TSTP Solution File: DAT038_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT038_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May 5 05:05:42 EDT 2024
% Result : Theorem 134.52s 19.51s
% Output : Refutation 134.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 637
% Syntax : Number of formulae : 2152 ( 60 unt; 7 typ; 0 def)
% Number of atoms : 7240 (1485 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 8971 (3876 ~;4437 |; 34 &)
% ( 619 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 9942 (1396 atm;3315 fun;2012 num;3219 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 609 ( 605 usr; 605 prp; 0-2 aty)
% Number of functors : 15 ( 5 usr; 9 con; 0-2 aty)
% Number of variables : 3619 (3616 !; 3 ?;3619 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_12,type,
sK0: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f97066,plain,
$false,
inference(avatar_sat_refutation,[],[f92,f97,f102,f107,f111,f115,f119,f124,f130,f134,f138,f142,f146,f150,f154,f160,f164,f168,f172,f182,f186,f190,f204,f208,f212,f216,f224,f228,f232,f277,f281,f285,f289,f319,f323,f327,f331,f336,f363,f378,f383,f388,f413,f418,f423,f448,f452,f456,f471,f475,f479,f483,f538,f542,f561,f565,f569,f573,f594,f636,f640,f644,f648,f652,f656,f835,f839,f843,f905,f909,f913,f917,f921,f925,f929,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1323,f1327,f1331,f1335,f1339,f1343,f1445,f1449,f1453,f1457,f1494,f1535,f1539,f1569,f1573,f1577,f1581,f1645,f1649,f1653,f1657,f1685,f1689,f1693,f1697,f1701,f1705,f1709,f1782,f1786,f1790,f1794,f1828,f1832,f1836,f1840,f1901,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1946,f1950,f1954,f1958,f1962,f2398,f2402,f2406,f2410,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2614,f3106,f3110,f3114,f3118,f3122,f3126,f3130,f3134,f3138,f3468,f3472,f3476,f3480,f3484,f3488,f3492,f3507,f3511,f3515,f3519,f3523,f3527,f3531,f3535,f3539,f3543,f3558,f4329,f5101,f5127,f5131,f5135,f5139,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5180,f5184,f5188,f5192,f5196,f5200,f5204,f5208,f6483,f7531,f7564,f7568,f7572,f7576,f7580,f7584,f7588,f7592,f7596,f7600,f7604,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7675,f7679,f7683,f7687,f7691,f8024,f8949,f10588,f10645,f10649,f10653,f10657,f10661,f10665,f10669,f10673,f10677,f10681,f10685,f10689,f10693,f10697,f10701,f10705,f10709,f10713,f10717,f10721,f10770,f10774,f10778,f10782,f10786,f10790,f10794,f10798,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f19000,f19289,f19293,f19297,f19301,f19305,f19309,f19313,f19331,f19335,f19339,f19343,f19347,f19351,f19355,f19359,f19363,f19367,f19420,f19424,f19428,f19432,f19436,f19440,f19444,f19448,f19452,f19456,f19460,f19464,f19468,f19472,f19476,f19480,f19484,f33523,f38144,f39533,f39537,f39541,f39545,f39549,f39553,f39557,f39561,f39565,f39569,f39573,f39577,f39581,f39585,f39589,f39593,f39597,f39601,f39605,f39609,f39613,f39617,f39621,f39625,f41622,f42614,f42962,f42966,f42970,f42974,f42978,f42982,f42986,f42990,f42994,f43038,f43042,f43046,f43050,f43054,f43058,f43062,f43066,f43070,f43074,f43078,f43082,f43086,f43090,f43094,f43098,f43102,f43106,f43110,f43114,f43118,f43142,f43146,f43150,f43154,f43158,f43162,f43166,f43170,f47057,f54303,f55109,f55113,f55117,f55121,f55125,f55146,f55150,f55154,f55158,f55162,f55166,f55170,f55174,f55178,f55182,f55235,f55239,f55243,f55247,f55251,f55256,f55261,f55265,f55269,f55273,f55277,f55281,f55285,f55289,f55293,f55297,f55301,f55305,f55309,f55313,f55317,f55361,f55365,f55369,f55373,f55377,f55381,f55385,f55389,f55393,f55397,f55401,f55405,f55409,f60755,f76970,f76974,f76978,f76982,f76986,f76990,f76994,f76998,f77002,f78905,f79175,f79179,f79183,f79187,f79191,f79195,f79199,f79220,f79224,f79228,f79232,f79236,f80485,f80489,f80493,f80550,f80554,f80558,f80562,f80566,f80570,f80574,f80578,f80582,f80586,f80630,f80634,f80638,f83831,f84347,f84415,f84419,f84423,f84427,f84431,f84435,f84439,f84443,f87200,f87204,f87208,f87212,f87216,f87220,f87224,f87228,f87232,f87236,f87240,f87244,f87716,f88311,f88315,f88319,f88323,f88327,f88331,f88335,f88339,f89594,f89670,f89674,f89678,f89682,f89686,f89690,f89814,f90428,f90432,f90436,f90665,f90695,f90699,f90703,f90707,f90711,f90715,f91248,f91776,f91780,f92116,f92120,f92349,f92535,f92539,f92543,f93107,f93304,f93308,f93312,f93316,f93410,f93414,f93418,f93432,f93441,f93445,f93449,f93453,f93457,f93461,f93465,f93469,f93473,f93477,f93481,f93485,f93489,f93493,f93497,f93501,f94211,f94327,f94331,f94335,f94339,f94343,f94347,f94351,f94355,f94359,f94364,f94368,f94372,f94376,f94423,f95569,f95704,f95708,f95712,f95717,f95721,f95725,f95729,f95769,f95774,f95778,f95782,f95786,f95790,f95794,f95798,f95802,f95806,f95810,f95814,f95819,f95823,f95827,f95831,f95835,f95839,f95843,f95847,f96531,f96535,f96539,f96543,f96547,f96552,f96556,f96560,f96564,f96568,f96877,f96881,f96885,f96889,f96893,f96897,f96901,f96906,f96910,f96914,f96918,f96922,f96926,f97047,f97052,f97056]) ).
tff(f97056,plain,
( ~ spl1_8
| ~ spl1_37
| ~ spl1_46
| ~ spl1_599 ),
inference(avatar_contradiction_clause,[],[f97055]) ).
tff(f97055,plain,
( $false
| ~ spl1_8
| ~ spl1_37
| ~ spl1_46
| ~ spl1_599 ),
inference(evaluation,[],[f97054]) ).
tff(f97054,plain,
( ( 0 = $sum(-1,0) )
| ~ spl1_8
| ~ spl1_37
| ~ spl1_46
| ~ spl1_599 ),
inference(forward_demodulation,[],[f97053,f123]) ).
tff(f123,plain,
( ( 0 = count(empty) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f121,plain,
( spl1_8
<=> ( 0 = count(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f97053,plain,
( ( 0 = $sum(-1,count(empty)) )
| ~ spl1_37
| ~ spl1_46
| ~ spl1_599 ),
inference(forward_demodulation,[],[f97028,f447]) ).
tff(f447,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl1_46 ),
inference(avatar_component_clause,[],[f446]) ).
tff(f446,plain,
( spl1_46
<=> ! [X0: $int] : ( 0 = count(remove(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f97028,plain,
( ( $sum(-1,count(empty)) = count(remove(3,empty)) )
| ~ spl1_37
| ~ spl1_599 ),
inference(resolution,[],[f96905,f330]) ).
tff(f330,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f329]) ).
tff(f329,plain,
( spl1_37
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
tff(f96905,plain,
( in(3,empty)
| ~ spl1_599 ),
inference(avatar_component_clause,[],[f96903]) ).
tff(f96903,plain,
( spl1_599
<=> in(3,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_599])]) ).
tff(f97052,plain,
( ~ spl1_8
| ~ spl1_28
| ~ spl1_48
| ~ spl1_599 ),
inference(avatar_contradiction_clause,[],[f97051]) ).
tff(f97051,plain,
( $false
| ~ spl1_8
| ~ spl1_28
| ~ spl1_48
| ~ spl1_599 ),
inference(evaluation,[],[f97050]) ).
tff(f97050,plain,
( ( 0 = 1 )
| ~ spl1_8
| ~ spl1_28
| ~ spl1_48
| ~ spl1_599 ),
inference(forward_demodulation,[],[f97049,f123]) ).
tff(f97049,plain,
( ( 1 = count(empty) )
| ~ spl1_28
| ~ spl1_48
| ~ spl1_599 ),
inference(forward_demodulation,[],[f97027,f455]) ).
tff(f455,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f454]) ).
tff(f454,plain,
( spl1_48
<=> ! [X0: $int] : ( 1 = count(add(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f97027,plain,
( ( count(empty) = count(add(3,empty)) )
| ~ spl1_28
| ~ spl1_599 ),
inference(resolution,[],[f96905,f227]) ).
tff(f227,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f226]) ).
tff(f226,plain,
( spl1_28
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f97047,plain,
( ~ spl1_6
| ~ spl1_599 ),
inference(avatar_contradiction_clause,[],[f97025]) ).
tff(f97025,plain,
( $false
| ~ spl1_6
| ~ spl1_599 ),
inference(resolution,[],[f96905,f114]) ).
tff(f114,plain,
( ! [X0: $int] : ~ in(X0,empty)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f113]) ).
tff(f113,plain,
( spl1_6
<=> ! [X0: $int] : ~ in(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f96926,plain,
( spl1_604
| ~ spl1_101
| ~ spl1_368 ),
inference(avatar_split_clause,[],[f55428,f55107,f1579,f96924]) ).
tff(f96924,plain,
( spl1_604
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(5,remove(5,add(5,add(X0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_604])]) ).
tff(f1579,plain,
( spl1_101
<=> ! [X0: $int] : ( count(add(X0,sK0)) = count(add(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
tff(f55107,plain,
( spl1_368
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| in(X0,remove(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_368])]) ).
tff(f55428,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(5,remove(5,add(5,add(X0,sK0)))) )
| ~ spl1_101
| ~ spl1_368 ),
inference(superposition,[],[f55108,f1580]) ).
tff(f1580,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(5,add(X0,sK0))) )
| ~ spl1_101 ),
inference(avatar_component_clause,[],[f1579]) ).
tff(f55108,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| in(X0,remove(X0,add(X0,X1))) )
| ~ spl1_368 ),
inference(avatar_component_clause,[],[f55107]) ).
tff(f96922,plain,
( spl1_603
| ~ spl1_100
| ~ spl1_368 ),
inference(avatar_split_clause,[],[f55427,f55107,f1575,f96920]) ).
tff(f96920,plain,
( spl1_603
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(3,remove(3,add(3,add(X0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_603])]) ).
tff(f1575,plain,
( spl1_100
<=> ! [X0: $int] : ( count(add(X0,sK0)) = count(add(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
tff(f55427,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(3,remove(3,add(3,add(X0,sK0)))) )
| ~ spl1_100
| ~ spl1_368 ),
inference(superposition,[],[f55108,f1576]) ).
tff(f1576,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(3,add(X0,sK0))) )
| ~ spl1_100 ),
inference(avatar_component_clause,[],[f1575]) ).
tff(f96918,plain,
( spl1_602
| ~ spl1_99
| ~ spl1_368 ),
inference(avatar_split_clause,[],[f55426,f55107,f1571,f96916]) ).
tff(f96916,plain,
( spl1_602
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(2,remove(2,add(2,add(X0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_602])]) ).
tff(f1571,plain,
( spl1_99
<=> ! [X0: $int] : ( count(add(X0,sK0)) = count(add(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
tff(f55426,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(2,remove(2,add(2,add(X0,sK0)))) )
| ~ spl1_99
| ~ spl1_368 ),
inference(superposition,[],[f55108,f1572]) ).
tff(f1572,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(2,add(X0,sK0))) )
| ~ spl1_99 ),
inference(avatar_component_clause,[],[f1571]) ).
tff(f96914,plain,
( spl1_601
| ~ spl1_102
| ~ spl1_302 ),
inference(avatar_split_clause,[],[f39649,f39531,f1643,f96912]) ).
tff(f96912,plain,
( spl1_601
<=> ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(2,remove(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_601])]) ).
tff(f1643,plain,
( spl1_102
<=> ! [X0: $int] : ( count(remove(2,add(X0,sK0))) = $sum(-1,count(add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).
tff(f39531,plain,
( spl1_302
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(remove(X0,X1))) )
| in(X0,remove(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_302])]) ).
tff(f39649,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(2,remove(2,add(X0,sK0))) )
| ~ spl1_102
| ~ spl1_302 ),
inference(evaluation,[],[f39632]) ).
tff(f39632,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-1,$sum(-1,count(add(X0,sK0)))) )
| in(2,remove(2,add(X0,sK0))) )
| ~ spl1_102
| ~ spl1_302 ),
inference(superposition,[],[f39532,f1644]) ).
tff(f1644,plain,
( ! [X0: $int] : ( count(remove(2,add(X0,sK0))) = $sum(-1,count(add(X0,sK0))) )
| ~ spl1_102 ),
inference(avatar_component_clause,[],[f1643]) ).
tff(f39532,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(remove(X0,X1))) )
| in(X0,remove(X0,X1)) )
| ~ spl1_302 ),
inference(avatar_component_clause,[],[f39531]) ).
tff(f96910,plain,
( spl1_600
| ~ spl1_104
| ~ spl1_302 ),
inference(avatar_split_clause,[],[f39648,f39531,f1651,f96908]) ).
tff(f96908,plain,
( spl1_600
<=> ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(3,remove(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_600])]) ).
tff(f1651,plain,
( spl1_104
<=> ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).
tff(f39648,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(3,remove(3,add(X0,sK0))) )
| ~ spl1_104
| ~ spl1_302 ),
inference(evaluation,[],[f39633]) ).
tff(f39633,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-1,$sum(-1,count(add(X0,sK0)))) )
| in(3,remove(3,add(X0,sK0))) )
| ~ spl1_104
| ~ spl1_302 ),
inference(superposition,[],[f39532,f1652]) ).
tff(f1652,plain,
( ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(3,add(X0,sK0))) )
| ~ spl1_104 ),
inference(avatar_component_clause,[],[f1651]) ).
tff(f96906,plain,
( spl1_599
| ~ spl1_33
| ~ spl1_587 ),
inference(avatar_split_clause,[],[f96723,f96549,f287,f96903]) ).
tff(f287,plain,
( spl1_33
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f96549,plain,
( spl1_587
<=> in(3,add(2,empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_587])]) ).
tff(f96723,plain,
( in(3,empty)
| ~ spl1_33
| ~ spl1_587 ),
inference(evaluation,[],[f96701]) ).
tff(f96701,plain,
( in(3,empty)
| ( 2 = 3 )
| ~ spl1_33
| ~ spl1_587 ),
inference(resolution,[],[f96551,f288]) ).
tff(f288,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) )
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f287]) ).
tff(f96551,plain,
( in(3,add(2,empty))
| ~ spl1_587 ),
inference(avatar_component_clause,[],[f96549]) ).
tff(f96901,plain,
( spl1_598
| ~ spl1_105
| ~ spl1_302 ),
inference(avatar_split_clause,[],[f39647,f39531,f1655,f96899]) ).
tff(f96899,plain,
( spl1_598
<=> ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(5,remove(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_598])]) ).
tff(f1655,plain,
( spl1_105
<=> ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).
tff(f39647,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-2,count(add(X0,sK0))) )
| in(5,remove(5,add(X0,sK0))) )
| ~ spl1_105
| ~ spl1_302 ),
inference(evaluation,[],[f39634]) ).
tff(f39634,plain,
( ! [X0: $int] :
( ( $sum(-1,count(add(X0,sK0))) != $sum(-1,$sum(-1,count(add(X0,sK0)))) )
| in(5,remove(5,add(X0,sK0))) )
| ~ spl1_105
| ~ spl1_302 ),
inference(superposition,[],[f39532,f1656]) ).
tff(f1656,plain,
( ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(5,add(X0,sK0))) )
| ~ spl1_105 ),
inference(avatar_component_clause,[],[f1655]) ).
tff(f96897,plain,
( spl1_597
| ~ spl1_108
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38130,f19442,f1691,f96895]) ).
tff(f96895,plain,
( spl1_597
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,add(5,remove(X0,sK0))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_597])]) ).
tff(f1691,plain,
( spl1_108
<=> ! [X0: $int] :
( ( 5 = X0 )
| ( count(remove(X0,sK0)) = count(add(5,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
tff(f19442,plain,
( spl1_289
<=> ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(add(X0,X1))) )
| ( empty = remove(X0,add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_289])]) ).
tff(f38130,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,add(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_108
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1692]) ).
tff(f1692,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = count(add(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_108 ),
inference(avatar_component_clause,[],[f1691]) ).
tff(f19443,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(add(X0,X1))) )
| ( empty = remove(X0,add(X0,X1)) ) )
| ~ spl1_289 ),
inference(avatar_component_clause,[],[f19442]) ).
tff(f96893,plain,
( spl1_596
| ~ spl1_107
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38129,f19442,f1687,f96891]) ).
tff(f96891,plain,
( spl1_596
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,add(3,remove(X0,sK0))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_596])]) ).
tff(f1687,plain,
( spl1_107
<=> ! [X0: $int] :
( ( 3 = X0 )
| ( count(remove(X0,sK0)) = count(add(3,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
tff(f38129,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,add(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_107
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1688]) ).
tff(f1688,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = count(add(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_107 ),
inference(avatar_component_clause,[],[f1687]) ).
tff(f96889,plain,
( spl1_595
| ~ spl1_106
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38128,f19442,f1683,f96887]) ).
tff(f96887,plain,
( spl1_595
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,add(2,remove(X0,sK0))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_595])]) ).
tff(f1683,plain,
( spl1_106
<=> ! [X0: $int] :
( ( 2 = X0 )
| ( count(remove(X0,sK0)) = count(add(2,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
tff(f38128,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,add(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_106
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1684]) ).
tff(f1684,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = count(add(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_106 ),
inference(avatar_component_clause,[],[f1683]) ).
tff(f96885,plain,
( spl1_594
| ~ spl1_115
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8939,f7618,f1788,f96883]) ).
tff(f96883,plain,
( spl1_594
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_594])]) ).
tff(f1788,plain,
( spl1_115
<=> ! [X0: $int] :
( ( 5 = X0 )
| ( $sum(-1,count(remove(X0,sK0))) = count(remove(5,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
tff(f7618,plain,
( spl1_212
<=> ! [X0: $int,X1: collection] :
( ( 0 != count(remove(X0,X1)) )
| ( empty = remove(X0,remove(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_212])]) ).
tff(f8939,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_115
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1789]) ).
tff(f1789,plain,
( ! [X0: $int] :
( ( $sum(-1,count(remove(X0,sK0))) = count(remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_115 ),
inference(avatar_component_clause,[],[f1788]) ).
tff(f7619,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(remove(X0,X1)) )
| ( empty = remove(X0,remove(X0,X1)) ) )
| ~ spl1_212 ),
inference(avatar_component_clause,[],[f7618]) ).
tff(f96881,plain,
( spl1_593
| ~ spl1_114
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8938,f7618,f1784,f96879]) ).
tff(f96879,plain,
( spl1_593
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_593])]) ).
tff(f1784,plain,
( spl1_114
<=> ! [X0: $int] :
( ( 3 = X0 )
| ( $sum(-1,count(remove(X0,sK0))) = count(remove(3,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
tff(f8938,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_114
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1785]) ).
tff(f1785,plain,
( ! [X0: $int] :
( ( $sum(-1,count(remove(X0,sK0))) = count(remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_114 ),
inference(avatar_component_clause,[],[f1784]) ).
tff(f96877,plain,
( spl1_592
| ~ spl1_113
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8937,f7618,f1780,f96875]) ).
tff(f96875,plain,
( spl1_592
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_592])]) ).
tff(f1780,plain,
( spl1_113
<=> ! [X0: $int] :
( ( 2 = X0 )
| ( count(remove(2,remove(X0,sK0))) = $sum(-1,count(remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
tff(f8937,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_113
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1781]) ).
tff(f1781,plain,
( ! [X0: $int] :
( ( count(remove(2,remove(X0,sK0))) = $sum(-1,count(remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_113 ),
inference(avatar_component_clause,[],[f1780]) ).
tff(f96568,plain,
( spl1_591
| ~ spl1_51
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f1821,f1788,f477,f96566]) ).
tff(f96566,plain,
( spl1_591
<=> ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_591])]) ).
tff(f477,plain,
( spl1_51
<=> ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f1821,plain,
( ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_51
| ~ spl1_115 ),
inference(superposition,[],[f478,f1789]) ).
tff(f478,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl1_51 ),
inference(avatar_component_clause,[],[f477]) ).
tff(f96564,plain,
( spl1_590
| ~ spl1_27
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f1820,f1788,f222,f96562]) ).
tff(f96562,plain,
( spl1_590
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(5,remove(X0,sK0))
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_590])]) ).
tff(f222,plain,
( spl1_27
<=> ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f1820,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(5,remove(X0,sK0))
| ( 5 = X0 ) )
| ~ spl1_27
| ~ spl1_115 ),
inference(superposition,[],[f223,f1789]) ).
tff(f223,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != count(X1) )
| ~ in(X0,X1) )
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f222]) ).
tff(f96560,plain,
( spl1_589
| ~ spl1_51
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f1811,f1784,f477,f96558]) ).
tff(f96558,plain,
( spl1_589
<=> ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_589])]) ).
tff(f1811,plain,
( ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_51
| ~ spl1_114 ),
inference(superposition,[],[f478,f1785]) ).
tff(f96556,plain,
( spl1_588
| ~ spl1_27
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f1810,f1784,f222,f96554]) ).
tff(f96554,plain,
( spl1_588
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(3,remove(X0,sK0))
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_588])]) ).
tff(f1810,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(3,remove(X0,sK0))
| ( 3 = X0 ) )
| ~ spl1_27
| ~ spl1_114 ),
inference(superposition,[],[f223,f1785]) ).
tff(f96552,plain,
( spl1_587
| ~ spl1_8
| ~ spl1_36
| ~ spl1_42
| ~ spl1_109
| ~ spl1_539
| ~ spl1_549 ),
inference(avatar_split_clause,[],[f96383,f94361,f94208,f1695,f385,f325,f121,f96549]) ).
tff(f325,plain,
( spl1_36
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f385,plain,
( spl1_42
<=> ( 1 = count(remove(5,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
tff(f1695,plain,
( spl1_109
<=> ! [X0: $int] :
( ( 2 = X0 )
| ( remove(X0,sK0) = add(2,remove(2,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
tff(f94208,plain,
( spl1_539
<=> ( empty = remove(2,remove(5,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_539])]) ).
tff(f94361,plain,
( spl1_549
<=> ( empty = remove(3,remove(5,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_549])]) ).
tff(f96383,plain,
( in(3,add(2,empty))
| ~ spl1_8
| ~ spl1_36
| ~ spl1_42
| ~ spl1_109
| ~ spl1_539
| ~ spl1_549 ),
inference(forward_demodulation,[],[f96382,f95967]) ).
tff(f95967,plain,
( ( remove(5,sK0) = add(2,empty) )
| ~ spl1_109
| ~ spl1_539 ),
inference(evaluation,[],[f95865]) ).
tff(f95865,plain,
( ( remove(5,sK0) = add(2,empty) )
| ( 2 = 5 )
| ~ spl1_109
| ~ spl1_539 ),
inference(superposition,[],[f1696,f94210]) ).
tff(f94210,plain,
( ( empty = remove(2,remove(5,sK0)) )
| ~ spl1_539 ),
inference(avatar_component_clause,[],[f94208]) ).
tff(f1696,plain,
( ! [X0: $int] :
( ( remove(X0,sK0) = add(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_109 ),
inference(avatar_component_clause,[],[f1695]) ).
tff(f96382,plain,
( in(3,remove(5,sK0))
| ~ spl1_8
| ~ spl1_36
| ~ spl1_42
| ~ spl1_549 ),
inference(trivial_inequality_removal,[],[f96381]) ).
tff(f96381,plain,
( ( 0 != 0 )
| in(3,remove(5,sK0))
| ~ spl1_8
| ~ spl1_36
| ~ spl1_42
| ~ spl1_549 ),
inference(forward_demodulation,[],[f96380,f123]) ).
tff(f96380,plain,
( ( 0 != count(empty) )
| in(3,remove(5,sK0))
| ~ spl1_36
| ~ spl1_42
| ~ spl1_549 ),
inference(evaluation,[],[f96379]) ).
tff(f96379,plain,
( ( count(empty) != $sum(-1,1) )
| in(3,remove(5,sK0))
| ~ spl1_36
| ~ spl1_42
| ~ spl1_549 ),
inference(forward_demodulation,[],[f96265,f387]) ).
tff(f387,plain,
( ( 1 = count(remove(5,sK0)) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f96265,plain,
( ( count(empty) != $sum(-1,count(remove(5,sK0))) )
| in(3,remove(5,sK0))
| ~ spl1_36
| ~ spl1_549 ),
inference(superposition,[],[f326,f94363]) ).
tff(f94363,plain,
( ( empty = remove(3,remove(5,sK0)) )
| ~ spl1_549 ),
inference(avatar_component_clause,[],[f94361]) ).
tff(f326,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) )
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f325]) ).
tff(f96547,plain,
( spl1_586
| ~ spl1_51
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1801,f1780,f477,f96545]) ).
tff(f96545,plain,
( spl1_586
<=> ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_586])]) ).
tff(f1801,plain,
( ! [X0: $int] :
( $less(0,$sum(-1,count(remove(X0,sK0))))
| ( 0 = $sum(-1,count(remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_51
| ~ spl1_113 ),
inference(superposition,[],[f478,f1781]) ).
tff(f96543,plain,
( spl1_585
| ~ spl1_27
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1800,f1780,f222,f96541]) ).
tff(f96541,plain,
( spl1_585
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(2,remove(X0,sK0))
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_585])]) ).
tff(f1800,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(-1,count(remove(X0,sK0))) )
| ~ in(2,remove(X0,sK0))
| ( 2 = X0 ) )
| ~ spl1_27
| ~ spl1_113 ),
inference(superposition,[],[f223,f1781]) ).
tff(f96539,plain,
( spl1_584
| ~ spl1_34
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f1743,f1691,f317,f96537]) ).
tff(f96537,plain,
( spl1_584
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(5,remove(X0,sK0))
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_584])]) ).
tff(f317,plain,
( spl1_34
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f1743,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(5,remove(X0,sK0))
| ( 5 = X0 ) )
| ~ spl1_34
| ~ spl1_108 ),
inference(superposition,[],[f318,f1692]) ).
tff(f318,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) )
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f317]) ).
tff(f96535,plain,
( spl1_583
| ~ spl1_34
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f1730,f1687,f317,f96533]) ).
tff(f96533,plain,
( spl1_583
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(3,remove(X0,sK0))
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_583])]) ).
tff(f1730,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(3,remove(X0,sK0))
| ( 3 = X0 ) )
| ~ spl1_34
| ~ spl1_107 ),
inference(superposition,[],[f318,f1688]) ).
tff(f96531,plain,
( spl1_582
| ~ spl1_34
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f1717,f1683,f317,f96529]) ).
tff(f96529,plain,
( spl1_582
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(2,remove(X0,sK0))
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_582])]) ).
tff(f1717,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != $sum(1,count(remove(X0,sK0))) )
| ~ in(2,remove(X0,sK0))
| ( 2 = X0 ) )
| ~ spl1_34
| ~ spl1_106 ),
inference(superposition,[],[f318,f1684]) ).
tff(f95847,plain,
( spl1_581
| ~ spl1_101
| ~ spl1_321 ),
inference(avatar_split_clause,[],[f42302,f39607,f1579,f95845]) ).
tff(f95845,plain,
( spl1_581
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(5,add(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_581])]) ).
tff(f39607,plain,
( spl1_321
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_321])]) ).
tff(f42302,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(5,add(5,add(X0,sK0))) )
| ~ spl1_101
| ~ spl1_321 ),
inference(superposition,[],[f39608,f1580]) ).
tff(f39608,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) )
| ~ spl1_321 ),
inference(avatar_component_clause,[],[f39607]) ).
tff(f95843,plain,
( spl1_580
| ~ spl1_100
| ~ spl1_321 ),
inference(avatar_split_clause,[],[f42301,f39607,f1575,f95841]) ).
tff(f95841,plain,
( spl1_580
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(3,add(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_580])]) ).
tff(f42301,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(3,add(3,add(X0,sK0))) )
| ~ spl1_100
| ~ spl1_321 ),
inference(superposition,[],[f39608,f1576]) ).
tff(f95839,plain,
( spl1_579
| ~ spl1_99
| ~ spl1_321 ),
inference(avatar_split_clause,[],[f42300,f39607,f1571,f95837]) ).
tff(f95837,plain,
( spl1_579
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(2,add(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_579])]) ).
tff(f42300,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(2,add(2,add(X0,sK0))) )
| ~ spl1_99
| ~ spl1_321 ),
inference(superposition,[],[f39608,f1572]) ).
tff(f95835,plain,
( spl1_578
| ~ spl1_101
| ~ spl1_304 ),
inference(avatar_split_clause,[],[f39672,f39539,f1579,f95833]) ).
tff(f95833,plain,
( spl1_578
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(5,add(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_578])]) ).
tff(f39539,plain,
( spl1_304
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_304])]) ).
tff(f39672,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(5,add(5,add(X0,sK0))) )
| ~ spl1_101
| ~ spl1_304 ),
inference(superposition,[],[f39540,f1580]) ).
tff(f39540,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) )
| ~ spl1_304 ),
inference(avatar_component_clause,[],[f39539]) ).
tff(f95831,plain,
( spl1_577
| ~ spl1_100
| ~ spl1_304 ),
inference(avatar_split_clause,[],[f39671,f39539,f1575,f95829]) ).
tff(f95829,plain,
( spl1_577
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(3,add(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_577])]) ).
tff(f39671,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(3,add(3,add(X0,sK0))) )
| ~ spl1_100
| ~ spl1_304 ),
inference(superposition,[],[f39540,f1576]) ).
tff(f95827,plain,
( spl1_576
| ~ spl1_99
| ~ spl1_304 ),
inference(avatar_split_clause,[],[f39670,f39539,f1571,f95825]) ).
tff(f95825,plain,
( spl1_576
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(2,add(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_576])]) ).
tff(f39670,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(2,add(2,add(X0,sK0))) )
| ~ spl1_99
| ~ spl1_304 ),
inference(superposition,[],[f39540,f1572]) ).
tff(f95823,plain,
( spl1_575
| ~ spl1_113
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38097,f19438,f1780,f95821]) ).
tff(f95821,plain,
( spl1_575
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_575])]) ).
tff(f19438,plain,
( spl1_288
<=> ! [X0: $int,X1: collection] :
( ( 0 != $sum(1,count(remove(X0,X1))) )
| ( empty = add(X0,remove(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_288])]) ).
tff(f38097,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_113
| ~ spl1_288 ),
inference(evaluation,[],[f38089]) ).
tff(f38089,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(remove(X0,sK0)))) )
| ( empty = add(2,remove(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_113
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1781]) ).
tff(f19439,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(1,count(remove(X0,X1))) )
| ( empty = add(X0,remove(X0,X1)) ) )
| ~ spl1_288 ),
inference(avatar_component_clause,[],[f19438]) ).
tff(f95819,plain,
( spl1_574
| ~ spl1_40
| ~ spl1_115
| ~ spl1_535 ),
inference(avatar_split_clause,[],[f93938,f93487,f1788,f375,f95816]) ).
tff(f95816,plain,
( spl1_574
<=> ( empty = remove(5,remove(2,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_574])]) ).
tff(f375,plain,
( spl1_40
<=> ( 1 = count(remove(2,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
tff(f93487,plain,
( spl1_535
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(2,sK0)) )
| ( 1 = count(remove(X0,remove(2,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_535])]) ).
tff(f93938,plain,
( ( empty = remove(5,remove(2,sK0)) )
| ~ spl1_40
| ~ spl1_115
| ~ spl1_535 ),
inference(evaluation,[],[f93937]) ).
tff(f93937,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(5,remove(2,sK0)) )
| ~ spl1_40
| ~ spl1_115
| ~ spl1_535 ),
inference(forward_demodulation,[],[f93933,f377]) ).
tff(f377,plain,
( ( 1 = count(remove(2,sK0)) )
| ~ spl1_40 ),
inference(avatar_component_clause,[],[f375]) ).
tff(f93933,plain,
( ( 1 = $sum(-1,count(remove(2,sK0))) )
| ( empty = remove(5,remove(2,sK0)) )
| ~ spl1_115
| ~ spl1_535 ),
inference(evaluation,[],[f93851]) ).
tff(f93851,plain,
( ( 1 = $sum(-1,count(remove(2,sK0))) )
| ( empty = remove(5,remove(2,sK0)) )
| ( 2 = 5 )
| ~ spl1_115
| ~ spl1_535 ),
inference(superposition,[],[f93488,f1789]) ).
tff(f93488,plain,
( ! [X0: $int] :
( ( 1 = count(remove(X0,remove(2,sK0))) )
| ( empty = remove(X0,remove(2,sK0)) ) )
| ~ spl1_535 ),
inference(avatar_component_clause,[],[f93487]) ).
tff(f95814,plain,
( spl1_573
| ~ spl1_114
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38096,f19438,f1784,f95812]) ).
tff(f95812,plain,
( spl1_573
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_573])]) ).
tff(f38096,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_114
| ~ spl1_288 ),
inference(evaluation,[],[f38090]) ).
tff(f38090,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(remove(X0,sK0)))) )
| ( empty = add(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_114
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1785]) ).
tff(f95810,plain,
( spl1_572
| ~ spl1_115
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38095,f19438,f1788,f95808]) ).
tff(f95808,plain,
( spl1_572
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_572])]) ).
tff(f38095,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_115
| ~ spl1_288 ),
inference(evaluation,[],[f38091]) ).
tff(f38091,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(remove(X0,sK0)))) )
| ( empty = add(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_115
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1789]) ).
tff(f95806,plain,
( spl1_571
| ~ spl1_108
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8972,f7622,f1691,f95804]) ).
tff(f95804,plain,
( spl1_571
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,add(5,remove(X0,sK0))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_571])]) ).
tff(f7622,plain,
( spl1_213
<=> ! [X0: $int,X1: collection] :
( ( 0 != count(add(X0,X1)) )
| ( empty = add(X0,add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_213])]) ).
tff(f8972,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,add(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_108
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1692]) ).
tff(f7623,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(add(X0,X1)) )
| ( empty = add(X0,add(X0,X1)) ) )
| ~ spl1_213 ),
inference(avatar_component_clause,[],[f7622]) ).
tff(f95802,plain,
( spl1_570
| ~ spl1_107
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8971,f7622,f1687,f95800]) ).
tff(f95800,plain,
( spl1_570
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,add(3,remove(X0,sK0))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_570])]) ).
tff(f8971,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,add(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_107
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1688]) ).
tff(f95798,plain,
( spl1_569
| ~ spl1_106
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8970,f7622,f1683,f95796]) ).
tff(f95796,plain,
( spl1_569
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,add(2,remove(X0,sK0))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_569])]) ).
tff(f8970,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,add(2,remove(X0,sK0))) )
| ( 2 = X0 ) )
| ~ spl1_106
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1684]) ).
tff(f95794,plain,
( spl1_568
| ~ spl1_15
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f1822,f1788,f152,f95792]) ).
tff(f95792,plain,
( spl1_568
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,remove(X0,sK0)) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_568])]) ).
tff(f152,plain,
( spl1_15
<=> ! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f1822,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(5,remove(X0,sK0)) )
| ( 5 = X0 ) )
| ~ spl1_15
| ~ spl1_115 ),
inference(superposition,[],[f153,f1789]) ).
tff(f153,plain,
( ! [X0: collection] :
( ( 0 != count(X0) )
| ( empty = X0 ) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f152]) ).
tff(f95790,plain,
( spl1_567
| ~ spl1_15
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f1812,f1784,f152,f95788]) ).
tff(f95788,plain,
( spl1_567
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,remove(X0,sK0)) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_567])]) ).
tff(f1812,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(3,remove(X0,sK0)) )
| ( 3 = X0 ) )
| ~ spl1_15
| ~ spl1_114 ),
inference(superposition,[],[f153,f1785]) ).
tff(f95786,plain,
( spl1_566
| ~ spl1_15
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1802,f1780,f152,f95784]) ).
tff(f95784,plain,
( spl1_566
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,remove(X0,sK0)) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_566])]) ).
tff(f1802,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(remove(X0,sK0))) )
| ( empty = remove(2,remove(X0,sK0)) )
| ( 2 = X0 ) )
| ~ spl1_15
| ~ spl1_113 ),
inference(superposition,[],[f153,f1781]) ).
tff(f95782,plain,
( spl1_565
| ~ spl1_3
| ~ spl1_29
| ~ spl1_90
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f1617,f1567,f1341,f230,f99,f95780]) ).
tff(f95780,plain,
( spl1_565
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(5,remove(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_565])]) ).
tff(f99,plain,
( spl1_3
<=> in(5,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f230,plain,
( spl1_29
<=> ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f1341,plain,
( spl1_90
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).
tff(f1567,plain,
( spl1_98
<=> ! [X0: $int] : ( add(X0,sK0) = add(5,remove(5,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
tff(f1617,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(5,remove(5,add(X0,sK0))) )
| ~ spl1_3
| ~ spl1_29
| ~ spl1_90
| ~ spl1_98 ),
inference(forward_demodulation,[],[f1609,f1441]) ).
tff(f1441,plain,
( ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(5,add(X0,sK0))) )
| ~ spl1_3
| ~ spl1_90 ),
inference(resolution,[],[f1342,f101]) ).
tff(f101,plain,
( in(5,sK0)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f99]) ).
tff(f1342,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,X2)
| ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) ) )
| ~ spl1_90 ),
inference(avatar_component_clause,[],[f1341]) ).
tff(f1609,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != count(remove(5,add(X0,sK0))) )
| in(5,remove(5,add(X0,sK0))) )
| ~ spl1_29
| ~ spl1_98 ),
inference(superposition,[],[f231,f1568]) ).
tff(f1568,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(5,remove(5,add(X0,sK0))) )
| ~ spl1_98 ),
inference(avatar_component_clause,[],[f1567]) ).
tff(f231,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) )
| ~ spl1_29 ),
inference(avatar_component_clause,[],[f230]) ).
tff(f95778,plain,
( spl1_564
| ~ spl1_2
| ~ spl1_29
| ~ spl1_90
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f1605,f1451,f1341,f230,f94,f95776]) ).
tff(f95776,plain,
( spl1_564
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(3,remove(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_564])]) ).
tff(f94,plain,
( spl1_2
<=> in(3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f1451,plain,
( spl1_93
<=> ! [X0: $int] : ( add(X0,sK0) = add(3,remove(3,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).
tff(f1605,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(3,remove(3,add(X0,sK0))) )
| ~ spl1_2
| ~ spl1_29
| ~ spl1_90
| ~ spl1_93 ),
inference(forward_demodulation,[],[f1597,f1440]) ).
tff(f1440,plain,
( ! [X0: $int] : ( $sum(-1,count(add(X0,sK0))) = count(remove(3,add(X0,sK0))) )
| ~ spl1_2
| ~ spl1_90 ),
inference(resolution,[],[f1342,f96]) ).
