TSTP Solution File: SWW642_2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW642_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 07:27:36 EDT 2024
% Result : Theorem 1.43s 0.60s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 399
% Syntax : Number of formulae : 1382 ( 77 unt; 29 typ; 0 def)
% Number of atoms : 4740 ( 915 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 5971 (2584 ~;2877 |; 119 &)
% ( 325 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 6073 ( 933 atm;2607 fun; 959 num;1574 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 24 ( 12 >; 12 *; 0 +; 0 <<)
% Number of predicates : 332 ( 328 usr; 326 prp; 0-3 aty)
% Number of functors : 31 ( 22 usr; 18 con; 0-4 aty)
% Number of variables : 1776 (1719 !; 57 ?;1776 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
ref: ty > ty ).
tff(func_def_13,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_14,type,
contents: ( ty * uni ) > uni ).
tff(func_def_18,type,
fact1: $int > $int ).
tff(func_def_21,type,
sK1: ( $int * $int * $int ) > $int ).
tff(func_def_22,type,
sK2: ( $int * $int * $int ) > $int ).
tff(func_def_23,type,
sK3: $int ).
tff(func_def_24,type,
sK4: $int ).
tff(func_def_25,type,
sK5: $int ).
tff(func_def_26,type,
sK6: $int ).
tff(func_def_27,type,
sK7: $int ).
tff(func_def_28,type,
sK8: $int > $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
even1: $int > $o ).
tff(pred_def_5,type,
sP0: ( $int * $int * $int ) > $o ).
tff(f7395,plain,
$false,
inference(avatar_sat_refutation,[],[f131,f136,f141,f146,f155,f165,f166,f172,f176,f181,f185,f191,f195,f199,f203,f205,f209,f213,f217,f221,f225,f229,f233,f237,f241,f245,f252,f256,f260,f272,f276,f280,f284,f294,f298,f314,f323,f327,f331,f335,f339,f376,f384,f388,f392,f442,f446,f450,f470,f474,f478,f554,f559,f571,f579,f584,f597,f614,f622,f635,f689,f710,f715,f734,f738,f753,f757,f761,f804,f808,f812,f816,f820,f824,f860,f891,f949,f953,f957,f961,f966,f970,f1046,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1432,f1436,f1440,f1444,f1448,f1473,f1532,f1536,f1540,f1544,f1548,f1552,f1556,f1564,f1568,f1572,f1576,f1580,f1675,f1690,f1974,f1978,f1982,f1986,f2175,f2185,f2189,f2193,f2250,f2254,f2324,f2412,f2416,f2420,f2424,f2428,f2432,f2688,f2692,f2883,f2887,f2930,f3168,f3213,f3217,f3221,f3230,f3237,f3324,f3331,f3336,f3396,f3402,f3406,f3410,f3415,f3463,f3469,f3489,f3496,f3501,f3508,f3514,f3518,f3522,f3527,f3532,f3536,f3540,f3544,f3548,f3895,f3902,f3910,f3917,f3928,f3931,f3939,f3946,f3953,f4007,f4013,f4021,f4061,f4067,f4072,f4078,f4086,f4091,f4135,f4143,f4149,f4155,f4162,f4168,f4175,f4182,f4187,f4193,f4197,f4205,f4213,f4223,f4227,f4238,f4245,f4251,f4372,f4376,f4519,f4527,f4534,f4542,f4549,f4555,f4565,f4573,f4580,f4594,f4601,f4608,f4615,f4624,f4637,f4646,f4650,f4658,f4662,f4783,f4792,f4797,f4806,f4821,f4835,f4843,f4850,f4861,f4865,f4875,f4883,f4890,f4905,f4912,f4920,f4927,f4935,f4945,f4954,f4963,f4972,f4980,f4988,f5112,f5121,f5130,f5141,f5150,f5159,f5182,f5192,f5202,f5208,f5215,f5225,f5235,f5239,f5246,f5253,f5263,f5273,f5283,f5292,f5301,f5311,f5318,f5441,f5450,f5454,f5458,f5462,f5466,f5470,f5475,f5518,f5639,f5650,f5660,f5670,f5682,f5686,f5696,f5708,f5720,f5732,f5736,f5740,f5744,f5748,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5929,f6298,f6356,f6360,f6374,f6388,f6392,f6396,f6400,f6404,f6408,f6412,f6416,f6424,f6428,f7053,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7394]) ).
tff(f7394,plain,
( ~ spl9_54
| ~ spl9_231
| ~ spl9_297 ),
inference(avatar_split_clause,[],[f6304,f5746,f4818,f568]) ).
tff(f568,plain,
( spl9_54
<=> $less(0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
tff(f4818,plain,
( spl9_231
<=> $less($sum(-1,sK6),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_231])]) ).
tff(f5746,plain,
( spl9_297
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_297])]) ).
tff(f6304,plain,
( ~ $less(0,sK6)
| ~ spl9_231
| ~ spl9_297 ),
inference(resolution,[],[f4820,f5747]) ).
tff(f5747,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(-1,X0),X1)
| ~ $less(X1,X0) )
| ~ spl9_297 ),
inference(avatar_component_clause,[],[f5746]) ).
tff(f4820,plain,
( $less($sum(-1,sK6),0)
| ~ spl9_231 ),
inference(avatar_component_clause,[],[f4818]) ).
tff(f7393,plain,
( spl9_325
| ~ spl9_26
| ~ spl9_84 ),
inference(avatar_split_clause,[],[f1051,f968,f250,f7391]) ).
tff(f7391,plain,
( spl9_325
<=> ! [X0: $int,X1: $int] :
( ~ even1($sum(X1,$sum(1,X0)))
| ~ even1($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_325])]) ).
tff(f250,plain,
( spl9_26
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
tff(f968,plain,
( spl9_84
<=> ! [X0: $int,X1: $int] :
( ~ even1($sum(X0,$sum(X1,1)))
| ~ even1($sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_84])]) ).
tff(f1051,plain,
( ! [X0: $int,X1: $int] :
( ~ even1($sum(X1,$sum(1,X0)))
| ~ even1($sum(X1,X0)) )
| ~ spl9_26
| ~ spl9_84 ),
inference(superposition,[],[f969,f251]) ).
tff(f251,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f250]) ).
tff(f969,plain,
( ! [X0: $int,X1: $int] :
( ~ even1($sum(X0,$sum(X1,1)))
| ~ even1($sum(X0,X1)) )
| ~ spl9_84 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f7389,plain,
( spl9_324
| ~ spl9_26
| ~ spl9_42
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f1039,f964,f374,f250,f7387]) ).
tff(f7387,plain,
( spl9_324
<=> ! [X0: $int,X1: $int] :
( even1($sum(X1,$sum(2,X0)))
| ~ even1($sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_324])]) ).
tff(f374,plain,
( spl9_42
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
tff(f964,plain,
( spl9_83
<=> ! [X0: $int,X1: $int] :
( even1($sum(X0,$sum(X1,2)))
| ~ even1($sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_83])]) ).
