fof(f495,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_57 ),
inference(resolution,[],[f471,f144]) ).
fof(f1620,plain,
( spl3_137
| ~ spl3_17
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f487,f466,f143,f1618]) ).
fof(f1618,plain,
( spl3_137
<=> ! [X6,X4,X5] :
( ~ int_leq(int_zero,X4)
| ~ int_less(X5,X6)
| int_less(X5,plus(X6,X4))
| plus(X6,X4) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_137])]) ).
fof(f487,plain,
( ! [X6,X4,X5] :
( ~ int_leq(int_zero,X4)
| ~ int_less(X5,X6)
| int_less(X5,plus(X6,X4))
| plus(X6,X4) = X5 )
| ~ spl3_17
| ~ spl3_56 ),
inference(resolution,[],[f467,f144]) ).
fof(f1588,plain,
( ~ spl3_2
| ~ spl3_16
| spl3_78 ),
inference(avatar_split_clause,[],[f780,f773,f137,f64]) ).
fof(f780,plain,
( ~ int_less(sK0,sK1)
| ~ spl3_16
| spl3_78 ),
inference(resolution,[],[f775,f138]) ).
fof(f775,plain,
( ~ int_less(int_zero,sK2(sK0,sK1))
| spl3_78 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f1587,plain,
( spl3_136
| ~ spl3_52
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f507,f504,f434,f1585]) ).
fof(f1585,plain,
( spl3_136
<=> ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_136])]) ).
fof(f434,plain,
( spl3_52
<=> ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).
fof(f507,plain,
( ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| int_less(X1,X0)
| X0 = X1 )
| ~ spl3_52
| ~ spl3_58 ),
inference(resolution,[],[f505,f435]) ).
fof(f435,plain,
( ! [X0,X1] :
( int_less(X1,X0)
| int_less(X0,X1)
| X0 = X1 )
| ~ spl3_52 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f1528,plain,
( spl3_135
| ~ spl3_18
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f475,f453,f147,f1526]) ).
fof(f1526,plain,
( spl3_135
<=> ! [X5,X7,X6,X8] :
( ~ int_less(X5,int_zero)
| ~ int_less(X6,X7)
| int_less(X8,sK2(X6,X7))
| ~ int_less(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_135])]) ).
fof(f475,plain,
( ! [X8,X6,X7,X5] :
( ~ int_less(X5,int_zero)
| ~ int_less(X6,X7)
| int_less(X8,sK2(X6,X7))
| ~ int_less(X8,X5) )
| ~ spl3_18
| ~ spl3_53 ),
inference(resolution,[],[f454,f148]) ).
fof(f1524,plain,
( spl3_134
| ~ spl3_19
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f422,f415,f160,f1522]) ).
fof(f1522,plain,
( spl3_134
<=> ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X1,X0) = plus(X1,sK2(X1,plus(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_134])]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| plus(X1,X0) = plus(X1,sK2(X1,plus(X1,X0))) )
| ~ spl3_19
| ~ spl3_51 ),
inference(resolution,[],[f416,f161]) ).
fof(f1461,plain,
( spl3_133
| ~ spl3_15
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f541,f521,f129,f1459]) ).
fof(f1459,plain,
( spl3_133
<=> ! [X5,X4,X6,X3] :
( int_leq(plus(X5,X6),plus(X4,X3))
| ~ int_leq(X5,X4)
| ~ int_less(X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_133])]) ).
fof(f541,plain,
( ! [X3,X6,X4,X5] :
( int_leq(plus(X5,X6),plus(X4,X3))
| ~ int_leq(X5,X4)
| ~ int_less(X6,X3) )
| ~ spl3_15
| ~ spl3_59 ),
inference(superposition,[],[f522,f130]) ).
fof(f1457,plain,
( spl3_132
| ~ spl3_19
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f438,f434,f160,f1455]) ).
fof(f1455,plain,
( spl3_132
<=> ! [X2,X1] :
( int_less(X2,X1)
| X1 = X2
| plus(X1,sK2(X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_132])]) ).
fof(f438,plain,
( ! [X2,X1] :
( int_less(X2,X1)
| X1 = X2
| plus(X1,sK2(X1,X2)) = X2 )
| ~ spl3_19
| ~ spl3_52 ),
inference(resolution,[],[f435,f161]) ).
fof(f1446,plain,
( spl3_131
| ~ spl3_17
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f420,f407,f143,f1444]) ).
fof(f1444,plain,
( spl3_131
<=> ! [X4,X5] :
( ~ int_less(X4,X5)
| int_less(int_one,sK2(X4,X5))
| int_one = sK2(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_131])]) ).
fof(f420,plain,
( ! [X4,X5] :
( ~ int_less(X4,X5)
| int_less(int_one,sK2(X4,X5))
| int_one = sK2(X4,X5) )
| ~ spl3_17
| ~ spl3_49 ),
inference(resolution,[],[f408,f144]) ).
fof(f1382,plain,
( spl3_130
| ~ spl3_45
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f512,f504,f368,f1380]) ).
fof(f1380,plain,
( spl3_130
<=> ! [X10] :
( sK2(int_zero,X10) = sK2(int_zero,sK2(int_zero,X10))
| int_less(X10,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_130])]) ).
fof(f512,plain,
( ! [X10] :
( sK2(int_zero,X10) = sK2(int_zero,sK2(int_zero,X10))
| int_less(X10,int_one) )
| ~ spl3_45
| ~ spl3_58 ),
inference(resolution,[],[f505,f369]) ).
fof(f1378,plain,
( spl3_129
| ~ spl3_45
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f509,f504,f368,f1376]) ).
fof(f1376,plain,
( spl3_129
<=> ! [X4] :
( sK2(X4,int_one) = sK2(int_zero,sK2(X4,int_one))
| int_less(int_zero,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_129])]) ).
fof(f509,plain,
( ! [X4] :
( sK2(X4,int_one) = sK2(int_zero,sK2(X4,int_one))
| int_less(int_zero,X4) )
| ~ spl3_45
| ~ spl3_58 ),
inference(resolution,[],[f505,f369]) ).
fof(f1374,plain,
( spl3_128
| ~ spl3_18
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f439,f434,f147,f1372]) ).
fof(f1372,plain,
( spl3_128
<=> ! [X4,X5,X3] :
( int_less(X4,X3)
| X3 = X4
| int_less(X5,X4)
| ~ int_less(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_128])]) ).
fof(f439,plain,
( ! [X3,X4,X5] :
( int_less(X4,X3)
| X3 = X4
| int_less(X5,X4)
| ~ int_less(X5,X3) )
| ~ spl3_18
| ~ spl3_52 ),
inference(resolution,[],[f435,f148]) ).
fof(f1224,plain,
( spl3_127
| ~ spl3_43
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f553,f530,f350,f1222]) ).
fof(f1222,plain,
( spl3_127
<=> ! [X13,X14,X15] :
( int_leq(X13,plus(X14,X15))
| ~ int_leq(X13,X14)
| ~ int_less(int_zero,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_127])]) ).
fof(f553,plain,
( ! [X14,X15,X13] :
( int_leq(X13,plus(X14,X15))
| ~ int_leq(X13,X14)
| ~ int_less(int_zero,X15) )
| ~ spl3_43
| ~ spl3_61 ),
inference(superposition,[],[f531,f351]) ).