tff(f96,plain,
( in(3,sK0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f1597,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != count(remove(3,add(X0,sK0))) )
| in(3,remove(3,add(X0,sK0))) )
| ~ spl1_29
| ~ spl1_93 ),
inference(superposition,[],[f231,f1452]) ).
tff(f1452,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(3,remove(3,add(X0,sK0))) )
| ~ spl1_93 ),
inference(avatar_component_clause,[],[f1451]) ).
tff(f95774,plain,
( spl1_563
| ~ spl1_40
| ~ spl1_114
| ~ spl1_535 ),
inference(avatar_split_clause,[],[f93936,f93487,f1784,f375,f95771]) ).
tff(f95771,plain,
( spl1_563
<=> ( empty = remove(3,remove(2,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_563])]) ).
tff(f93936,plain,
( ( empty = remove(3,remove(2,sK0)) )
| ~ spl1_40
| ~ spl1_114
| ~ spl1_535 ),
inference(evaluation,[],[f93935]) ).
tff(f93935,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(3,remove(2,sK0)) )
| ~ spl1_40
| ~ spl1_114
| ~ spl1_535 ),
inference(forward_demodulation,[],[f93934,f377]) ).
tff(f93934,plain,
( ( 1 = $sum(-1,count(remove(2,sK0))) )
| ( empty = remove(3,remove(2,sK0)) )
| ~ spl1_114
| ~ spl1_535 ),
inference(evaluation,[],[f93850]) ).
tff(f93850,plain,
( ( 1 = $sum(-1,count(remove(2,sK0))) )
| ( empty = remove(3,remove(2,sK0)) )
| ( 2 = 3 )
| ~ spl1_114
| ~ spl1_535 ),
inference(superposition,[],[f93488,f1785]) ).
tff(f95769,plain,
( spl1_562
| ~ spl1_1
| ~ spl1_29
| ~ spl1_87
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1593,f1341,f1329,f230,f89,f95767]) ).
tff(f95767,plain,
( spl1_562
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(2,remove(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_562])]) ).
tff(f89,plain,
( spl1_1
<=> in(2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f1329,plain,
( spl1_87
<=> ! [X0: $int] : ( add(X0,sK0) = add(2,remove(2,add(X0,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
tff(f1593,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| in(2,remove(2,add(X0,sK0))) )
| ~ spl1_1
| ~ spl1_29
| ~ spl1_87
| ~ spl1_90 ),
inference(forward_demodulation,[],[f1585,f1439]) ).
tff(f1439,plain,
( ! [X0: $int] : ( count(remove(2,add(X0,sK0))) = $sum(-1,count(add(X0,sK0))) )
| ~ spl1_1
| ~ spl1_90 ),
inference(resolution,[],[f1342,f91]) ).
tff(f91,plain,
( in(2,sK0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f89]) ).
tff(f1585,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != count(remove(2,add(X0,sK0))) )
| in(2,remove(2,add(X0,sK0))) )
| ~ spl1_29
| ~ spl1_87 ),
inference(superposition,[],[f231,f1330]) ).
tff(f1330,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(2,remove(2,add(X0,sK0))) )
| ~ spl1_87 ),
inference(avatar_component_clause,[],[f1329]) ).
tff(f95729,plain,
( spl1_561
| ~ spl1_101
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38125,f19442,f1579,f95727]) ).
tff(f95727,plain,
( spl1_561
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,add(5,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_561])]) ).
tff(f38125,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,add(5,add(X0,sK0))) ) )
| ~ spl1_101
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1580]) ).
tff(f95725,plain,
( spl1_560
| ~ spl1_100
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38124,f19442,f1575,f95723]) ).
tff(f95723,plain,
( spl1_560
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,add(3,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_560])]) ).
tff(f38124,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,add(3,add(X0,sK0))) ) )
| ~ spl1_100
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1576]) ).
tff(f95721,plain,
( spl1_559
| ~ spl1_99
| ~ spl1_289 ),
inference(avatar_split_clause,[],[f38123,f19442,f1571,f95719]) ).
tff(f95719,plain,
( spl1_559
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,add(2,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_559])]) ).
tff(f38123,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,add(2,add(X0,sK0))) ) )
| ~ spl1_99
| ~ spl1_289 ),
inference(superposition,[],[f19443,f1572]) ).
tff(f95717,plain,
( spl1_558
| ~ spl1_41
| ~ spl1_115
| ~ spl1_534 ),
inference(avatar_split_clause,[],[f93803,f93483,f1788,f380,f95714]) ).
tff(f95714,plain,
( spl1_558
<=> ( empty = remove(5,remove(3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_558])]) ).
tff(f380,plain,
( spl1_41
<=> ( 1 = count(remove(3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
tff(f93483,plain,
( spl1_534
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(3,sK0)) )
| ( 1 = count(remove(X0,remove(3,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_534])]) ).
tff(f93803,plain,
( ( empty = remove(5,remove(3,sK0)) )
| ~ spl1_41
| ~ spl1_115
| ~ spl1_534 ),
inference(evaluation,[],[f93802]) ).
tff(f93802,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(5,remove(3,sK0)) )
| ~ spl1_41
| ~ spl1_115
| ~ spl1_534 ),
inference(forward_demodulation,[],[f93798,f382]) ).
tff(f382,plain,
( ( 1 = count(remove(3,sK0)) )
| ~ spl1_41 ),
inference(avatar_component_clause,[],[f380]) ).
tff(f93798,plain,
( ( 1 = $sum(-1,count(remove(3,sK0))) )
| ( empty = remove(5,remove(3,sK0)) )
| ~ spl1_115
| ~ spl1_534 ),
inference(evaluation,[],[f93716]) ).
tff(f93716,plain,
( ( 1 = $sum(-1,count(remove(3,sK0))) )
| ( empty = remove(5,remove(3,sK0)) )
| ( 3 = 5 )
| ~ spl1_115
| ~ spl1_534 ),
inference(superposition,[],[f93484,f1789]) ).
tff(f93484,plain,
( ! [X0: $int] :
( ( 1 = count(remove(X0,remove(3,sK0))) )
| ( empty = remove(X0,remove(3,sK0)) ) )
| ~ spl1_534 ),
inference(avatar_component_clause,[],[f93483]) ).
tff(f95712,plain,
( spl1_557
| ~ spl1_105
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8934,f7618,f1655,f95710]) ).
tff(f95710,plain,
( spl1_557
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,remove(5,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_557])]) ).
tff(f8934,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,remove(5,add(X0,sK0))) ) )
| ~ spl1_105
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1656]) ).
tff(f95708,plain,
( spl1_556
| ~ spl1_104
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8933,f7618,f1651,f95706]) ).
tff(f95706,plain,
( spl1_556
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,remove(3,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_556])]) ).
tff(f8933,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,remove(3,add(X0,sK0))) ) )
| ~ spl1_104
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1652]) ).
tff(f95704,plain,
( spl1_555
| ~ spl1_102
| ~ spl1_212 ),
inference(avatar_split_clause,[],[f8932,f7618,f1643,f95702]) ).
tff(f95702,plain,
( spl1_555
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,remove(2,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_555])]) ).
tff(f8932,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,remove(2,add(X0,sK0))) ) )
| ~ spl1_102
| ~ spl1_212 ),
inference(superposition,[],[f7619,f1644]) ).
tff(f95569,plain,
( spl1_554
| ~ spl1_7
| ~ spl1_117 ),
inference(avatar_split_clause,[],[f1845,f1826,f117,f95567]) ).
tff(f95567,plain,
( spl1_554
<=> ! [X0: collection] : $less(-1,count(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_554])]) ).
tff(f117,plain,
( spl1_7
<=> ! [X0: collection] : ~ $less(count(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f1826,plain,
( spl1_117
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
tff(f1845,plain,
( ! [X0: collection] : $less(-1,count(X0))
| ~ spl1_7
| ~ spl1_117 ),
inference(resolution,[],[f1827,f118]) ).
tff(f118,plain,
( ! [X0: collection] : ~ $less(count(X0),0)
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f1827,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl1_117 ),
inference(avatar_component_clause,[],[f1826]) ).
tff(f94423,plain,
( spl1_553
| ~ spl1_41
| ~ spl1_113
| ~ spl1_534 ),
inference(avatar_split_clause,[],[f93801,f93483,f1780,f380,f94420]) ).
tff(f94420,plain,
( spl1_553
<=> ( empty = remove(2,remove(3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_553])]) ).
tff(f93801,plain,
( ( empty = remove(2,remove(3,sK0)) )
| ~ spl1_41
| ~ spl1_113
| ~ spl1_534 ),
inference(evaluation,[],[f93800]) ).
tff(f93800,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(2,remove(3,sK0)) )
| ~ spl1_41
| ~ spl1_113
| ~ spl1_534 ),
inference(forward_demodulation,[],[f93799,f382]) ).
tff(f93799,plain,
( ( 1 = $sum(-1,count(remove(3,sK0))) )
| ( empty = remove(2,remove(3,sK0)) )
| ~ spl1_113
| ~ spl1_534 ),
inference(evaluation,[],[f93714]) ).
tff(f93714,plain,
( ( 1 = $sum(-1,count(remove(3,sK0))) )
| ( empty = remove(2,remove(3,sK0)) )
| ( 2 = 3 )
| ~ spl1_113
| ~ spl1_534 ),
inference(superposition,[],[f93484,f1781]) ).
tff(f94376,plain,
( spl1_552
| ~ spl1_74
| ~ spl1_112 ),
inference(avatar_split_clause,[],[f1769,f1707,f923,f94374]) ).
tff(f94374,plain,
( spl1_552
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(5,remove(X0,sK0)))) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_552])]) ).
tff(f923,plain,
( spl1_74
<=> ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
tff(f1707,plain,
( spl1_112
<=> ! [X0: $int] :
( ( 5 = X0 )
| ( remove(X0,sK0) = add(5,remove(5,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
tff(f1769,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(5,remove(X0,sK0)))) )
| ( 5 = X0 ) )
| ~ spl1_74
| ~ spl1_112 ),
inference(superposition,[],[f924,f1708]) ).
tff(f1708,plain,
( ! [X0: $int] :
( ( remove(X0,sK0) = add(5,remove(5,remove(X0,sK0))) )
| ( 5 = X0 ) )
| ~ spl1_112 ),
inference(avatar_component_clause,[],[f1707]) ).
tff(f924,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) )
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f923]) ).
tff(f94372,plain,
( spl1_551
| ~ spl1_74
| ~ spl1_110 ),
inference(avatar_split_clause,[],[f1759,f1699,f923,f94370]) ).
tff(f94370,plain,
( spl1_551
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(3,remove(X0,sK0)))) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_551])]) ).
tff(f1699,plain,
( spl1_110
<=> ! [X0: $int] :
( ( 3 = X0 )
| ( remove(X0,sK0) = add(3,remove(3,remove(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).
tff(f1759,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(3,remove(X0,sK0)))) )
| ( 3 = X0 ) )
| ~ spl1_74
| ~ spl1_110 ),
inference(superposition,[],[f924,f1700]) ).
tff(f1700,plain,
( ! [X0: $int] :
( ( remove(X0,sK0) = add(3,remove(3,remove(X0,sK0))) )
| ( 3 = X0 ) )
| ~ spl1_110 ),
inference(avatar_component_clause,[],[f1699]) ).
tff(f94368,plain,
( spl1_550
| ~ spl1_74
| ~ spl1_109 ),
inference(avatar_split_clause,[],[f1749,f1695,f923,f94366]) ).
tff(f94366,plain,
( spl1_550
<=> ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(2,remove(X0,sK0)))) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_550])]) ).
tff(f1749,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) = $sum(1,count(remove(2,remove(X0,sK0)))) )
| ( 2 = X0 ) )
| ~ spl1_74
| ~ spl1_109 ),
inference(superposition,[],[f924,f1696]) ).
tff(f94364,plain,
( spl1_549
| ~ spl1_42
| ~ spl1_114
| ~ spl1_533 ),
inference(avatar_split_clause,[],[f93668,f93479,f1784,f385,f94361]) ).
tff(f93479,plain,
( spl1_533
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(5,sK0)) )
| ( 1 = count(remove(X0,remove(5,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_533])]) ).
tff(f93668,plain,
( ( empty = remove(3,remove(5,sK0)) )
| ~ spl1_42
| ~ spl1_114
| ~ spl1_533 ),
inference(evaluation,[],[f93667]) ).
tff(f93667,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(3,remove(5,sK0)) )
| ~ spl1_42
| ~ spl1_114
| ~ spl1_533 ),
inference(forward_demodulation,[],[f93663,f387]) ).
tff(f93663,plain,
( ( 1 = $sum(-1,count(remove(5,sK0))) )
| ( empty = remove(3,remove(5,sK0)) )
| ~ spl1_114
| ~ spl1_533 ),
inference(evaluation,[],[f93580]) ).
tff(f93580,plain,
( ( 1 = $sum(-1,count(remove(5,sK0))) )
| ( empty = remove(3,remove(5,sK0)) )
| ( 3 = 5 )
| ~ spl1_114
| ~ spl1_533 ),
inference(superposition,[],[f93480,f1785]) ).
tff(f93480,plain,
( ! [X0: $int] :
( ( 1 = count(remove(X0,remove(5,sK0))) )
| ( empty = remove(X0,remove(5,sK0)) ) )
| ~ spl1_533 ),
inference(avatar_component_clause,[],[f93479]) ).
tff(f94359,plain,
( spl1_548
| ~ spl1_15
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f1746,f1691,f152,f94357]) ).
tff(f94357,plain,
( spl1_548
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,remove(X0,sK0)) )
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_548])]) ).
tff(f1746,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(5,remove(X0,sK0)) )
| ( 5 = X0 ) )
| ~ spl1_15
| ~ spl1_108 ),
inference(superposition,[],[f153,f1692]) ).
tff(f94355,plain,
( spl1_547
| ~ spl1_15
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f1733,f1687,f152,f94353]) ).
tff(f94353,plain,
( spl1_547
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,remove(X0,sK0)) )
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_547])]) ).
tff(f1733,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(3,remove(X0,sK0)) )
| ( 3 = X0 ) )
| ~ spl1_15
| ~ spl1_107 ),
inference(superposition,[],[f153,f1688]) ).
tff(f94351,plain,
( spl1_546
| ~ spl1_15
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f1720,f1683,f152,f94349]) ).
tff(f94349,plain,
( spl1_546
<=> ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,remove(X0,sK0)) )
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_546])]) ).
tff(f1720,plain,
( ! [X0: $int] :
( ( 0 != count(remove(X0,sK0)) )
| ( empty = add(2,remove(X0,sK0)) )
| ( 2 = X0 ) )
| ~ spl1_15
| ~ spl1_106 ),
inference(superposition,[],[f153,f1684]) ).
tff(f94347,plain,
( spl1_545
| ~ spl1_27
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f1677,f1655,f222,f94345]) ).
tff(f94345,plain,
( spl1_545
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(5,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_545])]) ).
tff(f1677,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(5,add(X0,sK0)) )
| ~ spl1_27
| ~ spl1_105 ),
inference(superposition,[],[f223,f1656]) ).
tff(f94343,plain,
( spl1_544
| ~ spl1_27
| ~ spl1_104 ),
inference(avatar_split_clause,[],[f1669,f1651,f222,f94341]) ).
tff(f94341,plain,
( spl1_544
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(3,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_544])]) ).
tff(f1669,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(3,add(X0,sK0)) )
| ~ spl1_27
| ~ spl1_104 ),
inference(superposition,[],[f223,f1652]) ).
tff(f94339,plain,
( spl1_543
| ~ spl1_27
| ~ spl1_102 ),
inference(avatar_split_clause,[],[f1661,f1643,f222,f94337]) ).
tff(f94337,plain,
( spl1_543
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(2,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_543])]) ).
tff(f1661,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(-1,count(add(X0,sK0))) )
| ~ in(2,add(X0,sK0)) )
| ~ spl1_27
| ~ spl1_102 ),
inference(superposition,[],[f223,f1644]) ).
tff(f94335,plain,
( spl1_542
| ~ spl1_34
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1636,f1579,f317,f94333]) ).
tff(f94333,plain,
( spl1_542
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(5,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_542])]) ).
tff(f1636,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(5,add(X0,sK0)) )
| ~ spl1_34
| ~ spl1_101 ),
inference(superposition,[],[f318,f1580]) ).
tff(f94331,plain,
( spl1_541
| ~ spl1_34
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f1628,f1575,f317,f94329]) ).
tff(f94329,plain,
( spl1_541
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(3,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_541])]) ).
tff(f1628,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(3,add(X0,sK0)) )
| ~ spl1_34
| ~ spl1_100 ),
inference(superposition,[],[f318,f1576]) ).
tff(f94327,plain,
( spl1_540
| ~ spl1_34
| ~ spl1_99 ),
inference(avatar_split_clause,[],[f1620,f1571,f317,f94325]) ).
tff(f94325,plain,
( spl1_540
<=> ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(2,add(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_540])]) ).
tff(f1620,plain,
( ! [X0: $int] :
( ( count(add(X0,sK0)) != $sum(1,count(add(X0,sK0))) )
| ~ in(2,add(X0,sK0)) )
| ~ spl1_34
| ~ spl1_99 ),
inference(superposition,[],[f318,f1572]) ).
tff(f94211,plain,
( spl1_539
| ~ spl1_42
| ~ spl1_113
| ~ spl1_533 ),
inference(avatar_split_clause,[],[f93666,f93479,f1780,f385,f94208]) ).
tff(f93666,plain,
( ( empty = remove(2,remove(5,sK0)) )
| ~ spl1_42
| ~ spl1_113
| ~ spl1_533 ),
inference(evaluation,[],[f93665]) ).
tff(f93665,plain,
( ( 1 = $sum(-1,1) )
| ( empty = remove(2,remove(5,sK0)) )
| ~ spl1_42
| ~ spl1_113
| ~ spl1_533 ),
inference(forward_demodulation,[],[f93664,f387]) ).
tff(f93664,plain,
( ( 1 = $sum(-1,count(remove(5,sK0))) )
| ( empty = remove(2,remove(5,sK0)) )
| ~ spl1_113
| ~ spl1_533 ),
inference(evaluation,[],[f93579]) ).
tff(f93579,plain,
( ( 1 = $sum(-1,count(remove(5,sK0))) )
| ( empty = remove(2,remove(5,sK0)) )
| ( 2 = 5 )
| ~ spl1_113
| ~ spl1_533 ),
inference(superposition,[],[f93480,f1781]) ).
tff(f93501,plain,
( spl1_538
| ~ spl1_40
| ~ spl1_437 ),
inference(avatar_split_clause,[],[f80295,f79226,f375,f93499]) ).
tff(f93499,plain,
( spl1_538
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(2,sK0)) )
| ( 2 = count(add(X0,remove(2,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_538])]) ).
tff(f79226,plain,
( spl1_437
<=> ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_437])]) ).
tff(f80295,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(2,sK0)) )
| ( 2 = count(add(X0,remove(2,sK0))) ) )
| ~ spl1_40
| ~ spl1_437 ),
inference(evaluation,[],[f80289]) ).
tff(f80289,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(2,sK0)) )
| ( $sum(1,1) = count(add(X0,remove(2,sK0))) ) )
| ~ spl1_40
| ~ spl1_437 ),
inference(superposition,[],[f79227,f377]) ).
tff(f79227,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_437 ),
inference(avatar_component_clause,[],[f79226]) ).
tff(f93497,plain,
( spl1_537
| ~ spl1_41
| ~ spl1_437 ),
inference(avatar_split_clause,[],[f80294,f79226,f380,f93495]) ).
tff(f93495,plain,
( spl1_537
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(3,sK0)) )
| ( 2 = count(add(X0,remove(3,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_537])]) ).
tff(f80294,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(3,sK0)) )
| ( 2 = count(add(X0,remove(3,sK0))) ) )
| ~ spl1_41
| ~ spl1_437 ),
inference(evaluation,[],[f80290]) ).
tff(f80290,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(3,sK0)) )
| ( $sum(1,1) = count(add(X0,remove(3,sK0))) ) )
| ~ spl1_41
| ~ spl1_437 ),
inference(superposition,[],[f79227,f382]) ).
tff(f93493,plain,
( spl1_536
| ~ spl1_42
| ~ spl1_437 ),
inference(avatar_split_clause,[],[f80293,f79226,f385,f93491]) ).
tff(f93491,plain,
( spl1_536
<=> ! [X0: $int] :
( ( empty = remove(X0,remove(5,sK0)) )
| ( 2 = count(add(X0,remove(5,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_536])]) ).
tff(f80293,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(5,sK0)) )
| ( 2 = count(add(X0,remove(5,sK0))) ) )
| ~ spl1_42
| ~ spl1_437 ),
inference(evaluation,[],[f80291]) ).
tff(f80291,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(5,sK0)) )
| ( $sum(1,1) = count(add(X0,remove(5,sK0))) ) )
| ~ spl1_42
| ~ spl1_437 ),
inference(superposition,[],[f79227,f387]) ).
tff(f93489,plain,
( spl1_535
| ~ spl1_40
| ~ spl1_412 ),
inference(avatar_split_clause,[],[f76802,f55391,f375,f93487]) ).
tff(f55391,plain,
( spl1_412
<=> ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_412])]) ).
tff(f76802,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(2,sK0)) )
| ( 1 = count(remove(X0,remove(2,sK0))) ) )
| ~ spl1_40
| ~ spl1_412 ),
inference(evaluation,[],[f76796]) ).
tff(f76796,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(2,sK0)) )
| ( 1 = count(remove(X0,remove(2,sK0))) ) )
| ~ spl1_40
| ~ spl1_412 ),
inference(superposition,[],[f55392,f377]) ).
tff(f55392,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_412 ),
inference(avatar_component_clause,[],[f55391]) ).
tff(f93485,plain,
( spl1_534
| ~ spl1_41
| ~ spl1_412 ),
inference(avatar_split_clause,[],[f76801,f55391,f380,f93483]) ).
tff(f76801,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(3,sK0)) )
| ( 1 = count(remove(X0,remove(3,sK0))) ) )
| ~ spl1_41
| ~ spl1_412 ),
inference(evaluation,[],[f76797]) ).
tff(f76797,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(3,sK0)) )
| ( 1 = count(remove(X0,remove(3,sK0))) ) )
| ~ spl1_41
| ~ spl1_412 ),
inference(superposition,[],[f55392,f382]) ).
tff(f93481,plain,
( spl1_533
| ~ spl1_42
| ~ spl1_412 ),
inference(avatar_split_clause,[],[f76800,f55391,f385,f93479]) ).
tff(f76800,plain,
( ! [X0: $int] :
( ( empty = remove(X0,remove(5,sK0)) )
| ( 1 = count(remove(X0,remove(5,sK0))) ) )
| ~ spl1_42
| ~ spl1_412 ),
inference(evaluation,[],[f76798]) ).
tff(f76798,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,1) )
| ( empty = remove(X0,remove(5,sK0)) )
| ( 1 = count(remove(X0,remove(5,sK0))) ) )
| ~ spl1_42
| ~ spl1_412 ),
inference(superposition,[],[f55392,f387]) ).
tff(f93477,plain,
( spl1_532
| ~ spl1_52
| ~ spl1_314 ),
inference(avatar_split_clause,[],[f75855,f39579,f481,f93475]) ).
tff(f93475,plain,
( spl1_532
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_532])]) ).
tff(f481,plain,
( spl1_52
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f39579,plain,
( spl1_314
<=> ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less($sum(-1,X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_314])]) ).
tff(f75855,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum(1,X0)) )
| ~ spl1_52
| ~ spl1_314 ),
inference(evaluation,[],[f75825]) ).
tff(f75825,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum($uminus(-1),X0)) )
| ~ spl1_52
| ~ spl1_314 ),
inference(superposition,[],[f39580,f482]) ).
tff(f482,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl1_52 ),
inference(avatar_component_clause,[],[f481]) ).
tff(f39580,plain,
( ! [X0: $int] :
( ~ $less($sum(-1,X0),0)
| ~ $less(2,X0) )
| ~ spl1_314 ),
inference(avatar_component_clause,[],[f39579]) ).
tff(f93473,plain,
( spl1_531
| ~ spl1_102
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38100,f19438,f1643,f93471]) ).
tff(f93471,plain,
( spl1_531
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,remove(2,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_531])]) ).
tff(f38100,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,remove(2,add(X0,sK0))) ) )
| ~ spl1_102
| ~ spl1_288 ),
inference(evaluation,[],[f38084]) ).
tff(f38084,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(add(X0,sK0)))) )
| ( empty = add(2,remove(2,add(X0,sK0))) ) )
| ~ spl1_102
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1644]) ).
tff(f93469,plain,
( spl1_530
| ~ spl1_104
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38099,f19438,f1651,f93467]) ).
tff(f93467,plain,
( spl1_530
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,remove(3,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_530])]) ).
tff(f38099,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,remove(3,add(X0,sK0))) ) )
| ~ spl1_104
| ~ spl1_288 ),
inference(evaluation,[],[f38085]) ).
tff(f38085,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(add(X0,sK0)))) )
| ( empty = add(3,remove(3,add(X0,sK0))) ) )
| ~ spl1_104
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1652]) ).
tff(f93465,plain,
( spl1_529
| ~ spl1_105
| ~ spl1_288 ),
inference(avatar_split_clause,[],[f38098,f19438,f1655,f93463]) ).
tff(f93463,plain,
( spl1_529
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,remove(5,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_529])]) ).
tff(f38098,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,remove(5,add(X0,sK0))) ) )
| ~ spl1_105
| ~ spl1_288 ),
inference(evaluation,[],[f38086]) ).
tff(f38086,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$sum(-1,count(add(X0,sK0)))) )
| ( empty = add(5,remove(5,add(X0,sK0))) ) )
| ~ spl1_105
| ~ spl1_288 ),
inference(superposition,[],[f19439,f1656]) ).
tff(f93461,plain,
( spl1_528
| ~ spl1_101
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8967,f7622,f1579,f93459]) ).
tff(f93459,plain,
( spl1_528
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,add(5,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_528])]) ).
tff(f8967,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,add(5,add(X0,sK0))) ) )
| ~ spl1_101
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1580]) ).
tff(f93457,plain,
( spl1_527
| ~ spl1_100
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8966,f7622,f1575,f93455]) ).
tff(f93455,plain,
( spl1_527
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,add(3,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_527])]) ).
tff(f8966,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,add(3,add(X0,sK0))) ) )
| ~ spl1_100
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1576]) ).
tff(f93453,plain,
( spl1_526
| ~ spl1_99
| ~ spl1_213 ),
inference(avatar_split_clause,[],[f8965,f7622,f1571,f93451]) ).
tff(f93451,plain,
( spl1_526
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,add(2,add(X0,sK0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_526])]) ).
tff(f8965,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,add(2,add(X0,sK0))) ) )
| ~ spl1_99
| ~ spl1_213 ),
inference(superposition,[],[f7623,f1572]) ).
tff(f93449,plain,
( spl1_525
| ~ spl1_15
| ~ spl1_105 ),
inference(avatar_split_clause,[],[f1679,f1655,f152,f93447]) ).
tff(f93447,plain,
( spl1_525
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_525])]) ).
tff(f1679,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(5,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_105 ),
inference(superposition,[],[f153,f1656]) ).
tff(f93445,plain,
( spl1_524
| ~ spl1_15
| ~ spl1_104 ),
inference(avatar_split_clause,[],[f1671,f1651,f152,f93443]) ).
tff(f93443,plain,
( spl1_524
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_524])]) ).
tff(f1671,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(3,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_104 ),
inference(superposition,[],[f153,f1652]) ).
tff(f93441,plain,
( spl1_523
| ~ spl1_15
| ~ spl1_102 ),
inference(avatar_split_clause,[],[f1663,f1643,f152,f93439]) ).
tff(f93439,plain,
( spl1_523
<=> ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_523])]) ).
tff(f1663,plain,
( ! [X0: $int] :
( ( 0 != $sum(-1,count(add(X0,sK0))) )
| ( empty = remove(2,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_102 ),
inference(superposition,[],[f153,f1644]) ).
tff(f93432,plain,
( spl1_522
| ~ spl1_124
| ~ spl1_314 ),
inference(avatar_split_clause,[],[f75853,f39579,f1914,f93430]) ).
tff(f93430,plain,
( spl1_522
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_522])]) ).
tff(f1914,plain,
( spl1_124
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
tff(f75853,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum(X0,1)) )
| ~ spl1_124
| ~ spl1_314 ),
inference(evaluation,[],[f75834]) ).
tff(f75834,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(2,$sum(X0,$uminus(-1))) )
| ~ spl1_124
| ~ spl1_314 ),
inference(superposition,[],[f39580,f1915]) ).
tff(f1915,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 )
| ~ spl1_124 ),
inference(avatar_component_clause,[],[f1914]) ).
tff(f93418,plain,
( spl1_521
| ~ spl1_15
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1639,f1579,f152,f93416]) ).
tff(f93416,plain,
( spl1_521
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_521])]) ).
tff(f1639,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(5,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_101 ),
inference(superposition,[],[f153,f1580]) ).
tff(f93414,plain,
( spl1_520
| ~ spl1_15
| ~ spl1_100 ),
inference(avatar_split_clause,[],[f1631,f1575,f152,f93412]) ).
tff(f93412,plain,
( spl1_520
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_520])]) ).
tff(f1631,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(3,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_100 ),
inference(superposition,[],[f153,f1576]) ).
tff(f93410,plain,
( spl1_519
| ~ spl1_15
| ~ spl1_99 ),
inference(avatar_split_clause,[],[f1623,f1571,f152,f93408]) ).
tff(f93408,plain,
( spl1_519
<=> ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,add(X0,sK0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_519])]) ).
tff(f1623,plain,
( ! [X0: $int] :
( ( 0 != count(add(X0,sK0)) )
| ( empty = add(2,add(X0,sK0)) ) )
| ~ spl1_15
| ~ spl1_99 ),
inference(superposition,[],[f153,f1572]) ).
tff(f93316,plain,
( spl1_518
| ~ spl1_7
| ~ spl1_115 ),
inference(avatar_split_clause,[],[f1823,f1788,f117,f93314]) ).
tff(f93314,plain,
( spl1_518
<=> ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_518])]) ).
tff(f1823,plain,
( ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 5 = X0 ) )
| ~ spl1_7
| ~ spl1_115 ),
inference(superposition,[],[f118,f1789]) ).
tff(f93312,plain,
( spl1_517
| ~ spl1_7
| ~ spl1_114 ),
inference(avatar_split_clause,[],[f1813,f1784,f117,f93310]) ).
tff(f93310,plain,
( spl1_517
<=> ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_517])]) ).
tff(f1813,plain,
( ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 3 = X0 ) )
| ~ spl1_7
| ~ spl1_114 ),
inference(superposition,[],[f118,f1785]) ).
tff(f93308,plain,
( spl1_516
| ~ spl1_14
| ~ spl1_314 ),
inference(avatar_split_clause,[],[f75823,f39579,f148,f93306]) ).
tff(f93306,plain,
( spl1_516
<=> ! [X0: $int] :
( ~ $less($sum(X0,-1),0)
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_516])]) ).
tff(f148,plain,
( spl1_14
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f75823,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,-1),0)
| ~ $less(2,X0) )
| ~ spl1_14
| ~ spl1_314 ),
inference(superposition,[],[f39580,f149]) ).
tff(f149,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f148]) ).
tff(f93304,plain,
( spl1_515
| ~ spl1_7
| ~ spl1_113 ),
inference(avatar_split_clause,[],[f1803,f1780,f117,f93302]) ).
tff(f93302,plain,
( spl1_515
<=> ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_515])]) ).
tff(f1803,plain,
( ! [X0: $int] :
( ~ $less($sum(-1,count(remove(X0,sK0))),0)
| ( 2 = X0 ) )
| ~ spl1_7
| ~ spl1_113 ),
inference(superposition,[],[f118,f1781]) ).
tff(f93107,plain,
( spl1_514
| ~ spl1_96
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1554,f1537,f1533,f93105]) ).
tff(f93105,plain,
( spl1_514
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,add(X3,X2))) = $sum(1,count(add(X3,X2))) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_514])]) ).
tff(f1533,plain,
( spl1_96
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| in(X0,X2)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
tff(f1537,plain,
( spl1_97
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X1 )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
tff(f1554,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,add(X3,X2))) = $sum(1,count(add(X3,X2))) )
| ( X0 = X3 ) )
| ~ spl1_96
| ~ spl1_97 ),
inference(resolution,[],[f1538,f1534]) ).
tff(f1534,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( in(X0,X2)
| ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 ) )
| ~ spl1_96 ),
inference(avatar_component_clause,[],[f1533]) ).
tff(f1538,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,X2)
| ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) ) )
| ~ spl1_97 ),
inference(avatar_component_clause,[],[f1537]) ).
tff(f92543,plain,
( spl1_513
| ~ spl1_94
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1555,f1537,f1455,f92541]) ).
tff(f92541,plain,
( spl1_513
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X3 )
| ( count(add(X3,X2)) = count(remove(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_513])]) ).
tff(f1455,plain,
( spl1_94
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_94])]) ).
tff(f1555,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X3 )
| ( count(add(X3,X2)) = count(remove(X0,add(X3,X2))) ) )
| ~ spl1_94
| ~ spl1_97 ),
inference(resolution,[],[f1538,f1456]) ).
tff(f1456,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) )
| ~ spl1_94 ),
inference(avatar_component_clause,[],[f1455]) ).
tff(f92539,plain,
( spl1_512
| ~ spl1_92
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1547,f1533,f1447,f92537]) ).
tff(f92537,plain,
( spl1_512
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( X0 = X3 )
| ( remove(X3,X2) = add(X0,remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_512])]) ).
tff(f1447,plain,
( spl1_92
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).
tff(f1547,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( X0 = X3 )
| ( remove(X3,X2) = add(X0,remove(X0,remove(X3,X2))) ) )
| ~ spl1_92
| ~ spl1_96 ),
inference(resolution,[],[f1534,f1448]) ).
tff(f1448,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,X2)
| ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) )
| ~ spl1_92 ),
inference(avatar_component_clause,[],[f1447]) ).
tff(f92535,plain,
( spl1_511
| ~ spl1_91
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1546,f1533,f1443,f92533]) ).
tff(f92533,plain,
( spl1_511
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( X0 = X3 )
| ( count(add(X0,remove(X3,X2))) = count(remove(X3,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_511])]) ).
tff(f1443,plain,
( spl1_91
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).
tff(f1546,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( X0 = X3 )
| ( count(add(X0,remove(X3,X2))) = count(remove(X3,X2)) ) )
| ~ spl1_91
| ~ spl1_96 ),
inference(resolution,[],[f1534,f1444]) ).
tff(f1444,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,X2)
| ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) )
| ~ spl1_91 ),
inference(avatar_component_clause,[],[f1443]) ).
tff(f92349,plain,
( spl1_510
| ~ spl1_14
| ~ spl1_303 ),
inference(avatar_split_clause,[],[f55209,f39535,f148,f92347]) ).
tff(f92347,plain,
( spl1_510
<=> ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_510])]) ).
tff(f39535,plain,
( spl1_303
<=> ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_303])]) ).
tff(f55209,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,3) )
| ~ spl1_14
| ~ spl1_303 ),
inference(superposition,[],[f39536,f149]) ).
tff(f39536,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,3) )
| ~ spl1_303 ),
inference(avatar_component_clause,[],[f39535]) ).
tff(f92120,plain,
( spl1_509
| ~ spl1_88
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1556,f1537,f1333,f92118]) ).
tff(f92118,plain,
( spl1_509
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_509])]) ).
tff(f1333,plain,
( spl1_88
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
tff(f1556,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) )
| ~ spl1_88
| ~ spl1_97 ),
inference(resolution,[],[f1538,f1334]) ).
tff(f1334,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( in(X0,X2)
| ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) ) )
| ~ spl1_88 ),
inference(avatar_component_clause,[],[f1333]) ).
tff(f92116,plain,
( spl1_508
| ~ spl1_90
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1545,f1533,f1341,f92114]) ).
tff(f92114,plain,
( spl1_508
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(remove(X0,add(X3,X2))) = $sum(-1,count(add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_508])]) ).
tff(f1545,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(remove(X0,add(X3,X2))) = $sum(-1,count(add(X3,X2))) ) )
| ~ spl1_90
| ~ spl1_96 ),
inference(resolution,[],[f1534,f1342]) ).
tff(f91780,plain,
( spl1_507
| ~ spl1_92
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1485,f1455,f1447,f91778]) ).
tff(f91778,plain,
( spl1_507
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( X0 = X3 )
| ( remove(X3,X2) = add(X0,remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_507])]) ).
tff(f1485,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( X0 = X3 )
| ( remove(X3,X2) = add(X0,remove(X0,remove(X3,X2))) ) )
| ~ spl1_92
| ~ spl1_94 ),
inference(resolution,[],[f1456,f1448]) ).
tff(f91776,plain,
( spl1_506
| ~ spl1_91
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1484,f1455,f1443,f91774]) ).
tff(f91774,plain,
( spl1_506
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( X0 = X3 )
| ( count(add(X0,remove(X3,X2))) = count(remove(X3,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_506])]) ).
tff(f1484,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( X0 = X3 )
| ( count(add(X0,remove(X3,X2))) = count(remove(X3,X2)) ) )
| ~ spl1_91
| ~ spl1_94 ),
inference(resolution,[],[f1456,f1444]) ).
tff(f91248,plain,
( spl1_505
| ~ spl1_14
| ~ spl1_301 ),
inference(avatar_split_clause,[],[f43733,f38142,f148,f91246]) ).
tff(f91246,plain,
( spl1_505
<=> ! [X0: $int] :
( $less(0,$sum(1,X0))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_505])]) ).
tff(f38142,plain,
( spl1_301
<=> ! [X0: $int] :
( $less(0,$sum(X0,1))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_301])]) ).
tff(f43733,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| ~ $less(2,X0) )
| ~ spl1_14
| ~ spl1_301 ),
inference(superposition,[],[f38143,f149]) ).
tff(f38143,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| ~ $less(2,X0) )
| ~ spl1_301 ),
inference(avatar_component_clause,[],[f38142]) ).
tff(f90715,plain,
( spl1_504
| ~ spl1_77
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1557,f1537,f1069,f90713]) ).
tff(f90713,plain,
( spl1_504
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_504])]) ).
tff(f1069,plain,
( spl1_77
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
tff(f1557,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) )
| ~ spl1_77
| ~ spl1_97 ),
inference(resolution,[],[f1538,f1070]) ).
tff(f1070,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( in(X0,X2)
| ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) ) )
| ~ spl1_77 ),
inference(avatar_component_clause,[],[f1069]) ).
tff(f90711,plain,
( spl1_503
| ~ spl1_79
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1544,f1533,f1077,f90709]) ).
tff(f90709,plain,
( spl1_503
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_503])]) ).
tff(f1077,plain,
( spl1_79
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ~ in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
tff(f1544,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) )
| ~ spl1_79
| ~ spl1_96 ),
inference(resolution,[],[f1534,f1078]) ).
tff(f1078,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X2,X1)
| ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) ) )
| ~ spl1_79 ),
inference(avatar_component_clause,[],[f1077]) ).