tff(f1039,plain,
( ! [X0: $int,X1: $int] :
( even1($sum(X1,$sum(2,X0)))
| ~ even1($sum(X0,X1)) )
| ~ spl9_26
| ~ spl9_42
| ~ spl9_83 ),
inference(forward_demodulation,[],[f1035,f375]) ).
tff(f375,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl9_42 ),
inference(avatar_component_clause,[],[f374]) ).
tff(f1035,plain,
( ! [X0: $int,X1: $int] :
( even1($sum($sum(X1,2),X0))
| ~ even1($sum(X0,X1)) )
| ~ spl9_26
| ~ spl9_83 ),
inference(superposition,[],[f965,f251]) ).
tff(f965,plain,
( ! [X0: $int,X1: $int] :
( even1($sum(X0,$sum(X1,2)))
| ~ even1($sum(X0,X1)) )
| ~ spl9_83 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f7385,plain,
( spl9_323
| ~ spl9_26
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f1031,f964,f250,f7383]) ).
tff(f7383,plain,
( spl9_323
<=> ! [X0: $int,X1: $int] :
( even1($sum(X1,$sum(2,X0)))
| ~ even1($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_323])]) ).
tff(f1031,plain,
( ! [X0: $int,X1: $int] :
( even1($sum(X1,$sum(2,X0)))
| ~ even1($sum(X1,X0)) )
| ~ spl9_26
| ~ spl9_83 ),
inference(superposition,[],[f965,f251]) ).
tff(f7381,plain,
( spl9_322
| ~ spl9_26
| ~ spl9_80 ),
inference(avatar_split_clause,[],[f1000,f951,f250,f7379]) ).
tff(f7379,plain,
( spl9_322
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X2),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_322])]) ).
tff(f951,plain,
( spl9_80
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_80])]) ).
tff(f1000,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X2),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl9_26
| ~ spl9_80 ),
inference(superposition,[],[f952,f251]) ).
tff(f952,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl9_80 ),
inference(avatar_component_clause,[],[f951]) ).
tff(f7377,plain,
( spl9_321
| ~ spl9_72
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f979,f947,f806,f7375]) ).
tff(f7375,plain,
( spl9_321
<=> ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X0,X1)))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_321])]) ).
tff(f806,plain,
( spl9_72
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_72])]) ).
tff(f947,plain,
( spl9_79
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_79])]) ).
tff(f979,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X0,X1)))
| ~ $less(X1,$uminus(X0)) )
| ~ spl9_72
| ~ spl9_79 ),
inference(superposition,[],[f807,f948]) ).
tff(f948,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl9_79 ),
inference(avatar_component_clause,[],[f947]) ).
tff(f807,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl9_72 ),
inference(avatar_component_clause,[],[f806]) ).
tff(f7373,plain,
( spl9_320
| ~ spl9_73
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f978,f947,f810,f7371]) ).
tff(f7371,plain,
( spl9_320
<=> ! [X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),0)
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_320])]) ).
tff(f810,plain,
( spl9_73
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_73])]) ).
tff(f978,plain,
( ! [X0: $int,X1: $int] :
( $less($uminus($sum(X0,X1)),0)
| ~ $less($uminus(X0),X1) )
| ~ spl9_73
| ~ spl9_79 ),
inference(superposition,[],[f811,f948]) ).
tff(f811,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl9_73 ),
inference(avatar_component_clause,[],[f810]) ).
tff(f7369,plain,
( spl9_319
| ~ spl9_35
| ~ spl9_73 ),
inference(avatar_split_clause,[],[f915,f810,f312,f7367]) ).
tff(f7367,plain,
( spl9_319
<=> ! [X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),0)
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_319])]) ).
tff(f312,plain,
( spl9_35
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
tff(f915,plain,
( ! [X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),0)
| ~ $less($uminus(X0),X1) )
| ~ spl9_35
| ~ spl9_73 ),
inference(superposition,[],[f811,f313]) ).
tff(f313,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl9_35 ),
inference(avatar_component_clause,[],[f312]) ).
tff(f7365,plain,
( spl9_318
| ~ spl9_35
| ~ spl9_72 ),
inference(avatar_split_clause,[],[f907,f806,f312,f7363]) ).
tff(f7363,plain,
( spl9_318
<=> ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X1,X0)))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_318])]) ).
tff(f907,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$uminus($sum(X1,X0)))
| ~ $less(X1,$uminus(X0)) )
| ~ spl9_35
| ~ spl9_72 ),
inference(superposition,[],[f807,f313]) ).
tff(f7053,plain,
( spl9_185
| ~ spl9_115
| ~ spl9_148 ),
inference(avatar_split_clause,[],[f5934,f3333,f1672,f4088]) ).
tff(f4088,plain,
( spl9_185
<=> $less(1,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_185])]) ).
tff(f1672,plain,
( spl9_115
<=> $less(fact1(sK6),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_115])]) ).
tff(f3333,plain,
( spl9_148
<=> ( 1 = fact1(sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_148])]) ).
tff(f5934,plain,
( $less(1,sK5)
| ~ spl9_115
| ~ spl9_148 ),
inference(forward_demodulation,[],[f1674,f3335]) ).
tff(f3335,plain,
( ( 1 = fact1(sK6) )
| ~ spl9_148 ),
inference(avatar_component_clause,[],[f3333]) ).
tff(f1674,plain,
( $less(fact1(sK6),sK5)
| ~ spl9_115 ),
inference(avatar_component_clause,[],[f1672]) ).
tff(f6428,plain,
( spl9_317
| ~ spl9_21
| ~ spl9_117 ),
inference(avatar_split_clause,[],[f2027,f1972,f227,f6426]) ).
tff(f6426,plain,
( spl9_317
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum($uminus($sum(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_317])]) ).
tff(f227,plain,
( spl9_21
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
tff(f1972,plain,
( spl9_117
<=> ! [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,[spl9_117])]) ).
tff(f2027,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum($uminus($sum(X0,X1)),X0) )
| ~ spl9_21
| ~ spl9_117 ),
inference(evaluation,[],[f1990]) ).
tff(f1990,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus($sum(X0,X1)),$uminus($uminus(X0))) = $sum($uminus(X1),0) )
| ~ spl9_21
| ~ spl9_117 ),
inference(superposition,[],[f1973,f228]) ).
tff(f228,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl9_21 ),
inference(avatar_component_clause,[],[f227]) ).
tff(f1973,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl9_117 ),
inference(avatar_component_clause,[],[f1972]) ).
tff(f6424,plain,
( spl9_316
| ~ spl9_64
| ~ spl9_90 ),
inference(avatar_split_clause,[],[f1167,f1079,f708,f6422]) ).
tff(f6422,plain,
( spl9_316
<=> ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X1,$sum(X0,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_316])]) ).
tff(f708,plain,
( spl9_64
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_64])]) ).
tff(f1079,plain,
( spl9_90
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_90])]) ).