fof(f1220,plain,
( spl3_126
| ~ spl3_43
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f544,f521,f350,f1218]) ).
fof(f1218,plain,
( spl3_126
<=> ! [X13,X14,X15] :
( int_leq(plus(X14,X15),X13)
| ~ int_leq(X14,X13)
| ~ int_less(X15,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_126])]) ).
fof(f544,plain,
( ! [X14,X15,X13] :
( int_leq(plus(X14,X15),X13)
| ~ int_leq(X14,X13)
| ~ int_less(X15,int_zero) )
| ~ spl3_43
| ~ spl3_59 ),
inference(superposition,[],[f522,f351]) ).
fof(f1216,plain,
( spl3_125
| ~ spl3_15
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f498,f470,f129,f1214]) ).
fof(f1214,plain,
( spl3_125
<=> ! [X4,X2,X3] :
( int_leq(plus(X3,X2),X4)
| ~ int_leq(X3,int_zero)
| ~ int_less(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_125])]) ).
fof(f498,plain,
( ! [X2,X3,X4] :
( int_leq(plus(X3,X2),X4)
| ~ int_leq(X3,int_zero)
| ~ int_less(X2,X4) )
| ~ spl3_15
| ~ spl3_57 ),
inference(superposition,[],[f471,f130]) ).
fof(f1212,plain,
( spl3_124
| ~ spl3_15
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f489,f466,f129,f1210]) ).
fof(f1210,plain,
( spl3_124
<=> ! [X2,X4,X3] :
( int_leq(X4,plus(X3,X2))
| ~ int_leq(int_zero,X3)
| ~ int_less(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_124])]) ).
fof(f489,plain,
( ! [X2,X3,X4] :
( int_leq(X4,plus(X3,X2))
| ~ int_leq(int_zero,X3)
| ~ int_less(X4,X2) )
| ~ spl3_15
| ~ spl3_56 ),
inference(superposition,[],[f467,f130]) ).
fof(f1208,plain,
( spl3_123
| ~ spl3_63
| ~ spl3_67 ),
inference(avatar_split_clause,[],[f640,f623,f587,f1205]) ).
fof(f640,plain,
( int_less(sK1,sK0)
| ~ spl3_63
| ~ spl3_67 ),
inference(resolution,[],[f624,f589]) ).
fof(f1203,plain,
( spl3_122
| ~ spl3_9
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f486,f466,f97,f1201]) ).
fof(f1201,plain,
( spl3_122
<=> ! [X2,X3] :
( ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X3)
| int_less(int_zero,plus(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_122])]) ).
fof(f97,plain,
( spl3_9
<=> ! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f486,plain,
( ! [X2,X3] :
( ~ int_leq(int_zero,X2)
| ~ int_less(int_one,X3)
| int_less(int_zero,plus(X3,X2)) )
| ~ spl3_9
| ~ spl3_56 ),
inference(resolution,[],[f467,f98]) ).
fof(f98,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f1199,plain,
( spl3_121
| ~ spl3_12
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f476,f453,f109,f1197]) ).
fof(f1197,plain,
( spl3_121
<=> ! [X9,X11,X10] :
( ~ int_less(X9,int_zero)
| ~ int_less(X10,X11)
| int_leq(X9,sK2(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_121])]) ).
fof(f476,plain,
( ! [X10,X11,X9] :
( ~ int_less(X9,int_zero)
| ~ int_less(X10,X11)
| int_leq(X9,sK2(X10,X11)) )
| ~ spl3_12
| ~ spl3_53 ),
inference(resolution,[],[f454,f110]) ).
fof(f1195,plain,
( spl3_120
| ~ spl3_18
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f423,f415,f147,f1193]) ).
fof(f1193,plain,
( spl3_120
<=> ! [X2,X3,X4] :
( ~ int_less(int_zero,X2)
| int_less(X3,plus(X4,X2))
| ~ int_less(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_120])]) ).
fof(f423,plain,
( ! [X2,X3,X4] :
( ~ int_less(int_zero,X2)
| int_less(X3,plus(X4,X2))
| ~ int_less(X3,X4) )
| ~ spl3_18
| ~ spl3_51 ),
inference(resolution,[],[f416,f148]) ).
fof(f1191,plain,
( spl3_119
| ~ spl3_21
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f359,f350,f177,f1189]) ).
fof(f1189,plain,
( spl3_119
<=> ! [X9,X7,X8] :
( int_leq(plus(X8,X9),X7)
| ~ int_leq(X9,X7)
| ~ int_less(X8,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_119])]) ).
fof(f177,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(f359,plain,
( ! [X8,X9,X7] :
( int_leq(plus(X8,X9),X7)
| ~ int_leq(X9,X7)
| ~ int_less(X8,int_zero) )
| ~ spl3_21
| ~ spl3_43 ),
inference(superposition,[],[f178,f351]) ).
fof(f178,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,[],[f177]) ).
fof(f1187,plain,
( spl3_118
| ~ spl3_21
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f358,f350,f177,f1185]) ).
fof(f1185,plain,
( spl3_118
<=> ! [X6,X4,X5] :
( int_leq(X4,plus(X5,X6))
| ~ int_leq(X4,X6)
| ~ int_less(int_zero,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_118])]) ).
fof(f358,plain,
( ! [X6,X4,X5] :
( int_leq(X4,plus(X5,X6))
| ~ int_leq(X4,X6)
| ~ int_less(int_zero,X5) )
| ~ spl3_21
| ~ spl3_43 ),
inference(superposition,[],[f178,f351]) ).
fof(f1155,plain,
( spl3_117
| ~ spl3_44
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f496,f470,f361,f1153]) ).
fof(f1153,plain,
( spl3_117
<=> ! [X4,X3] :
( ~ int_leq(X3,int_zero)
| ~ int_less(X4,n)
| int_less(plus(X4,X3),int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_117])]) ).
fof(f496,plain,
( ! [X3,X4] :
( ~ int_leq(X3,int_zero)
| ~ int_less(X4,n)
| int_less(plus(X4,X3),int_one) )
| ~ spl3_44
| ~ spl3_57 ),
inference(resolution,[],[f471,f362]) ).
fof(f1151,plain,
( spl3_116
| ~ spl3_22
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f485,f466,f188,f1149]) ).
fof(f1149,plain,
( spl3_116
<=> ! [X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(int_one,X1)
| ~ int_leq(plus(X1,X0),n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_116])]) ).
fof(f485,plain,
( ! [X0,X1] :
( ~ int_leq(int_zero,X0)
| ~ int_less(int_one,X1)
| ~ int_leq(plus(X1,X0),n) )
| ~ spl3_22
| ~ spl3_56 ),
inference(resolution,[],[f467,f189]) ).
fof(f1130,plain,
( spl3_115
| ~ spl3_2
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f634,f619,f64,f1127]) ).
fof(f634,plain,
( int_less(sK0,n)
| ~ spl3_2
| ~ spl3_66 ),
inference(resolution,[],[f620,f66]) ).
fof(f66,plain,
( int_less(sK0,sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f1125,plain,
( spl3_114
| ~ spl3_19
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f375,f368,f160,f1123]) ).
fof(f1123,plain,
( spl3_114
<=> ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_114])]) ).