tff(f90707,plain,
( spl1_502
| ~ spl1_76
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1543,f1533,f1065,f90705]) ).
tff(f90705,plain,
( spl1_502
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_502])]) ).
tff(f1065,plain,
( spl1_76
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_76])]) ).
tff(f1543,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) )
| ~ spl1_76
| ~ spl1_96 ),
inference(resolution,[],[f1534,f1066]) ).
tff(f1066,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,X2)
| ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) ) )
| ~ spl1_76 ),
inference(avatar_component_clause,[],[f1065]) ).
tff(f90703,plain,
( spl1_501
| ~ spl1_90
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1483,f1455,f1341,f90701]) ).
tff(f90701,plain,
( spl1_501
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(remove(X0,add(X3,X2))) = $sum(-1,count(add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_501])]) ).
tff(f1483,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(remove(X0,add(X3,X2))) = $sum(-1,count(add(X3,X2))) ) )
| ~ spl1_90
| ~ spl1_94 ),
inference(resolution,[],[f1456,f1342]) ).
tff(f90699,plain,
( spl1_500
| ~ spl1_88
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1468,f1447,f1333,f90697]) ).
tff(f90697,plain,
( spl1_500
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_500])]) ).
tff(f1468,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) )
| ~ spl1_88
| ~ spl1_92 ),
inference(resolution,[],[f1448,f1334]) ).
tff(f90695,plain,
( spl1_499
| ~ spl1_88
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1458,f1443,f1333,f90693]) ).
tff(f90693,plain,
( spl1_499
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_499])]) ).
tff(f1458,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) )
| ~ spl1_88
| ~ spl1_91 ),
inference(resolution,[],[f1444,f1334]) ).
tff(f90665,plain,
( spl1_498
| ~ spl1_14
| ~ spl1_300 ),
inference(avatar_split_clause,[],[f43015,f33521,f148,f90663]) ).
tff(f90663,plain,
( spl1_498
<=> ! [X0: $int] :
( $less(0,$sum(2,X0))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_498])]) ).
tff(f33521,plain,
( spl1_300
<=> ! [X0: $int] :
( $less(0,$sum(X0,2))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_300])]) ).
tff(f43015,plain,
( ! [X0: $int] :
( $less(0,$sum(2,X0))
| ~ $less(0,X0) )
| ~ spl1_14
| ~ spl1_300 ),
inference(superposition,[],[f33522,f149]) ).
tff(f33522,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,2))
| ~ $less(0,X0) )
| ~ spl1_300 ),
inference(avatar_component_clause,[],[f33521]) ).
tff(f90436,plain,
( spl1_497
| ~ spl1_32
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1562,f1537,f283,f90434]) ).
tff(f90434,plain,
( spl1_497
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,remove(X2,X3)))) = $sum(-1,count(remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_497])]) ).
tff(f283,plain,
( spl1_32
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f1562,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,remove(X2,X3)))) = $sum(-1,count(remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) )
| ~ spl1_32
| ~ spl1_97 ),
inference(resolution,[],[f1538,f284]) ).
tff(f284,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) )
| ~ spl1_32 ),
inference(avatar_component_clause,[],[f283]) ).
tff(f90432,plain,
( spl1_496
| ~ spl1_33
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1549,f1533,f287,f90430]) ).
tff(f90430,plain,
( spl1_496
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(add(X0,add(X1,add(X2,X3)))) = $sum(1,count(add(X1,add(X2,X3)))) )
| ( X0 = X1 )
| in(X0,X3)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_496])]) ).
tff(f1549,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,add(X2,X3)))) = $sum(1,count(add(X1,add(X2,X3)))) )
| ( X0 = X1 )
| in(X0,X3)
| ( X0 = X2 ) )
| ~ spl1_33
| ~ spl1_96 ),
inference(resolution,[],[f1534,f288]) ).
tff(f90428,plain,
( spl1_495
| ~ spl1_88
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1432,f1341,f1333,f90426]) ).
tff(f90426,plain,
( spl1_495
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_495])]) ).
tff(f1432,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(add(X0,remove(X3,X2))) = $sum(1,count(remove(X3,X2))) ) )
| ~ spl1_88
| ~ spl1_90 ),
inference(resolution,[],[f1342,f1334]) ).
tff(f89814,plain,
( spl1_494
| ~ spl1_152
| ~ spl1_257 ),
inference(avatar_split_clause,[],[f11650,f10808,f3128,f89812]) ).
tff(f89812,plain,
( spl1_494
<=> ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_494])]) ).
tff(f3128,plain,
( spl1_152
<=> ! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_152])]) ).
tff(f10808,plain,
( spl1_257
<=> ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_257])]) ).
tff(f11650,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,3) )
| ~ spl1_152
| ~ spl1_257 ),
inference(evaluation,[],[f11633]) ).
tff(f11633,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,$sum(2,1)) )
| ~ spl1_152
| ~ spl1_257 ),
inference(resolution,[],[f10809,f3129]) ).
tff(f3129,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X0,1)) )
| ~ spl1_152 ),
inference(avatar_component_clause,[],[f3128]) ).
tff(f10809,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(X0,1) )
| ~ spl1_257 ),
inference(avatar_component_clause,[],[f10808]) ).
tff(f89690,plain,
( spl1_493
| ~ spl1_35
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1558,f1537,f321,f89688]) ).
tff(f89688,plain,
( spl1_493
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_493])]) ).
tff(f321,plain,
( spl1_35
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f1558,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) )
| ~ spl1_35
| ~ spl1_97 ),
inference(resolution,[],[f1538,f322]) ).
tff(f322,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f321]) ).
tff(f89686,plain,
( spl1_492
| ~ spl1_37
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1542,f1533,f329,f89684]) ).
tff(f89684,plain,
( spl1_492
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_492])]) ).
tff(f1542,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) )
| ~ spl1_37
| ~ spl1_96 ),
inference(resolution,[],[f1534,f330]) ).
tff(f89682,plain,
( spl1_491
| ~ spl1_79
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1482,f1455,f1077,f89680]) ).
tff(f89680,plain,
( spl1_491
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_491])]) ).
tff(f1482,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) )
| ~ spl1_79
| ~ spl1_94 ),
inference(resolution,[],[f1456,f1078]) ).
tff(f89678,plain,
( spl1_490
| ~ spl1_76
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1481,f1455,f1065,f89676]) ).
tff(f89676,plain,
( spl1_490
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_490])]) ).
tff(f1481,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) )
| ~ spl1_76
| ~ spl1_94 ),
inference(resolution,[],[f1456,f1066]) ).
tff(f89674,plain,
( spl1_489
| ~ spl1_77
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1469,f1447,f1069,f89672]) ).
tff(f89672,plain,
( spl1_489
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_489])]) ).
tff(f1469,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) )
| ~ spl1_77
| ~ spl1_92 ),
inference(resolution,[],[f1448,f1070]) ).
tff(f89670,plain,
( spl1_488
| ~ spl1_77
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1459,f1443,f1069,f89668]) ).
tff(f89668,plain,
( spl1_488
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_488])]) ).
tff(f1459,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) )
| ~ spl1_77
| ~ spl1_91 ),
inference(resolution,[],[f1444,f1070]) ).
tff(f89594,plain,
( spl1_487
| ~ spl1_122
| ~ spl1_257 ),
inference(avatar_split_clause,[],[f11632,f10808,f1906,f89592]) ).
tff(f89592,plain,
( spl1_487
<=> ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_487])]) ).
tff(f1906,plain,
( spl1_122
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
tff(f11632,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| ~ $less(2,X0) )
| ~ spl1_122
| ~ spl1_257 ),
inference(resolution,[],[f10809,f1907]) ).
tff(f1907,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| ~ $less(X0,X1) )
| ~ spl1_122 ),
inference(avatar_component_clause,[],[f1906]) ).
tff(f88339,plain,
( spl1_486
| ~ spl1_33
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1487,f1455,f287,f88337]) ).
tff(f88337,plain,
( spl1_486
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,add(X2,X3)))) = count(add(X1,add(X2,X3))) )
| in(X0,X3)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_486])]) ).
tff(f1487,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,add(X2,X3)))) = count(add(X1,add(X2,X3))) )
| in(X0,X3)
| ( X0 = X2 ) )
| ~ spl1_33
| ~ spl1_94 ),
inference(resolution,[],[f1456,f288]) ).
tff(f88335,plain,
( spl1_485
| ~ spl1_32
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1474,f1447,f283,f88333]) ).
tff(f88333,plain,
( spl1_485
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,remove(X2,X3)) = add(X0,remove(X0,remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_485])]) ).
tff(f1474,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,remove(X2,X3)) = add(X0,remove(X0,remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) )
| ~ spl1_32
| ~ spl1_92 ),
inference(resolution,[],[f1448,f284]) ).
tff(f88331,plain,
( spl1_484
| ~ spl1_32
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1464,f1443,f283,f88329]) ).
tff(f88329,plain,
( spl1_484
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,remove(X2,X3))) = count(add(X0,remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_484])]) ).
tff(f1464,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,remove(X2,X3))) = count(add(X0,remove(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) )
| ~ spl1_32
| ~ spl1_91 ),
inference(resolution,[],[f1444,f284]) ).
tff(f88327,plain,
( spl1_483
| ~ spl1_77
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1433,f1341,f1069,f88325]) ).
tff(f88325,plain,
( spl1_483
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_483])]) ).
tff(f1433,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(remove(X3,X2)) = count(remove(X0,remove(X3,X2))) ) )
| ~ spl1_77
| ~ spl1_90 ),
inference(resolution,[],[f1342,f1070]) ).
tff(f88323,plain,
( spl1_482
| ~ spl1_76
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1392,f1333,f1065,f88321]) ).
tff(f88321,plain,
( spl1_482
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_482])]) ).
tff(f1392,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) )
| ~ spl1_76
| ~ spl1_88 ),
inference(resolution,[],[f1334,f1066]) ).
tff(f88319,plain,
( spl1_481
| ~ spl1_79
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1391,f1333,f1077,f88317]) ).
tff(f88317,plain,
( spl1_481
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_481])]) ).
tff(f1391,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(add(X3,X2)) = count(add(X0,add(X3,X2))) ) )
| ~ spl1_79
| ~ spl1_88 ),
inference(resolution,[],[f1334,f1078]) ).
tff(f88315,plain,
( spl1_480
| ~ spl1_16
| ~ spl1_257 ),
inference(avatar_split_clause,[],[f11631,f10808,f158,f88313]) ).
tff(f88313,plain,
( spl1_480
<=> ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_480])]) ).
tff(f158,plain,
( spl1_16
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f11631,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,2) )
| ~ spl1_16
| ~ spl1_257 ),
inference(resolution,[],[f10809,f159]) ).
tff(f159,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f158]) ).
tff(f88311,plain,
( spl1_479
| ~ spl1_66
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1236,f1089,f833,f88309]) ).
tff(f88309,plain,
( spl1_479
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X2))
| ( $sum(X1,$sum(X2,X3)) = X4 )
| $less(X4,$sum(X1,$sum(X2,X3)))
| $less($sum(X0,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_479])]) ).
tff(f833,plain,
( spl1_66
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
tff(f1089,plain,
( spl1_82
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
tff(f1236,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X0,$sum(X1,X2))
| ( $sum(X1,$sum(X2,X3)) = X4 )
| $less(X4,$sum(X1,$sum(X2,X3)))
| $less($sum(X0,X3),X4) )
| ~ spl1_66
| ~ spl1_82 ),
inference(resolution,[],[f1090,f834]) ).
tff(f834,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| ( X0 = X1 )
| $less(X1,X0)
| $less(X2,X1) )
| ~ spl1_66 ),
inference(avatar_component_clause,[],[f833]) ).
tff(f1090,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_82 ),
inference(avatar_component_clause,[],[f1089]) ).
tff(f87716,plain,
( spl1_478
| ~ spl1_49
| ~ spl1_257 ),
inference(avatar_split_clause,[],[f11629,f10808,f469,f87714]) ).
tff(f87714,plain,
( spl1_478
<=> ! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_478])]) ).
tff(f469,plain,
( spl1_49
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f11629,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,2) )
| ~ spl1_49
| ~ spl1_257 ),
inference(resolution,[],[f10809,f470]) ).
tff(f470,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f469]) ).
tff(f87244,plain,
( spl1_477
| ~ spl1_19
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1561,f1537,f170,f87242]) ).
tff(f87242,plain,
( spl1_477
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,add(X2,X3)))) = $sum(-1,count(remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_477])]) ).
tff(f170,plain,
( spl1_19
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f1561,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,add(X2,X3)))) = $sum(-1,count(remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) )
| ~ spl1_19
| ~ spl1_97 ),
inference(resolution,[],[f1538,f171]) ).
tff(f171,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f170]) ).
tff(f87240,plain,
( spl1_476
| ~ spl1_26
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1559,f1537,f214,f87238]) ).
tff(f87238,plain,
( spl1_476
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_476])]) ).
tff(f214,plain,
( spl1_26
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f1559,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) )
| ~ spl1_26
| ~ spl1_97 ),
inference(resolution,[],[f1538,f215]) ).
tff(f215,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_26 ),
inference(avatar_component_clause,[],[f214]) ).
tff(f87236,plain,
( spl1_475
| ~ spl1_18
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1551,f1533,f166,f87234]) ).
tff(f87234,plain,
( spl1_475
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(add(X0,add(X1,remove(X2,X3)))) = $sum(1,count(add(X1,remove(X2,X3)))) )
| ( X0 = X1 )
| in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_475])]) ).
tff(f166,plain,
( spl1_18
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f1551,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,remove(X2,X3)))) = $sum(1,count(add(X1,remove(X2,X3)))) )
| ( X0 = X1 )
| in(X0,X3) )
| ~ spl1_18
| ~ spl1_96 ),
inference(resolution,[],[f1534,f167]) ).
tff(f167,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) )
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f166]) ).
tff(f87232,plain,
( spl1_474
| ~ spl1_28
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1541,f1533,f226,f87230]) ).
tff(f87230,plain,
( spl1_474
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(X2) = count(add(X0,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_474])]) ).
tff(f1541,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( count(X2) = count(add(X0,X2)) ) )
| ~ spl1_28
| ~ spl1_96 ),
inference(resolution,[],[f1534,f227]) ).
tff(f87228,plain,
( spl1_473
| ~ spl1_25
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1540,f1533,f210,f87226]) ).
tff(f87226,plain,
( spl1_473
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( add(X0,remove(X0,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_473])]) ).
tff(f210,plain,
( spl1_25
<=> ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f1540,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| ( X0 = X1 )
| ( add(X0,remove(X0,X2)) = X2 ) )
| ~ spl1_25
| ~ spl1_96 ),
inference(resolution,[],[f1534,f211]) ).
tff(f211,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl1_25 ),
inference(avatar_component_clause,[],[f210]) ).
tff(f87224,plain,
( spl1_472
| ~ spl1_37
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1480,f1455,f329,f87222]) ).
tff(f87222,plain,
( spl1_472
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_472])]) ).
tff(f1480,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) )
| ~ spl1_37
| ~ spl1_94 ),
inference(resolution,[],[f1456,f330]) ).
tff(f87220,plain,
( spl1_471
| ~ spl1_35
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1470,f1447,f321,f87218]) ).
tff(f87218,plain,
( spl1_471
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_471])]) ).
tff(f1470,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) )
| ~ spl1_35
| ~ spl1_92 ),
inference(resolution,[],[f1448,f322]) ).
tff(f87216,plain,
( spl1_470
| ~ spl1_35
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1460,f1443,f321,f87214]) ).
tff(f87214,plain,
( spl1_470
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_470])]) ).
tff(f1460,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) )
| ~ spl1_35
| ~ spl1_91 ),
inference(resolution,[],[f1444,f322]) ).
tff(f87212,plain,
( spl1_469
| ~ spl1_133
| ~ spl1_257 ),
inference(avatar_split_clause,[],[f11627,f10808,f1960,f87210]) ).
tff(f87210,plain,
( spl1_469
<=> ! [X0: $int] :
( ~ $less($sum(X0,2),1)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_469])]) ).
tff(f1960,plain,
( spl1_133
<=> ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
tff(f11627,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,2),1)
| ~ $less(0,X0) )
| ~ spl1_133
| ~ spl1_257 ),
inference(resolution,[],[f10809,f1961]) ).
tff(f1961,plain,
( ! [X2: $int,X1: $int] :
( $less(X1,$sum(X2,X1))
| ~ $less(0,X2) )
| ~ spl1_133 ),
inference(avatar_component_clause,[],[f1960]) ).
tff(f87208,plain,
( spl1_468
| ~ spl1_32
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1438,f1341,f283,f87206]) ).
tff(f87206,plain,
( spl1_468
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(remove(X0,add(X1,remove(X2,X3)))) = $sum(-1,count(add(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_468])]) ).
tff(f1438,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,remove(X2,X3)))) = $sum(-1,count(add(X1,remove(X2,X3)))) )
| ( X0 = X2 )
| ~ in(X0,X3) )
| ~ spl1_32
| ~ spl1_90 ),
inference(resolution,[],[f1342,f284]) ).
tff(f87204,plain,
( spl1_467
| ~ spl1_33
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1397,f1333,f287,f87202]) ).
tff(f87202,plain,
( spl1_467
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(add(X0,remove(X1,add(X2,X3)))) = $sum(1,count(remove(X1,add(X2,X3)))) )
| in(X0,X3)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_467])]) ).
tff(f1397,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,add(X2,X3)))) = $sum(1,count(remove(X1,add(X2,X3)))) )
| in(X0,X3)
| ( X0 = X2 ) )
| ~ spl1_33
| ~ spl1_88 ),
inference(resolution,[],[f1334,f288]) ).
tff(f87200,plain,
( spl1_466
| ~ spl1_67
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f932,f907,f837,f87198]) ).
tff(f87198,plain,
( spl1_466
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(X1,$sum(X2,1)) )
| ~ $less(X0,$sum(X1,$sum(X2,1)))
| ~ $less($sum(X1,X2),$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_466])]) ).
tff(f837,plain,
( spl1_67
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
tff(f907,plain,
( spl1_70
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
tff(f932,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(X1,$sum(X2,1)) )
| ~ $less(X0,$sum(X1,$sum(X2,1)))
| ~ $less($sum(X1,X2),$sum(X0,1)) )
| ~ spl1_67
| ~ spl1_70 ),
inference(resolution,[],[f908,f838]) ).
tff(f838,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_67 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f908,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f907]) ).
tff(f84443,plain,
( spl1_465
| ~ spl1_35
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1434,f1341,f321,f84441]) ).
tff(f84441,plain,
( spl1_465
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_465])]) ).
tff(f1434,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(add(X0,X2)) = $sum(1,count(X2)) ) )
| ~ spl1_35
| ~ spl1_90 ),
inference(resolution,[],[f1342,f322]) ).
tff(f84439,plain,
( spl1_464
| ~ spl1_37
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1393,f1333,f329,f84437]) ).
tff(f84437,plain,
( spl1_464
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_464])]) ).
tff(f1393,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) )
| ~ spl1_37
| ~ spl1_88 ),
inference(resolution,[],[f1334,f330]) ).
tff(f84435,plain,
( spl1_463
| ~ spl1_66
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1280,f1093,f833,f84433]) ).
tff(f84433,plain,
( spl1_463
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| ( $sum(X2,X3) = X4 )
| $less(X4,$sum(X2,X3))
| $less($sum(X0,$sum(X1,X3)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_463])]) ).
tff(f1093,plain,
( spl1_83
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).
tff(f1280,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less($sum(X0,X1),X2)
| ( $sum(X2,X3) = X4 )
| $less(X4,$sum(X2,X3))
| $less($sum(X0,$sum(X1,X3)),X4) )
| ~ spl1_66
| ~ spl1_83 ),
inference(resolution,[],[f1094,f834]) ).
tff(f1094,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_83 ),
inference(avatar_component_clause,[],[f1093]) ).
tff(f84431,plain,
( spl1_462
| ~ spl1_77
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1128,f1077,f1069,f84429]) ).
tff(f84429,plain,
( spl1_462
<=> ! [X0: $int,X3: $int,X2: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( count(remove(X2,remove(X3,X1))) = count(remove(X3,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_462])]) ).
tff(f1128,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( count(remove(X2,remove(X3,X1))) = count(remove(X3,X1)) ) )
| ~ spl1_77
| ~ spl1_79 ),
inference(resolution,[],[f1078,f1070]) ).
tff(f84427,plain,
( spl1_461
| ~ spl1_76
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1108,f1069,f1065,f84425]) ).
tff(f84425,plain,
( spl1_461
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_461])]) ).
tff(f1108,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( add(X3,X2) = add(X0,remove(X0,add(X3,X2))) ) )
| ~ spl1_76
| ~ spl1_77 ),
inference(resolution,[],[f1070,f1066]) ).
tff(f84423,plain,
( spl1_460
| ~ spl1_66
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f988,f919,f833,f84421]) ).
tff(f84421,plain,
( spl1_460
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| ( $uminus($sum(X2,X1)) = X3 )
| $less(X3,$uminus($sum(X2,X1)))
| $less($sum(X0,$uminus(X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_460])]) ).
tff(f919,plain,
( spl1_73
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
tff(f988,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| ( $uminus($sum(X2,X1)) = X3 )
| $less(X3,$uminus($sum(X2,X1)))
| $less($sum(X0,$uminus(X2)),X3) )
| ~ spl1_66
| ~ spl1_73 ),
inference(resolution,[],[f920,f834]) ).
tff(f920,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_73 ),
inference(avatar_component_clause,[],[f919]) ).
tff(f84419,plain,
( spl1_459
| ~ spl1_66
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f965,f915,f833,f84417]) ).
tff(f84417,plain,
( spl1_459
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| ( $sum(X1,$uminus(X2)) = X3 )
| $less(X3,$sum(X1,$uminus(X2)))
| $less($uminus($sum(X2,X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_459])]) ).
tff(f915,plain,
( spl1_72
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
tff(f965,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| ( $sum(X1,$uminus(X2)) = X3 )
| $less(X3,$sum(X1,$uminus(X2)))
| $less($uminus($sum(X2,X0)),X3) )
| ~ spl1_66
| ~ spl1_72 ),
inference(resolution,[],[f916,f834]) ).
tff(f916,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl1_72 ),
inference(avatar_component_clause,[],[f915]) ).
tff(f84415,plain,
( spl1_458
| ~ spl1_70
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f951,f911,f907,f84413]) ).
tff(f84413,plain,
( spl1_458
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,1),$sum(X1,X3))
| ( $sum(X2,1) = $sum(X0,X3) )
| ~ $less(X2,$sum(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_458])]) ).
tff(f911,plain,
( spl1_71
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
tff(f951,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,1),$sum(X1,X3))
| ( $sum(X2,1) = $sum(X0,X3) )
| ~ $less(X2,$sum(X0,X3)) )
| ~ spl1_70
| ~ spl1_71 ),
inference(resolution,[],[f912,f908]) ).
tff(f912,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,X3))
| ~ $less(X0,X1)
| $less(X2,$sum(X1,X3)) )
| ~ spl1_71 ),
inference(avatar_component_clause,[],[f911]) ).
tff(f84347,plain,
( spl1_457
| ~ spl1_66
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f883,f841,f833,f84345]) ).
tff(f84345,plain,
( spl1_457
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| ( $sum(X0,$sum(X1,1)) = X3 )
| $less(X3,$sum(X0,$sum(X1,1)))
| $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_457])]) ).
tff(f841,plain,
( spl1_68
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
tff(f883,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| ( $sum(X0,$sum(X1,1)) = X3 )
| $less(X3,$sum(X0,$sum(X1,1)))
| $less(X2,X3) )
| ~ spl1_66
| ~ spl1_68 ),
inference(resolution,[],[f842,f834]) ).
tff(f842,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl1_68 ),
inference(avatar_component_clause,[],[f841]) ).
tff(f83831,plain,
( spl1_456
| ~ spl1_122
| ~ spl1_326 ),
inference(avatar_split_clause,[],[f80588,f41620,f1906,f83829]) ).
tff(f83829,plain,
( spl1_456
<=> ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_456])]) ).
tff(f41620,plain,
( spl1_326
<=> ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_326])]) ).
tff(f80588,plain,
( ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,X0) )
| ~ spl1_122
| ~ spl1_326 ),
inference(resolution,[],[f41621,f1907]) ).
tff(f41621,plain,
( ! [X0: $int] :
( ~ $less(2,$sum(X0,1))
| $less(-1,X0) )
| ~ spl1_326 ),
inference(avatar_component_clause,[],[f41620]) ).
tff(f80638,plain,
( spl1_455
| ~ spl1_51
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f1510,f1492,f477,f80636]) ).
tff(f80636,plain,
( spl1_455
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(X1)))
| ( 0 = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_455])]) ).
tff(f1492,plain,
( spl1_95
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_95])]) ).
tff(f1510,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(X1)))
| ( 0 = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_51
| ~ spl1_95 ),
inference(superposition,[],[f478,f1493]) ).
tff(f1493,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_95 ),
inference(avatar_component_clause,[],[f1492]) ).
tff(f80634,plain,
( spl1_454
| ~ spl1_18
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1489,f1455,f166,f80632]) ).
tff(f80632,plain,
( spl1_454
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,remove(X2,X3)))) = count(add(X1,remove(X2,X3))) )
| in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_454])]) ).
tff(f1489,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,remove(X2,X3)))) = count(add(X1,remove(X2,X3))) )
| in(X0,X3) )
| ~ spl1_18
| ~ spl1_94 ),
inference(resolution,[],[f1456,f167]) ).
tff(f80630,plain,
( spl1_453
| ~ spl1_28
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1479,f1455,f226,f80628]) ).
tff(f80628,plain,
( spl1_453
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(X2) = count(add(X0,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_453])]) ).
tff(f1479,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( count(X2) = count(add(X0,X2)) ) )
| ~ spl1_28
| ~ spl1_94 ),
inference(resolution,[],[f1456,f227]) ).
tff(f80586,plain,
( spl1_452
| ~ spl1_25
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1478,f1455,f210,f80584]) ).
tff(f80584,plain,
( spl1_452
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( add(X0,remove(X0,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_452])]) ).
tff(f1478,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,X2))) = count(add(X1,X2)) )
| ( add(X0,remove(X0,X2)) = X2 ) )
| ~ spl1_25
| ~ spl1_94 ),
inference(resolution,[],[f1456,f211]) ).
tff(f80582,plain,
( spl1_451
| ~ spl1_19
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1473,f1447,f170,f80580]) ).
tff(f80580,plain,
( spl1_451
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,add(X2,X3)) = add(X0,remove(X0,remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_451])]) ).
tff(f1473,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,add(X2,X3)) = add(X0,remove(X0,remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) )
| ~ spl1_19
| ~ spl1_92 ),
inference(resolution,[],[f1448,f171]) ).
tff(f80578,plain,
( spl1_450
| ~ spl1_26
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1471,f1447,f214,f80576]) ).
tff(f80576,plain,
( spl1_450
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_450])]) ).
tff(f1471,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) )
| ~ spl1_26
| ~ spl1_92 ),
inference(resolution,[],[f1448,f215]) ).
tff(f80574,plain,
( spl1_449
| ~ spl1_19
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1463,f1443,f170,f80572]) ).
tff(f80572,plain,
( spl1_449
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,add(X2,X3))) = count(add(X0,remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_449])]) ).
tff(f1463,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,add(X2,X3))) = count(add(X0,remove(X1,add(X2,X3)))) )
| ~ in(X0,X3) )
| ~ spl1_19
| ~ spl1_91 ),
inference(resolution,[],[f1444,f171]) ).
tff(f80570,plain,
( spl1_448
| ~ spl1_26
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1461,f1443,f214,f80568]) ).
tff(f80568,plain,
( spl1_448
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_448])]) ).
tff(f1461,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) )
| ~ spl1_26
| ~ spl1_91 ),
inference(resolution,[],[f1444,f215]) ).
tff(f80566,plain,
( spl1_447
| ~ spl1_29
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f1382,f1325,f230,f80564]) ).
tff(f80564,plain,
( spl1_447
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != count(X1) )
| in(X0,remove(X0,X1))
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_447])]) ).
tff(f1325,plain,
( spl1_86
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
tff(f1382,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != count(X1) )
| in(X0,remove(X0,X1))
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_29
| ~ spl1_86 ),
inference(superposition,[],[f231,f1326]) ).
tff(f1326,plain,
( ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_86 ),
inference(avatar_component_clause,[],[f1325]) ).
tff(f80562,plain,
( spl1_446
| ~ spl1_81
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1310,f1093,f1085,f80560]) ).
tff(f80560,plain,
( spl1_446
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X4,$sum($uminus(X1),X2))),$sum($uminus($sum(X1,X0)),X2))
| ~ $less($sum(X3,X4),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_446])]) ).
tff(f1085,plain,
( spl1_81
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).
tff(f1310,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X4,$sum($uminus(X1),X2))),$sum($uminus($sum(X1,X0)),X2))
| ~ $less($sum(X3,X4),$uminus(X0)) )
| ~ spl1_81
| ~ spl1_83 ),
inference(superposition,[],[f1094,f1086]) ).
tff(f1086,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl1_81 ),
inference(avatar_component_clause,[],[f1085]) ).
tff(f80558,plain,
( spl1_445
| ~ spl1_81
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1291,f1093,f1085,f80556]) ).
tff(f80556,plain,
( spl1_445
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum($uminus($sum(X1,X0)),X2)),$sum(X4,$sum($uminus(X1),X2)))
| ~ $less($sum(X3,$uminus(X0)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_445])]) ).
tff(f1291,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum($uminus($sum(X1,X0)),X2)),$sum(X4,$sum($uminus(X1),X2)))
| ~ $less($sum(X3,$uminus(X0)),X4) )
| ~ spl1_81
| ~ spl1_83 ),
inference(superposition,[],[f1094,f1086]) ).
tff(f80554,plain,
( spl1_444
| ~ spl1_81
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1258,f1089,f1085,f80552]) ).
tff(f80552,plain,
( spl1_444
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum($uminus(X1),X2)),$sum(X4,$sum($uminus($sum(X1,X0)),X2)))
| ~ $less(X3,$sum(X4,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_444])]) ).
tff(f1258,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum($uminus(X1),X2)),$sum(X4,$sum($uminus($sum(X1,X0)),X2)))
| ~ $less(X3,$sum(X4,$uminus(X0))) )
| ~ spl1_81
| ~ spl1_82 ),
inference(superposition,[],[f1090,f1086]) ).
tff(f80550,plain,
( spl1_443
| ~ spl1_81
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1247,f1089,f1085,f80548]) ).
tff(f80548,plain,
( spl1_443
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$sum(X4,$sum($uminus(X1),X2))))
| ~ $less($uminus(X0),$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_443])]) ).
tff(f1247,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$sum(X4,$sum($uminus(X1),X2))))
| ~ $less($uminus(X0),$sum(X3,X4)) )
| ~ spl1_81
| ~ spl1_82 ),
inference(superposition,[],[f1090,f1086]) ).
tff(f80493,plain,
( spl1_442
| ~ spl1_32
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1133,f1077,f283,f80491]) ).
tff(f80491,plain,
( spl1_442
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = count(add(X3,add(X0,remove(X1,X2)))) )
| ( X1 = X3 )
| ~ in(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_442])]) ).
tff(f1133,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = count(add(X3,add(X0,remove(X1,X2)))) )
| ( X1 = X3 )
| ~ in(X3,X2) )
| ~ spl1_32
| ~ spl1_79 ),
inference(resolution,[],[f1078,f284]) ).
tff(f80489,plain,
( spl1_441
| ~ spl1_33
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1113,f1069,f287,f80487]) ).
tff(f80487,plain,
( spl1_441
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(remove(X0,remove(X1,add(X2,X3)))) = count(remove(X1,add(X2,X3))) )
| in(X0,X3)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_441])]) ).
tff(f1113,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,add(X2,X3)))) = count(remove(X1,add(X2,X3))) )
| in(X0,X3)
| ( X0 = X2 ) )
| ~ spl1_33
| ~ spl1_77 ),
inference(resolution,[],[f1070,f288]) ).
tff(f80485,plain,
( spl1_440
| ~ spl1_32
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1104,f1065,f283,f80483]) ).
tff(f80483,plain,
( spl1_440
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( add(X0,remove(X1,X2)) = add(X3,remove(X3,add(X0,remove(X1,X2)))) )
| ( X1 = X3 )
| ~ in(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_440])]) ).
tff(f1104,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( add(X0,remove(X1,X2)) = add(X3,remove(X3,add(X0,remove(X1,X2)))) )
| ( X1 = X3 )
| ~ in(X3,X2) )
| ~ spl1_32
| ~ spl1_76 ),
inference(resolution,[],[f1066,f284]) ).
tff(f79236,plain,
( spl1_439
| ~ spl1_12
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1560,f1537,f140,f79234]) ).
tff(f79234,plain,
( spl1_439
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,add(X0,X2)))) = $sum(-1,count(remove(X1,add(X0,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_439])]) ).
tff(f140,plain,
( spl1_12
<=> ! [X0: $int,X1: collection] : in(X0,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f1560,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,remove(X1,add(X0,X2)))) = $sum(-1,count(remove(X1,add(X0,X2)))) ) )
| ~ spl1_12
| ~ spl1_97 ),
inference(resolution,[],[f1538,f141]) ).
tff(f141,plain,
( ! [X0: $int,X1: collection] : in(X0,add(X0,X1))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f140]) ).
tff(f79232,plain,
( spl1_438
| ~ spl1_11
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1550,f1533,f136,f79230]) ).
tff(f79230,plain,
( spl1_438
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,remove(X0,X2)))) = $sum(1,count(add(X1,remove(X0,X2)))) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_438])]) ).
tff(f136,plain,
( spl1_11
<=> ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f1550,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,remove(X0,X2)))) = $sum(1,count(add(X1,remove(X0,X2)))) )
| ( X0 = X1 ) )
| ~ spl1_11
| ~ spl1_96 ),
inference(resolution,[],[f1534,f137]) ).
tff(f137,plain,
( ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f136]) ).
tff(f79228,plain,
( spl1_437
| ~ spl1_15
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f1511,f1492,f152,f79226]) ).
tff(f1511,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_15
| ~ spl1_95 ),
inference(superposition,[],[f153,f1493]) ).
tff(f79224,plain,
( spl1_436
| ~ spl1_19
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1437,f1341,f170,f79222]) ).
tff(f79222,plain,
( spl1_436
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(remove(X0,add(X1,add(X2,X3)))) = $sum(-1,count(add(X1,add(X2,X3)))) )
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_436])]) ).
tff(f1437,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,add(X2,X3)))) = $sum(-1,count(add(X1,add(X2,X3)))) )
| ~ in(X0,X3) )
| ~ spl1_19
| ~ spl1_90 ),
inference(resolution,[],[f1342,f171]) ).
tff(f79220,plain,
( spl1_435
| ~ spl1_26
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1435,f1341,f214,f79218]) ).
tff(f79218,plain,
( spl1_435
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_435])]) ).
tff(f1435,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ( count(remove(X0,X2)) = count(X2) ) )
| ~ spl1_26
| ~ spl1_90 ),
inference(resolution,[],[f1342,f215]) ).
tff(f79199,plain,
( spl1_434
| ~ spl1_18
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1399,f1333,f166,f79197]) ).
tff(f79197,plain,
( spl1_434
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(add(X0,remove(X1,remove(X2,X3)))) = $sum(1,count(remove(X1,remove(X2,X3)))) )
| in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_434])]) ).
tff(f1399,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,remove(X2,X3)))) = $sum(1,count(remove(X1,remove(X2,X3)))) )
| in(X0,X3) )
| ~ spl1_18
| ~ spl1_88 ),
inference(resolution,[],[f1334,f167]) ).
tff(f79195,plain,
( spl1_433
| ~ spl1_25
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1395,f1333,f210,f79193]) ).
tff(f79193,plain,
( spl1_433
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( add(X0,remove(X0,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_433])]) ).
tff(f1395,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( add(X0,remove(X0,X2)) = X2 ) )
| ~ spl1_25
| ~ spl1_88 ),
inference(resolution,[],[f1334,f211]) ).
tff(f79191,plain,
( spl1_432
| ~ spl1_28
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1394,f1333,f226,f79189]) ).
tff(f79189,plain,
( spl1_432
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(X2) = count(add(X0,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_432])]) ).
tff(f1394,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| ( count(X2) = count(add(X0,X2)) ) )
| ~ spl1_28
| ~ spl1_88 ),
inference(resolution,[],[f1334,f227]) ).
tff(f79187,plain,
( spl1_431
| ~ spl1_71
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1204,f1085,f911,f79185]) ).
tff(f79185,plain,
( spl1_431
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,$sum($uminus($sum(X1,X0)),X2))
| ~ $less($uminus(X0),X4)
| $less(X3,$sum(X4,$sum($uminus(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_431])]) ).
tff(f1204,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X3,$sum($uminus($sum(X1,X0)),X2))
| ~ $less($uminus(X0),X4)
| $less(X3,$sum(X4,$sum($uminus(X1),X2))) )
| ~ spl1_71
| ~ spl1_81 ),
inference(superposition,[],[f912,f1086]) ).
tff(f79183,plain,
( spl1_430
| ~ spl1_35
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1129,f1077,f321,f79181]) ).
tff(f79181,plain,
( spl1_430
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( $sum(1,count(X1)) = count(add(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_430])]) ).
tff(f1129,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( $sum(1,count(X1)) = count(add(X2,X1)) ) )
| ~ spl1_35
| ~ spl1_79 ),
inference(resolution,[],[f1078,f322]) ).
tff(f79179,plain,
( spl1_429
| ~ spl1_37
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1109,f1069,f329,f79177]) ).
tff(f79177,plain,
( spl1_429
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_429])]) ).
tff(f1109,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( count(remove(X0,X2)) = $sum(-1,count(X2)) ) )
| ~ spl1_37
| ~ spl1_77 ),
inference(resolution,[],[f1070,f330]) ).
tff(f79175,plain,
( spl1_428
| ~ spl1_35
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1100,f1065,f321,f79173]) ).
tff(f79173,plain,
( spl1_428
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( add(X0,X1) = add(X2,remove(X2,add(X0,X1))) )
| ( $sum(1,count(X1)) = count(add(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_428])]) ).
tff(f1100,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( add(X0,X1) = add(X2,remove(X2,add(X0,X1))) )
| ( $sum(1,count(X1)) = count(add(X2,X1)) ) )
| ~ spl1_35
| ~ spl1_76 ),
inference(resolution,[],[f1066,f322]) ).
tff(f78905,plain,
( spl1_427
| ~ spl1_142
| ~ spl1_314 ),
inference(avatar_split_clause,[],[f75796,f39579,f2428,f78903]) ).
tff(f78903,plain,
( spl1_427
<=> ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(-1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_427])]) ).
tff(f2428,plain,
( spl1_142
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_142])]) ).
tff(f75796,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(-1,$uminus(X0)) )
| ~ spl1_142
| ~ spl1_314 ),
inference(resolution,[],[f39580,f2429]) ).
tff(f2429,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) )
| ~ spl1_142 ),
inference(avatar_component_clause,[],[f2428]) ).
tff(f77002,plain,
( spl1_426
| ~ spl1_27
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f1504,f1492,f222,f77000]) ).