tff(f1167,plain,
( ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X1,$sum(X0,1)))
| ~ spl9_64
| ~ spl9_90 ),
inference(superposition,[],[f709,f1080]) ).
tff(f1080,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl9_90 ),
inference(avatar_component_clause,[],[f1079]) ).
tff(f709,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl9_64 ),
inference(avatar_component_clause,[],[f708]) ).
tff(f6416,plain,
( spl9_315
| ~ spl9_21
| ~ spl9_81 ),
inference(avatar_split_clause,[],[f1020,f955,f227,f6414]) ).
tff(f6414,plain,
( spl9_315
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_315])]) ).
tff(f955,plain,
( spl9_81
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_81])]) ).
tff(f1020,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,X0),0)
| ~ $less(X1,$uminus(X0)) )
| ~ spl9_21
| ~ spl9_81 ),
inference(superposition,[],[f956,f228]) ).
tff(f956,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl9_81 ),
inference(avatar_component_clause,[],[f955]) ).
tff(f6412,plain,
( spl9_314
| ~ spl9_21
| ~ spl9_80 ),
inference(avatar_split_clause,[],[f991,f951,f227,f6410]) ).
tff(f6410,plain,
( spl9_314
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_314])]) ).
tff(f991,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,X0))
| ~ $less($uminus(X0),X1) )
| ~ spl9_21
| ~ spl9_80 ),
inference(superposition,[],[f952,f228]) ).
tff(f6408,plain,
( spl9_313
| ~ spl9_70
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f976,f947,f759,f6406]) ).
tff(f6406,plain,
( spl9_313
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_313])]) ).
tff(f759,plain,
( spl9_70
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_70])]) ).
tff(f976,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X0,X1))) )
| ~ spl9_70
| ~ spl9_79 ),
inference(superposition,[],[f760,f948]) ).
tff(f760,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl9_70 ),
inference(avatar_component_clause,[],[f759]) ).
tff(f6404,plain,
( spl9_312
| ~ spl9_35
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f971,f947,f312,f6402]) ).
tff(f6402,plain,
( spl9_312
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_312])]) ).
tff(f971,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $uminus($sum(X1,X0)) )
| ~ spl9_35
| ~ spl9_79 ),
inference(superposition,[],[f948,f313]) ).
tff(f6400,plain,
( spl9_311
| ~ spl9_26
| ~ spl9_73 ),
inference(avatar_split_clause,[],[f912,f810,f250,f6398]) ).
tff(f6398,plain,
( spl9_311
<=> ! [X0: $int,X1: $int] :
( $less($sum($uminus(X1),X0),0)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_311])]) ).
tff(f912,plain,
( ! [X0: $int,X1: $int] :
( $less($sum($uminus(X1),X0),0)
| ~ $less(X0,X1) )
| ~ spl9_26
| ~ spl9_73 ),
inference(superposition,[],[f811,f251]) ).
tff(f6396,plain,
( spl9_310
| ~ spl9_26
| ~ spl9_72 ),
inference(avatar_split_clause,[],[f904,f806,f250,f6394]) ).
tff(f6394,plain,
( spl9_310
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum($uminus(X1),X0))
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_310])]) ).
tff(f904,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum($uminus(X1),X0))
| ~ $less(X1,X0) )
| ~ spl9_26
| ~ spl9_72 ),
inference(superposition,[],[f807,f251]) ).
tff(f6392,plain,
( spl9_309
| ~ spl9_35
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f782,f759,f312,f6390]) ).
tff(f6390,plain,
( spl9_309
<=> ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_309])]) ).
tff(f782,plain,
( ! [X0: $int,X1: $int] : ( $uminus(X1) = $sum(X0,$uminus($sum(X1,X0))) )
| ~ spl9_35
| ~ spl9_70 ),
inference(superposition,[],[f760,f313]) ).
tff(f6388,plain,
( spl9_308
| ~ spl9_42
| ~ spl9_64 ),
inference(avatar_split_clause,[],[f728,f708,f374,f6386]) ).
tff(f6386,plain,
( spl9_308
<=> ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X0,$sum(X1,1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_308])]) ).
tff(f728,plain,
( ! [X0: $int,X1: $int] : $less($sum(X0,X1),$sum(X0,$sum(X1,1)))
| ~ spl9_42
| ~ spl9_64 ),
inference(superposition,[],[f709,f375]) ).
tff(f6374,plain,
( spl9_307
| ~ spl9_58
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f2916,f2881,f612,f6372]) ).
tff(f6372,plain,
( spl9_307
<=> ! [X0: $int,X1: $int] :
( $less($product(X1,$sum(X0,fact1(sK6))),$sum(sK7,$product(sK7,X0)))
| $less(sK7,X1)
| $less($sum(X0,fact1(sK6)),0)
| ( $sum(sK7,$product(sK7,X0)) = $product(X1,$sum(X0,fact1(sK6))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_307])]) ).
tff(f612,plain,
( spl9_58
<=> ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum(sK7,$product(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_58])]) ).
tff(f2881,plain,
( spl9_136
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,X2)
| $less($product(X2,X0),$product(X1,X0))
| ( $product(X1,X0) = $product(X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_136])]) ).
tff(f2916,plain,
( ! [X0: $int,X1: $int] :
( $less($product(X1,$sum(X0,fact1(sK6))),$sum(sK7,$product(sK7,X0)))
| $less(sK7,X1)
| $less($sum(X0,fact1(sK6)),0)
| ( $sum(sK7,$product(sK7,X0)) = $product(X1,$sum(X0,fact1(sK6))) ) )
| ~ spl9_58
| ~ spl9_136 ),
inference(superposition,[],[f2882,f613]) ).
tff(f613,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum(sK7,$product(sK7,X0)) )
| ~ spl9_58 ),
inference(avatar_component_clause,[],[f612]) ).
tff(f2882,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($product(X2,X0),$product(X1,X0))
| $less(X1,X2)
| $less(X0,0)
| ( $product(X1,X0) = $product(X2,X0) ) )
| ~ spl9_136 ),
inference(avatar_component_clause,[],[f2881]) ).
tff(f6360,plain,
( spl9_306
| ~ spl9_58
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f2905,f2881,f612,f6358]) ).
tff(f6358,plain,
( spl9_306
<=> ! [X0: $int,X1: $int] :
( $less($sum(sK7,$product(sK7,X0)),$product(X1,$sum(X0,fact1(sK6))))
| $less(X1,sK7)
| $less($sum(X0,fact1(sK6)),0)
| ( $sum(sK7,$product(sK7,X0)) = $product(X1,$sum(X0,fact1(sK6))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_306])]) ).
tff(f2905,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(sK7,$product(sK7,X0)),$product(X1,$sum(X0,fact1(sK6))))
| $less(X1,sK7)
| $less($sum(X0,fact1(sK6)),0)
| ( $sum(sK7,$product(sK7,X0)) = $product(X1,$sum(X0,fact1(sK6))) ) )
| ~ spl9_58
| ~ spl9_136 ),
inference(superposition,[],[f2882,f613]) ).