fof(f375,plain,
( ! [X0] :
( int_less(int_zero,X0)
| int_one = plus(X0,sK2(X0,int_one)) )
| ~ spl3_19
| ~ spl3_45 ),
inference(resolution,[],[f369,f161]) ).
fof(f1063,plain,
( spl3_113
| ~ spl3_43
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f501,f470,f350,f1061]) ).
fof(f501,plain,
( ! [X10,X9] :
( int_leq(X9,X10)
| ~ int_leq(X9,int_zero)
| ~ int_less(int_zero,X10) )
| ~ spl3_43
| ~ spl3_57 ),
inference(superposition,[],[f471,f351]) ).
fof(f1059,plain,
( spl3_112
| ~ spl3_43
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f492,f466,f350,f1057]) ).
fof(f1057,plain,
( spl3_112
<=> ! [X9,X10] :
( int_leq(X10,X9)
| ~ int_leq(int_zero,X9)
| ~ int_less(X10,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_112])]) ).
fof(f492,plain,
( ! [X10,X9] :
( int_leq(X10,X9)
| ~ int_leq(int_zero,X9)
| ~ int_less(X10,int_zero) )
| ~ spl3_43
| ~ spl3_56 ),
inference(superposition,[],[f467,f351]) ).
fof(f1055,plain,
( spl3_111
| ~ spl3_8
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f443,f434,f93,f1053]) ).
fof(f1053,plain,
( spl3_111
<=> ! [X10] :
( int_less(X10,int_zero)
| int_zero = X10
| int_leq(int_one,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_111])]) ).
fof(f443,plain,
( ! [X10] :
( int_less(X10,int_zero)
| int_zero = X10
| int_leq(int_one,X10) )
| ~ spl3_8
| ~ spl3_52 ),
inference(resolution,[],[f435,f94]) ).
fof(f1051,plain,
( spl3_110
| ~ spl3_54
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f633,f619,f457,f1048]) ).
fof(f1048,plain,
( spl3_110
<=> int_less(int_one,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_110])]) ).
fof(f633,plain,
( int_less(int_one,n)
| ~ spl3_54
| ~ spl3_66 ),
inference(resolution,[],[f620,f459]) ).
fof(f1046,plain,
( spl3_109
| ~ spl3_18
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f382,f368,f147,f1044]) ).
fof(f1044,plain,
( spl3_109
<=> ! [X2,X3] :
( int_less(X2,int_one)
| int_less(X3,X2)
| ~ int_less(X3,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_109])]) ).
fof(f382,plain,
( ! [X2,X3] :
( int_less(X2,int_one)
| int_less(X3,X2)
| ~ int_less(X3,int_zero) )
| ~ spl3_18
| ~ spl3_45 ),
inference(resolution,[],[f369,f148]) ).
fof(f1042,plain,
( spl3_108
| ~ spl3_18
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f376,f368,f147,f1040]) ).
fof(f1040,plain,
( spl3_108
<=> ! [X2,X1] :
( int_less(int_zero,X1)
| int_less(X2,int_one)
| ~ int_less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_108])]) ).
fof(f376,plain,
( ! [X2,X1] :
( int_less(int_zero,X1)
| int_less(X2,int_one)
| ~ int_less(X2,X1) )
| ~ spl3_18
| ~ spl3_45 ),
inference(resolution,[],[f369,f148]) ).
fof(f1038,plain,
( spl3_107
| ~ spl3_20
| ~ spl3_43 ),
inference(avatar_split_clause,[],[f357,f350,f169,f1036]) ).
fof(f1036,plain,
( spl3_107
<=> ! [X2,X3] :
( X2 != X3
| ~ int_less(int_zero,X2)
| int_less(int_zero,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_107])]) ).
fof(f169,plain,
( spl3_20
<=> ! [X2,X0,X1] :
( int_less(X0,X1)
| ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f357,plain,
( ! [X2,X3] :
( X2 != X3
| ~ int_less(int_zero,X2)
| int_less(int_zero,X3) )
| ~ spl3_20
| ~ spl3_43 ),
inference(superposition,[],[f170,f351]) ).
fof(f170,plain,
( ! [X2,X0,X1] :
( plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| int_less(X0,X1) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f989,plain,
( spl3_106
| ~ spl3_34
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f473,f453,f274,f987]) ).
fof(f987,plain,
( spl3_106
<=> ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_106])]) ).
fof(f473,plain,
( ! [X0,X1] :
( ~ int_less(sK2(X0,X1),int_zero)
| ~ int_less(X0,X1) )
| ~ spl3_34
| ~ spl3_53 ),
inference(resolution,[],[f454,f275]) ).
fof(f985,plain,
( spl3_105
| ~ spl3_15
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f427,f415,f129,f983]) ).
fof(f427,plain,
( ! [X2,X1] :
( int_less(X1,plus(X2,X1))
| ~ int_less(int_zero,X2) )
| ~ spl3_15
| ~ spl3_51 ),
inference(superposition,[],[f416,f130]) ).
fof(f981,plain,
( spl3_104
| ~ spl3_12
| ~ spl3_51 ),
inference(avatar_split_clause,[],[f424,f415,f109,f979]) ).
fof(f979,plain,
( spl3_104
<=> ! [X6,X5] :
( ~ int_less(int_zero,X5)
| int_leq(X6,plus(X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_104])]) ).
fof(f424,plain,
( ! [X6,X5] :
( ~ int_less(int_zero,X5)
| int_leq(X6,plus(X6,X5)) )
| ~ spl3_12
| ~ spl3_51 ),
inference(resolution,[],[f416,f110]) ).
fof(f977,plain,
( spl3_103
| ~ spl3_48
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f631,f619,f394,f974]) ).
fof(f631,plain,
( int_less(int_zero,n)
| ~ spl3_48
| ~ spl3_66 ),
inference(resolution,[],[f620,f396]) ).
fof(f972,plain,
( spl3_102
| ~ spl3_19
| ~ spl3_43
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f386,f368,f350,f160,f970]) ).
fof(f386,plain,
( ! [X1] :
( sK2(int_zero,X1) = X1
| int_less(X1,int_one) )
| ~ spl3_19
| ~ spl3_43
| ~ spl3_45 ),
inference(forward_demodulation,[],[f381,f351]) ).
fof(f381,plain,
( ! [X1] :
( int_less(X1,int_one)
| plus(int_zero,sK2(int_zero,X1)) = X1 )
| ~ spl3_19
| ~ spl3_45 ),
inference(resolution,[],[f369,f161]) ).
fof(f963,plain,
( spl3_101
| ~ spl3_22
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f418,f407,f188,f961]) ).
fof(f961,plain,
( spl3_101
<=> ! [X0,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(sK2(X0,X1),n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_101])]) ).
fof(f418,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| ~ int_leq(sK2(X0,X1),n) )
| ~ spl3_22
| ~ spl3_49 ),
inference(resolution,[],[f408,f189]) ).
fof(f946,plain,
( spl3_100
| ~ spl3_12
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f383,f368,f109,f944]) ).
fof(f944,plain,
( spl3_100
<=> ! [X4] :
( int_less(X4,int_one)
| int_leq(int_zero,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_100])]) ).