tff(f77000,plain,
( spl1_426
<=> ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| ~ in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_426])]) ).
tff(f1504,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| ~ in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_27
| ~ spl1_95 ),
inference(superposition,[],[f223,f1493]) ).
tff(f76998,plain,
( spl1_425
| ~ spl1_51
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f1418,f1337,f477,f76996]) ).
tff(f76996,plain,
( spl1_425
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(X1)))
| ( 0 = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_425])]) ).
tff(f1337,plain,
( spl1_89
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
tff(f1418,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(X1)))
| ( 0 = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_51
| ~ spl1_89 ),
inference(superposition,[],[f478,f1338]) ).
tff(f1338,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_89 ),
inference(avatar_component_clause,[],[f1337]) ).
tff(f76994,plain,
( spl1_424
| ~ spl1_51
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f1361,f1321,f477,f76992]) ).
tff(f76992,plain,
( spl1_424
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(1,count(X1)))
| ( 0 = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_424])]) ).
tff(f1321,plain,
( spl1_85
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
tff(f1361,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(1,count(X1)))
| ( 0 = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_51
| ~ spl1_85 ),
inference(superposition,[],[f478,f1322]) ).
tff(f1322,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_85 ),
inference(avatar_component_clause,[],[f1321]) ).
tff(f76990,plain,
( spl1_423
| ~ spl1_60
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1281,f1093,f634,f76988]) ).
tff(f76988,plain,
( spl1_423
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| $less($sum(X0,$sum(X1,X3)),$sum(X4,1))
| $less(X4,$sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_423])]) ).
tff(f634,plain,
( spl1_60
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f1281,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less($sum(X0,X1),X2)
| $less($sum(X0,$sum(X1,X3)),$sum(X4,1))
| $less(X4,$sum(X2,X3)) )
| ~ spl1_60
| ~ spl1_83 ),
inference(resolution,[],[f1094,f635]) ).
tff(f635,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl1_60 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f76986,plain,
( spl1_422
| ~ spl1_60
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1237,f1089,f634,f76984]) ).
tff(f76984,plain,
( spl1_422
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X2))
| $less($sum(X0,X3),$sum(X4,1))
| $less(X4,$sum(X1,$sum(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_422])]) ).
tff(f1237,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X0,$sum(X1,X2))
| $less($sum(X0,X3),$sum(X4,1))
| $less(X4,$sum(X1,$sum(X2,X3))) )
| ~ spl1_60
| ~ spl1_82 ),
inference(resolution,[],[f1090,f635]) ).
tff(f76982,plain,
( spl1_421
| ~ spl1_54
| ~ spl1_314 ),
inference(avatar_split_clause,[],[f75795,f39579,f540,f76980]) ).
tff(f76980,plain,
( spl1_421
<=> ! [X0: $int] :
( ~ $less(2,$uminus(X0))
| ~ $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_421])]) ).
tff(f540,plain,
( spl1_54
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f75795,plain,
( ! [X0: $int] :
( ~ $less(2,$uminus(X0))
| ~ $less(-1,X0) )
| ~ spl1_54
| ~ spl1_314 ),
inference(resolution,[],[f39580,f541]) ).
tff(f541,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f540]) ).
tff(f76978,plain,
( spl1_420
| ~ spl1_64
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f939,f907,f650,f76976]) ).
tff(f76976,plain,
( spl1_420
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,1)),X2)
| ( $sum(X1,$sum(X0,1)) = X2 )
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_420])]) ).
tff(f650,plain,
( spl1_64
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
tff(f939,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,1)),X2)
| ( $sum(X1,$sum(X0,1)) = X2 )
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_64
| ~ spl1_70 ),
inference(superposition,[],[f908,f651]) ).
tff(f651,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f650]) ).
tff(f76974,plain,
( spl1_419
| ~ spl1_66
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f934,f907,f833,f76972]) ).
tff(f76972,plain,
( spl1_419
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| ( X1 = X2 )
| $less(X2,X1)
| $less($sum(X0,1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_419])]) ).
tff(f934,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| ( X1 = X2 )
| $less(X2,X1)
| $less($sum(X0,1),X2) )
| ~ spl1_66
| ~ spl1_70 ),
inference(resolution,[],[f908,f834]) ).
tff(f76970,plain,
( spl1_418
| ~ spl1_22
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f858,f837,f188,f76968]) ).
tff(f76968,plain,
( spl1_418
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| $less($sum(X0,$sum(X1,1)),X2)
| ( $sum(X0,$sum(X1,1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_418])]) ).
tff(f188,plain,
( spl1_22
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f858,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| $less($sum(X0,$sum(X1,1)),X2)
| ( $sum(X0,$sum(X1,1)) = X2 ) )
| ~ spl1_22
| ~ spl1_67 ),
inference(resolution,[],[f838,f189]) ).
tff(f189,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f60755,plain,
( spl1_417
| ~ spl1_161
| ~ spl1_303 ),
inference(avatar_split_clause,[],[f55226,f39535,f3490,f60753]) ).
tff(f60753,plain,
( spl1_417
<=> ! [X0: $int] :
( $less($uminus(X0),3)
| $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_417])]) ).
tff(f3490,plain,
( spl1_161
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X0),X1)
| ~ $less(X2,$sum($uminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_161])]) ).
tff(f55226,plain,
( ! [X0: $int] :
( $less($uminus(X0),3)
| $less(X0,1) )
| ~ spl1_161
| ~ spl1_303 ),
inference(evaluation,[],[f55195]) ).
tff(f55195,plain,
( ! [X0: $int] :
( $less($uminus(X0),3)
| $less($sum(0,X0),1) )
| ~ spl1_161
| ~ spl1_303 ),
inference(resolution,[],[f39536,f3491]) ).
tff(f3491,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum($uminus(X0),X1))
| $less($sum(X2,X0),X1) )
| ~ spl1_161 ),
inference(avatar_component_clause,[],[f3490]) ).
tff(f55409,plain,
( spl1_416
| ~ spl1_11
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1488,f1455,f136,f55407]) ).
tff(f55407,plain,
( spl1_416
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,remove(X0,X2)))) = count(add(X1,remove(X0,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_416])]) ).
tff(f1488,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,remove(X0,X2)))) = count(add(X1,remove(X0,X2))) ) )
| ~ spl1_11
| ~ spl1_94 ),
inference(resolution,[],[f1456,f137]) ).
tff(f55405,plain,
( spl1_415
| ~ spl1_12
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1472,f1447,f140,f55403]) ).
tff(f55403,plain,
( spl1_415
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,add(X0,X2)) = add(X0,remove(X0,remove(X1,add(X0,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_415])]) ).
tff(f1472,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( remove(X1,add(X0,X2)) = add(X0,remove(X0,remove(X1,add(X0,X2)))) ) )
| ~ spl1_12
| ~ spl1_92 ),
inference(resolution,[],[f1448,f141]) ).
tff(f55401,plain,
( spl1_414
| ~ spl1_117
| ~ spl1_393 ),
inference(avatar_split_clause,[],[f55318,f55275,f1826,f55399]) ).
tff(f55399,plain,
( spl1_414
<=> ! [X0: $int] :
( $less(X0,3)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_414])]) ).
tff(f55275,plain,
( spl1_393
<=> ! [X0: $int] :
( $less(X0,3)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_393])]) ).
tff(f55318,plain,
( ! [X0: $int] :
( $less(X0,3)
| $less(-1,X0) )
| ~ spl1_117
| ~ spl1_393 ),
inference(resolution,[],[f55276,f1827]) ).
tff(f55276,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,3) )
| ~ spl1_393 ),
inference(avatar_component_clause,[],[f55275]) ).
tff(f55397,plain,
( spl1_413
| ~ spl1_12
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1462,f1443,f140,f55395]) ).
tff(f55395,plain,
( spl1_413
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,add(X0,X2))) = count(add(X0,remove(X1,add(X0,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_413])]) ).
tff(f1462,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X1,add(X0,X2))) = count(add(X0,remove(X1,add(X0,X2)))) ) )
| ~ spl1_12
| ~ spl1_91 ),
inference(resolution,[],[f1444,f141]) ).
tff(f55393,plain,
( spl1_412
| ~ spl1_15
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f1419,f1337,f152,f55391]) ).
tff(f1419,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(X1)) )
| ( empty = remove(X0,X1) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_15
| ~ spl1_89 ),
inference(superposition,[],[f153,f1338]) ).
tff(f55389,plain,
( spl1_411
| ~ spl1_74
| ~ spl1_86 ),
inference(avatar_split_clause,[],[f1379,f1325,f923,f55387]) ).
tff(f55387,plain,
( spl1_411
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = $sum(1,count(remove(X0,X1))) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_411])]) ).
tff(f1379,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) = $sum(1,count(remove(X0,X1))) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_74
| ~ spl1_86 ),
inference(superposition,[],[f924,f1326]) ).
tff(f55385,plain,
( spl1_410
| ~ spl1_15
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f1362,f1321,f152,f55383]) ).
tff(f55383,plain,
( spl1_410
<=> ! [X0: $int,X1: collection] :
( ( 0 != $sum(1,count(X1)) )
| ( empty = add(X0,X1) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_410])]) ).
tff(f1362,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(1,count(X1)) )
| ( empty = add(X0,X1) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_85 ),
inference(superposition,[],[f153,f1322]) ).
tff(f55381,plain,
( spl1_409
| ~ spl1_31
| ~ spl1_64
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1318,f1093,f650,f279,f55379]) ).
tff(f55379,plain,
( spl1_409
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,$sum(X1,X2)),X4)
| $less($sum(X1,$sum(X0,$sum(X2,X3))),$sum(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_409])]) ).
tff(f279,plain,
( spl1_31
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f1318,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less($sum(X0,$sum(X1,X2)),X4)
| $less($sum(X1,$sum(X0,$sum(X2,X3))),$sum(X4,X3)) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_83 ),
inference(forward_demodulation,[],[f1300,f280]) ).
tff(f280,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f279]) ).
tff(f1300,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X1,$sum(X0,$sum(X2,X3))),$sum(X4,X3))
| ~ $less($sum($sum(X0,X1),X2),X4) )
| ~ spl1_64
| ~ spl1_83 ),
inference(superposition,[],[f1094,f651]) ).
tff(f55377,plain,
( spl1_408
| ~ spl1_64
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1311,f1093,f650,f55375]) ).
tff(f55375,plain,
( spl1_408
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X4,X2)),$sum(X1,$sum(X0,X2)))
| ~ $less($sum(X3,X4),$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_408])]) ).
tff(f1311,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X4,X2)),$sum(X1,$sum(X0,X2)))
| ~ $less($sum(X3,X4),$sum(X0,X1)) )
| ~ spl1_64
| ~ spl1_83 ),
inference(superposition,[],[f1094,f651]) ).
tff(f55373,plain,
( spl1_407
| ~ spl1_65
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1307,f1093,f654,f55371]) ).
tff(f55371,plain,
( spl1_407
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X4,$sum(X1,X2))),$sum(X2,$sum(X0,X1)))
| ~ $less($sum(X3,X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_407])]) ).
tff(f654,plain,
( spl1_65
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
tff(f1307,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X4,$sum(X1,X2))),$sum(X2,$sum(X0,X1)))
| ~ $less($sum(X3,X4),X0) )
| ~ spl1_65
| ~ spl1_83 ),
inference(superposition,[],[f1094,f655]) ).
tff(f655,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl1_65 ),
inference(avatar_component_clause,[],[f654]) ).
tff(f55369,plain,
( spl1_406
| ~ spl1_65
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1306,f1093,f654,f55367]) ).
tff(f55367,plain,
( spl1_406
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X4,$sum(X1,X2))),$sum(X1,$sum(X2,X0)))
| ~ $less($sum(X3,X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_406])]) ).
tff(f1306,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X4,$sum(X1,X2))),$sum(X1,$sum(X2,X0)))
| ~ $less($sum(X3,X4),X0) )
| ~ spl1_65
| ~ spl1_83 ),
inference(superposition,[],[f1094,f655]) ).
tff(f55365,plain,
( spl1_405
| ~ spl1_31
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1293,f1093,f279,f55363]) ).
tff(f55363,plain,
( spl1_405
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X0,$sum(X1,X2))),$sum(X4,X2))
| ~ $less($sum(X3,$sum(X0,X1)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_405])]) ).
tff(f1293,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X0,$sum(X1,X2))),$sum(X4,X2))
| ~ $less($sum(X3,$sum(X0,X1)),X4) )
| ~ spl1_31
| ~ spl1_83 ),
inference(superposition,[],[f1094,f280]) ).
tff(f55361,plain,
( spl1_404
| ~ spl1_64
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1292,f1093,f650,f55359]) ).
tff(f55359,plain,
( spl1_404
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X1,$sum(X0,X2))),$sum(X4,X2))
| ~ $less($sum(X3,$sum(X0,X1)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_404])]) ).
tff(f1292,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X1,$sum(X0,X2))),$sum(X4,X2))
| ~ $less($sum(X3,$sum(X0,X1)),X4) )
| ~ spl1_64
| ~ spl1_83 ),
inference(superposition,[],[f1094,f651]) ).
tff(f55317,plain,
( spl1_403
| ~ spl1_65
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1288,f1093,f654,f55315]) ).
tff(f55315,plain,
( spl1_403
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X2,$sum(X0,X1))),$sum(X4,$sum(X1,X2)))
| ~ $less($sum(X3,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_403])]) ).
tff(f1288,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X2,$sum(X0,X1))),$sum(X4,$sum(X1,X2)))
| ~ $less($sum(X3,X0),X4) )
| ~ spl1_65
| ~ spl1_83 ),
inference(superposition,[],[f1094,f655]) ).
tff(f55313,plain,
( spl1_402
| ~ spl1_65
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1287,f1093,f654,f55311]) ).
tff(f55311,plain,
( spl1_402
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X1,$sum(X2,X0))),$sum(X4,$sum(X1,X2)))
| ~ $less($sum(X3,X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_402])]) ).
tff(f1287,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X1,$sum(X2,X0))),$sum(X4,$sum(X1,X2)))
| ~ $less($sum(X3,X0),X4) )
| ~ spl1_65
| ~ spl1_83 ),
inference(superposition,[],[f1094,f655]) ).
tff(f55309,plain,
( spl1_401
| ~ spl1_31
| ~ spl1_64
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1274,f1089,f650,f279,f55307]) ).
tff(f55307,plain,
( spl1_401
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X4,$sum(X0,$sum(X1,X2)))
| $less($sum(X4,X3),$sum(X1,$sum(X0,$sum(X2,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_401])]) ).
tff(f1274,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X4,$sum(X0,$sum(X1,X2)))
| $less($sum(X4,X3),$sum(X1,$sum(X0,$sum(X2,X3)))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_82 ),
inference(forward_demodulation,[],[f1267,f280]) ).
tff(f1267,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X4,X3),$sum(X1,$sum(X0,$sum(X2,X3))))
| ~ $less(X4,$sum($sum(X0,X1),X2)) )
| ~ spl1_64
| ~ spl1_82 ),
inference(superposition,[],[f1090,f651]) ).
tff(f55305,plain,
( spl1_400
| ~ spl1_31
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1260,f1089,f279,f55303]) ).
tff(f55303,plain,
( spl1_400
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X4,$sum(X0,$sum(X1,X2))))
| ~ $less(X3,$sum(X4,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_400])]) ).
tff(f1260,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,X2),$sum(X4,$sum(X0,$sum(X1,X2))))
| ~ $less(X3,$sum(X4,$sum(X0,X1))) )
| ~ spl1_31
| ~ spl1_82 ),
inference(superposition,[],[f1090,f280]) ).
tff(f55301,plain,
( spl1_399
| ~ spl1_64
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1259,f1089,f650,f55299]) ).
tff(f55299,plain,
( spl1_399
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X4,$sum(X1,$sum(X0,X2))))
| ~ $less(X3,$sum(X4,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_399])]) ).
tff(f1259,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,X2),$sum(X4,$sum(X1,$sum(X0,X2))))
| ~ $less(X3,$sum(X4,$sum(X0,X1))) )
| ~ spl1_64
| ~ spl1_82 ),
inference(superposition,[],[f1090,f651]) ).
tff(f55297,plain,
( spl1_398
| ~ spl1_65
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1255,f1089,f654,f55295]) ).
tff(f55295,plain,
( spl1_398
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X4,$sum(X2,$sum(X0,X1))))
| ~ $less(X3,$sum(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_398])]) ).
tff(f1255,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X4,$sum(X2,$sum(X0,X1))))
| ~ $less(X3,$sum(X4,X0)) )
| ~ spl1_65
| ~ spl1_82 ),
inference(superposition,[],[f1090,f655]) ).
tff(f55293,plain,
( spl1_397
| ~ spl1_65
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1254,f1089,f654,f55291]) ).
tff(f55291,plain,
( spl1_397
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X4,$sum(X1,$sum(X2,X0))))
| ~ $less(X3,$sum(X4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_397])]) ).
tff(f1254,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X4,$sum(X1,$sum(X2,X0))))
| ~ $less(X3,$sum(X4,X0)) )
| ~ spl1_65
| ~ spl1_82 ),
inference(superposition,[],[f1090,f655]) ).
tff(f55289,plain,
( spl1_396
| ~ spl1_31
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1249,f1089,f279,f55287]) ).
tff(f55287,plain,
( spl1_396
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,$sum(X4,X2)))
| ~ $less($sum(X0,X1),$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_396])]) ).
tff(f1249,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,$sum(X4,X2)))
| ~ $less($sum(X0,X1),$sum(X3,X4)) )
| ~ spl1_31
| ~ spl1_82 ),
inference(superposition,[],[f1090,f280]) ).
tff(f55285,plain,
( spl1_395
| ~ spl1_64
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1248,f1089,f650,f55283]) ).
tff(f55283,plain,
( spl1_395
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,$sum(X4,X2)))
| ~ $less($sum(X0,X1),$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_395])]) ).
tff(f1248,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,$sum(X4,X2)))
| ~ $less($sum(X0,X1),$sum(X3,X4)) )
| ~ spl1_64
| ~ spl1_82 ),
inference(superposition,[],[f1090,f651]) ).
tff(f55281,plain,
( spl1_394
| ~ spl1_65
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1244,f1089,f654,f55279]) ).
tff(f55279,plain,
( spl1_394
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,$sum(X4,$sum(X1,X2))))
| ~ $less(X0,$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_394])]) ).
tff(f1244,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,$sum(X4,$sum(X1,X2))))
| ~ $less(X0,$sum(X3,X4)) )
| ~ spl1_65
| ~ spl1_82 ),
inference(superposition,[],[f1090,f655]) ).
tff(f55277,plain,
( spl1_393
| ~ spl1_17
| ~ spl1_303 ),
inference(avatar_split_clause,[],[f55188,f39535,f162,f55275]) ).
tff(f162,plain,
( spl1_17
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f55188,plain,
( ! [X0: $int] :
( $less(X0,3)
| ~ $less(X0,0) )
| ~ spl1_17
| ~ spl1_303 ),
inference(resolution,[],[f39536,f163]) ).
tff(f163,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f162]) ).
tff(f55273,plain,
( spl1_392
| ~ spl1_65
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1243,f1089,f654,f55271]) ).
tff(f55271,plain,
( spl1_392
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X2,X0)),$sum(X3,$sum(X4,$sum(X1,X2))))
| ~ $less(X0,$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_392])]) ).
tff(f1243,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( $less($sum(X1,$sum(X2,X0)),$sum(X3,$sum(X4,$sum(X1,X2))))
| ~ $less(X0,$sum(X3,X4)) )
| ~ spl1_65
| ~ spl1_82 ),
inference(superposition,[],[f1090,f655]) ).
tff(f55269,plain,
( spl1_391
| ~ spl1_31
| ~ spl1_65
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1232,f1085,f654,f279,f55267]) ).
tff(f55267,plain,
( spl1_391
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum($uminus($sum(X1,X0)),X2)) = $sum($uminus(X0),$sum($uminus(X1),$sum(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_391])]) ).
tff(f1232,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum($uminus($sum(X1,X0)),X2)) = $sum($uminus(X0),$sum($uminus(X1),$sum(X2,X3))) )
| ~ spl1_31
| ~ spl1_65
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1202,f280]) ).
tff(f1202,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($sum($uminus(X1),X2),X3)) = $sum(X3,$sum($uminus($sum(X1,X0)),X2)) )
| ~ spl1_65
| ~ spl1_81 ),
inference(superposition,[],[f655,f1086]) ).
tff(f55265,plain,
( spl1_390
| ~ spl1_31
| ~ spl1_64
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1231,f1085,f650,f279,f55263]) ).
tff(f55263,plain,
( spl1_390
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum($uminus(X1),X2),$sum($uminus(X0),X3)) = $sum($uminus($sum(X1,X0)),$sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_390])]) ).
tff(f1231,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum($uminus(X1),X2),$sum($uminus(X0),X3)) = $sum($uminus($sum(X1,X0)),$sum(X2,X3)) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1201,f280]) ).
tff(f1201,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum($uminus($sum(X1,X0)),X2),X3) = $sum($sum($uminus(X1),X2),$sum($uminus(X0),X3)) )
| ~ spl1_64
| ~ spl1_81 ),
inference(superposition,[],[f651,f1086]) ).
tff(f55261,plain,
( spl1_389
| ~ spl1_31
| ~ spl1_55
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1216,f1085,f559,f279,f55259]) ).
tff(f55259,plain,
( spl1_389
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum($uminus(X1),X2)) = $sum($uminus($sum(X3,$sum(X1,X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_389])]) ).
tff(f559,plain,
( spl1_55
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f1216,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum($uminus(X1),X2)) = $sum($uminus($sum(X3,$sum(X1,X0))),X2) )
| ~ spl1_31
| ~ spl1_55
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1174,f584]) ).
tff(f584,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X0,X1)),X2) )
| ~ spl1_31
| ~ spl1_55 ),
inference(superposition,[],[f280,f560]) ).
tff(f560,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl1_55 ),
inference(avatar_component_clause,[],[f559]) ).
tff(f1174,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum($uminus(X1),X2)) = $sum($uminus(X3),$sum($uminus($sum(X1,X0)),X2)) )
| ~ spl1_81 ),
inference(superposition,[],[f1086,f1086]) ).
tff(f55256,plain,
( spl1_388
| ~ spl1_72
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1208,f1085,f915,f55254]) ).
tff(f55254,plain,
( spl1_388
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum($uminus($sum(X1,X0)),X2)),$sum(X3,X0))
| ~ $less($uminus($sum($uminus(X1),X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_388])]) ).
tff(f1208,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum($uminus($sum(X1,X0)),X2)),$sum(X3,X0))
| ~ $less($uminus($sum($uminus(X1),X2)),X3) )
| ~ spl1_72
| ~ spl1_81 ),
inference(evaluation,[],[f1205]) ).
tff(f1205,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum($uminus($sum(X1,X0)),X2)),$sum(X3,$uminus($uminus(X0))))
| ~ $less($uminus($sum($uminus(X1),X2)),X3) )
| ~ spl1_72
| ~ spl1_81 ),
inference(superposition,[],[f916,f1086]) ).
tff(f55251,plain,
( spl1_387
| ~ spl1_73
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1207,f1085,f919,f55249]) ).
tff(f55249,plain,
( spl1_387
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X0),$uminus($sum($uminus($sum(X1,X0)),X2)))
| ~ $less(X3,$uminus($sum($uminus(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_387])]) ).
tff(f1207,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X0),$uminus($sum($uminus($sum(X1,X0)),X2)))
| ~ $less(X3,$uminus($sum($uminus(X1),X2))) )
| ~ spl1_73
| ~ spl1_81 ),
inference(evaluation,[],[f1206]) ).
tff(f1206,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus($uminus(X0))),$uminus($sum($uminus($sum(X1,X0)),X2)))
| ~ $less(X3,$uminus($sum($uminus(X1),X2))) )
| ~ spl1_73
| ~ spl1_81 ),
inference(superposition,[],[f920,f1086]) ).
tff(f55247,plain,
( spl1_386
| ~ spl1_65
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1203,f1085,f654,f55245]) ).
tff(f55245,plain,
( spl1_386
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum($uminus($sum(X1,X0)),X2)) = $sum($sum($uminus(X1),X2),$sum(X3,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_386])]) ).
tff(f1203,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum($uminus($sum(X1,X0)),X2)) = $sum($sum($uminus(X1),X2),$sum(X3,$uminus(X0))) )
| ~ spl1_65
| ~ spl1_81 ),
inference(superposition,[],[f655,f1086]) ).
tff(f55243,plain,
( spl1_385
| ~ spl1_65
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1180,f1085,f654,f55241]) ).
tff(f55241,plain,
( spl1_385
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum(X1,X2)) = $sum($uminus(X3),$sum(X2,$sum($uminus(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_385])]) ).
tff(f1180,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum(X1,X2)) = $sum($uminus(X3),$sum(X2,$sum($uminus(X0),X1))) )
| ~ spl1_65
| ~ spl1_81 ),
inference(superposition,[],[f1086,f655]) ).
tff(f55239,plain,
( spl1_384
| ~ spl1_65
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1179,f1085,f654,f55237]) ).
tff(f55237,plain,
( spl1_384
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum(X1,X2)) = $sum($uminus(X3),$sum(X1,$sum(X2,$uminus(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_384])]) ).
tff(f1179,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X3)),$sum(X1,X2)) = $sum($uminus(X3),$sum(X1,$sum(X2,$uminus(X0)))) )
| ~ spl1_65
| ~ spl1_81 ),
inference(superposition,[],[f1086,f655]) ).
tff(f55235,plain,
( spl1_383
| ~ spl1_19
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1132,f1077,f170,f55233]) ).
tff(f55233,plain,
( spl1_383
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( count(add(X0,add(X1,X2))) = count(add(X3,add(X0,add(X1,X2)))) )
| ~ in(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_383])]) ).
tff(f1132,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = count(add(X3,add(X0,add(X1,X2)))) )
| ~ in(X3,X2) )
| ~ spl1_19
| ~ spl1_79 ),
inference(resolution,[],[f1078,f171]) ).
tff(f55182,plain,
( spl1_382
| ~ spl1_26
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1130,f1077,f214,f55180]) ).
tff(f55180,plain,
( spl1_382
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( count(X1) = count(remove(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_382])]) ).
tff(f1130,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ( count(X1) = count(remove(X2,X1)) ) )
| ~ spl1_26
| ~ spl1_79 ),
inference(resolution,[],[f1078,f215]) ).
tff(f55178,plain,
( spl1_381
| ~ spl1_18
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1115,f1069,f166,f55176]) ).
tff(f55176,plain,
( spl1_381
<=> ! [X0: $int,X3: collection,X2: $int,X1: $int] :
( ( count(remove(X0,remove(X1,remove(X2,X3)))) = count(remove(X1,remove(X2,X3))) )
| in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_381])]) ).
tff(f1115,plain,
( ! [X2: $int,X3: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,remove(X2,X3)))) = count(remove(X1,remove(X2,X3))) )
| in(X0,X3) )
| ~ spl1_18
| ~ spl1_77 ),
inference(resolution,[],[f1070,f167]) ).
tff(f55174,plain,
( spl1_380
| ~ spl1_25
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1111,f1069,f210,f55172]) ).
tff(f55172,plain,
( spl1_380
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( add(X0,remove(X0,X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_380])]) ).
tff(f1111,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( add(X0,remove(X0,X2)) = X2 ) )
| ~ spl1_25
| ~ spl1_77 ),
inference(resolution,[],[f1070,f211]) ).
tff(f55170,plain,
( spl1_379
| ~ spl1_28
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1110,f1069,f226,f55168]) ).
tff(f55168,plain,
( spl1_379
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( count(X2) = count(add(X0,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_379])]) ).
tff(f1110,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| ( count(X2) = count(add(X0,X2)) ) )
| ~ spl1_28
| ~ spl1_77 ),
inference(resolution,[],[f1070,f227]) ).
tff(f55166,plain,
( spl1_378
| ~ spl1_19
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1103,f1065,f170,f55164]) ).
tff(f55164,plain,
( spl1_378
<=> ! [X0: $int,X3: $int,X2: collection,X1: $int] :
( ( add(X0,add(X1,X2)) = add(X3,remove(X3,add(X0,add(X1,X2)))) )
| ~ in(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_378])]) ).
tff(f1103,plain,
( ! [X2: collection,X3: $int,X0: $int,X1: $int] :
( ( add(X0,add(X1,X2)) = add(X3,remove(X3,add(X0,add(X1,X2)))) )
| ~ in(X3,X2) )
| ~ spl1_19
| ~ spl1_76 ),
inference(resolution,[],[f1066,f171]) ).
tff(f55162,plain,
( spl1_377
| ~ spl1_26
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1101,f1065,f214,f55160]) ).
tff(f55160,plain,
( spl1_377
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( add(X0,X1) = add(X2,remove(X2,add(X0,X1))) )
| ( count(X1) = count(remove(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_377])]) ).
tff(f1101,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( add(X0,X1) = add(X2,remove(X2,add(X0,X1))) )
| ( count(X1) = count(remove(X2,X1)) ) )
| ~ spl1_26
| ~ spl1_76 ),
inference(resolution,[],[f1066,f215]) ).
tff(f55158,plain,
( spl1_376
| ~ spl1_60
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f989,f919,f634,f55156]) ).
tff(f55156,plain,
( spl1_376
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| $less($sum(X0,$uminus(X2)),$sum(X3,1))
| $less(X3,$uminus($sum(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_376])]) ).
tff(f989,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| $less($sum(X0,$uminus(X2)),$sum(X3,1))
| $less(X3,$uminus($sum(X2,X1))) )
| ~ spl1_60
| ~ spl1_73 ),
inference(resolution,[],[f920,f635]) ).
tff(f55154,plain,
( spl1_375
| ~ spl1_60
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f966,f915,f634,f55152]) ).
tff(f55152,plain,
( spl1_375
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| $less($uminus($sum(X2,X0)),$sum(X3,1))
| $less(X3,$sum(X1,$uminus(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_375])]) ).
tff(f966,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| $less($uminus($sum(X2,X0)),$sum(X3,1))
| $less(X3,$sum(X1,$uminus(X2))) )
| ~ spl1_60
| ~ spl1_72 ),
inference(resolution,[],[f916,f635]) ).
tff(f55150,plain,
( spl1_374
| ~ spl1_22
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f946,f911,f188,f55148]) ).
tff(f55148,plain,
( spl1_374
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,X3))
| $less($sum(X0,X3),X2)
| ( $sum(X0,X3) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_374])]) ).
tff(f946,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,X3))
| $less($sum(X0,X3),X2)
| ( $sum(X0,X3) = X2 ) )
| ~ spl1_22
| ~ spl1_71 ),
inference(resolution,[],[f912,f189]) ).
tff(f55146,plain,
( spl1_373
| ~ spl1_60
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f935,f907,f634,f55144]) ).
tff(f55144,plain,
( spl1_373
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| $less($sum(X0,1),$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_373])]) ).
tff(f935,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| $less($sum(X0,1),$sum(X2,1))
| $less(X2,X1) )
| ~ spl1_60
| ~ spl1_70 ),
inference(resolution,[],[f908,f635]) ).
tff(f55125,plain,
( spl1_372
| ~ spl1_53
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f855,f833,f536,f55123]) ).
tff(f55123,plain,
( spl1_372
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,$uminus(X1)) = X2 )
| $less(X2,$sum(X0,$uminus(X1)))
| $less(0,X2)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_372])]) ).
tff(f536,plain,
( spl1_53
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f855,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,$uminus(X1)) = X2 )
| $less(X2,$sum(X0,$uminus(X1)))
| $less(0,X2)
| ~ $less(X1,X0) )
| ~ spl1_53
| ~ spl1_66 ),
inference(resolution,[],[f834,f537]) ).
tff(f537,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f536]) ).
tff(f55121,plain,
( spl1_371
| ~ spl1_57
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f852,f833,f567,f55119]) ).
tff(f55119,plain,
( spl1_371
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X3,X0),X2)
| ~ $less(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_371])]) ).
tff(f567,plain,
( spl1_57
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f852,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X3,X0),X2)
| ~ $less(X3,X1) )
| ~ spl1_57
| ~ spl1_66 ),
inference(resolution,[],[f834,f568]) ).
tff(f568,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl1_57 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f55117,plain,
( spl1_370
| ~ spl1_56
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f851,f833,f563,f55115]) ).
tff(f55115,plain,
( spl1_370
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X1,X3),X2)
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_370])]) ).
tff(f563,plain,
( spl1_56
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f851,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X1,X3),X2)
| ~ $less(X3,X0) )
| ~ spl1_56
| ~ spl1_66 ),
inference(resolution,[],[f834,f564]) ).
tff(f564,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl1_56 ),
inference(avatar_component_clause,[],[f563]) ).
tff(f55113,plain,
( spl1_369
| ~ spl1_24
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f850,f833,f206,f55111]) ).
tff(f55111,plain,
( spl1_369
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X3,X1),X2)
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_369])]) ).
tff(f206,plain,
( spl1_24
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f850,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $sum(X0,X1) = X2 )
| $less(X2,$sum(X0,X1))
| $less($sum(X3,X1),X2)
| ~ $less(X3,X0) )
| ~ spl1_24
| ~ spl1_66 ),
inference(resolution,[],[f834,f207]) ).
tff(f207,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f206]) ).
tff(f55109,plain,
( spl1_368
| ~ spl1_12
| ~ spl1_29
| ~ spl1_37
| ~ spl1_61 ),
inference(avatar_split_clause,[],[f678,f638,f329,f230,f140,f55107]) ).
tff(f638,plain,
( spl1_61
<=> ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
tff(f678,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| in(X0,remove(X0,add(X0,X1))) )
| ~ spl1_12
| ~ spl1_29
| ~ spl1_37
| ~ spl1_61 ),
inference(forward_demodulation,[],[f675,f347]) ).
tff(f347,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) )
| ~ spl1_12
| ~ spl1_37 ),
inference(resolution,[],[f330,f141]) ).
tff(f675,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != count(remove(X0,add(X0,X1))) )
| in(X0,remove(X0,add(X0,X1))) )
| ~ spl1_29
| ~ spl1_61 ),
inference(superposition,[],[f231,f639]) ).
tff(f639,plain,
( ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) )
| ~ spl1_61 ),
inference(avatar_component_clause,[],[f638]) ).
tff(f54303,plain,
( spl1_367
| ~ spl1_161
| ~ spl1_301 ),
inference(avatar_split_clause,[],[f43750,f38142,f3490,f54301]) ).
tff(f54301,plain,
( spl1_367
<=> ! [X0: $int] :
( ~ $less(2,$uminus(X0))
| $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_367])]) ).
tff(f43750,plain,
( ! [X0: $int] :
( ~ $less(2,$uminus(X0))
| $less(X0,1) )
| ~ spl1_161
| ~ spl1_301 ),
inference(evaluation,[],[f43719]) ).
tff(f43719,plain,
( ! [X0: $int] :
( ~ $less(2,$uminus(X0))
| $less($sum(0,X0),1) )
| ~ spl1_161
| ~ spl1_301 ),
inference(resolution,[],[f38143,f3491]) ).
tff(f47057,plain,
( spl1_366
| ~ spl1_17
| ~ spl1_301 ),
inference(avatar_split_clause,[],[f43714,f38142,f162,f47055]) ).
tff(f47055,plain,
( spl1_366
<=> ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_366])]) ).
tff(f43714,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(X0,0) )
| ~ spl1_17
| ~ spl1_301 ),
inference(resolution,[],[f38143,f163]) ).
tff(f43170,plain,
( spl1_365
| ~ spl1_12
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1436,f1341,f140,f43168]) ).
tff(f43168,plain,
( spl1_365
<=> ! [X2: collection,X0: $int,X1: $int] : ( count(remove(X0,add(X1,add(X0,X2)))) = $sum(-1,count(add(X1,add(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_365])]) ).
tff(f1436,plain,
( ! [X2: collection,X0: $int,X1: $int] : ( count(remove(X0,add(X1,add(X0,X2)))) = $sum(-1,count(add(X1,add(X0,X2)))) )
| ~ spl1_12
| ~ spl1_90 ),
inference(resolution,[],[f1342,f141]) ).
tff(f43166,plain,
( spl1_364
| ~ spl1_11
| ~ spl1_88 ),
inference(avatar_split_clause,[],[f1398,f1333,f136,f43164]) ).
tff(f43164,plain,
( spl1_364
<=> ! [X2: collection,X0: $int,X1: $int] : ( count(add(X0,remove(X1,remove(X0,X2)))) = $sum(1,count(remove(X1,remove(X0,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_364])]) ).
tff(f1398,plain,
( ! [X2: collection,X0: $int,X1: $int] : ( count(add(X0,remove(X1,remove(X0,X2)))) = $sum(1,count(remove(X1,remove(X0,X2)))) )
| ~ spl1_11
| ~ spl1_88 ),
inference(resolution,[],[f1334,f137]) ).
tff(f43162,plain,
( spl1_363
| ~ spl1_55
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1308,f1093,f559,f43160]) ).
tff(f43160,plain,
( spl1_363
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X3,$uminus(X1))),$uminus($sum(X0,X1)))
| ~ $less($sum(X2,X3),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_363])]) ).
tff(f1308,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X3,$uminus(X1))),$uminus($sum(X0,X1)))
| ~ $less($sum(X2,X3),$uminus(X0)) )
| ~ spl1_55
| ~ spl1_83 ),
inference(superposition,[],[f1094,f560]) ).
tff(f43158,plain,
( spl1_362
| ~ spl1_23
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1290,f1093,f202,f43156]) ).
tff(f43156,plain,
( spl1_362
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$uminus($sum(X1,X0))),$sum(X3,$uminus(X1)))
| ~ $less($sum(X2,$uminus(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_362])]) ).
tff(f202,plain,
( spl1_23
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f1290,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus($sum(X1,X0))),$sum(X3,$uminus(X1)))
| ~ $less($sum(X2,$uminus(X0)),X3) )
| ~ spl1_23
| ~ spl1_83 ),
inference(superposition,[],[f1094,f203]) ).
tff(f203,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f202]) ).
tff(f43154,plain,
( spl1_361
| ~ spl1_55
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1289,f1093,f559,f43152]) ).
tff(f43152,plain,
( spl1_361
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$uminus($sum(X0,X1))),$sum(X3,$uminus(X1)))
| ~ $less($sum(X2,$uminus(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_361])]) ).
tff(f1289,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus($sum(X0,X1))),$sum(X3,$uminus(X1)))
| ~ $less($sum(X2,$uminus(X0)),X3) )
| ~ spl1_55
| ~ spl1_83 ),
inference(superposition,[],[f1094,f560]) ).
tff(f43150,plain,
( spl1_360
| ~ spl1_71
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1278,f1093,f911,f43148]) ).
tff(f43148,plain,
( spl1_360
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| ~ $less(X2,X3)
| $less($sum(X0,$sum(X1,X4)),$sum(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_360])]) ).
tff(f1278,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less($sum(X0,X1),X2)
| ~ $less(X2,X3)
| $less($sum(X0,$sum(X1,X4)),$sum(X3,X4)) )
| ~ spl1_71
| ~ spl1_83 ),
inference(resolution,[],[f1094,f912]) ).
tff(f43146,plain,
( spl1_359
| ~ spl1_23
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1257,f1089,f202,f43144]) ).