tff(f6356,plain,
( ~ spl9_305
| ~ spl9_54
| ~ spl9_280 ),
inference(avatar_split_clause,[],[f5563,f5464,f568,f6353]) ).
tff(f6353,plain,
( spl9_305
<=> $less(sK6,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_305])]) ).
tff(f5464,plain,
( spl9_280
<=> ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_280])]) ).
tff(f5563,plain,
( ~ $less(sK6,1)
| ~ spl9_54
| ~ spl9_280 ),
inference(resolution,[],[f5465,f570]) ).
tff(f570,plain,
( $less(0,sK6)
| ~ spl9_54 ),
inference(avatar_component_clause,[],[f568]) ).
tff(f5465,plain,
( ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) )
| ~ spl9_280 ),
inference(avatar_component_clause,[],[f5464]) ).
tff(f6298,plain,
( spl9_230
| ~ spl9_303 ),
inference(avatar_contradiction_clause,[],[f6297]) ).
tff(f6297,plain,
( $false
| spl9_230
| ~ spl9_303 ),
inference(evaluation,[],[f6270]) ).
tff(f6270,plain,
( ~ $less(-1,0)
| spl9_230
| ~ spl9_303 ),
inference(resolution,[],[f5776,f4816]) ).
tff(f4816,plain,
( ~ $less($sum(-1,sK6),sK6)
| spl9_230 ),
inference(avatar_component_clause,[],[f4814]) ).
tff(f4814,plain,
( spl9_230
<=> $less($sum(-1,sK6),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_230])]) ).
tff(f5776,plain,
( ! [X2: $int,X1: $int] :
( $less($sum(X2,X1),X1)
| ~ $less(X2,0) )
| ~ spl9_303 ),
inference(avatar_component_clause,[],[f5775]) ).
tff(f5775,plain,
( spl9_303
<=> ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_303])]) ).
tff(f5929,plain,
( ~ spl9_235
| ~ spl9_37
| ~ spl9_280 ),
inference(avatar_split_clause,[],[f5562,f5464,f320,f4854]) ).
tff(f4854,plain,
( spl9_235
<=> $less(sK5,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_235])]) ).
tff(f320,plain,
( spl9_37
<=> $less(0,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
tff(f5562,plain,
( ~ $less(sK5,1)
| ~ spl9_37
| ~ spl9_280 ),
inference(resolution,[],[f5465,f322]) ).
tff(f322,plain,
( $less(0,sK5)
| ~ spl9_37 ),
inference(avatar_component_clause,[],[f320]) ).
tff(f5781,plain,
( spl9_304
| ~ spl9_21
| ~ spl9_70
| ~ spl9_119 ),
inference(avatar_split_clause,[],[f2151,f1980,f759,f227,f5779]) ).
tff(f5779,plain,
( spl9_304
<=> ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_304])]) ).
tff(f1980,plain,
( spl9_119
<=> ! [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,[spl9_119])]) ).
tff(f2151,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(0,X2)
| $less(X1,$sum(X2,X1)) )
| ~ spl9_21
| ~ spl9_70
| ~ spl9_119 ),
inference(forward_demodulation,[],[f2127,f228]) ).
tff(f2127,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,$sum(X2,X1))
| ~ $less($sum(X0,$uminus(X0)),X2) )
| ~ spl9_70
| ~ spl9_119 ),
inference(superposition,[],[f1981,f760]) ).
tff(f1981,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl9_119 ),
inference(avatar_component_clause,[],[f1980]) ).
tff(f5777,plain,
( spl9_303
| ~ spl9_21
| ~ spl9_70
| ~ spl9_118 ),
inference(avatar_split_clause,[],[f2099,f1976,f759,f227,f5775]) ).
tff(f1976,plain,
( spl9_118
<=> ! [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,[spl9_118])]) ).
tff(f2099,plain,
( ! [X2: $int,X1: $int] :
( ~ $less(X2,0)
| $less($sum(X2,X1),X1) )
| ~ spl9_21
| ~ spl9_70
| ~ spl9_118 ),
inference(forward_demodulation,[],[f2090,f228]) ).
tff(f2090,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),X1)
| ~ $less(X2,$sum(X0,$uminus(X0))) )
| ~ spl9_70
| ~ spl9_118 ),
inference(superposition,[],[f1977,f760]) ).
tff(f1977,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl9_118 ),
inference(avatar_component_clause,[],[f1976]) ).
tff(f5773,plain,
( spl9_302
| ~ spl9_21
| ~ spl9_91 ),
inference(avatar_split_clause,[],[f1257,f1083,f227,f5771]) ).
tff(f5771,plain,
( spl9_302
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_302])]) ).
tff(f1083,plain,
( spl9_91
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_91])]) ).
tff(f1257,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 )
| ~ spl9_21
| ~ spl9_91 ),
inference(evaluation,[],[f1184]) ).
tff(f1184,plain,
( ! [X0: $int,X1: $int] : ( $sum(X1,0) = $sum($uminus(X0),$sum(X1,X0)) )
| ~ spl9_21
| ~ spl9_91 ),
inference(superposition,[],[f1084,f228]) ).
tff(f1084,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl9_91 ),
inference(avatar_component_clause,[],[f1083]) ).
tff(f5769,plain,
( spl9_301
| ~ spl9_21
| ~ spl9_90 ),
inference(avatar_split_clause,[],[f1175,f1079,f227,f5767]) ).
tff(f5767,plain,
( spl9_301
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_301])]) ).
tff(f1175,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 )
| ~ spl9_21
| ~ spl9_90 ),
inference(evaluation,[],[f1137]) ).
tff(f1137,plain,
( ! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum($uminus(X0),$sum(X0,X1)) )
| ~ spl9_21
| ~ spl9_90 ),
inference(superposition,[],[f1080,f228]) ).
tff(f5765,plain,
( spl9_300
| ~ spl9_66
| ~ spl9_84 ),
inference(avatar_split_clause,[],[f1050,f968,f732,f5763]) ).
tff(f5763,plain,
( spl9_300
<=> ! [X0: $int] :
( ~ even1($sum(2,X0))
| ~ even1($sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_300])]) ).
tff(f732,plain,
( spl9_66
<=> ! [X0: $int] :
( even1($sum(2,X0))
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_66])]) ).
tff(f1050,plain,
( ! [X0: $int] :
( ~ even1($sum(2,X0))
| ~ even1($sum(X0,1)) )
| ~ spl9_66
| ~ spl9_84 ),
inference(resolution,[],[f969,f733]) ).
tff(f733,plain,
( ! [X0: $int] :
( even1($sum(2,X0))
| ~ even1(X0) )
| ~ spl9_66 ),
inference(avatar_component_clause,[],[f732]) ).
tff(f5761,plain,
( spl9_299
| ~ spl9_67
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f1029,f964,f736,f5759]) ).
tff(f5759,plain,
( spl9_299
<=> ! [X0: $int] :
( ~ even1($sum(1,X0))
| ~ even1($sum(X0,2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_299])]) ).