fof(f383,plain,
( ! [X4] :
( int_less(X4,int_one)
| int_leq(int_zero,X4) )
| ~ spl3_12
| ~ spl3_45 ),
inference(resolution,[],[f369,f110]) ).
fof(f942,plain,
( spl3_99
| ~ spl3_12
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f377,f368,f109,f940]) ).
fof(f940,plain,
( spl3_99
<=> ! [X3] :
( int_less(int_zero,X3)
| int_leq(X3,int_one) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_99])]) ).
fof(f377,plain,
( ! [X3] :
( int_less(int_zero,X3)
| int_leq(X3,int_one) )
| ~ spl3_12
| ~ spl3_45 ),
inference(resolution,[],[f369,f110]) ).
fof(f919,plain,
( spl3_98
| ~ spl3_10
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f364,f361,f101,f917]) ).
fof(f364,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(n,X0) )
| ~ spl3_10
| ~ spl3_44 ),
inference(resolution,[],[f362,f102]) ).
fof(f907,plain,
( spl3_97
| ~ spl3_43
| ~ spl3_47 ),
inference(avatar_split_clause,[],[f398,f389,f350,f904]) ).
fof(f904,plain,
( spl3_97
<=> int_one = sK2(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_97])]) ).
fof(f389,plain,
( spl3_47
<=> int_one = plus(int_zero,sK2(int_zero,int_one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).
fof(f398,plain,
( int_one = sK2(int_zero,int_one)
| ~ spl3_43
| ~ spl3_47 ),
inference(superposition,[],[f391,f351]) ).
fof(f391,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f894,plain,
( spl3_96
| ~ spl3_33
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f581,f564,f254,f892]) ).
fof(f892,plain,
( spl3_96
<=> ! [X11,X12] :
( int_less(plus(X11,X12),sK1)
| ~ int_less(X11,sK0)
| ~ int_leq(X12,sK2(sK0,sK1))
| sK1 = plus(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_96])]) ).
fof(f581,plain,
( ! [X11,X12] :
( int_less(plus(X11,X12),sK1)
| ~ int_less(X11,sK0)
| ~ int_leq(X12,sK2(sK0,sK1))
| sK1 = plus(X11,X12) )
| ~ spl3_33
| ~ spl3_62 ),
inference(superposition,[],[f565,f256]) ).
fof(f890,plain,
( spl3_95
| ~ spl3_33
| ~ spl3_62 ),
inference(avatar_split_clause,[],[f575,f564,f254,f888]) ).
fof(f888,plain,
( spl3_95
<=> ! [X11,X12] :
( int_less(sK1,plus(X11,X12))
| ~ int_less(sK0,X11)
| ~ int_leq(sK2(sK0,sK1),X12)
| sK1 = plus(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_95])]) ).
fof(f575,plain,
( ! [X11,X12] :
( int_less(sK1,plus(X11,X12))
| ~ int_less(sK0,X11)
| ~ int_leq(sK2(sK0,sK1),X12)
| sK1 = plus(X11,X12) )
| ~ spl3_33
| ~ spl3_62 ),
inference(superposition,[],[f565,f256]) ).
fof(f861,plain,
( spl3_94
| ~ spl3_12
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f608,f587,f109,f858]) ).
fof(f858,plain,
( spl3_94
<=> int_leq(sK1,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_94])]) ).
fof(f608,plain,
( int_leq(sK1,int_one)
| ~ spl3_12
| ~ spl3_63 ),
inference(resolution,[],[f589,f110]) ).
fof(f853,plain,
( spl3_93
| ~ spl3_33
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f558,f530,f254,f851]) ).
fof(f558,plain,
( ! [X11,X12] :
( int_leq(plus(X11,X12),sK1)
| ~ int_leq(X12,sK0)
| ~ int_less(X11,sK2(sK0,sK1)) )
| ~ spl3_33
| ~ spl3_61 ),
inference(superposition,[],[f531,f256]) ).
fof(f849,plain,
( spl3_92
| ~ spl3_33
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f552,f530,f254,f847]) ).
fof(f847,plain,
( spl3_92
<=> ! [X11,X12] :
( int_leq(sK1,plus(X11,X12))
| ~ int_leq(sK2(sK0,sK1),X11)
| ~ int_less(sK0,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_92])]) ).
fof(f552,plain,
( ! [X11,X12] :
( int_leq(sK1,plus(X11,X12))
| ~ int_leq(sK2(sK0,sK1),X11)
| ~ int_less(sK0,X12) )
| ~ spl3_33
| ~ spl3_61 ),
inference(superposition,[],[f531,f256]) ).
fof(f845,plain,
( spl3_91
| ~ spl3_33
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f543,f521,f254,f843]) ).
fof(f543,plain,
( ! [X11,X12] :
( int_leq(plus(X11,X12),sK1)
| ~ int_leq(X11,sK2(sK0,sK1))
| ~ int_less(X12,sK0) )
| ~ spl3_33
| ~ spl3_59 ),
inference(superposition,[],[f522,f256]) ).
fof(f841,plain,
( spl3_90
| ~ spl3_33
| ~ spl3_59 ),
inference(avatar_split_clause,[],[f537,f521,f254,f839]) ).
fof(f839,plain,
( spl3_90
<=> ! [X11,X12] :
( int_leq(sK1,plus(X11,X12))
| ~ int_leq(sK0,X12)
| ~ int_less(sK2(sK0,sK1),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_90])]) ).
fof(f537,plain,
( ! [X11,X12] :
( int_leq(sK1,plus(X11,X12))
| ~ int_leq(sK0,X12)
| ~ int_less(sK2(sK0,sK1),X11) )
| ~ spl3_33
| ~ spl3_59 ),
inference(superposition,[],[f522,f256]) ).
fof(f837,plain,
( spl3_89
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f260,f254,f177,f835]) ).
fof(f260,plain,
( ! [X3,X4] :
( int_leq(plus(X3,X4),sK1)
| ~ int_leq(X4,sK2(sK0,sK1))
| ~ int_less(X3,sK0) )
| ~ spl3_21
| ~ spl3_33 ),
inference(superposition,[],[f178,f256]) ).
fof(f833,plain,
( spl3_88
| ~ spl3_21
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f259,f254,f177,f831]) ).
fof(f831,plain,
( spl3_88
<=> ! [X2,X1] :
( int_leq(sK1,plus(X1,X2))
| ~ int_leq(sK2(sK0,sK1),X2)
| ~ int_less(sK0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_88])]) ).
fof(f259,plain,
( ! [X2,X1] :
( int_leq(sK1,plus(X1,X2))
| ~ int_leq(sK2(sK0,sK1),X2)
| ~ int_less(sK0,X1) )
| ~ spl3_21
| ~ spl3_33 ),
inference(superposition,[],[f178,f256]) ).
fof(f823,plain,
( spl3_87
| ~ spl3_36
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f365,f361,f284,f820]) ).
fof(f820,plain,
( spl3_87
<=> int_less(n,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_87])]) ).
fof(f365,plain,
( int_less(n,int_one)
| ~ spl3_36
| ~ spl3_44 ),
inference(resolution,[],[f362,f285]) ).
fof(f818,plain,
( spl3_86
| ~ spl3_12
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f604,f525,f109,f815]) ).
fof(f815,plain,
( spl3_86
<=> int_leq(n,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_86])]) ).