tff(f43144,plain,
( spl1_359
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$sum(X3,$uminus($sum(X1,X0))))
| ~ $less(X2,$sum(X3,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_359])]) ).
tff(f1257,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$sum(X3,$uminus($sum(X1,X0))))
| ~ $less(X2,$sum(X3,$uminus(X0))) )
| ~ spl1_23
| ~ spl1_82 ),
inference(superposition,[],[f1090,f203]) ).
tff(f43142,plain,
( spl1_358
| ~ spl1_55
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1256,f1089,f559,f43140]) ).
tff(f43140,plain,
( spl1_358
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less(X2,$sum(X3,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_358])]) ).
tff(f1256,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less(X2,$sum(X3,$uminus(X0))) )
| ~ spl1_55
| ~ spl1_82 ),
inference(superposition,[],[f1090,f560]) ).
tff(f43118,plain,
( spl1_357
| ~ spl1_55
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1245,f1089,f559,f43116]) ).
tff(f43116,plain,
( spl1_357
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum(X2,$sum(X3,$uminus(X1))))
| ~ $less($uminus(X0),$sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_357])]) ).
tff(f1245,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum(X2,$sum(X3,$uminus(X1))))
| ~ $less($uminus(X0),$sum(X2,X3)) )
| ~ spl1_55
| ~ spl1_82 ),
inference(superposition,[],[f1090,f560]) ).
tff(f43114,plain,
( spl1_356
| ~ spl1_21
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1238,f1089,f184,f43112]) ).
tff(f43112,plain,
( spl1_356
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X2))
| ~ $less(X3,$sum(X0,X4))
| $less(X3,$sum(X1,$sum(X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_356])]) ).
tff(f184,plain,
( spl1_21
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f1238,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X0,$sum(X1,X2))
| ~ $less(X3,$sum(X0,X4))
| $less(X3,$sum(X1,$sum(X2,X4))) )
| ~ spl1_21
| ~ spl1_82 ),
inference(resolution,[],[f1090,f185]) ).
tff(f185,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f43110,plain,
( spl1_355
| ~ spl1_71
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1234,f1089,f911,f43108]) ).
tff(f43108,plain,
( spl1_355
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X2))
| ~ $less(X1,X3)
| $less($sum(X0,X4),$sum(X3,$sum(X2,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_355])]) ).
tff(f1234,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X0,$sum(X1,X2))
| ~ $less(X1,X3)
| $less($sum(X0,X4),$sum(X3,$sum(X2,X4))) )
| ~ spl1_71
| ~ spl1_82 ),
inference(resolution,[],[f1090,f912]) ).
tff(f43106,plain,
( spl1_354
| ~ spl1_31
| ~ spl1_57
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1230,f1085,f567,f279,f43104]) ).
tff(f43104,plain,
( spl1_354
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum($uminus(X1),$sum(X2,X3)))
| ~ $less($uminus(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_354])]) ).
tff(f1230,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum($uminus(X1),$sum(X2,X3)))
| ~ $less($uminus(X0),X3) )
| ~ spl1_31
| ~ spl1_57
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1200,f280]) ).
tff(f1200,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum($sum($uminus(X1),X2),X3))
| ~ $less($uminus(X0),X3) )
| ~ spl1_57
| ~ spl1_81 ),
inference(superposition,[],[f568,f1086]) ).
tff(f43102,plain,
( spl1_353
| ~ spl1_31
| ~ spl1_56
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1229,f1085,f563,f279,f43100]) ).
tff(f43100,plain,
( spl1_353
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum($uminus(X1),$sum(X2,X3)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_353])]) ).
tff(f1229,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X1),$sum(X2,X3)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$uminus(X0)) )
| ~ spl1_31
| ~ spl1_56
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1198,f280]) ).
tff(f1198,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($sum($uminus(X1),X2),X3),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$uminus(X0)) )
| ~ spl1_56
| ~ spl1_81 ),
inference(superposition,[],[f564,f1086]) ).
tff(f43098,plain,
( spl1_352
| ~ spl1_57
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1199,f1085,f567,f43096]) ).
tff(f43096,plain,
( spl1_352
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$sum($uminus(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_352])]) ).
tff(f1199,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$sum($uminus(X1),X2)) )
| ~ spl1_57
| ~ spl1_81 ),
inference(superposition,[],[f568,f1086]) ).
tff(f43094,plain,
( spl1_351
| ~ spl1_56
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1197,f1085,f563,f43092]) ).
tff(f43092,plain,
( spl1_351
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$uminus(X0)))
| ~ $less($sum($uminus(X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_351])]) ).
tff(f1197,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$uminus(X0)))
| ~ $less($sum($uminus(X1),X2),X3) )
| ~ spl1_56
| ~ spl1_81 ),
inference(superposition,[],[f564,f1086]) ).
tff(f43090,plain,
( spl1_350
| ~ spl1_24
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1195,f1085,f206,f43088]) ).
tff(f43088,plain,
( spl1_350
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$sum($uminus(X1),X2)))
| ~ $less($uminus(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_350])]) ).
tff(f1195,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($uminus($sum(X1,X0)),X2),$sum(X3,$sum($uminus(X1),X2)))
| ~ $less($uminus(X0),X3) )
| ~ spl1_24
| ~ spl1_81 ),
inference(superposition,[],[f207,f1086]) ).
tff(f43086,plain,
( spl1_349
| ~ spl1_24
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1194,f1085,f206,f43084]) ).
tff(f43084,plain,
( spl1_349
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum($uminus(X1),X2)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_349])]) ).
tff(f1194,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$sum($uminus(X1),X2)),$sum($uminus($sum(X1,X0)),X2))
| ~ $less(X3,$uminus(X0)) )
| ~ spl1_24
| ~ spl1_81 ),
inference(superposition,[],[f207,f1086]) ).
tff(f43082,plain,
( spl1_348
| ~ spl1_36
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f1142,f1081,f325,f43080]) ).
tff(f43080,plain,
( spl1_348
<=> ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_348])]) ).
tff(f1081,plain,
( spl1_80
<=> ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
tff(f1142,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_36
| ~ spl1_80 ),
inference(superposition,[],[f326,f1082]) ).
tff(f1082,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = count(remove(X1,X0)) )
| ( count(X0) = count(add(X1,X0)) ) )
| ~ spl1_80 ),
inference(avatar_component_clause,[],[f1081]) ).
tff(f43078,plain,
( spl1_347
| ~ spl1_161
| ~ spl1_300 ),
inference(avatar_split_clause,[],[f43032,f33521,f3490,f43076]) ).
tff(f43076,plain,
( spl1_347
<=> ! [X0: $int] :
( ~ $less(0,$uminus(X0))
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_347])]) ).
tff(f43032,plain,
( ! [X0: $int] :
( ~ $less(0,$uminus(X0))
| $less(X0,2) )
| ~ spl1_161
| ~ spl1_300 ),
inference(evaluation,[],[f43001]) ).
tff(f43001,plain,
( ! [X0: $int] :
( ~ $less(0,$uminus(X0))
| $less($sum(0,X0),2) )
| ~ spl1_161
| ~ spl1_300 ),
inference(resolution,[],[f33522,f3491]) ).
tff(f43074,plain,
( spl1_346
| ~ spl1_31
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f1007,f919,f279,f43072]) ).
tff(f43072,plain,
( spl1_346
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$uminus($sum(X0,X1))),$uminus($sum(X0,$sum(X1,X2))))
| ~ $less(X3,$uminus(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_346])]) ).
tff(f1007,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus($sum(X0,X1))),$uminus($sum(X0,$sum(X1,X2))))
| ~ $less(X3,$uminus(X2)) )
| ~ spl1_31
| ~ spl1_73 ),
inference(superposition,[],[f920,f280]) ).
tff(f43070,plain,
( spl1_345
| ~ spl1_64
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f1006,f919,f650,f43068]) ).
tff(f43068,plain,
( spl1_345
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$uminus($sum(X0,X1))),$uminus($sum(X1,$sum(X0,X2))))
| ~ $less(X3,$uminus(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_345])]) ).
tff(f1006,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus($sum(X0,X1))),$uminus($sum(X1,$sum(X0,X2))))
| ~ $less(X3,$uminus(X2)) )
| ~ spl1_64
| ~ spl1_73 ),
inference(superposition,[],[f920,f651]) ).
tff(f43066,plain,
( spl1_344
| ~ spl1_65
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f1003,f919,f654,f43064]) ).
tff(f43064,plain,
( spl1_344
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$uminus($sum(X2,$sum(X0,X1))))
| ~ $less(X3,$uminus($sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_344])]) ).
tff(f1003,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$uminus($sum(X2,$sum(X0,X1))))
| ~ $less(X3,$uminus($sum(X1,X2))) )
| ~ spl1_65
| ~ spl1_73 ),
inference(superposition,[],[f920,f655]) ).
tff(f43062,plain,
( spl1_343
| ~ spl1_65
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f1002,f919,f654,f43060]) ).
tff(f43060,plain,
( spl1_343
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$uminus($sum(X1,$sum(X2,X0))))
| ~ $less(X3,$uminus($sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_343])]) ).
tff(f1002,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$uminus(X0)),$uminus($sum(X1,$sum(X2,X0))))
| ~ $less(X3,$uminus($sum(X1,X2))) )
| ~ spl1_65
| ~ spl1_73 ),
inference(superposition,[],[f920,f655]) ).
tff(f43058,plain,
( spl1_342
| ~ spl1_31
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f997,f919,f279,f43056]) ).
tff(f43056,plain,
( spl1_342
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,$uminus(X2))),$uminus($sum(X2,X3)))
| ~ $less($sum(X0,X1),$uminus(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_342])]) ).
tff(f997,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,$uminus(X2))),$uminus($sum(X2,X3)))
| ~ $less($sum(X0,X1),$uminus(X3)) )
| ~ spl1_31
| ~ spl1_73 ),
inference(superposition,[],[f920,f280]) ).
tff(f43054,plain,
( spl1_341
| ~ spl1_64
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f996,f919,f650,f43052]) ).
tff(f43052,plain,
( spl1_341
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X0,$uminus(X2))),$uminus($sum(X2,X3)))
| ~ $less($sum(X0,X1),$uminus(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_341])]) ).
tff(f996,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,$uminus(X2))),$uminus($sum(X2,X3)))
| ~ $less($sum(X0,X1),$uminus(X3)) )
| ~ spl1_64
| ~ spl1_73 ),
inference(superposition,[],[f920,f651]) ).
tff(f43050,plain,
( spl1_340
| ~ spl1_31
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f984,f915,f279,f43048]) ).
tff(f43048,plain,
( spl1_340
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X2,X3)),$sum(X0,$sum(X1,$uminus(X2))))
| ~ $less($uminus(X3),$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_340])]) ).
tff(f984,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X2,X3)),$sum(X0,$sum(X1,$uminus(X2))))
| ~ $less($uminus(X3),$sum(X0,X1)) )
| ~ spl1_31
| ~ spl1_72 ),
inference(superposition,[],[f916,f280]) ).
tff(f43046,plain,
( spl1_339
| ~ spl1_64
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f983,f915,f650,f43044]) ).
tff(f43044,plain,
( spl1_339
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X2,X3)),$sum(X1,$sum(X0,$uminus(X2))))
| ~ $less($uminus(X3),$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_339])]) ).
tff(f983,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X2,X3)),$sum(X1,$sum(X0,$uminus(X2))))
| ~ $less($uminus(X3),$sum(X0,X1)) )
| ~ spl1_64
| ~ spl1_72 ),
inference(superposition,[],[f916,f651]) ).
tff(f43042,plain,
( spl1_338
| ~ spl1_31
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f977,f915,f279,f43040]) ).
tff(f43040,plain,
( spl1_338
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X0,$sum(X1,X2))),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less($uminus(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_338])]) ).
tff(f977,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,$sum(X1,X2))),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less($uminus(X2),X3) )
| ~ spl1_31
| ~ spl1_72 ),
inference(superposition,[],[f916,f280]) ).
tff(f43038,plain,
( spl1_337
| ~ spl1_64
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f976,f915,f650,f43036]) ).
tff(f43036,plain,
( spl1_337
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X1,$sum(X0,X2))),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less($uminus(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_337])]) ).
tff(f976,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,$sum(X0,X2))),$sum(X3,$uminus($sum(X0,X1))))
| ~ $less($uminus(X2),X3) )
| ~ spl1_64
| ~ spl1_72 ),
inference(superposition,[],[f916,f651]) ).
tff(f42994,plain,
( spl1_336
| ~ spl1_65
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f973,f915,f654,f42992]) ).
tff(f42992,plain,
( spl1_336
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X2,$sum(X0,X1))),$sum(X3,$uminus(X0)))
| ~ $less($uminus($sum(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_336])]) ).
tff(f973,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X2,$sum(X0,X1))),$sum(X3,$uminus(X0)))
| ~ $less($uminus($sum(X1,X2)),X3) )
| ~ spl1_65
| ~ spl1_72 ),
inference(superposition,[],[f916,f655]) ).
tff(f42990,plain,
( spl1_335
| ~ spl1_65
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f972,f915,f654,f42988]) ).
tff(f42988,plain,
( spl1_335
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($uminus($sum(X1,$sum(X2,X0))),$sum(X3,$uminus(X0)))
| ~ $less($uminus($sum(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_335])]) ).
tff(f972,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,$sum(X2,X0))),$sum(X3,$uminus(X0)))
| ~ $less($uminus($sum(X1,X2)),X3) )
| ~ spl1_65
| ~ spl1_72 ),
inference(superposition,[],[f916,f655]) ).
tff(f42986,plain,
( spl1_334
| ~ spl1_31
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f962,f911,f279,f42984]) ).
tff(f42984,plain,
( spl1_334
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,$sum(X0,$sum(X1,X2)))
| ~ $less($sum(X0,X1),X4)
| $less(X3,$sum(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_334])]) ).
tff(f962,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X3,$sum(X0,$sum(X1,X2)))
| ~ $less($sum(X0,X1),X4)
| $less(X3,$sum(X4,X2)) )
| ~ spl1_31
| ~ spl1_71 ),
inference(superposition,[],[f912,f280]) ).
tff(f42982,plain,
( spl1_333
| ~ spl1_64
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f961,f911,f650,f42980]) ).
tff(f42980,plain,
( spl1_333
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,$sum(X1,$sum(X0,X2)))
| ~ $less($sum(X0,X1),X4)
| $less(X3,$sum(X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_333])]) ).
tff(f961,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X3,$sum(X1,$sum(X0,X2)))
| ~ $less($sum(X0,X1),X4)
| $less(X3,$sum(X4,X2)) )
| ~ spl1_64
| ~ spl1_71 ),
inference(superposition,[],[f912,f651]) ).
tff(f42978,plain,
( spl1_332
| ~ spl1_65
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f958,f911,f654,f42976]) ).
tff(f42976,plain,
( spl1_332
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,$sum(X2,$sum(X0,X1)))
| ~ $less(X0,X4)
| $less(X3,$sum(X4,$sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_332])]) ).
tff(f958,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X3,$sum(X2,$sum(X0,X1)))
| ~ $less(X0,X4)
| $less(X3,$sum(X4,$sum(X1,X2))) )
| ~ spl1_65
| ~ spl1_71 ),
inference(superposition,[],[f912,f655]) ).
tff(f42974,plain,
( spl1_331
| ~ spl1_65
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f957,f911,f654,f42972]) ).
tff(f42972,plain,
( spl1_331
<=> ! [X4: $int,X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X3,$sum(X1,$sum(X2,X0)))
| ~ $less(X0,X4)
| $less(X3,$sum(X4,$sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_331])]) ).
tff(f957,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int,X4: $int] :
( ~ $less(X3,$sum(X1,$sum(X2,X0)))
| ~ $less(X0,X4)
| $less(X3,$sum(X4,$sum(X1,X2))) )
| ~ spl1_65
| ~ spl1_71 ),
inference(superposition,[],[f912,f655]) ).
tff(f42970,plain,
( spl1_330
| ~ spl1_50
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f933,f907,f473,f42968]) ).
tff(f42968,plain,
( spl1_330
<=> ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(1,X1) )
| ~ $less(X0,$sum(1,X1))
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_330])]) ).
tff(f473,plain,
( spl1_50
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f933,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(1,X1) )
| ~ $less(X0,$sum(1,X1))
| ~ $less(X1,$sum(X0,1)) )
| ~ spl1_50
| ~ spl1_70 ),
inference(resolution,[],[f908,f474]) ).
tff(f474,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl1_50 ),
inference(avatar_component_clause,[],[f473]) ).
tff(f42966,plain,
( spl1_329
| ~ spl1_17
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f931,f907,f162,f42964]) ).
tff(f42964,plain,
( spl1_329
<=> ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(X1,1) )
| ~ $less(X0,$sum(X1,1))
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_329])]) ).
tff(f931,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = $sum(X1,1) )
| ~ $less(X0,$sum(X1,1))
| ~ $less(X1,$sum(X0,1)) )
| ~ spl1_17
| ~ spl1_70 ),
inference(resolution,[],[f908,f163]) ).
tff(f42962,plain,
( spl1_328
| ~ spl1_60
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f884,f841,f634,f42960]) ).
tff(f42960,plain,
( spl1_328
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| $less(X2,$sum(X3,1))
| $less(X3,$sum(X0,$sum(X1,1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_328])]) ).
tff(f884,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| $less(X2,$sum(X3,1))
| $less(X3,$sum(X0,$sum(X1,1))) )
| ~ spl1_60
| ~ spl1_68 ),
inference(resolution,[],[f842,f635]) ).
tff(f42614,plain,
( spl1_327
| ~ spl1_52
| ~ spl1_224 ),
inference(avatar_split_clause,[],[f10764,f8022,f481,f42612]) ).
tff(f42612,plain,
( spl1_327
<=> ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_327])]) ).
tff(f8022,plain,
( spl1_224
<=> ! [X0: $int] :
( $less(-1,$sum(-1,X0))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_224])]) ).
tff(f10764,plain,
( ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum(1,X0)) )
| ~ spl1_52
| ~ spl1_224 ),
inference(evaluation,[],[f10748]) ).
tff(f10748,plain,
( ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum($uminus(-1),X0)) )
| ~ spl1_52
| ~ spl1_224 ),
inference(superposition,[],[f8023,f482]) ).
tff(f8023,plain,
( ! [X0: $int] :
( $less(-1,$sum(-1,X0))
| ~ $less(2,X0) )
| ~ spl1_224 ),
inference(avatar_component_clause,[],[f8022]) ).
tff(f41622,plain,
( spl1_326
| ~ spl1_124
| ~ spl1_224 ),
inference(avatar_split_clause,[],[f10762,f8022,f1914,f41620]) ).
tff(f10762,plain,
( ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum(X0,1)) )
| ~ spl1_124
| ~ spl1_224 ),
inference(evaluation,[],[f10757]) ).
tff(f10757,plain,
( ! [X0: $int] :
( $less(-1,X0)
| ~ $less(2,$sum(X0,$uminus(-1))) )
| ~ spl1_124
| ~ spl1_224 ),
inference(superposition,[],[f8023,f1915]) ).
tff(f39625,plain,
( spl1_325
| ~ spl1_14
| ~ spl1_224 ),
inference(avatar_split_clause,[],[f10746,f8022,f148,f39623]) ).
tff(f39623,plain,
( spl1_325
<=> ! [X0: $int] :
( $less(-1,$sum(X0,-1))
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_325])]) ).
tff(f10746,plain,
( ! [X0: $int] :
( $less(-1,$sum(X0,-1))
| ~ $less(2,X0) )
| ~ spl1_14
| ~ spl1_224 ),
inference(superposition,[],[f8023,f149]) ).
tff(f39621,plain,
( spl1_324
| ~ spl1_67
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1277,f1093,f837,f39619]) ).
tff(f39619,plain,
( spl1_324
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| ~ $less($sum(X2,X3),$sum(X0,$sum(X1,$sum(X3,1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_324])]) ).
tff(f1277,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),X2)
| ~ $less($sum(X2,X3),$sum(X0,$sum(X1,$sum(X3,1)))) )
| ~ spl1_67
| ~ spl1_83 ),
inference(resolution,[],[f1094,f838]) ).
tff(f39617,plain,
( spl1_323
| ~ spl1_74
| ~ spl1_78 ),
inference(avatar_split_clause,[],[f1119,f1073,f923,f39615]) ).
tff(f39615,plain,
( spl1_323
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = $sum(1,count(remove(X0,X1))) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_323])]) ).
tff(f1073,plain,
( spl1_78
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
tff(f1119,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) = $sum(1,count(remove(X0,X1))) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_74
| ~ spl1_78 ),
inference(superposition,[],[f924,f1074]) ).
tff(f1074,plain,
( ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_78 ),
inference(avatar_component_clause,[],[f1073]) ).
tff(f39613,plain,
( spl1_322
| ~ spl1_51
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f1054,f927,f477,f39611]) ).
tff(f39611,plain,
( spl1_322
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(add(X0,X1))))
| ( 0 = $sum(-1,count(add(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_322])]) ).
tff(f927,plain,
( spl1_75
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
tff(f1054,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(-1,count(add(X0,X1))))
| ( 0 = $sum(-1,count(add(X0,X1))) ) )
| ~ spl1_51
| ~ spl1_75 ),
inference(superposition,[],[f478,f928]) ).
tff(f928,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) )
| ~ spl1_75 ),
inference(avatar_component_clause,[],[f927]) ).
tff(f39609,plain,
( spl1_321
| ~ spl1_27
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f1053,f927,f222,f39607]) ).
tff(f1053,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(-1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) )
| ~ spl1_27
| ~ spl1_75 ),
inference(superposition,[],[f223,f928]) ).
tff(f39605,plain,
( spl1_320
| ~ spl1_51
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1035,f923,f477,f39603]) ).
tff(f39603,plain,
( spl1_320
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(1,count(remove(X0,X1))))
| ( 0 = $sum(1,count(remove(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_320])]) ).
tff(f1035,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(1,count(remove(X0,X1))))
| ( 0 = $sum(1,count(remove(X0,X1))) ) )
| ~ spl1_51
| ~ spl1_74 ),
inference(superposition,[],[f478,f924]) ).
tff(f39601,plain,
( spl1_319
| ~ spl1_29
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1034,f923,f230,f39599]) ).
tff(f39599,plain,
( spl1_319
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(1,count(remove(X0,X1))) )
| in(X0,remove(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_319])]) ).
tff(f1034,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(1,count(remove(X0,X1))) )
| in(X0,remove(X0,X1)) )
| ~ spl1_29
| ~ spl1_74 ),
inference(superposition,[],[f231,f924]) ).
tff(f39597,plain,
( spl1_318
| ~ spl1_21
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f990,f919,f184,f39595]) ).
tff(f39595,plain,
( spl1_318
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| ~ $less(X2,$sum(X0,$uminus(X3)))
| $less(X2,$uminus($sum(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_318])]) ).
tff(f990,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,$uminus(X1))
| ~ $less(X2,$sum(X0,$uminus(X3)))
| $less(X2,$uminus($sum(X3,X1))) )
| ~ spl1_21
| ~ spl1_73 ),
inference(resolution,[],[f920,f185]) ).
tff(f39593,plain,
( spl1_317
| ~ spl1_71
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f963,f915,f911,f39591]) ).
tff(f39591,plain,
( spl1_317
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| ~ $less(X1,X2)
| $less($uminus($sum(X3,X0)),$sum(X2,$uminus(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_317])]) ).
tff(f963,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($uminus(X0),X1)
| ~ $less(X1,X2)
| $less($uminus($sum(X3,X0)),$sum(X2,$uminus(X3))) )
| ~ spl1_71
| ~ spl1_72 ),
inference(resolution,[],[f916,f912]) ).
tff(f39589,plain,
( spl1_316
| ~ spl1_23
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f960,f911,f202,f39587]) ).
tff(f39587,plain,
( spl1_316
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,$uminus($sum(X1,X0)))
| ~ $less($uminus(X0),X3)
| $less(X2,$sum(X3,$uminus(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_316])]) ).
tff(f960,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$uminus($sum(X1,X0)))
| ~ $less($uminus(X0),X3)
| $less(X2,$sum(X3,$uminus(X1))) )
| ~ spl1_23
| ~ spl1_71 ),
inference(superposition,[],[f912,f203]) ).
tff(f39585,plain,
( spl1_315
| ~ spl1_55
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f959,f911,f559,f39583]) ).
tff(f39583,plain,
( spl1_315
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,$uminus($sum(X0,X1)))
| ~ $less($uminus(X0),X3)
| $less(X2,$sum(X3,$uminus(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_315])]) ).
tff(f959,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$uminus($sum(X0,X1)))
| ~ $less($uminus(X0),X3)
| $less(X2,$sum(X3,$uminus(X1))) )
| ~ spl1_55
| ~ spl1_71 ),
inference(superposition,[],[f912,f560]) ).
tff(f39581,plain,
( spl1_314
| ~ spl1_118
| ~ spl1_224 ),
inference(avatar_split_clause,[],[f10722,f8022,f1830,f39579]) ).
tff(f1830,plain,
( spl1_118
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).
tff(f10722,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less($sum(-1,X0),0) )
| ~ spl1_118
| ~ spl1_224 ),
inference(resolution,[],[f8023,f1831]) ).
tff(f1831,plain,
( ! [X0: $int] :
( ~ $less(-1,X0)
| ~ $less(X0,0) )
| ~ spl1_118 ),
inference(avatar_component_clause,[],[f1830]) ).
tff(f39577,plain,
( spl1_313
| ~ spl1_21
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f936,f907,f184,f39575]) ).
tff(f39575,plain,
( spl1_313
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_313])]) ).
tff(f936,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,1))
| $less(X2,X1) )
| ~ spl1_21
| ~ spl1_70 ),
inference(resolution,[],[f908,f185]) ).
tff(f39573,plain,
( spl1_312
| ~ spl1_31
| ~ spl1_64
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f900,f841,f650,f279,f39571]) ).
tff(f39571,plain,
( spl1_312
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),X3)
| $less(X3,$sum(X1,$sum(X0,$sum(X2,1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_312])]) ).
tff(f900,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),X3)
| $less(X3,$sum(X1,$sum(X0,$sum(X2,1)))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_68 ),
inference(forward_demodulation,[],[f895,f280]) ).
tff(f895,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less(X3,$sum(X1,$sum(X0,$sum(X2,1))))
| $less($sum($sum(X0,X1),X2),X3) )
| ~ spl1_64
| ~ spl1_68 ),
inference(superposition,[],[f842,f651]) ).
tff(f39569,plain,
( spl1_311
| ~ spl1_31
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f889,f841,f279,f39567]) ).
tff(f39567,plain,
( spl1_311
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less(X2,$sum(X3,$sum(X0,$sum(X1,1))))
| $less($sum(X3,$sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_311])]) ).
tff(f889,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X3,$sum(X0,$sum(X1,1))))
| $less($sum(X3,$sum(X0,X1)),X2) )
| ~ spl1_31
| ~ spl1_68 ),
inference(superposition,[],[f842,f280]) ).
tff(f39565,plain,
( spl1_310
| ~ spl1_64
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f888,f841,f650,f39563]) ).
tff(f39563,plain,
( spl1_310
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less(X2,$sum(X3,$sum(X1,$sum(X0,1))))
| $less($sum(X3,$sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_310])]) ).
tff(f888,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X3,$sum(X1,$sum(X0,1))))
| $less($sum(X3,$sum(X0,X1)),X2) )
| ~ spl1_64
| ~ spl1_68 ),
inference(superposition,[],[f842,f651]) ).
tff(f39561,plain,
( spl1_309
| ~ spl1_31
| ~ spl1_64
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f878,f837,f650,f279,f39559]) ).
tff(f39559,plain,
( spl1_309
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($sum(X0,$sum(X1,X2)),X3)
| ~ $less(X3,$sum(X1,$sum(X0,$sum(X2,1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_309])]) ).
tff(f878,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,$sum(X1,X2)),X3)
| ~ $less(X3,$sum(X1,$sum(X0,$sum(X2,1)))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_67 ),
inference(forward_demodulation,[],[f872,f280]) ).
tff(f872,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X3,$sum(X1,$sum(X0,$sum(X2,1))))
| ~ $less($sum($sum(X0,X1),X2),X3) )
| ~ spl1_64
| ~ spl1_67 ),
inference(superposition,[],[f838,f651]) ).
tff(f39557,plain,
( spl1_308
| ~ spl1_31
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f866,f837,f279,f39555]) ).
tff(f39555,plain,
( spl1_308
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,$sum(X3,$sum(X0,$sum(X1,1))))
| ~ $less($sum(X3,$sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_308])]) ).
tff(f866,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X3,$sum(X0,$sum(X1,1))))
| ~ $less($sum(X3,$sum(X0,X1)),X2) )
| ~ spl1_31
| ~ spl1_67 ),
inference(superposition,[],[f838,f280]) ).
tff(f39553,plain,
( spl1_307
| ~ spl1_64
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f865,f837,f650,f39551]) ).
tff(f39551,plain,
( spl1_307
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,$sum(X3,$sum(X1,$sum(X0,1))))
| ~ $less($sum(X3,$sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_307])]) ).
tff(f865,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X3,$sum(X1,$sum(X0,1))))
| ~ $less($sum(X3,$sum(X0,X1)),X2) )
| ~ spl1_64
| ~ spl1_67 ),
inference(superposition,[],[f838,f651]) ).
tff(f39549,plain,
( spl1_306
| ~ spl1_49
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f846,f833,f469,f39547]) ).
tff(f39547,plain,
( spl1_306
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(1,X0) = X1 )
| $less(X1,$sum(1,X0))
| $less(X2,X1)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_306])]) ).
tff(f846,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(1,X0) = X1 )
| $less(X1,$sum(1,X0))
| $less(X2,X1)
| $less(X0,X2) )
| ~ spl1_49
| ~ spl1_66 ),
inference(resolution,[],[f834,f470]) ).
tff(f39545,plain,
( spl1_305
| ~ spl1_16
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f844,f833,f158,f39543]) ).
tff(f39543,plain,
( spl1_305
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| $less(X1,$sum(X0,1))
| $less(X2,X1)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_305])]) ).
tff(f844,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| $less(X1,$sum(X0,1))
| $less(X2,X1)
| $less(X0,X2) )
| ~ spl1_16
| ~ spl1_66 ),
inference(resolution,[],[f834,f159]) ).
tff(f39541,plain,
( spl1_304
| ~ spl1_34
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f699,f646,f317,f39539]) ).
tff(f646,plain,
( spl1_63
<=> ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f699,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(add(X0,X1))) )
| ~ in(X0,add(X0,X1)) )
| ~ spl1_34
| ~ spl1_63 ),
inference(superposition,[],[f318,f647]) ).
tff(f647,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl1_63 ),
inference(avatar_component_clause,[],[f646]) ).
tff(f39537,plain,
( spl1_303
| ~ spl1_152
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f7669,f7602,f3128,f39535]) ).
tff(f7602,plain,
( spl1_208
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less(2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_208])]) ).
tff(f7669,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,3) )
| ~ spl1_152
| ~ spl1_208 ),
inference(evaluation,[],[f7654]) ).
tff(f7654,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,$sum(2,1)) )
| ~ spl1_152
| ~ spl1_208 ),
inference(resolution,[],[f7603,f3129]) ).
tff(f7603,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| $less(0,X0) )
| ~ spl1_208 ),
inference(avatar_component_clause,[],[f7602]) ).
tff(f39533,plain,
( spl1_302
| ~ spl1_36
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f688,f642,f325,f39531]) ).
tff(f642,plain,
( spl1_62
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
tff(f688,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(remove(X0,X1))) )
| in(X0,remove(X0,X1)) )
| ~ spl1_36
| ~ spl1_62 ),
inference(superposition,[],[f326,f643]) ).
tff(f643,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) )
| ~ spl1_62 ),
inference(avatar_component_clause,[],[f642]) ).
tff(f38144,plain,
( spl1_301
| ~ spl1_122
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f7656,f7602,f1906,f38142]) ).
tff(f7656,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| ~ $less(2,X0) )
| ~ spl1_122
| ~ spl1_208 ),
inference(resolution,[],[f7603,f1907]) ).
tff(f33523,plain,
( spl1_300
| ~ spl1_133
| ~ spl1_208 ),
inference(avatar_split_clause,[],[f7651,f7602,f1960,f33521]) ).
tff(f7651,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,2))
| ~ $less(0,X0) )
| ~ spl1_133
| ~ spl1_208 ),
inference(resolution,[],[f7603,f1961]) ).
tff(f19484,plain,
( spl1_299
| ~ spl1_7
| ~ spl1_95 ),
inference(avatar_split_clause,[],[f1512,f1492,f117,f19482]) ).
tff(f19482,plain,
( spl1_299
<=> ! [X0: $int,X1: collection] :
( ~ $less($sum(-1,count(X1)),0)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_299])]) ).
tff(f1512,plain,
( ! [X0: $int,X1: collection] :
( ~ $less($sum(-1,count(X1)),0)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_7
| ~ spl1_95 ),
inference(superposition,[],[f118,f1493]) ).
tff(f19480,plain,
( spl1_298
| ~ spl1_52
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1305,f1093,f481,f19478]) ).
tff(f19478,plain,
( spl1_298
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X3,$sum($uminus(X0),X1))),X1)
| ~ $less($sum(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_298])]) ).
tff(f1305,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X3,$sum($uminus(X0),X1))),X1)
| ~ $less($sum(X2,X3),X0) )
| ~ spl1_52
| ~ spl1_83 ),
inference(superposition,[],[f1094,f482]) ).
tff(f19476,plain,
( spl1_297
| ~ spl1_52
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1286,f1093,f481,f19474]) ).
tff(f19474,plain,
( spl1_297
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X3,$sum($uminus(X0),X1)))
| ~ $less($sum(X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_297])]) ).
tff(f1286,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X3,$sum($uminus(X0),X1)))
| ~ $less($sum(X2,X0),X3) )
| ~ spl1_52
| ~ spl1_83 ),
inference(superposition,[],[f1094,f482]) ).
tff(f19472,plain,
( spl1_296
| ~ spl1_52
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1253,f1089,f481,f19470]) ).
tff(f19470,plain,
( spl1_296
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum($uminus(X0),X1)),$sum(X3,X1))
| ~ $less(X2,$sum(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_296])]) ).
tff(f1253,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum($uminus(X0),X1)),$sum(X3,X1))
| ~ $less(X2,$sum(X3,X0)) )
| ~ spl1_52
| ~ spl1_82 ),
inference(superposition,[],[f1090,f482]) ).
tff(f19468,plain,
( spl1_295
| ~ spl1_52
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1242,f1089,f481,f19466]) ).
tff(f19466,plain,
( spl1_295
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less(X1,$sum(X2,$sum(X3,$sum($uminus(X0),X1))))
| ~ $less(X0,$sum(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_295])]) ).
tff(f1242,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$sum(X3,$sum($uminus(X0),X1))))
| ~ $less(X0,$sum(X2,X3)) )
| ~ spl1_52
| ~ spl1_82 ),
inference(superposition,[],[f1090,f482]) ).
tff(f19464,plain,
( spl1_294
| ~ spl1_15
| ~ spl1_80 ),
inference(avatar_split_clause,[],[f1171,f1081,f152,f19462]) ).
tff(f19462,plain,
( spl1_294
<=> ! [X0: $int,X1: collection] :
( ( 0 != count(X1) )
| ( empty = remove(X0,X1) )
| ( 0 = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_294])]) ).
tff(f1171,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(X1) )
| ( empty = remove(X0,X1) )
| ( 0 = count(add(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_80 ),
inference(inner_rewriting,[],[f1150]) ).
tff(f1150,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(X1) )
| ( empty = remove(X0,X1) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_80 ),
inference(superposition,[],[f153,f1082]) ).
tff(f19460,plain,
( spl1_293
| ~ spl1_176
| ~ spl1_236 ),
inference(avatar_split_clause,[],[f19415,f10679,f5129,f19458]) ).
tff(f19458,plain,
( spl1_293
<=> ! [X0: $int] :
( $less($uminus(X0),2)
| ~ $less(1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_293])]) ).
tff(f5129,plain,
( spl1_176
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,$uminus(X1)))
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_176])]) ).
tff(f10679,plain,
( spl1_236
<=> ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_236])]) ).
tff(f19415,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| ~ $less(1,X0) )
| ~ spl1_176
| ~ spl1_236 ),
inference(evaluation,[],[f19380]) ).
tff(f19380,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| ~ $less(1,X0)
| $less(0,0) )
| ~ spl1_176
| ~ spl1_236 ),
inference(resolution,[],[f10680,f5130]) ).
tff(f5130,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$uminus(X1)))
| ~ $less(X0,X1)
| $less(X2,0) )
| ~ spl1_176 ),
inference(avatar_component_clause,[],[f5129]) ).
tff(f10680,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,2) )
| ~ spl1_236 ),
inference(avatar_component_clause,[],[f10679]) ).
tff(f19456,plain,
( spl1_292
| ~ spl1_12
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1131,f1077,f140,f19454]) ).
tff(f19454,plain,
( spl1_292
<=> ! [X2: collection,X0: $int,X1: $int] : ( count(add(X0,add(X1,X2))) = count(add(X1,add(X0,add(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_292])]) ).
tff(f1131,plain,
( ! [X2: collection,X0: $int,X1: $int] : ( count(add(X0,add(X1,X2))) = count(add(X1,add(X0,add(X1,X2)))) )
| ~ spl1_12
| ~ spl1_79 ),
inference(resolution,[],[f1078,f141]) ).
tff(f19452,plain,
( spl1_291
| ~ spl1_11
| ~ spl1_77 ),
inference(avatar_split_clause,[],[f1114,f1069,f136,f19450]) ).
tff(f19450,plain,
( spl1_291
<=> ! [X2: collection,X0: $int,X1: $int] : ( count(remove(X0,remove(X1,remove(X0,X2)))) = count(remove(X1,remove(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_291])]) ).
tff(f1114,plain,
( ! [X2: collection,X0: $int,X1: $int] : ( count(remove(X0,remove(X1,remove(X0,X2)))) = count(remove(X1,remove(X0,X2))) )
| ~ spl1_11
| ~ spl1_77 ),
inference(resolution,[],[f1070,f137]) ).
tff(f19448,plain,
( spl1_290
| ~ spl1_12
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1102,f1065,f140,f19446]) ).
tff(f19446,plain,
( spl1_290
<=> ! [X2: collection,X0: $int,X1: $int] : ( add(X0,add(X1,X2)) = add(X1,remove(X1,add(X0,add(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_290])]) ).
tff(f1102,plain,
( ! [X2: collection,X0: $int,X1: $int] : ( add(X0,add(X1,X2)) = add(X1,remove(X1,add(X0,add(X1,X2)))) )
| ~ spl1_12
| ~ spl1_76 ),
inference(resolution,[],[f1066,f141]) ).
tff(f19444,plain,
( spl1_289
| ~ spl1_15
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f1055,f927,f152,f19442]) ).
tff(f1055,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(-1,count(add(X0,X1))) )
| ( empty = remove(X0,add(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_75 ),
inference(superposition,[],[f153,f928]) ).
tff(f19440,plain,
( spl1_288
| ~ spl1_15
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1036,f923,f152,f19438]) ).