tff(f736,plain,
( spl9_67
<=> ! [X0: $int] :
( ~ even1($sum(1,X0))
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_67])]) ).
tff(f1029,plain,
( ! [X0: $int] :
( ~ even1($sum(1,X0))
| ~ even1($sum(X0,2)) )
| ~ spl9_67
| ~ spl9_83 ),
inference(resolution,[],[f965,f737]) ).
tff(f737,plain,
( ! [X0: $int] :
( ~ even1($sum(1,X0))
| ~ even1(X0) )
| ~ spl9_67 ),
inference(avatar_component_clause,[],[f736]) ).
tff(f5757,plain,
( spl9_298
| ~ spl9_69
| ~ spl9_80 ),
inference(avatar_split_clause,[],[f988,f951,f755,f5755]) ).
tff(f5755,plain,
( spl9_298
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_298])]) ).
tff(f755,plain,
( spl9_69
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_69])]) ).
tff(f988,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) )
| ~ spl9_69
| ~ spl9_80 ),
inference(resolution,[],[f952,f756]) ).
tff(f756,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl9_69 ),
inference(avatar_component_clause,[],[f755]) ).
tff(f5748,plain,
( spl9_297
| ~ spl9_69
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f798,f759,f755,f5746]) ).
tff(f798,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) )
| ~ spl9_69
| ~ spl9_70 ),
inference(evaluation,[],[f793]) ).
tff(f793,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum($uminus(1),X0),X1) )
| ~ spl9_69
| ~ spl9_70 ),
inference(superposition,[],[f756,f760]) ).
tff(f5744,plain,
( spl9_296
| ~ spl9_68
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f797,f759,f751,f5742]) ).
tff(f5742,plain,
( spl9_296
<=> ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_296])]) ).
tff(f751,plain,
( spl9_68
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_68])]) ).
tff(f797,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) )
| ~ spl9_68
| ~ spl9_70 ),
inference(evaluation,[],[f794]) ).
tff(f794,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum($uminus(1),X0),X1) )
| ~ spl9_68
| ~ spl9_70 ),
inference(superposition,[],[f752,f760]) ).
tff(f752,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl9_68 ),
inference(avatar_component_clause,[],[f751]) ).
tff(f5740,plain,
( spl9_295
| ~ spl9_26
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f784,f759,f250,f5738]) ).
tff(f5738,plain,
( spl9_295
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_295])]) ).
tff(f784,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 )
| ~ spl9_26
| ~ spl9_70 ),
inference(superposition,[],[f760,f251]) ).
tff(f5736,plain,
( spl9_294
| ~ spl9_38
| ~ spl9_69 ),
inference(avatar_split_clause,[],[f777,f755,f325,f5734]) ).
tff(f5734,plain,
( spl9_294
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_294])]) ).
tff(f325,plain,
( spl9_38
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
tff(f777,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) )
| ~ spl9_38
| ~ spl9_69 ),
inference(resolution,[],[f756,f326]) ).
tff(f326,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl9_38 ),
inference(avatar_component_clause,[],[f325]) ).
tff(f5732,plain,
( spl9_293
| ~ spl9_33
| ~ spl9_64 ),
inference(avatar_split_clause,[],[f725,f708,f292,f5730]) ).
tff(f5730,plain,
( spl9_293
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_293])]) ).
tff(f292,plain,
( spl9_33
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
tff(f725,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) )
| ~ spl9_33
| ~ spl9_64 ),
inference(resolution,[],[f709,f293]) ).
tff(f293,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f292]) ).
tff(f5720,plain,
( spl9_292
| ~ spl9_57
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f2915,f2881,f595,f5718]) ).
tff(f5718,plain,
( spl9_292
<=> ! [X0: $int,X1: $int] :
( $less($product(X1,$product(fact1(sK6),X0)),$product(sK7,X0))
| $less(sK7,X1)
| $less($product(fact1(sK6),X0),0)
| ( $product(sK7,X0) = $product(X1,$product(fact1(sK6),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_292])]) ).
tff(f595,plain,
( spl9_57
<=> ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(sK7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_57])]) ).
tff(f2915,plain,
( ! [X0: $int,X1: $int] :
( $less($product(X1,$product(fact1(sK6),X0)),$product(sK7,X0))
| $less(sK7,X1)
| $less($product(fact1(sK6),X0),0)
| ( $product(sK7,X0) = $product(X1,$product(fact1(sK6),X0)) ) )
| ~ spl9_57
| ~ spl9_136 ),
inference(superposition,[],[f2882,f596]) ).
tff(f596,plain,
( ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(sK7,X0) )
| ~ spl9_57 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f5708,plain,
( spl9_291
| ~ spl9_57
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f2904,f2881,f595,f5706]) ).
tff(f5706,plain,
( spl9_291
<=> ! [X0: $int,X1: $int] :
( $less($product(sK7,X0),$product(X1,$product(fact1(sK6),X0)))
| $less(X1,sK7)
| $less($product(fact1(sK6),X0),0)
| ( $product(sK7,X0) = $product(X1,$product(fact1(sK6),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_291])]) ).
tff(f2904,plain,
( ! [X0: $int,X1: $int] :
( $less($product(sK7,X0),$product(X1,$product(fact1(sK6),X0)))
| $less(X1,sK7)
| $less($product(fact1(sK6),X0),0)
| ( $product(sK7,X0) = $product(X1,$product(fact1(sK6),X0)) ) )
| ~ spl9_57
| ~ spl9_136 ),
inference(superposition,[],[f2882,f596]) ).
tff(f5696,plain,
( spl9_290
| ~ spl9_69
| ~ spl9_72 ),
inference(avatar_split_clause,[],[f900,f806,f755,f5694]) ).
tff(f5694,plain,
( spl9_290
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_290])]) ).
tff(f900,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl9_69
| ~ spl9_72 ),
inference(resolution,[],[f807,f756]) ).
tff(f5686,plain,
( spl9_289
| ~ spl9_58
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2859,f2690,f612,f5684]) ).
tff(f5684,plain,
( spl9_289
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) != $product($sum(sK7,$product(sK7,X0)),X2) )
| ( 0 = $sum(sK7,$product(sK7,X0)) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_289])]) ).
tff(f2690,plain,
( spl9_135
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ( $product(X0,$product(X1,X2)) != $product($product(X0,X1),X3) )
| ( 0 = $product(X0,X1) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_135])]) ).
tff(f2859,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) != $product($sum(sK7,$product(sK7,X0)),X2) )
| ( 0 = $sum(sK7,$product(sK7,X0)) )
| ( X1 = X2 ) )
| ~ spl9_58
| ~ spl9_135 ),
inference(superposition,[],[f2691,f613]) ).
tff(f2691,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $product(X0,$product(X1,X2)) != $product($product(X0,X1),X3) )
| ( 0 = $product(X0,X1) )
| ( X2 = X3 ) )
| ~ spl9_135 ),
inference(avatar_component_clause,[],[f2690]) ).