fof(f604,plain,
( int_leq(n,sK0)
| ~ spl3_12
| ~ spl3_60 ),
inference(resolution,[],[f527,f110]) ).
fof(f813,plain,
( ~ spl3_85
| ~ spl3_22
| ~ spl3_36 ),
inference(avatar_split_clause,[],[f337,f284,f188,f810]) ).
fof(f337,plain,
( ~ int_leq(int_one,n)
| ~ spl3_22
| ~ spl3_36 ),
inference(resolution,[],[f189,f285]) ).
fof(f807,plain,
( ~ spl3_83
| spl3_84
| ~ spl3_33
| ~ spl3_57 ),
inference(avatar_split_clause,[],[f500,f470,f254,f805,f801]) ).
fof(f805,plain,
( spl3_84
<=> ! [X8] :
( int_leq(sK1,X8)
| ~ int_less(sK0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_84])]) ).
fof(f500,plain,
( ! [X8] :
( int_leq(sK1,X8)
| ~ int_leq(sK2(sK0,sK1),int_zero)
| ~ int_less(sK0,X8) )
| ~ spl3_33
| ~ spl3_57 ),
inference(superposition,[],[f471,f256]) ).
fof(f797,plain,
( ~ spl3_81
| spl3_82
| ~ spl3_33
| ~ spl3_56 ),
inference(avatar_split_clause,[],[f491,f466,f254,f795,f791]) ).
fof(f795,plain,
( spl3_82
<=> ! [X8] :
( int_leq(X8,sK1)
| ~ int_less(X8,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_82])]) ).
fof(f491,plain,
( ! [X8] :
( int_leq(X8,sK1)
| ~ int_leq(int_zero,sK2(sK0,sK1))
| ~ int_less(X8,sK0) )
| ~ spl3_33
| ~ spl3_56 ),
inference(superposition,[],[f467,f256]) ).
fof(f788,plain,
( ~ spl3_14
| spl3_80
| ~ spl3_33
| ~ spl3_55 ),
inference(avatar_split_clause,[],[f481,f462,f254,f786,f120]) ).
fof(f462,plain,
( spl3_55
<=> ! [X4,X2,X3] :
( plus(X3,X2) != X4
| ~ int_less(int_zero,X3)
| int_less(X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
fof(f481,plain,
( ! [X8] :
( sK1 != X8
| ~ int_less(int_zero,sK0)
| int_less(sK2(sK0,sK1),X8) )
| ~ spl3_33
| ~ spl3_55 ),
inference(superposition,[],[f463,f256]) ).
fof(f463,plain,
( ! [X2,X3,X4] :
( plus(X3,X2) != X4
| ~ int_less(int_zero,X3)
| int_less(X2,X4) )
| ~ spl3_55 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f779,plain,
( ~ spl3_78
| spl3_79
| ~ spl3_20
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f258,f254,f169,f777,f773]) ).
fof(f777,plain,
( spl3_79
<=> ! [X0] :
( sK1 != X0
| int_less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_79])]) ).
fof(f258,plain,
( ! [X0] :
( sK1 != X0
| ~ int_less(int_zero,sK2(sK0,sK1))
| int_less(sK0,X0) )
| ~ spl3_20
| ~ spl3_33 ),
inference(superposition,[],[f170,f256]) ).
fof(f767,plain,
( spl3_77
| ~ spl3_32
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f600,f525,f249,f764]) ).
fof(f600,plain,
( int_less(n,sK1)
| ~ spl3_32
| ~ spl3_60 ),
inference(resolution,[],[f527,f250]) ).
fof(f737,plain,
( spl3_76
| ~ spl3_30
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f518,f504,f237,f734]) ).
fof(f734,plain,
( spl3_76
<=> sK2(sK1,n) = sK2(int_zero,sK2(sK1,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_76])]) ).
fof(f237,plain,
( spl3_30
<=> int_less(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f518,plain,
( sK2(sK1,n) = sK2(int_zero,sK2(sK1,n))
| ~ spl3_30
| ~ spl3_58 ),
inference(resolution,[],[f505,f239]) ).
fof(f239,plain,
( int_less(sK1,n)
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f732,plain,
( spl3_75
| ~ spl3_2
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f517,f504,f64,f729]) ).
fof(f729,plain,
( spl3_75
<=> sK2(sK0,sK1) = sK2(int_zero,sK2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_75])]) ).
fof(f517,plain,
( sK2(sK0,sK1) = sK2(int_zero,sK2(sK0,sK1))
| ~ spl3_2
| ~ spl3_58 ),
inference(resolution,[],[f505,f66]) ).
fof(f727,plain,
( spl3_74
| ~ spl3_28
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f516,f504,f223,f724]) ).
fof(f724,plain,
( spl3_74
<=> sK2(int_one,sK0) = sK2(int_zero,sK2(int_one,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_74])]) ).
fof(f223,plain,
( spl3_28
<=> int_less(int_one,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f516,plain,
( sK2(int_one,sK0) = sK2(int_zero,sK2(int_one,sK0))
| ~ spl3_28
| ~ spl3_58 ),
inference(resolution,[],[f505,f225]) ).
fof(f225,plain,
( int_less(int_one,sK0)
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f721,plain,
( spl3_73
| ~ spl3_14
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f514,f504,f120,f718]) ).
fof(f718,plain,
( spl3_73
<=> sK2(int_zero,sK0) = sK2(int_zero,sK2(int_zero,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_73])]) ).
fof(f514,plain,
( sK2(int_zero,sK0) = sK2(int_zero,sK2(int_zero,sK0))
| ~ spl3_14
| ~ spl3_58 ),
inference(resolution,[],[f505,f122]) ).
fof(f716,plain,
( spl3_72
| ~ spl3_32
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f442,f434,f249,f714]) ).
fof(f714,plain,
( spl3_72
<=> ! [X9] :
( int_less(sK0,X9)
| sK0 = X9
| int_less(X9,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).
fof(f442,plain,
( ! [X9] :
( int_less(sK0,X9)
| sK0 = X9
| int_less(X9,sK1) )
| ~ spl3_32
| ~ spl3_52 ),
inference(resolution,[],[f435,f250]) ).
fof(f686,plain,
( spl3_71
| ~ spl3_12
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f595,f394,f109,f683]) ).
fof(f595,plain,
( int_leq(int_zero,sK1)
| ~ spl3_12
| ~ spl3_48 ),
inference(resolution,[],[f396,f110]) ).
fof(f655,plain,
( spl3_70
| ~ spl3_19
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f339,f223,f160,f652]) ).
fof(f339,plain,
( sK0 = plus(int_one,sK2(int_one,sK0))
| ~ spl3_19
| ~ spl3_28 ),
inference(resolution,[],[f225,f161]) ).
fof(f650,plain,
( spl3_69
| ~ spl3_19
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f328,f237,f160,f647]) ).
fof(f328,plain,
( n = plus(sK1,sK2(sK1,n))
| ~ spl3_19
| ~ spl3_30 ),
inference(resolution,[],[f239,f161]) ).
fof(f645,plain,
( spl3_68
| ~ spl3_14
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f166,f160,f120,f642]) ).
fof(f166,plain,
( sK0 = plus(int_zero,sK2(int_zero,sK0))
| ~ spl3_14
| ~ spl3_19 ),
inference(resolution,[],[f161,f122]) ).