tff(f1036,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != $sum(1,count(remove(X0,X1))) )
| ( empty = add(X0,remove(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_74 ),
inference(superposition,[],[f153,f924]) ).
tff(f19436,plain,
( spl1_287
| ~ spl1_68
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f945,f911,f841,f19434]) ).
tff(f19434,plain,
( spl1_287
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,$sum(X3,1)))
| $less($sum(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_287])]) ).
tff(f945,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,$sum(X3,1)))
| $less($sum(X0,X3),X2) )
| ~ spl1_68
| ~ spl1_71 ),
inference(resolution,[],[f912,f842]) ).
tff(f19432,plain,
( spl1_286
| ~ spl1_21
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f885,f841,f184,f19430]) ).
tff(f19430,plain,
( spl1_286
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| ~ $less(X3,X2)
| $less(X3,$sum(X0,$sum(X1,1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_286])]) ).
tff(f885,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),X2)
| ~ $less(X3,X2)
| $less(X3,$sum(X0,$sum(X1,1))) )
| ~ spl1_21
| ~ spl1_68 ),
inference(resolution,[],[f842,f185]) ).
tff(f19428,plain,
( spl1_285
| ~ spl1_51
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f854,f833,f477,f19426]) ).
tff(f19426,plain,
( spl1_285
<=> ! [X0: collection,X1: $int] :
( ( count(X0) = X1 )
| $less(X1,count(X0))
| $less(0,X1)
| ( 0 = count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_285])]) ).
tff(f854,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = X1 )
| $less(X1,count(X0))
| $less(0,X1)
| ( 0 = count(X0) ) )
| ~ spl1_51
| ~ spl1_66 ),
inference(resolution,[],[f834,f478]) ).
tff(f19424,plain,
( spl1_284
| ~ spl1_54
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f853,f833,f540,f19422]) ).
tff(f19422,plain,
( spl1_284
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| $less(X0,0)
| $less($sum(X1,$uminus(X2)),X0)
| ~ $less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_284])]) ).
tff(f853,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| $less(X0,0)
| $less($sum(X1,$uminus(X2)),X0)
| ~ $less(X1,X2) )
| ~ spl1_54
| ~ spl1_66 ),
inference(resolution,[],[f834,f541]) ).
tff(f19420,plain,
( spl1_283
| ~ spl1_22
| ~ spl1_66 ),
inference(avatar_split_clause,[],[f848,f833,f188,f19418]) ).
tff(f19418,plain,
( spl1_283
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X2,X1)
| $less(X0,X2)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_283])]) ).
tff(f848,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X2,X1)
| $less(X0,X2)
| ( X0 = X2 ) )
| ~ spl1_22
| ~ spl1_66 ),
inference(resolution,[],[f834,f189]) ).
tff(f19367,plain,
( spl1_282
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f823,f654,f650,f279,f19365]) ).
tff(f19365,plain,
( spl1_282
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X2,$sum(X0,$sum(X1,X3))) = $sum(X2,$sum(X1,$sum(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_282])]) ).
tff(f823,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X2,$sum(X0,$sum(X1,X3))) = $sum(X2,$sum(X1,$sum(X0,X3))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(forward_demodulation,[],[f822,f280]) ).
tff(f822,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X2,$sum($sum(X0,X1),X3)) = $sum(X2,$sum(X1,$sum(X0,X3))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(forward_demodulation,[],[f821,f651]) ).
tff(f821,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X2,$sum($sum(X0,X1),X3)) = $sum($sum(X1,X2),$sum(X0,X3)) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(forward_demodulation,[],[f786,f280]) ).
tff(f786,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X1,X2),$sum(X0,X3)) = $sum($sum(X2,$sum(X0,X1)),X3) )
| ~ spl1_64
| ~ spl1_65 ),
inference(superposition,[],[f651,f655]) ).
tff(f19363,plain,
( spl1_281
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f818,f654,f279,f19361]) ).
tff(f19361,plain,
( spl1_281
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum($sum(X2,$sum(X0,X1)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_281])]) ).
tff(f818,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum($sum(X2,$sum(X0,X1)),X3) )
| ~ spl1_31
| ~ spl1_65 ),
inference(forward_demodulation,[],[f781,f280]) ).
tff(f781,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum($sum(X1,X2),X3)) = $sum($sum(X2,$sum(X0,X1)),X3) )
| ~ spl1_31
| ~ spl1_65 ),
inference(superposition,[],[f280,f655]) ).
tff(f19359,plain,
( spl1_280
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f816,f654,f279,f19357]) ).
tff(f19357,plain,
( spl1_280
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X3,$sum(X2,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_280])]) ).
tff(f816,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X3,$sum(X2,$sum(X0,X1))) )
| ~ spl1_31
| ~ spl1_65 ),
inference(forward_demodulation,[],[f766,f280]) ).
tff(f766,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum($sum(X1,X2),X3)) = $sum(X3,$sum(X2,$sum(X0,X1))) )
| ~ spl1_65 ),
inference(superposition,[],[f655,f655]) ).
tff(f19355,plain,
( spl1_279
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f815,f654,f279,f19353]) ).
tff(f19353,plain,
( spl1_279
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X3,$sum(X1,$sum(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_279])]) ).
tff(f815,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X3,$sum(X1,$sum(X2,X0))) )
| ~ spl1_31
| ~ spl1_65 ),
inference(forward_demodulation,[],[f765,f280]) ).
tff(f765,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum($sum(X1,X2),X3)) = $sum(X3,$sum(X1,$sum(X2,X0))) )
| ~ spl1_65 ),
inference(superposition,[],[f655,f655]) ).
tff(f19351,plain,
( spl1_278
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f812,f654,f650,f279,f19349]) ).
tff(f19349,plain,
( spl1_278
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum(X0,$sum(X1,X2))) = $sum(X1,$sum(X0,$sum(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_278])]) ).
tff(f812,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum(X0,$sum(X1,X2))) = $sum(X1,$sum(X0,$sum(X2,X3))) )
| ~ spl1_31
| ~ spl1_64
| ~ spl1_65 ),
inference(forward_demodulation,[],[f759,f280]) ).
tff(f759,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X1,$sum(X0,$sum(X2,X3))) = $sum(X3,$sum($sum(X0,X1),X2)) )
| ~ spl1_64
| ~ spl1_65 ),
inference(superposition,[],[f655,f651]) ).
tff(f19347,plain,
( spl1_277
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f775,f654,f279,f19345]) ).
tff(f19345,plain,
( spl1_277
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X2,$sum(X3,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_277])]) ).
tff(f775,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X2,$sum(X3,$sum(X0,X1))) )
| ~ spl1_31
| ~ spl1_65 ),
inference(superposition,[],[f655,f280]) ).
tff(f19343,plain,
( spl1_276
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f770,f654,f279,f19341]) ).
tff(f19341,plain,
( spl1_276
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum(X0,X1),$sum(X2,X3)) = $sum(X3,$sum(X0,$sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_276])]) ).
tff(f770,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),$sum(X2,X3)) = $sum(X3,$sum(X0,$sum(X1,X2))) )
| ~ spl1_31
| ~ spl1_65 ),
inference(superposition,[],[f655,f280]) ).
tff(f19339,plain,
( spl1_275
| ~ spl1_64
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f769,f654,f650,f19337]) ).
tff(f19337,plain,
( spl1_275
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum(X0,X1),$sum(X2,X3)) = $sum(X3,$sum(X1,$sum(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_275])]) ).
tff(f769,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),$sum(X2,X3)) = $sum(X3,$sum(X1,$sum(X0,X2))) )
| ~ spl1_64
| ~ spl1_65 ),
inference(superposition,[],[f655,f651]) ).
tff(f19335,plain,
( spl1_274
| ~ spl1_31
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f754,f654,f279,f19333]) ).
tff(f19333,plain,
( spl1_274
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum(X0,$sum(X1,X2))) = $sum(X2,$sum(X3,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_274])]) ).
tff(f754,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum(X0,$sum(X1,X2))) = $sum(X2,$sum(X3,$sum(X0,X1))) )
| ~ spl1_31
| ~ spl1_65 ),
inference(superposition,[],[f655,f280]) ).
tff(f19331,plain,
( spl1_273
| ~ spl1_64
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f753,f654,f650,f19329]) ).
tff(f19329,plain,
( spl1_273
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum(X1,$sum(X0,X2))) = $sum(X2,$sum(X3,$sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_273])]) ).
tff(f753,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum(X1,$sum(X0,X2))) = $sum(X2,$sum(X3,$sum(X0,X1))) )
| ~ spl1_64
| ~ spl1_65 ),
inference(superposition,[],[f655,f651]) ).
tff(f19313,plain,
( spl1_272
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f750,f654,f19311]) ).
tff(f19311,plain,
( spl1_272
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum(X3,$sum(X2,$sum(X0,X1))) = $sum($sum(X1,X2),$sum(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_272])]) ).
tff(f750,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$sum(X2,$sum(X0,X1))) = $sum($sum(X1,X2),$sum(X3,X0)) )
| ~ spl1_65 ),
inference(superposition,[],[f655,f655]) ).
tff(f19309,plain,
( spl1_271
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f749,f654,f19307]) ).
tff(f19307,plain,
( spl1_271
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum(X1,X2),$sum(X3,X0)) = $sum(X3,$sum(X1,$sum(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_271])]) ).
tff(f749,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X1,X2),$sum(X3,X0)) = $sum(X3,$sum(X1,$sum(X2,X0))) )
| ~ spl1_65 ),
inference(superposition,[],[f655,f655]) ).
tff(f19305,plain,
( spl1_270
| ~ spl1_31
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f740,f650,f279,f19303]) ).
tff(f19303,plain,
( spl1_270
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum(X0,$sum(X1,X2)),X3) = $sum(X2,$sum(X0,$sum(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_270])]) ).
tff(f740,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X0,$sum(X1,X2)),X3) = $sum(X2,$sum(X0,$sum(X1,X3))) )
| ~ spl1_31
| ~ spl1_64 ),
inference(forward_demodulation,[],[f715,f280]) ).
tff(f715,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X0,$sum(X1,X2)),X3) = $sum(X2,$sum($sum(X0,X1),X3)) )
| ~ spl1_31
| ~ spl1_64 ),
inference(superposition,[],[f651,f280]) ).
tff(f19301,plain,
( spl1_269
| ~ spl1_31
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f739,f650,f279,f19299]) ).
tff(f19299,plain,
( spl1_269
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($sum(X1,$sum(X0,X2)),X3) = $sum(X2,$sum(X0,$sum(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_269])]) ).
tff(f739,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($sum(X1,$sum(X0,X2)),X3) = $sum(X2,$sum(X0,$sum(X1,X3))) )
| ~ spl1_31
| ~ spl1_64 ),
inference(forward_demodulation,[],[f714,f280]) ).
tff(f714,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X2,$sum($sum(X0,X1),X3)) = $sum($sum(X1,$sum(X0,X2)),X3) )
| ~ spl1_64 ),
inference(superposition,[],[f651,f651]) ).
tff(f19297,plain,
( spl1_268
| ~ spl1_57
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f665,f634,f567,f19295]) ).
tff(f19295,plain,
( spl1_268
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X1,X3))
| ~ $less(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_268])]) ).
tff(f665,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X1,X3))
| ~ $less(X0,X3) )
| ~ spl1_57
| ~ spl1_60 ),
inference(resolution,[],[f635,f568]) ).
tff(f19293,plain,
( spl1_267
| ~ spl1_56
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f664,f634,f563,f19291]) ).
tff(f19291,plain,
( spl1_267
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X3,X0))
| ~ $less(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_267])]) ).
tff(f664,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X3,X0))
| ~ $less(X1,X3) )
| ~ spl1_56
| ~ spl1_60 ),
inference(resolution,[],[f635,f564]) ).
tff(f19289,plain,
( spl1_266
| ~ spl1_24
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f663,f634,f206,f19287]) ).
tff(f19287,plain,
( spl1_266
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X3,X1))
| ~ $less(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_266])]) ).
tff(f663,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,X1),$sum(X2,1))
| $less(X2,$sum(X3,X1))
| ~ $less(X0,X3) )
| ~ spl1_24
| ~ spl1_60 ),
inference(resolution,[],[f635,f207]) ).
tff(f19000,plain,
( spl1_265
| ~ spl1_161
| ~ spl1_226 ),
inference(avatar_split_clause,[],[f16302,f10586,f3490,f18998]) ).
tff(f18998,plain,
( spl1_265
<=> ! [X0: $int] :
( $less($uminus(X0),2)
| $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_265])]) ).
tff(f10586,plain,
( spl1_226
<=> ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_226])]) ).
tff(f16302,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| $less(X0,1) )
| ~ spl1_161
| ~ spl1_226 ),
inference(evaluation,[],[f16283]) ).
tff(f16283,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| $less($sum(0,X0),1) )
| ~ spl1_161
| ~ spl1_226 ),
inference(resolution,[],[f10587,f3491]) ).
tff(f10587,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,2) )
| ~ spl1_226 ),
inference(avatar_component_clause,[],[f10586]) ).
tff(f10838,plain,
( spl1_264
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f1421,f1337,f10836]) ).
tff(f10836,plain,
( spl1_264
<=> ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_264])]) ).
tff(f1421,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_89 ),
inference(equality_factoring,[],[f1338]) ).
tff(f10834,plain,
( spl1_263
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f1364,f1321,f10832]) ).
tff(f10832,plain,
( spl1_263
<=> ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_263])]) ).
tff(f1364,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_85 ),
inference(equality_factoring,[],[f1322]) ).
tff(f10830,plain,
( spl1_262
| ~ spl1_14
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1284,f1093,f148,f10828]) ).
tff(f10828,plain,
( spl1_262
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X1,X0)),$sum(X3,X1))
| ~ $less($sum(X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_262])]) ).
tff(f1284,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X1,X0)),$sum(X3,X1))
| ~ $less($sum(X2,X0),X3) )
| ~ spl1_14
| ~ spl1_83 ),
inference(superposition,[],[f1094,f149]) ).
tff(f10826,plain,
( spl1_261
| ~ spl1_14
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1251,f1089,f148,f10824]) ).
tff(f10824,plain,
( spl1_261
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X3,$sum(X1,X0)))
| ~ $less(X2,$sum(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_261])]) ).
tff(f1251,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X3,$sum(X1,X0)))
| ~ $less(X2,$sum(X3,X0)) )
| ~ spl1_14
| ~ spl1_82 ),
inference(superposition,[],[f1090,f149]) ).
tff(f10822,plain,
( spl1_260
| ~ spl1_14
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1184,f1085,f148,f10820]) ).
tff(f10820,plain,
( spl1_260
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X1,X0)),X2) = $sum($sum($uminus(X1),X2),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_260])]) ).
tff(f1184,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X1,X0)),X2) = $sum($sum($uminus(X1),X2),$uminus(X0)) )
| ~ spl1_14
| ~ spl1_81 ),
inference(superposition,[],[f1086,f149]) ).
tff(f10818,plain,
( spl1_259
| ~ spl1_65
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1182,f1085,f654,f10816]) ).
tff(f10816,plain,
( spl1_259
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X1,X0)),X2) = $sum($uminus(X1),$sum(X2,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_259])]) ).
tff(f1182,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X1,X0)),X2) = $sum($uminus(X1),$sum(X2,$uminus(X0))) )
| ~ spl1_65
| ~ spl1_81 ),
inference(superposition,[],[f1086,f655]) ).
tff(f10814,plain,
( spl1_258
| ~ spl1_14
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1176,f1085,f148,f10812]) ).
tff(f10812,plain,
( spl1_258
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X2)),X1) = $sum($uminus(X2),$sum(X1,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_258])]) ).
tff(f1176,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X2)),X1) = $sum($uminus(X2),$sum(X1,$uminus(X0))) )
| ~ spl1_14
| ~ spl1_81 ),
inference(superposition,[],[f1086,f149]) ).
tff(f10810,plain,
( spl1_257
| ~ spl1_127
| ~ spl1_224 ),
inference(avatar_split_clause,[],[f10723,f8022,f1926,f10808]) ).
tff(f1926,plain,
( spl1_127
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
tff(f10723,plain,
( ! [X0: $int] :
( ~ $less(2,X0)
| ~ $less(X0,1) )
| ~ spl1_127
| ~ spl1_224 ),
inference(resolution,[],[f8023,f1927]) ).
tff(f1927,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X1,X0))
| ~ $less(X0,1) )
| ~ spl1_127 ),
inference(avatar_component_clause,[],[f1926]) ).
tff(f10806,plain,
( spl1_256
| ~ spl1_55
| ~ spl1_73 ),
inference(avatar_split_clause,[],[f994,f919,f559,f10804]) ).
tff(f10804,plain,
( spl1_256
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$uminus($sum(X1,X2)))
| ~ $less($uminus(X0),$uminus(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_256])]) ).
tff(f994,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$uminus($sum(X1,X2)))
| ~ $less($uminus(X0),$uminus(X2)) )
| ~ spl1_55
| ~ spl1_73 ),
inference(superposition,[],[f920,f560]) ).
tff(f10802,plain,
( spl1_255
| ~ spl1_23
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f982,f915,f202,f10800]) ).
tff(f10800,plain,
( spl1_255
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X2)),$uminus($sum(X1,X0)))
| ~ $less($uminus(X2),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_255])]) ).
tff(f982,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X2)),$uminus($sum(X1,X0)))
| ~ $less($uminus(X2),$uminus(X0)) )
| ~ spl1_23
| ~ spl1_72 ),
inference(superposition,[],[f916,f203]) ).
tff(f10798,plain,
( spl1_254
| ~ spl1_55
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f981,f915,f559,f10796]) ).
tff(f10796,plain,
( spl1_254
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X2)),$uminus($sum(X0,X1)))
| ~ $less($uminus(X2),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_254])]) ).
tff(f981,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X2)),$uminus($sum(X0,X1)))
| ~ $less($uminus(X2),$uminus(X0)) )
| ~ spl1_55
| ~ spl1_72 ),
inference(superposition,[],[f916,f560]) ).
tff(f10794,plain,
( spl1_253
| ~ spl1_52
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f956,f911,f481,f10792]) ).
tff(f10792,plain,
( spl1_253
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X2,X1)
| ~ $less(X0,X3)
| $less(X2,$sum(X3,$sum($uminus(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_253])]) ).
tff(f956,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X2,X1)
| ~ $less(X0,X3)
| $less(X2,$sum(X3,$sum($uminus(X0),X1))) )
| ~ spl1_52
| ~ spl1_71 ),
inference(superposition,[],[f912,f482]) ).
tff(f10790,plain,
( spl1_252
| ~ spl1_31
| ~ spl1_56
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f828,f654,f563,f279,f10788]) ).
tff(f10788,plain,
( spl1_252
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X2,X3)),$sum(X1,$sum(X2,X0)))
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_252])]) ).
tff(f828,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X2,X3)),$sum(X1,$sum(X2,X0)))
| ~ $less(X3,X0) )
| ~ spl1_31
| ~ spl1_56
| ~ spl1_65 ),
inference(forward_demodulation,[],[f799,f280]) ).
tff(f799,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($sum(X1,X2),X3),$sum(X1,$sum(X2,X0)))
| ~ $less(X3,X0) )
| ~ spl1_56
| ~ spl1_65 ),
inference(superposition,[],[f564,f655]) ).
tff(f10786,plain,
( spl1_251
| ~ spl1_31
| ~ spl1_57
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f820,f654,f567,f279,f10784]) ).
tff(f10784,plain,
( spl1_251
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X1,$sum(X2,X3)))
| ~ $less(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_251])]) ).
tff(f820,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X1,$sum(X2,X3)))
| ~ $less(X0,X3) )
| ~ spl1_31
| ~ spl1_57
| ~ spl1_65 ),
inference(forward_demodulation,[],[f785,f280]) ).
tff(f785,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum($sum(X1,X2),X3))
| ~ $less(X0,X3) )
| ~ spl1_57
| ~ spl1_65 ),
inference(superposition,[],[f568,f655]) ).
tff(f10782,plain,
( spl1_250
| ~ spl1_31
| ~ spl1_56
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f819,f654,f563,f279,f10780]) ).
tff(f10780,plain,
( spl1_250
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X2,X3)),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_250])]) ).
tff(f819,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X2,X3)),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,X0) )
| ~ spl1_31
| ~ spl1_56
| ~ spl1_65 ),
inference(forward_demodulation,[],[f783,f280]) ).
tff(f783,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum($sum(X1,X2),X3),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,X0) )
| ~ spl1_56
| ~ spl1_65 ),
inference(superposition,[],[f564,f655]) ).
tff(f10778,plain,
( spl1_249
| ~ spl1_57
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f784,f654,f567,f10776]) ).
tff(f10776,plain,
( spl1_249
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X0),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_249])]) ).
tff(f784,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X0),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,$sum(X1,X2)) )
| ~ spl1_57
| ~ spl1_65 ),
inference(superposition,[],[f568,f655]) ).
tff(f10774,plain,
( spl1_248
| ~ spl1_56
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f782,f654,f563,f10772]) ).
tff(f10772,plain,
( spl1_248
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,X0))
| ~ $less($sum(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_248])]) ).
tff(f782,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,X0))
| ~ $less($sum(X1,X2),X3) )
| ~ spl1_56
| ~ spl1_65 ),
inference(superposition,[],[f564,f655]) ).
tff(f10770,plain,
( spl1_247
| ~ spl1_24
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f780,f654,f206,f10768]) ).
tff(f10768,plain,
( spl1_247
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,$sum(X1,X2)))
| ~ $less(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_247])]) ).
tff(f780,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum(X0,X1)),$sum(X3,$sum(X1,X2)))
| ~ $less(X0,X3) )
| ~ spl1_24
| ~ spl1_65 ),
inference(superposition,[],[f207,f655]) ).
tff(f10721,plain,
( spl1_246
| ~ spl1_24
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f779,f654,f206,f10719]) ).
tff(f10719,plain,
( spl1_246
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_246])]) ).
tff(f779,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$sum(X1,X2)),$sum(X2,$sum(X0,X1)))
| ~ $less(X3,X0) )
| ~ spl1_24
| ~ spl1_65 ),
inference(superposition,[],[f207,f655]) ).
tff(f10717,plain,
( spl1_245
| ~ spl1_23
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f768,f654,f202,f10715]) ).
tff(f10715,plain,
( spl1_245
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum(X2,$uminus($sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_245])]) ).
tff(f768,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum(X2,$uminus($sum(X1,X0))) )
| ~ spl1_23
| ~ spl1_65 ),
inference(superposition,[],[f655,f203]) ).
tff(f10713,plain,
( spl1_244
| ~ spl1_55
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f767,f654,f559,f10711]) ).
tff(f10711,plain,
( spl1_244
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum(X2,$uminus($sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_244])]) ).
tff(f767,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum(X2,$uminus($sum(X0,X1))) )
| ~ spl1_55
| ~ spl1_65 ),
inference(superposition,[],[f655,f560]) ).
tff(f10709,plain,
( spl1_243
| ~ spl1_23
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f752,f654,f202,f10707]) ).
tff(f10707,plain,
( spl1_243
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$uminus($sum(X1,X0))) = $sum($uminus(X1),$sum(X2,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_243])]) ).
tff(f752,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$uminus($sum(X1,X0))) = $sum($uminus(X1),$sum(X2,$uminus(X0))) )
| ~ spl1_23
| ~ spl1_65 ),
inference(superposition,[],[f655,f203]) ).
tff(f10705,plain,
( spl1_242
| ~ spl1_55
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f751,f654,f559,f10703]) ).
tff(f10703,plain,
( spl1_242
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$uminus($sum(X0,X1))) = $sum($uminus(X1),$sum(X2,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_242])]) ).
tff(f751,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$uminus($sum(X0,X1))) = $sum($uminus(X1),$sum(X2,$uminus(X0))) )
| ~ spl1_55
| ~ spl1_65 ),
inference(superposition,[],[f655,f560]) ).
tff(f10701,plain,
( spl1_241
| ~ spl1_57
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f730,f650,f567,f10699]) ).
tff(f10699,plain,
( spl1_241
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X2,X3))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_241])]) ).
tff(f730,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X2,X3))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_57
| ~ spl1_64 ),
inference(superposition,[],[f568,f651]) ).
tff(f10697,plain,
( spl1_240
| ~ spl1_57
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f729,f650,f567,f10695]) ).
tff(f10695,plain,
( spl1_240
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X0,X1)),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_240])]) ).
tff(f729,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$sum(X0,X1)),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,X2) )
| ~ spl1_57
| ~ spl1_64 ),
inference(superposition,[],[f568,f651]) ).
tff(f10693,plain,
( spl1_239
| ~ spl1_56
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f728,f650,f563,f10691]) ).
tff(f10691,plain,
( spl1_239
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,X3),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_239])]) ).
tff(f728,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,X3),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_56
| ~ spl1_64 ),
inference(superposition,[],[f564,f651]) ).
tff(f10689,plain,
( spl1_238
| ~ spl1_56
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f727,f650,f563,f10687]) ).
tff(f10687,plain,
( spl1_238
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,$sum(X0,X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_238])]) ).
tff(f727,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,$sum(X0,X1)))
| ~ $less(X2,X3) )
| ~ spl1_56
| ~ spl1_64 ),
inference(superposition,[],[f564,f651]) ).
tff(f10685,plain,
( spl1_237
| ~ spl1_24
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f725,f650,f206,f10683]) ).
tff(f10683,plain,
( spl1_237
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_237])]) ).
tff(f725,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_24
| ~ spl1_64 ),
inference(superposition,[],[f207,f651]) ).
tff(f10681,plain,
( spl1_236
| ~ spl1_52
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f7559,f6481,f481,f10679]) ).
tff(f6481,plain,
( spl1_196
<=> ! [X0: $int] :
( $less($sum(-1,X0),2)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_196])]) ).
tff(f7559,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum(1,X0)) )
| ~ spl1_52
| ~ spl1_196 ),
inference(evaluation,[],[f7544]) ).
tff(f7544,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum($uminus(-1),X0)) )
| ~ spl1_52
| ~ spl1_196 ),
inference(superposition,[],[f6482,f482]) ).
tff(f6482,plain,
( ! [X0: $int] :
( $less($sum(-1,X0),2)
| $less(0,X0) )
| ~ spl1_196 ),
inference(avatar_component_clause,[],[f6481]) ).
tff(f10677,plain,
( spl1_235
| ~ spl1_24
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f724,f650,f206,f10675]) ).
tff(f10675,plain,
( spl1_235
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_235])]) ).
tff(f724,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X1,$sum(X0,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_24
| ~ spl1_64 ),
inference(superposition,[],[f207,f651]) ).
tff(f10673,plain,
( spl1_234
| ~ spl1_53
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f668,f634,f536,f10671]) ).
tff(f10671,plain,
( spl1_234
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X0,1))
| $less(X0,$sum(X1,$uminus(X2)))
| ~ $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_234])]) ).
tff(f668,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X0,1))
| $less(X0,$sum(X1,$uminus(X2)))
| ~ $less(X2,X1) )
| ~ spl1_53
| ~ spl1_60 ),
inference(resolution,[],[f635,f537]) ).
tff(f10669,plain,
( spl1_233
| ~ spl1_54
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f666,f634,f540,f10667]) ).
tff(f10667,plain,
( spl1_233
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),$sum(X2,1))
| $less(X2,0)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_233])]) ).
tff(f666,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),$sum(X2,1))
| $less(X2,0)
| ~ $less(X0,X1) )
| ~ spl1_54
| ~ spl1_60 ),
inference(resolution,[],[f635,f541]) ).
tff(f10665,plain,
( spl1_232
| ~ spl1_22
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f661,f634,f188,f10663]) ).
tff(f10663,plain,
( spl1_232
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,X2)
| $less(X2,X0)
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_232])]) ).
tff(f661,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,X2)
| $less(X2,X0)
| ( X0 = X2 ) )
| ~ spl1_22
| ~ spl1_60 ),
inference(resolution,[],[f635,f189]) ).
tff(f10661,plain,
( spl1_231
| ~ spl1_31
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f631,f567,f279,f10659]) ).
tff(f10659,plain,
( spl1_231
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$sum(X0,X1)),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_231])]) ).
tff(f631,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$sum(X0,X1)),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,X2) )
| ~ spl1_31
| ~ spl1_57 ),
inference(superposition,[],[f568,f280]) ).
tff(f10657,plain,
( spl1_230
| ~ spl1_31
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f624,f567,f279,f10655]) ).
tff(f10655,plain,
( spl1_230
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X2,X3))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_230])]) ).
tff(f624,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X2,X3))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_31
| ~ spl1_57 ),
inference(superposition,[],[f568,f280]) ).
tff(f10653,plain,
( spl1_229
| ~ spl1_31
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f612,f563,f279,f10651]) ).
tff(f10651,plain,
( spl1_229
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X2,X3),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_229])]) ).
tff(f612,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X2,X3),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_31
| ~ spl1_56 ),
inference(superposition,[],[f564,f280]) ).
tff(f10649,plain,
( spl1_228
| ~ spl1_31
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f605,f563,f279,f10647]) ).
tff(f10647,plain,
( spl1_228
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,$sum(X0,X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_228])]) ).
tff(f605,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,$sum(X0,X1)))
| ~ $less(X2,X3) )
| ~ spl1_31
| ~ spl1_56 ),
inference(superposition,[],[f564,f280]) ).
tff(f10645,plain,
( spl1_227
| ~ spl1_31
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f584,f559,f279,f10643]) ).
tff(f10643,plain,
( spl1_227
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_227])]) ).
tff(f10588,plain,
( spl1_226
| ~ spl1_124
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f7557,f6481,f1914,f10586]) ).
tff(f7557,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum(X0,1)) )
| ~ spl1_124
| ~ spl1_196 ),
inference(evaluation,[],[f7552]) ).
tff(f7552,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(0,$sum(X0,$uminus(-1))) )
| ~ spl1_124
| ~ spl1_196 ),
inference(superposition,[],[f6482,f1915]) ).
tff(f8949,plain,
( spl1_225
| ~ spl1_14
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f7542,f6481,f148,f8947]) ).
tff(f8947,plain,
( spl1_225
<=> ! [X0: $int] :
( $less($sum(X0,-1),2)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_225])]) ).
tff(f7542,plain,
( ! [X0: $int] :
( $less($sum(X0,-1),2)
| $less(0,X0) )
| ~ spl1_14
| ~ spl1_196 ),
inference(superposition,[],[f6482,f149]) ).
tff(f8024,plain,
( spl1_224
| ~ spl1_126
| ~ spl1_185 ),
inference(avatar_split_clause,[],[f5216,f5166,f1922,f8022]) ).
tff(f1922,plain,
( spl1_126
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
tff(f5166,plain,
( spl1_185
<=> ! [X0: $int] :
( $less(X0,2)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_185])]) ).
tff(f5216,plain,
( ! [X0: $int] :
( $less(-1,$sum(-1,X0))
| ~ $less(2,X0) )
| ~ spl1_126
| ~ spl1_185 ),
inference(resolution,[],[f5167,f1923]) ).
tff(f1923,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(-1,X0),X1)
| ~ $less(X1,X0) )
| ~ spl1_126 ),
inference(avatar_component_clause,[],[f1922]) ).
tff(f5167,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(-1,X0) )
| ~ spl1_185 ),
inference(avatar_component_clause,[],[f5166]) ).
tff(f7691,plain,
( spl1_223
| ~ spl1_7
| ~ spl1_89 ),
inference(avatar_split_clause,[],[f1420,f1337,f117,f7689]) ).
tff(f7689,plain,
( spl1_223
<=> ! [X0: $int,X1: collection] :
( ~ $less($sum(-1,count(X1)),0)
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_223])]) ).
tff(f1420,plain,
( ! [X0: $int,X1: collection] :
( ~ $less($sum(-1,count(X1)),0)
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_7
| ~ spl1_89 ),
inference(superposition,[],[f118,f1338]) ).
tff(f7687,plain,
( spl1_222
| ~ spl1_7
| ~ spl1_85 ),
inference(avatar_split_clause,[],[f1363,f1321,f117,f7685]) ).
tff(f7685,plain,
( spl1_222
<=> ! [X0: $int,X1: collection] :
( ~ $less($sum(1,count(X1)),0)
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_222])]) ).
tff(f1363,plain,
( ! [X0: $int,X1: collection] :
( ~ $less($sum(1,count(X1)),0)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_7
| ~ spl1_85 ),
inference(superposition,[],[f118,f1322]) ).
tff(f7683,plain,
( spl1_221
| ~ spl1_23
| ~ spl1_31
| ~ spl1_55
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1213,f1085,f559,f279,f202,f7681]) ).
tff(f7681,plain,
( spl1_221
<=> ! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum(X0,$sum(X1,X2))) = $uminus($sum(X1,$sum(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_221])]) ).
tff(f1213,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum(X0,$sum(X1,X2))) = $uminus($sum(X1,$sum(X0,X2))) )
| ~ spl1_23
| ~ spl1_31
| ~ spl1_55
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1212,f280]) ).
tff(f1212,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum($sum(X0,X1),X2)) = $uminus($sum(X1,$sum(X0,X2))) )
| ~ spl1_23
| ~ spl1_55
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1211,f203]) ).
tff(f1211,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $uminus($sum($sum(X0,X1),X2)) = $sum($uminus($sum(X0,X2)),$uminus(X1)) )
| ~ spl1_23
| ~ spl1_55
| ~ spl1_81 ),
inference(forward_demodulation,[],[f1172,f203]) ).
tff(f1172,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X2)),$uminus(X1)) = $sum($uminus(X2),$uminus($sum(X0,X1))) )
| ~ spl1_55
| ~ spl1_81 ),
inference(superposition,[],[f1086,f560]) ).
tff(f7679,plain,
( spl1_220
| ~ spl1_52
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1209,f1085,f481,f7677]) ).
tff(f7677,plain,
( spl1_220
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X2),X1) = $sum($uminus($sum(X0,X2)),$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_220])]) ).
tff(f1209,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X2),X1) = $sum($uminus($sum(X0,X2)),$sum(X0,X1)) )
| ~ spl1_52
| ~ spl1_81 ),
inference(evaluation,[],[f1178]) ).
tff(f1178,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X2),X1) = $sum($uminus($sum(X0,X2)),$sum($uminus($uminus(X0)),X1)) )
| ~ spl1_52
| ~ spl1_81 ),
inference(superposition,[],[f1086,f482]) ).
tff(f7675,plain,
( spl1_219
| ~ spl1_52
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1186,f1085,f481,f7673]) ).
tff(f7673,plain,
( spl1_219
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X1),X2) = $sum(X0,$sum($uminus($sum(X1,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_219])]) ).
tff(f1186,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X1),X2) = $sum(X0,$sum($uminus($sum(X1,X0)),X2)) )
| ~ spl1_52
| ~ spl1_81 ),
inference(superposition,[],[f482,f1086]) ).
tff(f7644,plain,
( spl1_218
| ~ spl1_57
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f950,f911,f567,f7642]) ).
tff(f7642,plain,
( spl1_218
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X0),$sum(X1,X3))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_218])]) ).
tff(f950,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X0),$sum(X1,X3))
| ~ $less(X2,X3) )
| ~ spl1_57
| ~ spl1_71 ),
inference(resolution,[],[f912,f568]) ).
tff(f7640,plain,
( spl1_217
| ~ spl1_56
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f949,f911,f563,f7638]) ).
tff(f7638,plain,
( spl1_217
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X3),$sum(X1,X2))
| ~ $less(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_217])]) ).
tff(f949,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X3),$sum(X1,X2))
| ~ $less(X3,X0) )
| ~ spl1_56
| ~ spl1_71 ),
inference(resolution,[],[f912,f564]) ).
tff(f7636,plain,
( spl1_216
| ~ spl1_24
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f948,f911,f206,f7634]) ).
tff(f7634,plain,
( spl1_216
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X3),$sum(X1,X3))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_216])]) ).
tff(f948,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X2,X3),$sum(X1,X3))
| ~ $less(X2,X0) )
| ~ spl1_24
| ~ spl1_71 ),
inference(resolution,[],[f912,f207]) ).
tff(f7632,plain,
( spl1_215
| ~ spl1_53
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f737,f650,f536,f7630]) ).
tff(f7630,plain,
( spl1_215
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X1,$sum(X0,$uminus(X2))))
| ~ $less(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_215])]) ).
tff(f737,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X1,$sum(X0,$uminus(X2))))
| ~ $less(X2,$sum(X0,X1)) )
| ~ spl1_53
| ~ spl1_64 ),
inference(superposition,[],[f537,f651]) ).
tff(f7628,plain,
( spl1_214
| ~ spl1_54
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f736,f650,f540,f7626]) ).
tff(f7626,plain,
( spl1_214
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,$uminus(X2))),0)
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_214])]) ).
tff(f736,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(X0,$uminus(X2))),0)
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_54
| ~ spl1_64 ),
inference(superposition,[],[f541,f651]) ).
tff(f7624,plain,
( spl1_213
| ~ spl1_15
| ~ spl1_63 ),
inference(avatar_split_clause,[],[f702,f646,f152,f7622]) ).
tff(f702,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(add(X0,X1)) )
| ( empty = add(X0,add(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_63 ),
inference(superposition,[],[f153,f647]) ).
tff(f7620,plain,
( spl1_212
| ~ spl1_15
| ~ spl1_62 ),
inference(avatar_split_clause,[],[f691,f642,f152,f7618]) ).
tff(f691,plain,
( ! [X0: $int,X1: collection] :
( ( 0 != count(remove(X0,X1)) )
| ( empty = remove(X0,remove(X0,X1)) ) )
| ~ spl1_15
| ~ spl1_62 ),
inference(superposition,[],[f153,f643]) ).
tff(f7616,plain,
( spl1_211
| ~ spl1_51
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f667,f634,f477,f7614]) ).
tff(f7614,plain,
( spl1_211
<=> ! [X0: $int,X1: collection] :
( $less(0,$sum(X0,1))
| $less(X0,count(X1))
| ( 0 = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_211])]) ).
tff(f667,plain,
( ! [X0: $int,X1: collection] :
( $less(0,$sum(X0,1))
| $less(X0,count(X1))
| ( 0 = count(X1) ) )
| ~ spl1_51
| ~ spl1_60 ),
inference(resolution,[],[f635,f478]) ).
tff(f7612,plain,
( spl1_210
| ~ spl1_49
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f659,f634,f469,f7610]) ).
tff(f7610,plain,
( spl1_210
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(1,X2))
| $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_210])]) ).
tff(f659,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(1,X2))
| $less(X2,X0) )
| ~ spl1_49
| ~ spl1_60 ),
inference(resolution,[],[f635,f470]) ).
tff(f7608,plain,
( spl1_209
| ~ spl1_16
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f657,f634,f158,f7606]) ).
tff(f7606,plain,
( spl1_209
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X2,1))
| $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_209])]) ).
tff(f657,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X2,1))
| $less(X2,X0) )
| ~ spl1_16
| ~ spl1_60 ),
inference(resolution,[],[f635,f159]) ).
tff(f7604,plain,
( spl1_208
| ~ spl1_126
| ~ spl1_196 ),
inference(avatar_split_clause,[],[f7532,f6481,f1922,f7602]) ).
tff(f7532,plain,
( ! [X0: $int] :
( $less(0,X0)
| ~ $less(2,X0) )
| ~ spl1_126
| ~ spl1_196 ),
inference(resolution,[],[f6482,f1923]) ).