tff(f5682,plain,
( spl9_288
| spl9_2
| ~ spl9_276 ),
inference(avatar_split_clause,[],[f5481,f5448,f133,f5679]) ).
tff(f5679,plain,
( spl9_288
<=> $less(-1,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_288])]) ).
tff(f133,plain,
( spl9_2
<=> $less(sK6,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
tff(f5448,plain,
( spl9_276
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_276])]) ).
tff(f5481,plain,
( $less(-1,sK6)
| spl9_2
| ~ spl9_276 ),
inference(resolution,[],[f5449,f135]) ).
tff(f135,plain,
( ~ $less(sK6,0)
| spl9_2 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f5449,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl9_276 ),
inference(avatar_component_clause,[],[f5448]) ).
tff(f5670,plain,
( spl9_287
| ~ spl9_58
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f2659,f2430,f612,f5668]) ).
tff(f5668,plain,
( spl9_287
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(X0,fact1(sK6))),$product(X2,$sum(sK7,$product(sK7,X0))))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,$product(X2,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_287])]) ).
tff(f2430,plain,
( spl9_133
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($product(X3,X2),$product(X0,$product(X1,X2)))
| $less(X2,0)
| $less(X3,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_133])]) ).
tff(f2659,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(X0,fact1(sK6))),$product(X2,$sum(sK7,$product(sK7,X0))))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,$product(X2,sK7)) )
| ~ spl9_58
| ~ spl9_133 ),
inference(superposition,[],[f2431,f613]) ).
tff(f2431,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($product(X3,X2),$product(X0,$product(X1,X2)))
| $less(X2,0)
| $less(X3,$product(X0,X1)) )
| ~ spl9_133 ),
inference(avatar_component_clause,[],[f2430]) ).
tff(f5660,plain,
( spl9_286
| ~ spl9_58
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f2648,f2430,f612,f5658]) ).
tff(f5658,plain,
( spl9_286
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,$product(X2,$sum(X0,fact1(sK6)))))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,$product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_286])]) ).
tff(f2648,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,$product(X2,$sum(X0,fact1(sK6)))))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,$product(X1,X2)) )
| ~ spl9_58
| ~ spl9_133 ),
inference(superposition,[],[f2431,f613]) ).
tff(f5650,plain,
( spl9_285
| ~ spl9_58
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f2618,f2426,f612,f5648]) ).
tff(f5648,plain,
( spl9_285
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X2,$sum(X0,fact1(sK6)))),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less($product(X1,X2),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_285])]) ).
tff(f2426,plain,
( spl9_132
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less($product(X0,$product(X1,X2)),$product(X3,X2))
| $less(X2,0)
| $less($product(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_132])]) ).
tff(f2618,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X2,$sum(X0,fact1(sK6)))),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less($product(X1,X2),sK7) )
| ~ spl9_58
| ~ spl9_132 ),
inference(superposition,[],[f2427,f613]) ).
tff(f2427,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($product(X0,$product(X1,X2)),$product(X3,X2))
| $less(X2,0)
| $less($product(X0,X1),X3) )
| ~ spl9_132 ),
inference(avatar_component_clause,[],[f2426]) ).
tff(f5639,plain,
( spl9_284
| ~ spl9_58
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f2599,f2426,f612,f5637]) ).
tff(f5637,plain,
( spl9_284
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(sK7,$product(sK7,X0))),$product(X2,$sum(X0,fact1(sK6))))
| $less($sum(X0,fact1(sK6)),0)
| $less($product(X1,sK7),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_284])]) ).
tff(f2599,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(sK7,$product(sK7,X0))),$product(X2,$sum(X0,fact1(sK6))))
| $less($sum(X0,fact1(sK6)),0)
| $less($product(X1,sK7),X2) )
| ~ spl9_58
| ~ spl9_132 ),
inference(superposition,[],[f2427,f613]) ).
tff(f5518,plain,
( spl9_283
| spl9_1
| ~ spl9_276 ),
inference(avatar_split_clause,[],[f5480,f5448,f128,f5515]) ).
tff(f5515,plain,
( spl9_283
<=> $less(-1,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_283])]) ).
tff(f128,plain,
( spl9_1
<=> $less(sK5,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
tff(f5480,plain,
( $less(-1,sK5)
| spl9_1
| ~ spl9_276 ),
inference(resolution,[],[f5449,f130]) ).
tff(f130,plain,
( ~ $less(sK5,0)
| spl9_1 ),
inference(avatar_component_clause,[],[f128]) ).
tff(f5475,plain,
( spl9_282
| ~ spl9_3
| ~ spl9_129 ),
inference(avatar_split_clause,[],[f2456,f2414,f138,f5472]) ).
tff(f5472,plain,
( spl9_282
<=> ( 2 = $sum(2,sK8(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_282])]) ).
tff(f138,plain,
( spl9_3
<=> even1(0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
tff(f2414,plain,
( spl9_129
<=> ! [X0: $int] :
( ( 0 = $sum(X0,2) )
| ( $sum(X0,2) = $sum(2,sK8($sum(X0,2))) )
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_129])]) ).
tff(f2456,plain,
( ( 2 = $sum(2,sK8(2)) )
| ~ spl9_3
| ~ spl9_129 ),
inference(evaluation,[],[f2448]) ).
tff(f2448,plain,
( ( $sum(0,2) = $sum(2,sK8($sum(0,2))) )
| ( 0 = $sum(0,2) )
| ~ spl9_3
| ~ spl9_129 ),
inference(resolution,[],[f2415,f140]) ).
tff(f140,plain,
( even1(0)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f138]) ).
tff(f2415,plain,
( ! [X0: $int] :
( ~ even1(X0)
| ( $sum(X0,2) = $sum(2,sK8($sum(X0,2))) )
| ( 0 = $sum(X0,2) ) )
| ~ spl9_129 ),
inference(avatar_component_clause,[],[f2414]) ).
tff(f5470,plain,
( spl9_281
| ~ spl9_21
| ~ spl9_70
| ~ spl9_101 ),
inference(avatar_split_clause,[],[f1524,f1446,f759,f227,f5468]) ).
tff(f5468,plain,
( spl9_281
<=> ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_281])]) ).
tff(f1446,plain,
( spl9_101
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_101])]) ).
tff(f1524,plain,
( ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) )
| ~ spl9_21
| ~ spl9_70
| ~ spl9_101 ),
inference(forward_demodulation,[],[f1515,f228]) ).
tff(f1515,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less($sum(X0,$uminus(X0)),X1) )
| ~ spl9_70
| ~ spl9_101 ),
inference(superposition,[],[f1447,f760]) ).
tff(f1447,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl9_101 ),
inference(avatar_component_clause,[],[f1446]) ).
tff(f5466,plain,
( spl9_280
| ~ spl9_21
| ~ spl9_70
| ~ spl9_100 ),
inference(avatar_split_clause,[],[f1499,f1442,f759,f227,f5464]) ).
tff(f1442,plain,
( spl9_100
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_100])]) ).