fof(f625,plain,
( spl3_67
| ~ spl3_18
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f340,f223,f147,f623]) ).
fof(f340,plain,
( ! [X0] :
( int_less(X0,sK0)
| ~ int_less(X0,int_one) )
| ~ spl3_18
| ~ spl3_28 ),
inference(resolution,[],[f225,f148]) ).
fof(f621,plain,
( spl3_66
| ~ spl3_18
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f329,f237,f147,f619]) ).
fof(f329,plain,
( ! [X0] :
( int_less(X0,n)
| ~ int_less(X0,sK1) )
| ~ spl3_18
| ~ spl3_30 ),
inference(resolution,[],[f239,f148]) ).
fof(f617,plain,
( spl3_65
| ~ spl3_14
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f158,f147,f120,f615]) ).
fof(f615,plain,
( spl3_65
<=> ! [X5] :
( int_less(X5,sK0)
| ~ int_less(X5,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
fof(f158,plain,
( ! [X5] :
( int_less(X5,sK0)
| ~ int_less(X5,int_zero) )
| ~ spl3_14
| ~ spl3_18 ),
inference(resolution,[],[f148,f122]) ).
fof(f613,plain,
( spl3_64
| ~ spl3_8
| ~ spl3_48 ),
inference(avatar_split_clause,[],[f591,f394,f93,f610]) ).
fof(f591,plain,
( int_leq(int_one,sK1)
| ~ spl3_8
| ~ spl3_48 ),
inference(resolution,[],[f396,f94]) ).
fof(f590,plain,
( spl3_63
| ~ spl3_3
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f366,f361,f69,f587]) ).
fof(f366,plain,
( int_less(sK1,int_one)
| ~ spl3_3
| ~ spl3_44 ),
inference(resolution,[],[f362,f71]) ).
fof(f71,plain,
( int_leq(sK1,n)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f566,plain,
( spl3_62
| ~ spl3_17
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f180,f177,f143,f564]) ).
fof(f180,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,[],[f178,f144]) ).
fof(f532,plain,
( spl3_61
| ~ spl3_15
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f185,f177,f129,f530]) ).
fof(f185,plain,
( ! [X3,X6,X4,X5] :
( int_leq(plus(X5,X6),plus(X4,X3))
| ~ int_leq(X6,X4)
| ~ int_less(X5,X3) )
| ~ spl3_15
| ~ spl3_21 ),
inference(superposition,[],[f178,f130]) ).
fof(f528,plain,
( spl3_60
| ~ spl3_10
| spl3_42 ),
inference(avatar_split_clause,[],[f347,f343,f101,f525]) ).
fof(f347,plain,
( int_less(n,sK0)
| ~ spl3_10
| spl3_42 ),
inference(resolution,[],[f345,f102]) ).
fof(f523,plain,
( spl3_59
| ~ spl3_15
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f182,f177,f129,f521]) ).
fof(f182,plain,
( ! [X3,X6,X4,X5] :
( int_leq(plus(X4,X3),plus(X5,X6))
| ~ int_leq(X4,X6)
| ~ int_less(X3,X5) )
| ~ spl3_15
| ~ spl3_21 ),
inference(superposition,[],[f178,f130]) ).
fof(f506,plain,
( spl3_58
| ~ spl3_7
| ~ spl3_15
| ~ spl3_16
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f167,f160,f137,f129,f89,f504]) ).
fof(f89,plain,
( spl3_7
<=> ! [X0] : plus(X0,int_zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f167,plain,
( ! [X0,X1] :
( sK2(X0,X1) = sK2(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) )
| ~ spl3_7
| ~ spl3_15
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f165,f132]) ).
fof(f132,plain,
( ! [X0] : plus(int_zero,X0) = X0
| ~ spl3_7
| ~ spl3_15 ),
inference(superposition,[],[f130,f90]) ).
fof(f90,plain,
( ! [X0] : plus(X0,int_zero) = X0
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f165,plain,
( ! [X0,X1] :
( sK2(X0,X1) = plus(int_zero,sK2(int_zero,sK2(X0,X1)))
| ~ int_less(X0,X1) )
| ~ spl3_16
| ~ spl3_19 ),
inference(resolution,[],[f161,f138]) ).
fof(f472,plain,
( spl3_57
| ~ spl3_7
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f184,f177,f89,f470]) ).
fof(f184,plain,
( ! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_leq(X2,int_zero)
| ~ int_less(X1,X0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(superposition,[],[f178,f90]) ).
fof(f468,plain,
( spl3_56
| ~ spl3_7
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f181,f177,f89,f466]) ).
fof(f181,plain,
( ! [X2,X0,X1] :
( int_leq(X0,plus(X1,X2))
| ~ int_leq(int_zero,X2)
| ~ int_less(X0,X1) )
| ~ spl3_7
| ~ spl3_21 ),
inference(superposition,[],[f178,f90]) ).
fof(f464,plain,
( spl3_55
| ~ spl3_15
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f173,f169,f129,f462]) ).
fof(f173,plain,
( ! [X2,X3,X4] :
( plus(X3,X2) != X4
| ~ int_less(int_zero,X3)
| int_less(X2,X4) )
| ~ spl3_15
| ~ spl3_20 ),
inference(superposition,[],[f170,f130]) ).
fof(f460,plain,
( spl3_54
| ~ spl3_28
| ~ spl3_32 ),
inference(avatar_split_clause,[],[f338,f249,f223,f457]) ).
fof(f338,plain,
( int_less(int_one,sK1)
| ~ spl3_28
| ~ spl3_32 ),
inference(resolution,[],[f225,f250]) ).
fof(f455,plain,
( spl3_53
| ~ spl3_16
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f157,f147,f137,f453]) ).
fof(f157,plain,
( ! [X2,X3,X4] :
( int_less(X2,sK2(X3,X4))
| ~ int_less(X2,int_zero)
| ~ int_less(X3,X4) )
| ~ spl3_16
| ~ spl3_18 ),
inference(resolution,[],[f148,f138]) ).
fof(f436,plain,
( spl3_52
| ~ spl3_10
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f152,f143,f101,f434]) ).
fof(f152,plain,
( ! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| int_less(X1,X0) )
| ~ spl3_10
| ~ spl3_17 ),
inference(resolution,[],[f144,f102]) ).
fof(f417,plain,
( spl3_51
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f175,f169,f415]) ).
fof(f175,plain,
( ! [X0,X1] :
( ~ int_less(int_zero,X0)
| int_less(X1,plus(X1,X0)) )
| ~ spl3_20 ),
inference(equality_resolution,[],[f170]) ).
fof(f413,plain,
( spl3_50
| ~ spl3_12
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f141,f137,f109,f411]) ).
fof(f141,plain,
( ! [X2,X3] :
( ~ int_less(X2,X3)
| int_leq(int_zero,sK2(X2,X3)) )
| ~ spl3_12
| ~ spl3_16 ),
inference(resolution,[],[f138,f110]) ).
fof(f409,plain,
( spl3_49
| ~ spl3_8
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f140,f137,f93,f407]) ).
fof(f140,plain,
( ! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(int_one,sK2(X0,X1)) )
| ~ spl3_8
| ~ spl3_16 ),
inference(resolution,[],[f138,f94]) ).