tff(f7600,plain,
( spl1_207
| ~ spl1_23
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f623,f567,f202,f7598]) ).
tff(f7598,plain,
( spl1_207
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum($uminus(X1),X2))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_207])]) ).
tff(f623,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum($uminus(X1),X2))
| ~ $less($uminus(X0),X2) )
| ~ spl1_23
| ~ spl1_57 ),
inference(superposition,[],[f568,f203]) ).
tff(f7596,plain,
( spl1_206
| ~ spl1_55
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f622,f567,f559,f7594]) ).
tff(f7594,plain,
( spl1_206
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum($uminus(X1),X2))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_206])]) ).
tff(f622,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum($uminus(X1),X2))
| ~ $less($uminus(X0),X2) )
| ~ spl1_55
| ~ spl1_57 ),
inference(superposition,[],[f568,f560]) ).
tff(f7592,plain,
( spl1_205
| ~ spl1_21
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f617,f567,f184,f7590]) ).
tff(f7590,plain,
( spl1_205
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_205])]) ).
tff(f617,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X3,X1)) )
| ~ spl1_21
| ~ spl1_57 ),
inference(resolution,[],[f568,f185]) ).
tff(f7588,plain,
( spl1_204
| ~ spl1_23
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f611,f563,f202,f7586]) ).
tff(f7586,plain,
( spl1_204
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X1),X2),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_204])]) ).
tff(f611,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X1),X2),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_23
| ~ spl1_56 ),
inference(superposition,[],[f564,f203]) ).
tff(f7584,plain,
( spl1_203
| ~ spl1_55
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f610,f563,f559,f7582]) ).
tff(f7582,plain,
( spl1_203
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X1),X2),$uminus($sum(X0,X1)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_203])]) ).
tff(f610,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X1),X2),$uminus($sum(X0,X1)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_55
| ~ spl1_56 ),
inference(superposition,[],[f564,f560]) ).
tff(f7580,plain,
( spl1_202
| ~ spl1_21
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f598,f563,f184,f7578]) ).
tff(f7578,plain,
( spl1_202
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X3,X0))
| $less(X2,$sum(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_202])]) ).
tff(f598,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X3,X0))
| $less(X2,$sum(X1,X3)) )
| ~ spl1_21
| ~ spl1_56 ),
inference(resolution,[],[f564,f185]) ).
tff(f7576,plain,
( spl1_201
| ~ spl1_24
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f586,f559,f206,f7574]) ).
tff(f7574,plain,
( spl1_201
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_201])]) ).
tff(f586,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl1_24
| ~ spl1_55 ),
inference(superposition,[],[f207,f560]) ).
tff(f7572,plain,
( spl1_200
| ~ spl1_24
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f585,f559,f206,f7570]) ).
tff(f7570,plain,
( spl1_200
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X0,X1)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_200])]) ).
tff(f585,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X0,X1)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_24
| ~ spl1_55 ),
inference(superposition,[],[f207,f560]) ).
tff(f7568,plain,
( spl1_199
| ~ spl1_31
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f556,f540,f279,f7566]) ).
tff(f7566,plain,
( spl1_199
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,$uminus(X2))),0)
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_199])]) ).
tff(f556,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,$uminus(X2))),0)
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_31
| ~ spl1_54 ),
inference(superposition,[],[f541,f280]) ).
tff(f7564,plain,
( spl1_198
| ~ spl1_31
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f549,f536,f279,f7562]) ).
tff(f7562,plain,
( spl1_198
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X0,$sum(X1,$uminus(X2))))
| ~ $less(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_198])]) ).
tff(f549,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(0,$sum(X0,$sum(X1,$uminus(X2))))
| ~ $less(X2,$sum(X0,X1)) )
| ~ spl1_31
| ~ spl1_53 ),
inference(superposition,[],[f537,f280]) ).
tff(f7531,plain,
( spl1_197
| ~ spl1_22
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f494,f473,f188,f7529]) ).
tff(f7529,plain,
( spl1_197
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_197])]) ).
tff(f494,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 ) )
| ~ spl1_22
| ~ spl1_50 ),
inference(resolution,[],[f474,f189]) ).
tff(f6483,plain,
( spl1_196
| ~ spl1_125
| ~ spl1_173 ),
inference(avatar_split_clause,[],[f5114,f4327,f1918,f6481]) ).
tff(f1918,plain,
( spl1_125
<=> ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
tff(f4327,plain,
( spl1_173
<=> ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_173])]) ).
tff(f5114,plain,
( ! [X0: $int] :
( $less($sum(-1,X0),2)
| $less(0,X0) )
| ~ spl1_125
| ~ spl1_173 ),
inference(resolution,[],[f4328,f1919]) ).
tff(f1919,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(-1,X0),X1)
| $less(X1,X0) )
| ~ spl1_125 ),
inference(avatar_component_clause,[],[f1918]) ).
tff(f4328,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,2) )
| ~ spl1_173 ),
inference(avatar_component_clause,[],[f4327]) ).
tff(f5208,plain,
( spl1_195
| ~ spl1_50
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1279,f1093,f473,f5206]) ).
tff(f5206,plain,
( spl1_195
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),1)
| ~ $less(X2,$sum(X0,$sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_195])]) ).
tff(f1279,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),1)
| ~ $less(X2,$sum(X0,$sum(X1,X2))) )
| ~ spl1_50
| ~ spl1_83 ),
inference(resolution,[],[f1094,f474]) ).
tff(f5204,plain,
( spl1_194
| ~ spl1_50
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1235,f1089,f473,f5202]) ).
tff(f5202,plain,
( spl1_194
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,$sum(1,X1))
| ~ $less($sum(X1,X2),$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_194])]) ).
tff(f1235,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,$sum(1,X1))
| ~ $less($sum(X1,X2),$sum(X0,X2)) )
| ~ spl1_50
| ~ spl1_82 ),
inference(resolution,[],[f1090,f474]) ).
tff(f5200,plain,
( spl1_193
| ~ spl1_53
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f952,f911,f536,f5198]) ).
tff(f5198,plain,
( spl1_193
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(0,$sum(X1,$uminus(X2)))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_193])]) ).
tff(f952,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(0,$sum(X1,$uminus(X2)))
| ~ $less(X2,X0) )
| ~ spl1_53
| ~ spl1_71 ),
inference(resolution,[],[f912,f537]) ).
tff(f5196,plain,
( spl1_192
| ~ spl1_14
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f886,f841,f148,f5194]) ).
tff(f5194,plain,
( spl1_192
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$sum(1,X0)))
| $less($sum(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_192])]) ).
tff(f886,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$sum(1,X0)))
| $less($sum(X2,X0),X1) )
| ~ spl1_14
| ~ spl1_68 ),
inference(superposition,[],[f842,f149]) ).
tff(f5192,plain,
( spl1_191
| ~ spl1_31
| ~ spl1_56
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f874,f837,f563,f279,f5190]) ).
tff(f5190,plain,
( spl1_191
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X1,$sum(1,X2)))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_191])]) ).
tff(f874,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X1,$sum(1,X2)))
| ~ $less(X2,X0) )
| ~ spl1_31
| ~ spl1_56
| ~ spl1_67 ),
inference(forward_demodulation,[],[f861,f280]) ).
tff(f861,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum($sum(X1,1),X2))
| ~ $less(X2,X0) )
| ~ spl1_56
| ~ spl1_67 ),
inference(resolution,[],[f838,f564]) ).
tff(f5188,plain,
( spl1_190
| ~ spl1_14
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f863,f837,f148,f5186]) ).
tff(f5186,plain,
( spl1_190
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,$sum(X2,$sum(1,X0)))
| ~ $less($sum(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_190])]) ).
tff(f863,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,$sum(X2,$sum(1,X0)))
| ~ $less($sum(X2,X0),X1) )
| ~ spl1_14
| ~ spl1_67 ),
inference(superposition,[],[f838,f149]) ).
tff(f5184,plain,
( spl1_189
| ~ spl1_57
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f862,f837,f567,f5182]) ).
tff(f5182,plain,
( spl1_189
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,X0))
| ~ $less(X2,$sum(X1,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_189])]) ).
tff(f862,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,X0))
| ~ $less(X2,$sum(X1,1)) )
| ~ spl1_57
| ~ spl1_67 ),
inference(resolution,[],[f838,f568]) ).
tff(f5180,plain,
( spl1_188
| ~ spl1_24
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f860,f837,f206,f5178]) ).
tff(f5178,plain,
( spl1_188
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,$sum(X1,1)))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_188])]) ).
tff(f860,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,$sum(X1,1)))
| ~ $less(X2,X0) )
| ~ spl1_24
| ~ spl1_67 ),
inference(resolution,[],[f838,f207]) ).
tff(f5176,plain,
( spl1_187
| ~ spl1_31
| ~ spl1_52
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f814,f654,f481,f279,f5174]) ).
tff(f5174,plain,
( spl1_187
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,X1) = $sum(X0,$sum($uminus(X0),$sum(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_187])]) ).
tff(f814,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,X1) = $sum(X0,$sum($uminus(X0),$sum(X1,X2))) )
| ~ spl1_31
| ~ spl1_52
| ~ spl1_65 ),
inference(forward_demodulation,[],[f764,f280]) ).
tff(f764,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,X1) = $sum(X0,$sum($sum($uminus(X0),X1),X2)) )
| ~ spl1_52
| ~ spl1_65 ),
inference(superposition,[],[f655,f482]) ).
tff(f5172,plain,
( spl1_186
| ~ spl1_52
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f808,f654,f481,f5170]) ).
tff(f5170,plain,
( spl1_186
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum(X0,$sum(X1,$sum(X2,$uminus(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_186])]) ).
tff(f808,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum(X0,$sum(X1,$sum(X2,$uminus(X0)))) )
| ~ spl1_52
| ~ spl1_65 ),
inference(superposition,[],[f482,f655]) ).
tff(f5168,plain,
( spl1_185
| ~ spl1_117
| ~ spl1_173 ),
inference(avatar_split_clause,[],[f5103,f4327,f1826,f5166]) ).
tff(f5103,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(-1,X0) )
| ~ spl1_117
| ~ spl1_173 ),
inference(resolution,[],[f4328,f1827]) ).
tff(f5164,plain,
( spl1_184
| ~ spl1_52
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f792,f654,f481,f5162]) ).
tff(f5162,plain,
( spl1_184
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum(X0,$sum(X2,$sum($uminus(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_184])]) ).
tff(f792,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum(X0,$sum(X2,$sum($uminus(X0),X1))) )
| ~ spl1_52
| ~ spl1_65 ),
inference(superposition,[],[f482,f655]) ).
tff(f5160,plain,
( spl1_183
| ~ spl1_49
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f789,f654,f469,f5158]) ).
tff(f5158,plain,
( spl1_183
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X1,$sum(1,X0)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_183])]) ).
tff(f789,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X1,$sum(1,X0)))
| $less($sum(X0,X1),X2) )
| ~ spl1_49
| ~ spl1_65 ),
inference(superposition,[],[f470,f655]) ).
tff(f5156,plain,
( spl1_182
| ~ spl1_50
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f788,f654,f473,f5154]) ).
tff(f5154,plain,
( spl1_182
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X1,$sum(1,X0)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_182])]) ).
tff(f788,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X1,$sum(1,X0)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_50
| ~ spl1_65 ),
inference(superposition,[],[f474,f655]) ).
tff(f5152,plain,
( spl1_181
| ~ spl1_52
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f748,f654,f481,f5150]) ).
tff(f5150,plain,
( spl1_181
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,X1) = $sum($sum($uminus(X0),X1),$sum(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_181])]) ).
tff(f748,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,X1) = $sum($sum($uminus(X0),X1),$sum(X2,X0)) )
| ~ spl1_52
| ~ spl1_65 ),
inference(superposition,[],[f655,f482]) ).
tff(f5148,plain,
( spl1_180
| ~ spl1_16
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f733,f650,f158,f5146]) ).
tff(f5146,plain,
( spl1_180
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X1,$sum(X0,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_180])]) ).
tff(f733,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X1,$sum(X0,1)))
| $less($sum(X0,X1),X2) )
| ~ spl1_16
| ~ spl1_64 ),
inference(superposition,[],[f159,f651]) ).
tff(f5144,plain,
( spl1_179
| ~ spl1_17
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f732,f650,f162,f5142]) ).
tff(f5142,plain,
( spl1_179
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X1,$sum(X0,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_179])]) ).
tff(f732,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X1,$sum(X0,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_17
| ~ spl1_64 ),
inference(superposition,[],[f163,f651]) ).
tff(f5139,plain,
( spl1_178
| ~ spl1_52
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f720,f650,f481,f5137]) ).
tff(f5137,plain,
( spl1_178
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,$sum(X0,$sum($uminus($sum(X0,X1)),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_178])]) ).
tff(f720,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,$sum(X0,$sum($uminus($sum(X0,X1)),X2))) = X2 )
| ~ spl1_52
| ~ spl1_64 ),
inference(superposition,[],[f651,f482]) ).
tff(f5135,plain,
( spl1_177
| ~ spl1_52
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f711,f650,f481,f5133]) ).
tff(f5133,plain,
( spl1_177
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum($sum($uminus(X0),X1),$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_177])]) ).
tff(f711,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X1,X2) = $sum($sum($uminus(X0),X1),$sum(X0,X2)) )
| ~ spl1_52
| ~ spl1_64 ),
inference(superposition,[],[f651,f482]) ).
tff(f5131,plain,
( spl1_176
| ~ spl1_21
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f551,f540,f184,f5129]) ).
tff(f551,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,$uminus(X1)))
| $less(X2,0) )
| ~ spl1_21
| ~ spl1_54 ),
inference(resolution,[],[f541,f185]) ).
tff(f5127,plain,
( spl1_175
| ~ spl1_21
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f544,f536,f184,f5125]) ).
tff(f5125,plain,
( spl1_175
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,0)
| $less(X2,$sum(X1,$uminus(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_175])]) ).
tff(f544,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,0)
| $less(X2,$sum(X1,$uminus(X0))) )
| ~ spl1_21
| ~ spl1_53 ),
inference(resolution,[],[f537,f185]) ).
tff(f5101,plain,
( spl1_174
| ~ spl1_31
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f523,f481,f279,f5099]) ).
tff(f5099,plain,
( spl1_174
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum($uminus($sum(X0,X1)),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_174])]) ).
tff(f523,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$sum($uminus($sum(X0,X1)),X2))) = X2 )
| ~ spl1_31
| ~ spl1_52 ),
inference(superposition,[],[f482,f280]) ).
tff(f4329,plain,
( spl1_173
| ~ spl1_30
| ~ spl1_156 ),
inference(avatar_split_clause,[],[f3645,f3470,f274,f4327]) ).
tff(f274,plain,
( spl1_30
<=> ( 2 = count(add(2,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f3470,plain,
( spl1_156
<=> ! [X0: collection,X1: $int] :
( ( 0 = count(X0) )
| ~ $less(X1,0)
| $less(X1,count(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_156])]) ).
tff(f3645,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,0) )
| ~ spl1_30
| ~ spl1_156 ),
inference(evaluation,[],[f3620]) ).
tff(f3620,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,0)
| ( 0 = 2 ) )
| ~ spl1_30
| ~ spl1_156 ),
inference(superposition,[],[f3471,f276]) ).
tff(f276,plain,
( ( 2 = count(add(2,sK0)) )
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f274]) ).
tff(f3471,plain,
( ! [X0: collection,X1: $int] :
( $less(X1,count(X0))
| ~ $less(X1,0)
| ( 0 = count(X0) ) )
| ~ spl1_156 ),
inference(avatar_component_clause,[],[f3470]) ).
tff(f3558,plain,
( spl1_172
| ~ spl1_6
| ~ spl1_48
| ~ spl1_96 ),
inference(avatar_split_clause,[],[f1553,f1533,f454,f113,f3556]) ).
tff(f3556,plain,
( spl1_172
<=> ! [X0: $int,X1: $int] :
( ( 2 = count(add(X0,add(X1,empty))) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_172])]) ).
tff(f1553,plain,
( ! [X0: $int,X1: $int] :
( ( 2 = count(add(X0,add(X1,empty))) )
| ( X0 = X1 ) )
| ~ spl1_6
| ~ spl1_48
| ~ spl1_96 ),
inference(evaluation,[],[f1552]) ).
tff(f1552,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(1,1) = count(add(X0,add(X1,empty))) )
| ( X0 = X1 ) )
| ~ spl1_6
| ~ spl1_48
| ~ spl1_96 ),
inference(forward_demodulation,[],[f1548,f455]) ).
tff(f1548,plain,
( ! [X0: $int,X1: $int] :
( ( count(add(X0,add(X1,empty))) = $sum(1,count(add(X1,empty))) )
| ( X0 = X1 ) )
| ~ spl1_6
| ~ spl1_96 ),
inference(resolution,[],[f1534,f114]) ).
tff(f3543,plain,
( spl1_171
| ~ spl1_6
| ~ spl1_48
| ~ spl1_94 ),
inference(avatar_split_clause,[],[f1490,f1455,f454,f113,f3541]) ).
tff(f3541,plain,
( spl1_171
<=> ! [X0: $int,X1: $int] :
( ( 1 = count(remove(X0,add(X1,empty))) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_171])]) ).
tff(f1490,plain,
( ! [X0: $int,X1: $int] :
( ( 1 = count(remove(X0,add(X1,empty))) )
| ( X0 = X1 ) )
| ~ spl1_6
| ~ spl1_48
| ~ spl1_94 ),
inference(forward_demodulation,[],[f1486,f455]) ).
tff(f1486,plain,
( ! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(remove(X0,add(X1,empty))) = count(add(X1,empty)) ) )
| ~ spl1_6
| ~ spl1_94 ),
inference(resolution,[],[f1456,f114]) ).
tff(f3539,plain,
( spl1_170
| ~ spl1_13
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1313,f1093,f144,f3537]) ).
tff(f3537,plain,
( spl1_170
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$uminus(X0)))
| ~ $less($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_170])]) ).
tff(f144,plain,
( spl1_13
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f1313,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$uminus(X0)))
| ~ $less($sum(X1,X0),X2) )
| ~ spl1_13
| ~ spl1_83 ),
inference(evaluation,[],[f1283]) ).
tff(f1283,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,0),$sum(X2,$uminus(X0)))
| ~ $less($sum(X1,X0),X2) )
| ~ spl1_13
| ~ spl1_83 ),
inference(superposition,[],[f1094,f145]) ).
tff(f145,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f3535,plain,
( spl1_169
| ~ spl1_13
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1269,f1089,f144,f3533]) ).
tff(f3533,plain,
( spl1_169
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),X2)
| ~ $less(X1,$sum(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_169])]) ).
tff(f1269,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),X2)
| ~ $less(X1,$sum(X2,X0)) )
| ~ spl1_13
| ~ spl1_82 ),
inference(evaluation,[],[f1250]) ).
tff(f1250,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),$sum(X2,0))
| ~ $less(X1,$sum(X2,X0)) )
| ~ spl1_13
| ~ spl1_82 ),
inference(superposition,[],[f1090,f145]) ).
tff(f3531,plain,
( spl1_168
| ~ spl1_50
| ~ spl1_72 ),
inference(avatar_split_clause,[],[f964,f915,f473,f3529]) ).
tff(f3529,plain,
( spl1_168
<=> ! [X0: $int,X1: $int] :
( ~ $less($uminus(X0),1)
| ~ $less($uminus(X1),$uminus($sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_168])]) ).
tff(f964,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($uminus(X0),1)
| ~ $less($uminus(X1),$uminus($sum(X1,X0))) )
| ~ spl1_50
| ~ spl1_72 ),
inference(resolution,[],[f916,f474]) ).
tff(f3527,plain,
( spl1_167
| ~ spl1_16
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f943,f911,f158,f3525]) ).
tff(f3525,plain,
( spl1_167
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,1))
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_167])]) ).
tff(f943,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X2,$sum(X1,1))
| $less(X0,X2) )
| ~ spl1_16
| ~ spl1_71 ),
inference(resolution,[],[f912,f159]) ).
tff(f3523,plain,
( spl1_166
| ~ spl1_49
| ~ spl1_71 ),
inference(avatar_split_clause,[],[f942,f911,f469,f3521]) ).
tff(f3521,plain,
( spl1_166
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(1,X0)
| $less(X1,$sum(X0,X2))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_166])]) ).
tff(f942,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(1,X0)
| $less(X1,$sum(X0,X2))
| $less(X2,X1) )
| ~ spl1_49
| ~ spl1_71 ),
inference(resolution,[],[f912,f470]) ).
tff(f3519,plain,
( spl1_165
| ~ spl1_14
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f757,f654,f148,f3517]) ).
tff(f3517,plain,
( spl1_165
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$sum(X0,X1)) = $sum($sum(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_165])]) ).
tff(f757,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$sum(X0,X1)) = $sum($sum(X1,X2),X0) )
| ~ spl1_14
| ~ spl1_65 ),
inference(superposition,[],[f655,f149]) ).
tff(f3515,plain,
( spl1_164
| ~ spl1_14
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f718,f650,f148,f3513]) ).
tff(f3513,plain,
( spl1_164
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$sum(X0,X1)) = $sum(X1,$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_164])]) ).
tff(f718,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X2,$sum(X0,X1)) = $sum(X1,$sum(X0,X2)) )
| ~ spl1_14
| ~ spl1_64 ),
inference(superposition,[],[f651,f149]) ).
tff(f3511,plain,
( spl1_163
| ~ spl1_31
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f716,f650,f279,f3509]) ).
tff(f3509,plain,
( spl1_163
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_163])]) ).
tff(f716,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) )
| ~ spl1_31
| ~ spl1_64 ),
inference(superposition,[],[f651,f280]) ).
tff(f3507,plain,
( spl1_162
| ~ spl1_31
| ~ spl1_52
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f632,f567,f481,f279,f3505]) ).
tff(f3505,plain,
( spl1_162
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum($uminus(X0),$sum(X1,X2)))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_162])]) ).
tff(f632,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum($uminus(X0),$sum(X1,X2)))
| ~ $less(X0,X2) )
| ~ spl1_31
| ~ spl1_52
| ~ spl1_57 ),
inference(forward_demodulation,[],[f621,f280]) ).
tff(f621,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum($sum($uminus(X0),X1),X2))
| ~ $less(X0,X2) )
| ~ spl1_52
| ~ spl1_57 ),
inference(superposition,[],[f568,f482]) ).
tff(f3492,plain,
( spl1_161
| ~ spl1_52
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f628,f567,f481,f3490]) ).
tff(f628,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X0),X1)
| ~ $less(X2,$sum($uminus(X0),X1)) )
| ~ spl1_52
| ~ spl1_57 ),
inference(superposition,[],[f568,f482]) ).
tff(f3488,plain,
( spl1_160
| ~ spl1_31
| ~ spl1_52
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f613,f563,f481,f279,f3486]) ).
tff(f3486,plain,
( spl1_160
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X0),$sum(X1,X2)),X1)
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_160])]) ).
tff(f613,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($uminus(X0),$sum(X1,X2)),X1)
| ~ $less(X2,X0) )
| ~ spl1_31
| ~ spl1_52
| ~ spl1_56 ),
inference(forward_demodulation,[],[f609,f280]) ).
tff(f609,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum($sum($uminus(X0),X1),X2),X1)
| ~ $less(X2,X0) )
| ~ spl1_52
| ~ spl1_56 ),
inference(superposition,[],[f564,f482]) ).
tff(f3484,plain,
( spl1_159
| ~ spl1_52
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f602,f563,f481,f3482]) ).
tff(f3482,plain,
( spl1_159
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,X0))
| ~ $less($sum($uminus(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_159])]) ).
tff(f602,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,X0))
| ~ $less($sum($uminus(X0),X1),X2) )
| ~ spl1_52
| ~ spl1_56 ),
inference(superposition,[],[f564,f482]) ).
tff(f3480,plain,
( spl1_158
| ~ spl1_24
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f526,f481,f206,f3478]) ).
tff(f3478,plain,
( spl1_158
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$sum($uminus(X0),X1)))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_158])]) ).
tff(f526,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,$sum($uminus(X0),X1)))
| ~ $less(X0,X2) )
| ~ spl1_24
| ~ spl1_52 ),
inference(superposition,[],[f207,f482]) ).
tff(f3476,plain,
( spl1_157
| ~ spl1_24
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f525,f481,f206,f3474]) ).
tff(f3474,plain,
( spl1_157
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum($uminus(X0),X1)),X1)
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_157])]) ).
tff(f525,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$sum($uminus(X0),X1)),X1)
| ~ $less(X2,X0) )
| ~ spl1_24
| ~ spl1_52 ),
inference(superposition,[],[f207,f482]) ).
tff(f3472,plain,
( spl1_156
| ~ spl1_21
| ~ spl1_51 ),
inference(avatar_split_clause,[],[f501,f477,f184,f3470]) ).
tff(f501,plain,
( ! [X0: collection,X1: $int] :
( ( 0 = count(X0) )
| ~ $less(X1,0)
| $less(X1,count(X0)) )
| ~ spl1_21
| ~ spl1_51 ),
inference(resolution,[],[f478,f185]) ).
tff(f3468,plain,
( spl1_155
| ~ spl1_21
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f486,f469,f184,f3466]) ).
tff(f3466,plain,
( spl1_155
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(X2,X1)
| $less(X2,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_155])]) ).
tff(f486,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(X2,X1)
| $less(X2,$sum(1,X0)) )
| ~ spl1_21
| ~ spl1_49 ),
inference(resolution,[],[f470,f185]) ).
tff(f3138,plain,
( spl1_154
| ~ spl1_50
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f881,f841,f473,f3136]) ).
tff(f3136,plain,
( spl1_154
<=> ! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ~ $less($sum(X0,1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_154])]) ).
tff(f881,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ~ $less($sum(X0,1),X1) )
| ~ spl1_50
| ~ spl1_68 ),
inference(resolution,[],[f842,f474]) ).
tff(f3134,plain,
( spl1_153
| ~ spl1_49
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f856,f837,f469,f3132]) ).
tff(f3132,plain,
( spl1_153
<=> ! [X0: $int,X1: $int] :
( ~ $less($sum(1,X0),X1)
| $less($sum(X0,1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_153])]) ).
tff(f856,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(1,X0),X1)
| $less($sum(X0,1),X1) )
| ~ spl1_49
| ~ spl1_67 ),
inference(resolution,[],[f838,f470]) ).
tff(f3130,plain,
( spl1_152
| ~ spl1_20
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f658,f634,f180,f3128]) ).
tff(f180,plain,
( spl1_20
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f658,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,1))
| $less(X1,$sum(X0,1)) )
| ~ spl1_20
| ~ spl1_60 ),
inference(resolution,[],[f635,f181]) ).
tff(f181,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f180]) ).
tff(f3126,plain,
( spl1_151
| ~ spl1_14
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f607,f563,f148,f3124]) ).
tff(f3124,plain,
( spl1_151
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X2),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_151])]) ).
tff(f607,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X2),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl1_14
| ~ spl1_56 ),
inference(superposition,[],[f564,f149]) ).
tff(f3122,plain,
( spl1_150
| ~ spl1_53
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f583,f559,f536,f3120]) ).
tff(f3120,plain,
( spl1_150
<=> ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X0,X1)))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_150])]) ).
tff(f583,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X0,X1)))
| ~ $less(X1,$uminus(X0)) )
| ~ spl1_53
| ~ spl1_55 ),
inference(superposition,[],[f537,f560]) ).
tff(f3118,plain,
( spl1_149
| ~ spl1_29
| ~ spl1_108 ),
inference(avatar_split_clause,[],[f1748,f1691,f230,f3116]) ).
tff(f3116,plain,
( spl1_149
<=> ! [X0: $int] :
( in(5,remove(X0,sK0))
| ( 5 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_149])]) ).
tff(f1748,plain,
( ! [X0: $int] :
( in(5,remove(X0,sK0))
| ( 5 = X0 ) )
| ~ spl1_29
| ~ spl1_108 ),
inference(trivial_inequality_removal,[],[f1744]) ).
tff(f1744,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != count(remove(X0,sK0)) )
| in(5,remove(X0,sK0))
| ( 5 = X0 ) )
| ~ spl1_29
| ~ spl1_108 ),
inference(superposition,[],[f231,f1692]) ).
tff(f3114,plain,
( spl1_148
| ~ spl1_54
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f582,f559,f540,f3112]) ).
tff(f3112,plain,
( spl1_148
<=> ! [X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),0)
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_148])]) ).
tff(f582,plain,
( ! [X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),0)
| ~ $less($uminus(X0),X1) )
| ~ spl1_54
| ~ spl1_55 ),
inference(superposition,[],[f541,f560]) ).
tff(f3110,plain,
( spl1_147
| ~ spl1_23
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f555,f540,f202,f3108]) ).
tff(f3108,plain,
( spl1_147
<=> ! [X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),0)
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_147])]) ).
tff(f555,plain,
( ! [X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),0)
| ~ $less($uminus(X0),X1) )
| ~ spl1_23
| ~ spl1_54 ),
inference(superposition,[],[f541,f203]) ).
tff(f3106,plain,
( spl1_146
| ~ spl1_23
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f548,f536,f202,f3104]) ).
tff(f3104,plain,
( spl1_146
<=> ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X1,X0)))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_146])]) ).
tff(f548,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X1,X0)))
| ~ $less(X1,$uminus(X0)) )
| ~ spl1_23
| ~ spl1_53 ),
inference(superposition,[],[f537,f203]) ).
tff(f2614,plain,
( spl1_145
| ~ spl1_29
| ~ spl1_107 ),
inference(avatar_split_clause,[],[f1735,f1687,f230,f2612]) ).
tff(f2612,plain,
( spl1_145
<=> ! [X0: $int] :
( in(3,remove(X0,sK0))
| ( 3 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_145])]) ).
tff(f1735,plain,
( ! [X0: $int] :
( in(3,remove(X0,sK0))
| ( 3 = X0 ) )
| ~ spl1_29
| ~ spl1_107 ),
inference(trivial_inequality_removal,[],[f1731]) ).
tff(f1731,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != count(remove(X0,sK0)) )
| in(3,remove(X0,sK0))
| ( 3 = X0 ) )
| ~ spl1_29
| ~ spl1_107 ),
inference(superposition,[],[f231,f1688]) ).
tff(f2438,plain,
( spl1_144
| ~ spl1_13
| ~ spl1_81 ),
inference(avatar_split_clause,[],[f1210,f1085,f144,f2436]) ).
tff(f2436,plain,
( spl1_144
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum($uminus($sum(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_144])]) ).
tff(f1210,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum($uminus($sum(X0,X1)),X0) )
| ~ spl1_13
| ~ spl1_81 ),
inference(evaluation,[],[f1175]) ).
tff(f1175,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X1)),$uminus($uminus(X0))) = $sum($uminus(X1),0) )
| ~ spl1_13
| ~ spl1_81 ),
inference(superposition,[],[f1086,f145]) ).
tff(f2434,plain,
( spl1_143
| ~ spl1_20
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f731,f650,f180,f2432]) ).
tff(f2432,plain,
( spl1_143
<=> ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X1,$sum(X0,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_143])]) ).
tff(f731,plain,
( ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X1,$sum(X0,1)))
| ~ spl1_20
| ~ spl1_64 ),
inference(superposition,[],[f181,f651]) ).
tff(f2430,plain,
( spl1_142
| ~ spl1_13
| ~ spl1_57 ),
inference(avatar_split_clause,[],[f625,f567,f144,f2428]) ).
tff(f625,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) )
| ~ spl1_13
| ~ spl1_57 ),
inference(superposition,[],[f568,f145]) ).
tff(f2426,plain,
( spl1_141
| ~ spl1_13
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f599,f563,f144,f2424]) ).
tff(f2424,plain,
( spl1_141
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
tff(f599,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) )
| ~ spl1_13
| ~ spl1_56 ),
inference(superposition,[],[f564,f145]) ).
tff(f2422,plain,
( spl1_140
| ~ spl1_52
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f580,f559,f481,f2420]) ).
tff(f2420,plain,
( spl1_140
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
tff(f580,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X0,X1))) )
| ~ spl1_52
| ~ spl1_55 ),
inference(superposition,[],[f482,f560]) ).
tff(f2418,plain,
( spl1_139
| ~ spl1_23
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f575,f559,f202,f2416]) ).
tff(f2416,plain,
( spl1_139
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
tff(f575,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $uminus($sum(X1,X0)) )
| ~ spl1_23
| ~ spl1_55 ),
inference(superposition,[],[f560,f203]) ).
tff(f2414,plain,
( spl1_138
| ~ spl1_14
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f553,f540,f148,f2412]) ).
tff(f2412,plain,
( spl1_138
<=> ! [X0: $int,X1: $int] :
( $less($sum($uminus(X1),X0),0)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
tff(f553,plain,
( ! [X0: $int,X1: $int] :
( $less($sum($uminus(X1),X0),0)
| ~ $less(X0,X1) )
| ~ spl1_14
| ~ spl1_54 ),
inference(superposition,[],[f541,f149]) ).
tff(f2410,plain,
( spl1_137
| ~ spl1_29
| ~ spl1_106 ),
inference(avatar_split_clause,[],[f1722,f1683,f230,f2408]) ).
tff(f2408,plain,
( spl1_137
<=> ! [X0: $int] :
( in(2,remove(X0,sK0))
| ( 2 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
tff(f1722,plain,
( ! [X0: $int] :
( in(2,remove(X0,sK0))
| ( 2 = X0 ) )
| ~ spl1_29
| ~ spl1_106 ),
inference(trivial_inequality_removal,[],[f1718]) ).
tff(f1718,plain,
( ! [X0: $int] :
( ( count(remove(X0,sK0)) != count(remove(X0,sK0)) )
| in(2,remove(X0,sK0))
| ( 2 = X0 ) )
| ~ spl1_29
| ~ spl1_106 ),
inference(superposition,[],[f231,f1684]) ).
tff(f2406,plain,
( spl1_136
| ~ spl1_14
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f546,f536,f148,f2404]) ).
tff(f2404,plain,
( spl1_136
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum($uminus(X1),X0))
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
tff(f546,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum($uminus(X1),X0))
| ~ $less(X1,X0) )
| ~ spl1_14
| ~ spl1_53 ),
inference(superposition,[],[f537,f149]) ).
tff(f2402,plain,
( spl1_135
| ~ spl1_23
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f518,f481,f202,f2400]) ).
tff(f2400,plain,
( spl1_135
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
tff(f518,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) )
| ~ spl1_23
| ~ spl1_52 ),
inference(superposition,[],[f482,f203]) ).
tff(f2398,plain,
( spl1_134
| ~ spl1_20
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f303,f279,f180,f2396]) ).
tff(f2396,plain,
( spl1_134
<=> ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X0,$sum(X1,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
tff(f303,plain,
( ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X0,$sum(X1,1)))
| ~ spl1_20
| ~ spl1_31 ),
inference(superposition,[],[f181,f280]) ).
tff(f1962,plain,
( spl1_133
| ~ spl1_13
| ~ spl1_52
| ~ spl1_83 ),
inference(avatar_split_clause,[],[f1314,f1093,f481,f144,f1960]) ).
tff(f1314,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) )
| ~ spl1_13
| ~ spl1_52
| ~ spl1_83 ),
inference(forward_demodulation,[],[f1294,f145]) ).
tff(f1294,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X0)),X2) )
| ~ spl1_52
| ~ spl1_83 ),
inference(superposition,[],[f1094,f482]) ).
tff(f1958,plain,
( spl1_132
| ~ spl1_13
| ~ spl1_52
| ~ spl1_82 ),
inference(avatar_split_clause,[],[f1270,f1089,f481,f144,f1956]) ).
tff(f1956,plain,
( spl1_132
<=> ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
tff(f1270,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) )
| ~ spl1_13
| ~ spl1_52
| ~ spl1_82 ),
inference(forward_demodulation,[],[f1261,f145]) ).
tff(f1261,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),X1)
| ~ $less(X2,$sum(X0,$uminus(X0))) )
| ~ spl1_52
| ~ spl1_82 ),
inference(superposition,[],[f1090,f482]) ).
tff(f1954,plain,
( spl1_131
| ~ spl1_7
| ~ spl1_75 ),
inference(avatar_split_clause,[],[f1056,f927,f117,f1952]) ).
tff(f1952,plain,
( spl1_131
<=> ! [X0: $int,X1: collection] : ~ $less($sum(-1,count(add(X0,X1))),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
tff(f1056,plain,
( ! [X0: $int,X1: collection] : ~ $less($sum(-1,count(add(X0,X1))),0)
| ~ spl1_7
| ~ spl1_75 ),
inference(superposition,[],[f118,f928]) ).
tff(f1950,plain,
( spl1_130
| ~ spl1_7
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1037,f923,f117,f1948]) ).
tff(f1948,plain,
( spl1_130
<=> ! [X0: $int,X1: collection] : ~ $less($sum(1,count(remove(X0,X1))),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).
tff(f1037,plain,
( ! [X0: $int,X1: collection] : ~ $less($sum(1,count(remove(X0,X1))),0)
| ~ spl1_7
| ~ spl1_74 ),
inference(superposition,[],[f118,f924]) ).
tff(f1946,plain,
( spl1_129
| ~ spl1_13
| ~ spl1_65 ),
inference(avatar_split_clause,[],[f810,f654,f144,f1944]) ).
tff(f1944,plain,
( spl1_129
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
tff(f810,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 )
| ~ spl1_13
| ~ spl1_65 ),
inference(evaluation,[],[f745]) ).
tff(f745,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = $sum(X1,0) )
| ~ spl1_13
| ~ spl1_65 ),
inference(superposition,[],[f655,f145]) ).
tff(f1932,plain,
( spl1_128
| ~ spl1_13
| ~ spl1_64 ),
inference(avatar_split_clause,[],[f738,f650,f144,f1930]) ).
tff(f1930,plain,
( spl1_128
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
tff(f738,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 )
| ~ spl1_13
| ~ spl1_64 ),
inference(evaluation,[],[f708]) ).
tff(f708,plain,
( ! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum($uminus(X0),$sum(X0,X1)) )
| ~ spl1_13
| ~ spl1_64 ),
inference(superposition,[],[f651,f145]) ).
tff(f1928,plain,
( spl1_127
| ~ spl1_50
| ~ spl1_56 ),
inference(avatar_split_clause,[],[f596,f563,f473,f1926]) ).
tff(f596,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) )
| ~ spl1_50
| ~ spl1_56 ),
inference(resolution,[],[f564,f474]) ).
tff(f1924,plain,
( spl1_126
| ~ spl1_50
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f532,f481,f473,f1922]) ).
tff(f532,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) )
| ~ spl1_50
| ~ spl1_52 ),
inference(evaluation,[],[f528]) ).
tff(f528,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum($uminus(1),X0),X1) )
| ~ spl1_50
| ~ spl1_52 ),
inference(superposition,[],[f474,f482]) ).
tff(f1920,plain,
( spl1_125
| ~ spl1_49
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f531,f481,f469,f1918]) ).
tff(f531,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) )
| ~ spl1_49
| ~ spl1_52 ),
inference(evaluation,[],[f529]) ).
tff(f529,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum($uminus(1),X0),X1) )
| ~ spl1_49
| ~ spl1_52 ),
inference(superposition,[],[f470,f482]) ).