tff(f1499,plain,
( ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) )
| ~ spl9_21
| ~ spl9_70
| ~ spl9_100 ),
inference(forward_demodulation,[],[f1491,f228]) ).
tff(f1491,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,1)
| ~ $less($sum(X0,$uminus(X0)),X1) )
| ~ spl9_70
| ~ spl9_100 ),
inference(superposition,[],[f1443,f760]) ).
tff(f1443,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl9_100 ),
inference(avatar_component_clause,[],[f1442]) ).
tff(f5462,plain,
( spl9_279
| ~ spl9_66
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f799,f759,f732,f5460]) ).
tff(f5460,plain,
( spl9_279
<=> ! [X0: $int] :
( even1(X0)
| ~ even1($sum(-2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_279])]) ).
tff(f799,plain,
( ! [X0: $int] :
( even1(X0)
| ~ even1($sum(-2,X0)) )
| ~ spl9_66
| ~ spl9_70 ),
inference(evaluation,[],[f791]) ).
tff(f791,plain,
( ! [X0: $int] :
( even1(X0)
| ~ even1($sum($uminus(2),X0)) )
| ~ spl9_66
| ~ spl9_70 ),
inference(superposition,[],[f733,f760]) ).
tff(f5458,plain,
( spl9_278
| ~ spl9_67
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f796,f759,f736,f5456]) ).
tff(f5456,plain,
( spl9_278
<=> ! [X0: $int] :
( ~ even1(X0)
| ~ even1($sum(-1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_278])]) ).
tff(f796,plain,
( ! [X0: $int] :
( ~ even1(X0)
| ~ even1($sum(-1,X0)) )
| ~ spl9_67
| ~ spl9_70 ),
inference(evaluation,[],[f795]) ).
tff(f795,plain,
( ! [X0: $int] :
( ~ even1(X0)
| ~ even1($sum($uminus(1),X0)) )
| ~ spl9_67
| ~ spl9_70 ),
inference(superposition,[],[f737,f760]) ).
tff(f5454,plain,
( spl9_277
| ~ spl9_21
| ~ spl9_69 ),
inference(avatar_split_clause,[],[f781,f755,f227,f5452]) ).
tff(f5452,plain,
( spl9_277
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_277])]) ).
tff(f781,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) )
| ~ spl9_21
| ~ spl9_69 ),
inference(evaluation,[],[f778]) ).
tff(f778,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) )
| ~ spl9_21
| ~ spl9_69 ),
inference(superposition,[],[f756,f228]) ).
tff(f5450,plain,
( spl9_276
| ~ spl9_21
| ~ spl9_68 ),
inference(avatar_split_clause,[],[f769,f751,f227,f5448]) ).
tff(f769,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl9_21
| ~ spl9_68 ),
inference(evaluation,[],[f766]) ).
tff(f766,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl9_21
| ~ spl9_68 ),
inference(superposition,[],[f752,f228]) ).
tff(f5441,plain,
( spl9_275
| ~ spl9_58
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2840,f2690,f612,f5439]) ).
tff(f5439,plain,
( spl9_275
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,$sum(sK7,$product(sK7,X0))) != $product($product(X1,sK7),X2) )
| ( 0 = $product(X1,sK7) )
| ( $sum(X0,fact1(sK6)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_275])]) ).
tff(f2840,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,$sum(sK7,$product(sK7,X0))) != $product($product(X1,sK7),X2) )
| ( 0 = $product(X1,sK7) )
| ( $sum(X0,fact1(sK6)) = X2 ) )
| ~ spl9_58
| ~ spl9_135 ),
inference(superposition,[],[f2691,f613]) ).
tff(f5318,plain,
( spl9_274
| ~ spl9_53
| ~ spl9_164
| ~ spl9_273 ),
inference(avatar_split_clause,[],[f5314,f5309,f3530,f556,f5316]) ).
tff(f5316,plain,
( spl9_274
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X1,$sum(1,$sum(X2,X0))) = $sum($product(X1,X2),$product(X1,$sum(1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_274])]) ).
tff(f556,plain,
( spl9_53
<=> ( 1 = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
tff(f3530,plain,
( spl9_164
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$product(X0,X1)) = $product(X0,$sum(1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_164])]) ).
tff(f5309,plain,
( spl9_273
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(X1,$product(sK7,X2)),$product(X1,$sum(sK7,$product(sK7,X0)))) = $product(X1,$sum(sK7,$product(sK7,$sum(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_273])]) ).
tff(f5314,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X1,$sum(1,$sum(X2,X0))) = $sum($product(X1,X2),$product(X1,$sum(1,X0))) )
| ~ spl9_53
| ~ spl9_164
| ~ spl9_273 ),
inference(evaluation,[],[f5313]) ).
tff(f5313,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(X1,$product(1,X2)),$product(X1,$sum(1,$product(1,X0)))) = $product(X1,$product(1,$sum(1,$sum(X2,X0)))) )
| ~ spl9_53
| ~ spl9_164
| ~ spl9_273 ),
inference(forward_demodulation,[],[f5312,f558]) ).
tff(f558,plain,
( ( 1 = sK7 )
| ~ spl9_53 ),
inference(avatar_component_clause,[],[f556]) ).
tff(f5312,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(X1,$product(sK7,X2)),$product(X1,$sum(sK7,$product(sK7,X0)))) = $product(X1,$product(sK7,$sum(1,$sum(X2,X0)))) )
| ~ spl9_164
| ~ spl9_273 ),
inference(forward_demodulation,[],[f5310,f3531]) ).
tff(f3531,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$product(X0,X1)) = $product(X0,$sum(1,X1)) )
| ~ spl9_164 ),
inference(avatar_component_clause,[],[f3530]) ).
tff(f5310,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(X1,$product(sK7,X2)),$product(X1,$sum(sK7,$product(sK7,X0)))) = $product(X1,$sum(sK7,$product(sK7,$sum(X2,X0)))) )
| ~ spl9_273 ),
inference(avatar_component_clause,[],[f5309]) ).
tff(f5311,plain,
( spl9_273
| ~ spl9_42
| ~ spl9_58
| ~ spl9_134 ),
inference(avatar_split_clause,[],[f2806,f2686,f612,f374,f5309]) ).
tff(f2686,plain,
( spl9_134
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($product(X0,$product(X1,X2)),$product(X0,$product(X1,X3))) = $product(X0,$product(X1,$sum(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_134])]) ).
tff(f2806,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(X1,$product(sK7,X2)),$product(X1,$sum(sK7,$product(sK7,X0)))) = $product(X1,$sum(sK7,$product(sK7,$sum(X2,X0)))) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_134 ),
inference(forward_demodulation,[],[f2722,f642]) ).
tff(f642,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X0,$sum(X1,fact1(sK6)))) )
| ~ spl9_42
| ~ spl9_58 ),
inference(superposition,[],[f613,f375]) ).
tff(f2722,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X1,$product(sK7,$sum(X2,$sum(X0,fact1(sK6))))) = $sum($product(X1,$product(sK7,X2)),$product(X1,$sum(sK7,$product(sK7,X0)))) )
| ~ spl9_58
| ~ spl9_134 ),
inference(superposition,[],[f2687,f613]) ).