fof(f397,plain,
( spl3_48
| ~ spl3_14
| ~ spl3_32 ),
inference(avatar_split_clause,[],[f252,f249,f120,f394]) ).
fof(f252,plain,
( int_less(int_zero,sK1)
| ~ spl3_14
| ~ spl3_32 ),
inference(resolution,[],[f250,f122]) ).
fof(f392,plain,
( spl3_47
| ~ spl3_6
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f164,f160,f84,f389]) ).
fof(f164,plain,
( int_one = plus(int_zero,sK2(int_zero,int_one))
| ~ spl3_6
| ~ spl3_19 ),
inference(resolution,[],[f161,f86]) ).
fof(f86,plain,
( int_less(int_zero,int_one)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f374,plain,
( spl3_46
| ~ spl3_6
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f156,f147,f84,f372]) ).
fof(f372,plain,
( spl3_46
<=> ! [X1] :
( int_less(X1,int_one)
| ~ int_less(X1,int_zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).
fof(f156,plain,
( ! [X1] :
( int_less(X1,int_one)
| ~ int_less(X1,int_zero) )
| ~ spl3_6
| ~ spl3_18 ),
inference(resolution,[],[f148,f86]) ).
fof(f370,plain,
( spl3_45
| ~ spl3_9
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f118,f101,f97,f368]) ).
fof(f118,plain,
( ! [X0] :
( int_less(X0,int_one)
| int_less(int_zero,X0) )
| ~ spl3_9
| ~ spl3_10 ),
inference(resolution,[],[f102,f98]) ).
fof(f363,plain,
( spl3_44
| ~ spl3_10
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f336,f188,f101,f361]) ).
fof(f336,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| int_less(X0,int_one) )
| ~ spl3_10
| ~ spl3_22 ),
inference(resolution,[],[f189,f102]) ).
fof(f352,plain,
( spl3_43
| ~ spl3_7
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f132,f129,f89,f350]) ).
fof(f346,plain,
( ~ spl3_42
| ~ spl3_1
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f335,f188,f59,f343]) ).
fof(f335,plain,
( ~ int_leq(sK0,n)
| ~ spl3_1
| ~ spl3_22 ),
inference(resolution,[],[f189,f61]) ).
fof(f334,plain,
( spl3_41
| ~ spl3_10
| ~ spl3_23
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f325,f219,f191,f101,f332]) ).
fof(f332,plain,
( spl3_41
<=> ! [X2,X1] :
( int_less(X2,sK0)
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
fof(f219,plain,
( spl3_27
<=> int_one = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f325,plain,
( ! [X2,X1] :
( int_less(X2,sK0)
| ~ int_leq(sK0,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1) )
| ~ spl3_10
| ~ spl3_23
| ~ spl3_27 ),
inference(forward_demodulation,[],[f324,f221]) ).
fof(f221,plain,
( int_one = sK0
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f324,plain,
( ! [X2,X1] :
( ~ int_leq(sK0,X1)
| ~ int_leq(X1,n)
| real_one = a(X2,X2)
| ~ int_leq(X2,X1)
| int_less(X2,int_one) )
| ~ spl3_10
| ~ spl3_23
| ~ spl3_27 ),
inference(forward_demodulation,[],[f195,f221]) ).
fof(f315,plain,
( spl3_40
| ~ spl3_22
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f309,f219,f188,f313]) ).
fof(f313,plain,
( spl3_40
<=> ! [X0] :
( ~ int_leq(sK0,X0)
| ~ int_leq(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
fof(f309,plain,
( ! [X0] :
( ~ int_leq(sK0,X0)
| ~ int_leq(X0,n) )
| ~ spl3_22
| ~ spl3_27 ),
inference(forward_demodulation,[],[f189,f221]) ).
fof(f308,plain,
( spl3_39
| ~ spl3_22
| ~ spl3_27
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f303,f233,f219,f188,f306]) ).
fof(f306,plain,
( spl3_39
<=> ! [X0] :
( ~ int_leq(sK0,X0)
| ~ int_leq(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
fof(f303,plain,
( ! [X0] :
( ~ int_leq(sK0,X0)
| ~ int_leq(X0,sK1) )
| ~ spl3_22
| ~ spl3_27
| ~ spl3_29 ),
inference(forward_demodulation,[],[f302,f221]) ).
fof(f302,plain,
( ! [X0] :
( ~ int_leq(X0,sK1)
| ~ int_leq(int_one,X0) )
| ~ spl3_22
| ~ spl3_29 ),
inference(forward_demodulation,[],[f189,f235]) ).
fof(f301,plain,
( spl3_37
| spl3_38
| ~ spl3_1
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f194,f191,f59,f299,f295]) ).
fof(f295,plain,
( spl3_37
<=> real_one = a(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f299,plain,
( spl3_38
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f194,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| real_one = a(sK0,sK0)
| ~ int_leq(sK0,X0) )
| ~ spl3_1
| ~ spl3_23 ),
inference(resolution,[],[f192,f61]) ).
fof(f286,plain,
( spl3_36
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f127,f113,f284]) ).
fof(f113,plain,
( spl3_13
<=> ! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f127,plain,
( ! [X0] : int_leq(X0,X0)
| ~ spl3_13 ),
inference(equality_resolution,[],[f114]) ).
fof(f114,plain,
( ! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f281,plain,
( spl3_35
| ~ spl3_6
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f126,f109,f84,f278]) ).
fof(f278,plain,
( spl3_35
<=> int_leq(int_zero,int_one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f126,plain,
( int_leq(int_zero,int_one)
| ~ spl3_6
| ~ spl3_12 ),
inference(resolution,[],[f110,f86]) ).
fof(f276,plain,
( spl3_34
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f124,f105,f274]) ).
fof(f105,plain,
( spl3_11
<=> ! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f124,plain,
( ! [X0] : ~ int_less(X0,X0)
| ~ spl3_11 ),
inference(equality_resolution,[],[f106]) ).
fof(f106,plain,
( ! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f257,plain,
( spl3_33
| ~ spl3_2
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f163,f160,f64,f254]) ).
fof(f163,plain,
( sK1 = plus(sK0,sK2(sK0,sK1))
| ~ spl3_2
| ~ spl3_19 ),
inference(resolution,[],[f161,f66]) ).
fof(f251,plain,
( spl3_32
| ~ spl3_2
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f155,f147,f64,f249]) ).
fof(f155,plain,
( ! [X0] :
( int_less(X0,sK1)
| ~ int_less(X0,sK0) )
| ~ spl3_2
| ~ spl3_18 ),
inference(resolution,[],[f148,f66]) ).
fof(f247,plain,
( spl3_31
| ~ spl3_12
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f154,f120,f109,f244]) ).
fof(f244,plain,
( spl3_31
<=> int_leq(int_zero,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f154,plain,
( int_leq(int_zero,sK0)
| ~ spl3_12
| ~ spl3_14 ),
inference(resolution,[],[f122,f110]) ).
fof(f240,plain,
( spl3_29
| spl3_30
| ~ spl3_3
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f151,f143,f69,f237,f233]) ).
fof(f151,plain,
( int_less(sK1,n)
| n = sK1
| ~ spl3_3
| ~ spl3_17 ),
inference(resolution,[],[f144,f71]) ).