tff(f1916,plain,
( spl1_124
| ~ spl1_14
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f520,f481,f148,f1914]) ).
tff(f520,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 )
| ~ spl1_14
| ~ spl1_52 ),
inference(superposition,[],[f482,f149]) ).
tff(f1912,plain,
( spl1_123
| ~ spl1_24
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f496,f473,f206,f1910]) ).
tff(f1910,plain,
( spl1_123
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
tff(f496,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) )
| ~ spl1_24
| ~ spl1_50 ),
inference(resolution,[],[f474,f207]) ).
tff(f1908,plain,
( spl1_122
| ~ spl1_20
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f218,f184,f180,f1906]) ).
tff(f218,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) )
| ~ spl1_20
| ~ spl1_21 ),
inference(resolution,[],[f181,f185]) ).
tff(f1901,plain,
( spl1_121
| ~ spl1_50
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f543,f536,f473,f1899]) ).
tff(f1899,plain,
( spl1_121
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).
tff(f543,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl1_50
| ~ spl1_53 ),
inference(resolution,[],[f537,f474]) ).
tff(f1840,plain,
( spl1_120
| ~ spl1_13
| ~ spl1_52
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f897,f841,f481,f144,f1838]) ).
tff(f1838,plain,
( spl1_120
<=> ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
tff(f897,plain,
( ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) )
| ~ spl1_13
| ~ spl1_52
| ~ spl1_68 ),
inference(forward_demodulation,[],[f890,f145]) ).
tff(f890,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less($sum(X0,$uminus(X0)),X1) )
| ~ spl1_52
| ~ spl1_68 ),
inference(superposition,[],[f842,f482]) ).
tff(f1836,plain,
( spl1_119
| ~ spl1_13
| ~ spl1_52
| ~ spl1_67 ),
inference(avatar_split_clause,[],[f875,f837,f481,f144,f1834]) ).
tff(f1834,plain,
( spl1_119
<=> ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
tff(f875,plain,
( ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) )
| ~ spl1_13
| ~ spl1_52
| ~ spl1_67 ),
inference(forward_demodulation,[],[f867,f145]) ).
tff(f867,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,1)
| ~ $less($sum(X0,$uminus(X0)),X1) )
| ~ spl1_52
| ~ spl1_67 ),
inference(superposition,[],[f838,f482]) ).
tff(f1832,plain,
( spl1_118
| ~ spl1_13
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f500,f473,f144,f1830]) ).
tff(f500,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) )
| ~ spl1_13
| ~ spl1_50 ),
inference(evaluation,[],[f497]) ).
tff(f497,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) )
| ~ spl1_13
| ~ spl1_50 ),
inference(superposition,[],[f474,f145]) ).
tff(f1828,plain,
( spl1_117
| ~ spl1_13
| ~ spl1_49 ),
inference(avatar_split_clause,[],[f490,f469,f144,f1826]) ).
tff(f490,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl1_13
| ~ spl1_49 ),
inference(evaluation,[],[f487]) ).
tff(f487,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl1_13
| ~ spl1_49 ),
inference(superposition,[],[f470,f145]) ).
tff(f1794,plain,
( spl1_116
| ~ spl1_12
| ~ spl1_98 ),
inference(avatar_split_clause,[],[f1607,f1567,f140,f1792]) ).
tff(f1792,plain,
( spl1_116
<=> ! [X0: $int] : in(5,add(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
tff(f1607,plain,
( ! [X0: $int] : in(5,add(X0,sK0))
| ~ spl1_12
| ~ spl1_98 ),
inference(superposition,[],[f141,f1568]) ).
tff(f1790,plain,
( spl1_115
| ~ spl1_3
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1565,f1537,f99,f1788]) ).
tff(f1565,plain,
( ! [X0: $int] :
( ( 5 = X0 )
| ( $sum(-1,count(remove(X0,sK0))) = count(remove(5,remove(X0,sK0))) ) )
| ~ spl1_3
| ~ spl1_97 ),
inference(resolution,[],[f1538,f101]) ).
tff(f1786,plain,
( spl1_114
| ~ spl1_2
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1564,f1537,f94,f1784]) ).
tff(f1564,plain,
( ! [X0: $int] :
( ( 3 = X0 )
| ( $sum(-1,count(remove(X0,sK0))) = count(remove(3,remove(X0,sK0))) ) )
| ~ spl1_2
| ~ spl1_97 ),
inference(resolution,[],[f1538,f96]) ).
tff(f1782,plain,
( spl1_113
| ~ spl1_1
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1563,f1537,f89,f1780]) ).
tff(f1563,plain,
( ! [X0: $int] :
( ( 2 = X0 )
| ( count(remove(2,remove(X0,sK0))) = $sum(-1,count(remove(X0,sK0))) ) )
| ~ spl1_1
| ~ spl1_97 ),
inference(resolution,[],[f1538,f91]) ).
tff(f1709,plain,
( spl1_112
| ~ spl1_3
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1477,f1447,f99,f1707]) ).
tff(f1477,plain,
( ! [X0: $int] :
( ( 5 = X0 )
| ( remove(X0,sK0) = add(5,remove(5,remove(X0,sK0))) ) )
| ~ spl1_3
| ~ spl1_92 ),
inference(resolution,[],[f1448,f101]) ).
tff(f1705,plain,
( spl1_111
| ~ spl1_12
| ~ spl1_93 ),
inference(avatar_split_clause,[],[f1595,f1451,f140,f1703]) ).
tff(f1703,plain,
( spl1_111
<=> ! [X0: $int] : in(3,add(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
tff(f1595,plain,
( ! [X0: $int] : in(3,add(X0,sK0))
| ~ spl1_12
| ~ spl1_93 ),
inference(superposition,[],[f141,f1452]) ).
tff(f1701,plain,
( spl1_110
| ~ spl1_2
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1476,f1447,f94,f1699]) ).
tff(f1476,plain,
( ! [X0: $int] :
( ( 3 = X0 )
| ( remove(X0,sK0) = add(3,remove(3,remove(X0,sK0))) ) )
| ~ spl1_2
| ~ spl1_92 ),
inference(resolution,[],[f1448,f96]) ).
tff(f1697,plain,
( spl1_109
| ~ spl1_1
| ~ spl1_92 ),
inference(avatar_split_clause,[],[f1475,f1447,f89,f1695]) ).
tff(f1475,plain,
( ! [X0: $int] :
( ( 2 = X0 )
| ( remove(X0,sK0) = add(2,remove(2,remove(X0,sK0))) ) )
| ~ spl1_1
| ~ spl1_92 ),
inference(resolution,[],[f1448,f91]) ).
tff(f1693,plain,
( spl1_108
| ~ spl1_3
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1467,f1443,f99,f1691]) ).
tff(f1467,plain,
( ! [X0: $int] :
( ( 5 = X0 )
| ( count(remove(X0,sK0)) = count(add(5,remove(X0,sK0))) ) )
| ~ spl1_3
| ~ spl1_91 ),
inference(resolution,[],[f1444,f101]) ).
tff(f1689,plain,
( spl1_107
| ~ spl1_2
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1466,f1443,f94,f1687]) ).
tff(f1466,plain,
( ! [X0: $int] :
( ( 3 = X0 )
| ( count(remove(X0,sK0)) = count(add(3,remove(X0,sK0))) ) )
| ~ spl1_2
| ~ spl1_91 ),
inference(resolution,[],[f1444,f96]) ).
tff(f1685,plain,
( spl1_106
| ~ spl1_1
| ~ spl1_91 ),
inference(avatar_split_clause,[],[f1465,f1443,f89,f1683]) ).
tff(f1465,plain,
( ! [X0: $int] :
( ( 2 = X0 )
| ( count(remove(X0,sK0)) = count(add(2,remove(X0,sK0))) ) )
| ~ spl1_1
| ~ spl1_91 ),
inference(resolution,[],[f1444,f91]) ).
tff(f1657,plain,
( spl1_105
| ~ spl1_3
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1441,f1341,f99,f1655]) ).
tff(f1653,plain,
( spl1_104
| ~ spl1_2
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1440,f1341,f94,f1651]) ).
tff(f1649,plain,
( spl1_103
| ~ spl1_12
| ~ spl1_87 ),
inference(avatar_split_clause,[],[f1583,f1329,f140,f1647]) ).
tff(f1647,plain,
( spl1_103
<=> ! [X0: $int] : in(2,add(X0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).
tff(f1583,plain,
( ! [X0: $int] : in(2,add(X0,sK0))
| ~ spl1_12
| ~ spl1_87 ),
inference(superposition,[],[f141,f1330]) ).
tff(f1645,plain,
( spl1_102
| ~ spl1_1
| ~ spl1_90 ),
inference(avatar_split_clause,[],[f1439,f1341,f89,f1643]) ).
tff(f1581,plain,
( spl1_101
| ~ spl1_3
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1136,f1077,f99,f1579]) ).
tff(f1136,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(5,add(X0,sK0))) )
| ~ spl1_3
| ~ spl1_79 ),
inference(resolution,[],[f1078,f101]) ).
tff(f1577,plain,
( spl1_100
| ~ spl1_2
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1135,f1077,f94,f1575]) ).
tff(f1135,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(3,add(X0,sK0))) )
| ~ spl1_2
| ~ spl1_79 ),
inference(resolution,[],[f1078,f96]) ).
tff(f1573,plain,
( spl1_99
| ~ spl1_1
| ~ spl1_79 ),
inference(avatar_split_clause,[],[f1134,f1077,f89,f1571]) ).
tff(f1134,plain,
( ! [X0: $int] : ( count(add(X0,sK0)) = count(add(2,add(X0,sK0))) )
| ~ spl1_1
| ~ spl1_79 ),
inference(resolution,[],[f1078,f91]) ).
tff(f1569,plain,
( spl1_98
| ~ spl1_3
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1107,f1065,f99,f1567]) ).
tff(f1107,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(5,remove(5,add(X0,sK0))) )
| ~ spl1_3
| ~ spl1_76 ),
inference(resolution,[],[f1066,f101]) ).
tff(f1539,plain,
( spl1_97
| ~ spl1_32
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f349,f329,f283,f1537]) ).
tff(f349,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X1 )
| ~ in(X0,X2) )
| ~ spl1_32
| ~ spl1_37 ),
inference(resolution,[],[f330,f284]) ).
tff(f1535,plain,
( spl1_96
| ~ spl1_33
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f340,f321,f287,f1533]) ).
tff(f340,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| in(X0,X2)
| ( X0 = X1 ) )
| ~ spl1_33
| ~ spl1_35 ),
inference(resolution,[],[f322,f288]) ).
tff(f1494,plain,
( spl1_95
| ~ spl1_35
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f345,f329,f321,f1492]) ).
tff(f345,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl1_35
| ~ spl1_37 ),
inference(resolution,[],[f330,f322]) ).
tff(f1457,plain,
( spl1_94
| ~ spl1_26
| ~ spl1_33 ),
inference(avatar_split_clause,[],[f315,f287,f214,f1455]) ).
tff(f315,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) )
| ~ spl1_26
| ~ spl1_33 ),
inference(resolution,[],[f288,f215]) ).
tff(f1453,plain,
( spl1_93
| ~ spl1_2
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1106,f1065,f94,f1451]) ).
tff(f1106,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(3,remove(3,add(X0,sK0))) )
| ~ spl1_2
| ~ spl1_76 ),
inference(resolution,[],[f1066,f96]) ).
tff(f1449,plain,
( spl1_92
| ~ spl1_25
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f312,f283,f210,f1447]) ).
tff(f312,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) )
| ~ spl1_25
| ~ spl1_32 ),
inference(resolution,[],[f284,f211]) ).
tff(f1445,plain,
( spl1_91
| ~ spl1_28
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f311,f283,f226,f1443]) ).
tff(f311,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) )
| ~ spl1_28
| ~ spl1_32 ),
inference(resolution,[],[f284,f227]) ).
tff(f1343,plain,
( spl1_90
| ~ spl1_19
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f348,f329,f170,f1341]) ).
tff(f348,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl1_19
| ~ spl1_37 ),
inference(resolution,[],[f330,f171]) ).
tff(f1339,plain,
( spl1_89
| ~ spl1_26
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f346,f329,f214,f1337]) ).
tff(f346,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl1_26
| ~ spl1_37 ),
inference(resolution,[],[f330,f215]) ).
tff(f1335,plain,
( spl1_88
| ~ spl1_18
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f342,f321,f166,f1333]) ).
tff(f342,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| in(X0,X2) )
| ~ spl1_18
| ~ spl1_35 ),
inference(resolution,[],[f322,f167]) ).
tff(f1331,plain,
( spl1_87
| ~ spl1_1
| ~ spl1_76 ),
inference(avatar_split_clause,[],[f1105,f1065,f89,f1329]) ).
tff(f1105,plain,
( ! [X0: $int] : ( add(X0,sK0) = add(2,remove(2,add(X0,sK0))) )
| ~ spl1_1
| ~ spl1_76 ),
inference(resolution,[],[f1066,f91]) ).
tff(f1327,plain,
( spl1_86
| ~ spl1_25
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f338,f321,f210,f1325]) ).
tff(f338,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl1_25
| ~ spl1_35 ),
inference(resolution,[],[f322,f211]) ).
tff(f1323,plain,
( spl1_85
| ~ spl1_28
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f337,f321,f226,f1321]) ).
tff(f337,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl1_28
| ~ spl1_35 ),
inference(resolution,[],[f322,f227]) ).
tff(f1099,plain,
( spl1_84
| ~ spl1_14
| ~ spl1_69 ),
inference(avatar_split_clause,[],[f1019,f903,f148,f1097]) ).
tff(f1097,plain,
( spl1_84
<=> ! [X0: $int] : $less($sum(X0,-1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).
tff(f903,plain,
( spl1_69
<=> ! [X0: $int] : $less($sum(-1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
tff(f1019,plain,
( ! [X0: $int] : $less($sum(X0,-1),X0)
| ~ spl1_14
| ~ spl1_69 ),
inference(superposition,[],[f904,f149]) ).
tff(f904,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl1_69 ),
inference(avatar_component_clause,[],[f903]) ).
tff(f1095,plain,
( spl1_83
| ~ spl1_24
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f300,f279,f206,f1093]) ).
tff(f300,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl1_24
| ~ spl1_31 ),
inference(superposition,[],[f207,f280]) ).
tff(f1091,plain,
( spl1_82
| ~ spl1_24
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f299,f279,f206,f1089]) ).
tff(f299,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl1_24
| ~ spl1_31 ),
inference(superposition,[],[f207,f280]) ).
tff(f1087,plain,
( spl1_81
| ~ spl1_23
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f293,f279,f202,f1085]) ).
tff(f293,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl1_23
| ~ spl1_31 ),
inference(superposition,[],[f280,f203]) ).
tff(f1083,plain,
( spl1_80
| ~ spl1_26
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f269,f226,f214,f1081]) ).
tff(f269,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) )
| ~ spl1_26
| ~ spl1_28 ),
inference(resolution,[],[f227,f215]) ).
tff(f1079,plain,
( spl1_79
| ~ spl1_19
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f268,f226,f170,f1077]) ).
tff(f268,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ~ in(X2,X1) )
| ~ spl1_19
| ~ spl1_28 ),
inference(resolution,[],[f227,f171]) ).
tff(f1075,plain,
( spl1_78
| ~ spl1_25
| ~ spl1_26 ),
inference(avatar_split_clause,[],[f262,f214,f210,f1073]) ).
tff(f262,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl1_25
| ~ spl1_26 ),
inference(resolution,[],[f215,f211]) ).
tff(f1071,plain,
( spl1_77
| ~ spl1_18
| ~ spl1_26 ),
inference(avatar_split_clause,[],[f261,f214,f166,f1069]) ).
tff(f261,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| in(X0,X2) )
| ~ spl1_18
| ~ spl1_26 ),
inference(resolution,[],[f215,f167]) ).
tff(f1067,plain,
( spl1_76
| ~ spl1_19
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f258,f210,f170,f1065]) ).
tff(f258,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl1_19
| ~ spl1_25 ),
inference(resolution,[],[f211,f171]) ).
tff(f929,plain,
( spl1_75
| ~ spl1_12
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f347,f329,f140,f927]) ).
tff(f925,plain,
( spl1_74
| ~ spl1_11
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f341,f321,f136,f923]) ).
tff(f341,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) )
| ~ spl1_11
| ~ spl1_35 ),
inference(resolution,[],[f322,f137]) ).
tff(f921,plain,
( spl1_73
| ~ spl1_23
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f253,f206,f202,f919]) ).
tff(f253,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl1_23
| ~ spl1_24 ),
inference(superposition,[],[f207,f203]) ).
tff(f917,plain,
( spl1_72
| ~ spl1_23
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f249,f206,f202,f915]) ).
tff(f249,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl1_23
| ~ spl1_24 ),
inference(superposition,[],[f207,f203]) ).
tff(f913,plain,
( spl1_71
| ~ spl1_21
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f245,f206,f184,f911]) ).
tff(f245,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl1_21
| ~ spl1_24 ),
inference(resolution,[],[f207,f185]) ).
tff(f909,plain,
( spl1_70
| ~ spl1_17
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f193,f188,f162,f907]) ).
tff(f193,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl1_17
| ~ spl1_22 ),
inference(resolution,[],[f189,f163]) ).
tff(f905,plain,
( spl1_69
| ~ spl1_47
| ~ spl1_52 ),
inference(avatar_split_clause,[],[f533,f481,f450,f903]) ).
tff(f450,plain,
( spl1_47
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
tff(f533,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl1_47
| ~ spl1_52 ),
inference(evaluation,[],[f527]) ).
tff(f527,plain,
( ! [X0: $int] : $less($sum($uminus(1),X0),X0)
| ~ spl1_47
| ~ spl1_52 ),
inference(superposition,[],[f451,f482]) ).
tff(f451,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f450]) ).
tff(f843,plain,
( spl1_68
| ~ spl1_16
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f305,f279,f158,f841]) ).
tff(f305,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl1_16
| ~ spl1_31 ),
inference(superposition,[],[f159,f280]) ).
tff(f839,plain,
( spl1_67
| ~ spl1_17
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f304,f279,f162,f837]) ).
tff(f304,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl1_17
| ~ spl1_31 ),
inference(superposition,[],[f163,f280]) ).
tff(f835,plain,
( spl1_66
| ~ spl1_21
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f194,f188,f184,f833]) ).
tff(f194,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl1_21
| ~ spl1_22 ),
inference(resolution,[],[f189,f185]) ).
tff(f656,plain,
( spl1_65
| ~ spl1_14
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f296,f279,f148,f654]) ).
tff(f296,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl1_14
| ~ spl1_31 ),
inference(superposition,[],[f280,f149]) ).
tff(f652,plain,
( spl1_64
| ~ spl1_14
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f291,f279,f148,f650]) ).
tff(f291,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl1_14
| ~ spl1_31 ),
inference(superposition,[],[f280,f149]) ).
tff(f648,plain,
( spl1_63
| ~ spl1_12
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f267,f226,f140,f646]) ).
tff(f267,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl1_12
| ~ spl1_28 ),
inference(resolution,[],[f227,f141]) ).
tff(f644,plain,
( spl1_62
| ~ spl1_11
| ~ spl1_26 ),
inference(avatar_split_clause,[],[f260,f214,f136,f642]) ).
tff(f260,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) )
| ~ spl1_11
| ~ spl1_26 ),
inference(resolution,[],[f215,f137]) ).
tff(f640,plain,
( spl1_61
| ~ spl1_12
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f257,f210,f140,f638]) ).
tff(f257,plain,
( ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) )
| ~ spl1_12
| ~ spl1_25 ),
inference(resolution,[],[f211,f141]) ).
tff(f636,plain,
( spl1_60
| ~ spl1_16
| ~ spl1_21 ),
inference(avatar_split_clause,[],[f191,f184,f158,f634]) ).
tff(f191,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl1_16
| ~ spl1_21 ),
inference(resolution,[],[f185,f159]) ).
tff(f594,plain,
( spl1_59
| ~ spl1_15
| ~ spl1_46 ),
inference(avatar_split_clause,[],[f461,f446,f152,f592]) ).
tff(f592,plain,
( spl1_59
<=> ! [X0: $int] : ( empty = remove(X0,empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
tff(f461,plain,
( ! [X0: $int] : ( empty = remove(X0,empty) )
| ~ spl1_15
| ~ spl1_46 ),
inference(trivial_inequality_removal,[],[f459]) ).
tff(f459,plain,
( ! [X0: $int] :
( ( 0 != 0 )
| ( empty = remove(X0,empty) ) )
| ~ spl1_15
| ~ spl1_46 ),
inference(superposition,[],[f153,f447]) ).
tff(f573,plain,
( spl1_58
| ~ spl1_13
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f295,f279,f144,f571]) ).
tff(f571,plain,
( spl1_58
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
tff(f295,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl1_13
| ~ spl1_31 ),
inference(superposition,[],[f280,f145]) ).
tff(f569,plain,
( spl1_57
| ~ spl1_14
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f251,f206,f148,f567]) ).
tff(f251,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl1_14
| ~ spl1_24 ),
inference(superposition,[],[f207,f149]) ).
tff(f565,plain,
( spl1_56
| ~ spl1_14
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f247,f206,f148,f563]) ).
tff(f247,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl1_14
| ~ spl1_24 ),
inference(superposition,[],[f207,f149]) ).
tff(f561,plain,
( spl1_55
| ~ spl1_14
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f234,f202,f148,f559]) ).
tff(f234,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl1_14
| ~ spl1_23 ),
inference(superposition,[],[f203,f149]) ).
tff(f542,plain,
( spl1_54
| ~ spl1_13
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f250,f206,f144,f540]) ).
tff(f250,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl1_13
| ~ spl1_24 ),
inference(superposition,[],[f207,f145]) ).
tff(f538,plain,
( spl1_53
| ~ spl1_13
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f246,f206,f144,f536]) ).
tff(f246,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl1_13
| ~ spl1_24 ),
inference(superposition,[],[f207,f145]) ).
tff(f483,plain,
( spl1_52
| ~ spl1_13
| ~ spl1_31 ),
inference(avatar_split_clause,[],[f306,f279,f144,f481]) ).
tff(f306,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl1_13
| ~ spl1_31 ),
inference(evaluation,[],[f290]) ).
tff(f290,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl1_13
| ~ spl1_31 ),
inference(superposition,[],[f280,f145]) ).
tff(f479,plain,
( spl1_51
| ~ spl1_7
| ~ spl1_22 ),
inference(avatar_split_clause,[],[f195,f188,f117,f477]) ).
tff(f195,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl1_7
| ~ spl1_22 ),
inference(resolution,[],[f189,f118]) ).
tff(f475,plain,
( spl1_50
| ~ spl1_14
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f177,f162,f148,f473]) ).
tff(f177,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl1_14
| ~ spl1_17 ),
inference(superposition,[],[f163,f149]) ).
tff(f471,plain,
( spl1_49
| ~ spl1_14
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f174,f158,f148,f469]) ).
tff(f174,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl1_14
| ~ spl1_16 ),
inference(superposition,[],[f159,f149]) ).
tff(f456,plain,
( spl1_48
| ~ spl1_6
| ~ spl1_8
| ~ spl1_35 ),
inference(avatar_split_clause,[],[f344,f321,f121,f113,f454]) ).
tff(f344,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_35 ),
inference(evaluation,[],[f343]) ).
tff(f343,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,0) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_35 ),
inference(forward_demodulation,[],[f339,f123]) ).
tff(f339,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) )
| ~ spl1_6
| ~ spl1_35 ),
inference(resolution,[],[f322,f114]) ).
tff(f452,plain,
( spl1_47
| ~ spl1_14
| ~ spl1_20 ),
inference(avatar_split_clause,[],[f219,f180,f148,f450]) ).
tff(f219,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl1_14
| ~ spl1_20 ),
inference(superposition,[],[f181,f149]) ).
tff(f448,plain,
( spl1_46
| ~ spl1_6
| ~ spl1_8
| ~ spl1_26 ),
inference(avatar_split_clause,[],[f263,f214,f121,f113,f446]) ).
tff(f263,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_26 ),
inference(forward_demodulation,[],[f259,f123]) ).
tff(f259,plain,
( ! [X0: $int] : ( count(empty) = count(remove(X0,empty)) )
| ~ spl1_6
| ~ spl1_26 ),
inference(resolution,[],[f215,f114]) ).
tff(f423,plain,
( spl1_45
| ~ spl1_3
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f256,f210,f99,f420]) ).
tff(f420,plain,
( spl1_45
<=> ( sK0 = add(5,remove(5,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f256,plain,
( ( sK0 = add(5,remove(5,sK0)) )
| ~ spl1_3
| ~ spl1_25 ),
inference(resolution,[],[f211,f101]) ).
tff(f418,plain,
( spl1_44
| ~ spl1_2
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f255,f210,f94,f415]) ).
tff(f415,plain,
( spl1_44
<=> ( sK0 = add(3,remove(3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f255,plain,
( ( sK0 = add(3,remove(3,sK0)) )
| ~ spl1_2
| ~ spl1_25 ),
inference(resolution,[],[f211,f96]) ).
tff(f413,plain,
( spl1_43
| ~ spl1_1
| ~ spl1_25 ),
inference(avatar_split_clause,[],[f254,f210,f89,f410]) ).
tff(f410,plain,
( spl1_43
<=> ( sK0 = add(2,remove(2,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f254,plain,
( ( sK0 = add(2,remove(2,sK0)) )
| ~ spl1_1
| ~ spl1_25 ),
inference(resolution,[],[f211,f91]) ).
tff(f388,plain,
( spl1_42
| ~ spl1_3
| ~ spl1_4
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f358,f329,f104,f99,f385]) ).
tff(f104,plain,
( spl1_4
<=> ( 2 = count(sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f358,plain,
( ( 1 = count(remove(5,sK0)) )
| ~ spl1_3
| ~ spl1_4
| ~ spl1_37 ),
inference(evaluation,[],[f357]) ).
tff(f357,plain,
( ( count(remove(5,sK0)) = $sum(-1,2) )
| ~ spl1_3
| ~ spl1_4
| ~ spl1_37 ),
inference(forward_demodulation,[],[f352,f106]) ).
tff(f106,plain,
( ( 2 = count(sK0) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f352,plain,
( ( $sum(-1,count(sK0)) = count(remove(5,sK0)) )
| ~ spl1_3
| ~ spl1_37 ),
inference(resolution,[],[f330,f101]) ).
tff(f383,plain,
( spl1_41
| ~ spl1_2
| ~ spl1_4
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f356,f329,f104,f94,f380]) ).
tff(f356,plain,
( ( 1 = count(remove(3,sK0)) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_37 ),
inference(evaluation,[],[f355]) ).
tff(f355,plain,
( ( count(remove(3,sK0)) = $sum(-1,2) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_37 ),
inference(forward_demodulation,[],[f351,f106]) ).
tff(f351,plain,
( ( $sum(-1,count(sK0)) = count(remove(3,sK0)) )
| ~ spl1_2
| ~ spl1_37 ),
inference(resolution,[],[f330,f96]) ).
tff(f378,plain,
( spl1_40
| ~ spl1_1
| ~ spl1_4
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f354,f329,f104,f89,f375]) ).
tff(f354,plain,
( ( 1 = count(remove(2,sK0)) )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_37 ),
inference(evaluation,[],[f353]) ).
tff(f353,plain,
( ( count(remove(2,sK0)) = $sum(-1,2) )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_37 ),
inference(forward_demodulation,[],[f350,f106]) ).
tff(f350,plain,
( ( count(remove(2,sK0)) = $sum(-1,count(sK0)) )
| ~ spl1_1
| ~ spl1_37 ),
inference(resolution,[],[f330,f91]) ).
tff(f363,plain,
( spl1_39
| ~ spl1_3
| ~ spl1_4
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f272,f226,f104,f99,f360]) ).
tff(f360,plain,
( spl1_39
<=> ( 2 = count(add(5,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
tff(f272,plain,
( ( 2 = count(add(5,sK0)) )
| ~ spl1_3
| ~ spl1_4
| ~ spl1_28 ),
inference(forward_demodulation,[],[f266,f106]) ).
tff(f266,plain,
( ( count(sK0) = count(add(5,sK0)) )
| ~ spl1_3
| ~ spl1_28 ),
inference(resolution,[],[f227,f101]) ).
tff(f336,plain,
( spl1_38
| ~ spl1_2
| ~ spl1_4
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f271,f226,f104,f94,f333]) ).
tff(f333,plain,
( spl1_38
<=> ( 2 = count(add(3,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
tff(f271,plain,
( ( 2 = count(add(3,sK0)) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_28 ),
inference(forward_demodulation,[],[f265,f106]) ).
tff(f265,plain,
( ( count(sK0) = count(add(3,sK0)) )
| ~ spl1_2
| ~ spl1_28 ),
inference(resolution,[],[f227,f96]) ).
tff(f331,plain,
spl1_37,
inference(avatar_split_clause,[],[f87,f329]) ).
tff(f87,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f82,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f82,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f71]) ).
tff(f71,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) )
& ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,plain,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f327,plain,
spl1_36,
inference(avatar_split_clause,[],[f86,f325]) ).
tff(f86,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f83,f17]) ).
tff(f83,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),-1) ) ),
inference(evaluation,[],[f72]) ).
tff(f72,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) ),
inference(cnf_transformation,[],[f49]) ).
tff(f323,plain,
spl1_35,
inference(avatar_split_clause,[],[f85,f321]) ).
tff(f85,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f67,f17]) ).
tff(f67,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X13: $int,X14: collection] :
( ~ in(X13,X14)
<=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f319,plain,
spl1_34,
inference(avatar_split_clause,[],[f84,f317]) ).
tff(f84,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f68,f17]) ).
tff(f68,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f289,plain,
spl1_33,
inference(avatar_split_clause,[],[f78,f287]) ).
tff(f78,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f52]) ).
tff(f52,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f285,plain,
spl1_32,
inference(avatar_split_clause,[],[f73,f283]) ).
tff(f73,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f50]) ).
tff(f50,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f281,plain,
spl1_31,
inference(avatar_split_clause,[],[f18,f279]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f277,plain,
( spl1_30
| ~ spl1_1
| ~ spl1_4
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f270,f226,f104,f89,f274]) ).
tff(f270,plain,
( ( 2 = count(add(2,sK0)) )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_28 ),
inference(forward_demodulation,[],[f264,f106]) ).
tff(f264,plain,
( ( count(sK0) = count(add(2,sK0)) )
| ~ spl1_1
| ~ spl1_28 ),
inference(resolution,[],[f227,f91]) ).
tff(f232,plain,
spl1_29,
inference(avatar_split_clause,[],[f70,f230]) ).
tff(f70,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) )
& ( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(X1) = count(add(X0,X1)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X15: $int,X16: collection] :
( in(X15,X16)
<=> ( count(add(X15,X16)) = count(X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f228,plain,
spl1_28,
inference(avatar_split_clause,[],[f69,f226]) ).
tff(f69,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f224,plain,
spl1_27,
inference(avatar_split_clause,[],[f66,f222]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) )
& ( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(remove(X0,X1)) = count(X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X19: $int,X20: collection] :
( ~ in(X19,X20)
<=> ( count(remove(X19,X20)) = count(X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
tff(f216,plain,
spl1_26,
inference(avatar_split_clause,[],[f65,f214]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f212,plain,
spl1_25,
inference(avatar_split_clause,[],[f64,f210]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
=> ( add(X0,remove(X0,X1)) = X1 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X21: $int,X22: collection] :
( in(X21,X22)
=> ( add(X21,remove(X21,X22)) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
tff(f208,plain,
spl1_24,
inference(avatar_split_clause,[],[f25,f206]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f204,plain,
spl1_23,
inference(avatar_split_clause,[],[f20,f202]) ).
tff(f20,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f190,plain,
spl1_22,
inference(avatar_split_clause,[],[f24,f188]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f186,plain,
spl1_21,
inference(avatar_split_clause,[],[f23,f184]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f182,plain,
( spl1_20
| ~ spl1_5
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f173,f158,f109,f180]) ).
tff(f109,plain,
( spl1_5
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f173,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl1_5
| ~ spl1_16 ),
inference(resolution,[],[f159,f110]) ).
tff(f110,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f109]) ).
tff(f172,plain,
spl1_19,
inference(avatar_split_clause,[],[f76,f170]) ).
tff(f76,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f168,plain,
spl1_18,
inference(avatar_split_clause,[],[f74,f166]) ).
tff(f74,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f164,plain,
spl1_17,
inference(avatar_split_clause,[],[f28,f162]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f160,plain,
spl1_16,
inference(avatar_split_clause,[],[f26,f158]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f154,plain,
spl1_15,
inference(avatar_split_clause,[],[f61,f152]) ).
tff(f61,plain,
! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: collection] :
( ( ( empty = X0 )
| ( 0 != count(X0) ) )
& ( ( 0 = count(X0) )
| ( empty != X0 ) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: collection] :
( ( empty = X0 )
<=> ( 0 = count(X0) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X12: collection] :
( ( empty = X12 )
<=> ( 0 = count(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f150,plain,
spl1_14,
inference(avatar_split_clause,[],[f17,f148]) ).
tff(f146,plain,
spl1_13,
inference(avatar_split_clause,[],[f21,f144]) ).
tff(f21,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f142,plain,
spl1_12,
inference(avatar_split_clause,[],[f63,f140]) ).
tff(f63,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f138,plain,
spl1_11,
inference(avatar_split_clause,[],[f62,f136]) ).
tff(f62,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f134,plain,
spl1_10,
inference(avatar_split_clause,[],[f27,f132]) ).
tff(f132,plain,
( spl1_10
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f27,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f130,plain,
spl1_9,
inference(avatar_split_clause,[],[f19,f128]) ).
tff(f128,plain,
( spl1_9
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f19,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f124,plain,
spl1_8,
inference(avatar_split_clause,[],[f79,f121]) ).
tff(f79,plain,
0 = count(empty),
inference(equality_resolution,[],[f60]) ).
tff(f60,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f119,plain,
spl1_7,
inference(avatar_split_clause,[],[f59,f117]) ).
tff(f59,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(rectify,[],[f15]) ).
tff(f15,plain,
! [X11: collection] : ~ $less(count(X11),0),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
! [X11: collection] : $greatereq(count(X11),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f115,plain,
spl1_6,
inference(avatar_split_clause,[],[f58,f113]) ).
tff(f58,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f111,plain,
spl1_5,
inference(avatar_split_clause,[],[f22,f109]) ).
tff(f22,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f107,plain,
spl1_4,
inference(avatar_split_clause,[],[f56,f104]) ).
tff(f56,plain,
2 = count(sK0),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
( in(5,sK0)
& ( 2 = count(sK0) )
& in(3,sK0)
& in(2,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f41,f43]) ).
tff(f43,plain,
( ? [X0: collection] :
( in(5,X0)
& ( 2 = count(X0) )
& in(3,X0)
& in(2,X0) )
=> ( in(5,sK0)
& ( 2 = count(sK0) )
& in(3,sK0)
& in(2,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0: collection] :
( in(5,X0)
& ( 2 = count(X0) )
& in(3,X0)
& in(2,X0) ),
inference(flattening,[],[f40]) ).
tff(f40,plain,
? [X0: collection] :
( in(5,X0)
& ( 2 = count(X0) )
& in(3,X0)
& in(2,X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection] :
( ( ( 2 = count(X0) )
& in(3,X0)
& in(2,X0) )
=> ~ in(5,X0) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection] :
( ( ( 2 = count(X0) )
& in(3,X0)
& in(2,X0) )
=> ~ in(5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f102,plain,
spl1_3,
inference(avatar_split_clause,[],[f57,f99]) ).
tff(f57,plain,
in(5,sK0),
inference(cnf_transformation,[],[f44]) ).
tff(f97,plain,
spl1_2,
inference(avatar_split_clause,[],[f55,f94]) ).
tff(f55,plain,
in(3,sK0),
inference(cnf_transformation,[],[f44]) ).
tff(f92,plain,
spl1_1,
inference(avatar_split_clause,[],[f54,f89]) ).
tff(f54,plain,
in(2,sK0),
inference(cnf_transformation,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT038_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 13:26:06 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (1058)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (1064)WARNING: value z3 for option sas not known
% 0.14/0.38 % (1063)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (1066)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (1065)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (1068)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (1069)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (1064)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (1063)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (1065)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (1063)Terminated due to inappropriate strategy.
% 0.14/0.38 % (1063)------------------------------
% 0.14/0.38 % (1063)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (1065)Terminated due to inappropriate strategy.
% 0.14/0.38 % (1065)------------------------------
% 0.14/0.38 % (1065)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (1063)Termination reason: Inappropriate
% 0.14/0.38 % (1065)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (1063)Memory used [KB]: 767
% 0.14/0.38 % (1065)Memory used [KB]: 767
% 0.14/0.38 % (1063)Time elapsed: 0.002 s
% 0.14/0.38 % (1065)Time elapsed: 0.003 s
% 0.14/0.38 % (1065)Instructions burned: 3 (million)
% 0.14/0.38 % (1063)Instructions burned: 3 (million)
% 0.14/0.38 % (1065)------------------------------
% 0.14/0.38 % (1065)------------------------------
% 0.14/0.38 % (1063)------------------------------
% 0.14/0.38 % (1063)------------------------------
% 0.14/0.38 % (1062)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (1062)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (1062)Terminated due to inappropriate strategy.
% 0.14/0.38 % (1062)------------------------------
% 0.14/0.38 % (1062)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (1062)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (1062)Memory used [KB]: 767
% 0.14/0.38 % (1062)Time elapsed: 0.004 s
% 0.14/0.38 % (1062)Instructions burned: 3 (million)
% 0.14/0.38 % (1062)------------------------------
% 0.14/0.38 % (1062)------------------------------
% 0.14/0.40 % (1078)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.40 % (1079)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.40 % (1078)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (1078)Terminated due to inappropriate strategy.
% 0.21/0.40 % (1078)------------------------------
% 0.21/0.40 % (1078)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40 % (1078)Termination reason: Inappropriate
% 0.21/0.40
% 0.21/0.40 % (1078)Memory used [KB]: 766
% 0.21/0.40 % (1078)Time elapsed: 0.002 s
% 0.21/0.40 % (1078)Instructions burned: 3 (million)
% 0.21/0.40 % (1078)------------------------------
% 0.21/0.40 % (1078)------------------------------
% 0.21/0.40 % (1083)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.42 % (1089)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 134.07/19.48 % (1066)First to succeed.
% 134.52/19.51 % (1066)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1058"
% 134.52/19.51 % (1066)Refutation found. Thanks to Tanya!
% 134.52/19.51 % SZS status Theorem for theBenchmark
% 134.52/19.51 % SZS output start Proof for theBenchmark
% See solution above
% 134.52/19.53 % (1066)------------------------------
% 134.52/19.53 % (1066)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 134.52/19.53 % (1066)Termination reason: Refutation
% 134.52/19.53
% 134.52/19.53 % (1066)Memory used [KB]: 71251
% 134.52/19.53 % (1066)Time elapsed: 19.127 s
% 134.52/19.53 % (1066)Instructions burned: 63906 (million)
% 134.52/19.53 % (1058)Success in time 18.892 s
%------------------------------------------------------------------------------