fof(f226,plain,
( spl3_27
| spl3_28
| ~ spl3_1
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f150,f143,f59,f223,f219]) ).
fof(f150,plain,
( int_less(int_one,sK0)
| int_one = sK0
| ~ spl3_1
| ~ spl3_17 ),
inference(resolution,[],[f144,f61]) ).
fof(f208,plain,
spl3_26,
inference(avatar_split_clause,[],[f41,f206]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
& ! [X5] :
( ! [X6] :
( real_zero = a(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6) )
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
& ! [X5] :
( ! [X6] :
( real_zero = a(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6) )
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( plus(X0,X2) = X1
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> real_zero = a(X3,plus(X3,X2)) ) )
& ! [X4] :
( ( int_leq(X4,X1)
& int_leq(int_one,X4) )
=> real_one = a(X4,X4) )
& ! [X5] :
( ( plus(X1,X5) = X0
& int_less(int_zero,X5) )
=> ! [X6] :
( ( int_leq(X6,X1)
& int_leq(int_one,X6) )
=> real_zero = a(plus(X6,X5),X6) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X7] :
( ( plus(X0,X7) = X1
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X0)
& int_leq(int_one,X2) )
=> real_zero = a(X2,plus(X2,X7)) ) )
& ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> real_one = a(X2,X2) )
& ! [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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',qii) ).
fof(f204,plain,
( spl3_25
| ~ spl3_2
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f125,f109,f64,f201]) ).
fof(f125,plain,
( int_leq(sK0,sK1)
| ~ spl3_2
| ~ spl3_12 ),
inference(resolution,[],[f110,f66]) ).
fof(f199,plain,
spl3_24,
inference(avatar_split_clause,[],[f39,f197]) ).
fof(f39,plain,
! [X0,X1,X6,X5] :
( real_zero = a(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6)
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f193,plain,
( spl3_22
| spl3_23 ),
inference(avatar_split_clause,[],[f40,f191,f188]) ).
fof(f40,plain,
! [X0,X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f179,plain,
spl3_21,
inference(avatar_split_clause,[],[f57,f177]) ).
fof(f57,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',plus_and_order1) ).
fof(f171,plain,
spl3_20,
inference(avatar_split_clause,[],[f52,f169]) ).
fof(f52,plain,
! [X2,X0,X1] :
( int_less(X0,X1)
| ~ int_less(int_zero,X2)
| plus(X0,X2) != 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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',plus_and_inverse) ).
fof(f162,plain,
spl3_19,
inference(avatar_split_clause,[],[f50,f160]) ).
fof(f50,plain,
! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f149,plain,
spl3_18,
inference(avatar_split_clause,[],[f56,f147]) ).
fof(f56,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',int_less_transitive) ).
fof(f145,plain,
spl3_17,
inference(avatar_split_clause,[],[f53,f143]) ).
fof(f53,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',int_leq) ).
fof(f139,plain,
spl3_16,
inference(avatar_split_clause,[],[f51,f137]) ).
fof(f51,plain,
! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f131,plain,
spl3_15,
inference(avatar_split_clause,[],[f47,f129]) ).
fof(f47,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',plus_commutative) ).
fof(f123,plain,
( spl3_14
| ~ spl3_1
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f117,f97,f59,f120]) ).
fof(f117,plain,
( int_less(int_zero,sK0)
| ~ spl3_1
| ~ spl3_9 ),
inference(resolution,[],[f98,f61]) ).
fof(f115,plain,
spl3_13,
inference(avatar_split_clause,[],[f55,f113]) ).
fof(f55,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f111,plain,
spl3_12,
inference(avatar_split_clause,[],[f54,f109]) ).
fof(f54,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f107,plain,
spl3_11,
inference(avatar_split_clause,[],[f49,f105]) ).
fof(f49,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',int_less_irreflexive) ).
fof(f103,plain,
spl3_10,
inference(avatar_split_clause,[],[f48,f101]) ).
fof(f48,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',int_less_total) ).
fof(f99,plain,
spl3_9,
inference(avatar_split_clause,[],[f46,f97]) ).
fof(f46,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/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',one_successor_of_zero) ).
fof(f95,plain,
spl3_8,
inference(avatar_split_clause,[],[f45,f93]) ).
fof(f45,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f91,plain,
spl3_7,
inference(avatar_split_clause,[],[f44,f89]) ).
fof(f44,plain,
! [X0] : plus(X0,int_zero) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : plus(X0,int_zero) = X0,
file('/export/starexec/sandbox/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',plus_zero) ).
fof(f87,plain,
spl3_6,
inference(avatar_split_clause,[],[f43,f84]) ).
fof(f43,plain,
int_less(int_zero,int_one),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
int_less(int_zero,int_one),
file('/export/starexec/sandbox/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',int_zero_one) ).
fof(f82,plain,
~ spl3_5,
inference(avatar_split_clause,[],[f42,f79]) ).
fof(f79,plain,
( spl3_5
<=> real_zero = real_one ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f42,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',real_constants) ).
fof(f77,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f38,f74]) ).
fof(f38,plain,
real_zero != a(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( real_zero != a(sK0,sK1)
& int_leq(sK1,n)
& int_less(sK0,sK1)
& int_leq(int_one,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f26]) ).
fof(f26,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> ( real_zero != a(sK0,sK1)
& int_leq(sK1,n)
& int_less(sK0,sK1)
& int_leq(int_one,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.vWQVAf3xMF/Vampire---4.8_4428',lt) ).
fof(f72,plain,
spl3_3,
inference(avatar_split_clause,[],[f37,f69]) ).
fof(f37,plain,
int_leq(sK1,n),
inference(cnf_transformation,[],[f27]) ).
fof(f67,plain,
spl3_2,
inference(avatar_split_clause,[],[f36,f64]) ).
fof(f36,plain,
int_less(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
fof(f62,plain,
spl3_1,
inference(avatar_split_clause,[],[f35,f59]) ).
fof(f35,plain,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV486+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 30 18:00:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % (4536)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (4537)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.42 % (4538)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.42 % (4539)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.42 % (4540)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42 % (4541)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.42 % (4542)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.42 % (4543)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 TRYING [3]
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 TRYING [4]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [5]
% 0.22/0.45 TRYING [6]
% 0.22/0.46 TRYING [4]
% 0.22/0.48 TRYING [7]
% 0.22/0.49 TRYING [5]
% 0.22/0.53 TRYING [8]
% 1.00/0.59 % (4541)First to succeed.
% 1.00/0.60 % (4541)Refutation found. Thanks to Tanya!
% 1.00/0.60 % SZS status Theorem for Vampire---4
% 1.00/0.60 % SZS output start Proof for Vampire---4
% See solution above
% 1.00/0.60 % (4541)------------------------------
% 1.00/0.60 % (4541)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.00/0.60 % (4541)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.00/0.60 % (4541)Termination reason: Refutation
% 1.00/0.60
% 1.00/0.60 % (4541)Memory used [KB]: 8187
% 1.00/0.60 % (4541)Time elapsed: 0.172 s
% 1.00/0.60 % (4541)------------------------------
% 1.00/0.60 % (4541)------------------------------
% 1.00/0.60 % (4536)Success in time 0.217 s
% 1.00/0.60 % Vampire---4.8 exiting
%------------------------------------------------------------------------------