tff(f2687,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,$product(X1,X2)),$product(X0,$product(X1,X3))) = $product(X0,$product(X1,$sum(X2,X3))) )
| ~ spl9_134 ),
inference(avatar_component_clause,[],[f2686]) ).
tff(f5301,plain,
( spl9_272
| ~ spl9_57
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f2658,f2430,f595,f5299]) ).
tff(f5299,plain,
( spl9_272
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(fact1(sK6),X0)),$product(X2,$product(sK7,X0)))
| $less($product(fact1(sK6),X0),0)
| $less(X1,$product(X2,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_272])]) ).
tff(f2658,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(fact1(sK6),X0)),$product(X2,$product(sK7,X0)))
| $less($product(fact1(sK6),X0),0)
| $less(X1,$product(X2,sK7)) )
| ~ spl9_57
| ~ spl9_133 ),
inference(superposition,[],[f2431,f596]) ).
tff(f5292,plain,
( spl9_271
| ~ spl9_57
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f2647,f2430,f595,f5290]) ).
tff(f5290,plain,
( spl9_271
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,$product(X2,$product(fact1(sK6),X0))))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,$product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_271])]) ).
tff(f2647,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,$product(X2,$product(fact1(sK6),X0))))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,$product(X1,X2)) )
| ~ spl9_57
| ~ spl9_133 ),
inference(superposition,[],[f2431,f596]) ).
tff(f5283,plain,
( spl9_270
| ~ spl9_57
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f2617,f2426,f595,f5281]) ).
tff(f5281,plain,
( spl9_270
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X2,$product(fact1(sK6),X0))),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less($product(X1,X2),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_270])]) ).
tff(f2617,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X2,$product(fact1(sK6),X0))),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less($product(X1,X2),sK7) )
| ~ spl9_57
| ~ spl9_132 ),
inference(superposition,[],[f2427,f596]) ).
tff(f5273,plain,
( spl9_269
| ~ spl9_57
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f2598,f2426,f595,f5271]) ).
tff(f5271,plain,
( spl9_269
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(sK7,X0)),$product(X2,$product(fact1(sK6),X0)))
| $less($product(fact1(sK6),X0),0)
| $less($product(X1,sK7),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_269])]) ).
tff(f2598,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(sK7,X0)),$product(X2,$product(fact1(sK6),X0)))
| $less($product(fact1(sK6),X0),0)
| $less($product(X1,sK7),X2) )
| ~ spl9_57
| ~ spl9_132 ),
inference(superposition,[],[f2427,f596]) ).
tff(f5263,plain,
( spl9_268
| ~ spl9_43
| ~ spl9_57
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2878,f2690,f595,f382,f5261]) ).
tff(f5261,plain,
( spl9_268
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(sK7,$product(fact1(sK6),$product(X0,X1))) != $product($product(sK7,X0),X2) )
| ( 0 = $product(sK7,X0) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_268])]) ).
tff(f382,plain,
( spl9_43
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
tff(f2878,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(sK7,$product(fact1(sK6),$product(X0,X1))) != $product($product(sK7,X0),X2) )
| ( 0 = $product(sK7,X0) )
| ( X1 = X2 ) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2858,f383]) ).
tff(f383,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) )
| ~ spl9_43 ),
inference(avatar_component_clause,[],[f382]) ).
tff(f2858,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(sK7,$product($product(fact1(sK6),X0),X1)) != $product($product(sK7,X0),X2) )
| ( 0 = $product(sK7,X0) )
| ( X1 = X2 ) )
| ~ spl9_57
| ~ spl9_135 ),
inference(superposition,[],[f2691,f596]) ).
tff(f5253,plain,
( spl9_267
| ~ spl9_57
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2839,f2690,f595,f5251]) ).
tff(f5251,plain,
( spl9_267
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,$product(sK7,X0)) != $product($product(X1,sK7),X2) )
| ( 0 = $product(X1,sK7) )
| ( $product(fact1(sK6),X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_267])]) ).
tff(f2839,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,$product(sK7,X0)) != $product($product(X1,sK7),X2) )
| ( 0 = $product(X1,sK7) )
| ( $product(fact1(sK6),X0) = X2 ) )
| ~ spl9_57
| ~ spl9_135 ),
inference(superposition,[],[f2691,f596]) ).
tff(f5246,plain,
( spl9_266
| ~ spl9_42
| ~ spl9_58
| ~ spl9_131 ),
inference(avatar_split_clause,[],[f2562,f2422,f612,f374,f5244]) ).
tff(f5244,plain,
( spl9_266
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,X1),$sum(sK7,$sum($product(sK7,X0),X2))) = $sum(sK7,$sum($product(sK7,$sum(X1,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_266])]) ).
tff(f2422,plain,
( spl9_131
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] : ( $sum($product(X0,X1),$sum($product(X0,X2),X3)) = $sum($product(X0,$sum(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_131])]) ).
tff(f2562,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,X1),$sum(sK7,$sum($product(sK7,X0),X2))) = $sum(sK7,$sum($product(sK7,$sum(X1,X0)),X2)) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2561,f375]) ).
tff(f2561,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,X1),$sum(sK7,$sum($product(sK7,X0),X2))) = $sum($sum(sK7,$product(sK7,$sum(X1,X0))),X2) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2560,f642]) ).
tff(f2560,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X1,$sum(X0,fact1(sK6)))),X2) = $sum($product(sK7,X1),$sum(sK7,$sum($product(sK7,X0),X2))) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2485,f375]) ).
tff(f2485,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X1,$sum(X0,fact1(sK6)))),X2) = $sum($product(sK7,X1),$sum($sum(sK7,$product(sK7,X0)),X2)) )
| ~ spl9_58
| ~ spl9_131 ),
inference(superposition,[],[f2423,f613]) ).
tff(f2423,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,X1),$sum($product(X0,X2),X3)) = $sum($product(X0,$sum(X1,X2)),X3) )
| ~ spl9_131 ),
inference(avatar_component_clause,[],[f2422]) ).
tff(f5239,plain,
( spl9_265
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111
| ~ spl9_131 ),
inference(avatar_split_clause,[],[f2546,f2422,f1566,f1083,f612,f468,f374,f5237]) ).
tff(f5237,plain,
( spl9_265
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$sum($product(sK7,X1),X2)) = $sum(sK7,$sum($product(sK7,$sum(X0,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_265])]) ).
tff(f468,plain,
( spl9_49
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
tff(f1566,plain,
( spl9_111
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X2),$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_111])]) ).
tff(f2546,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$sum($product(sK7,X1),X2)) = $sum(sK7,$sum($product(sK7,$sum(X0,X1)),X2)) )
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2545,f375]) ).
tff(f2545,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$sum($product(sK7,X1),X2)) = $sum($sum(sK7,$product(sK7,$sum(X0,X1))),X2) )
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2544,f1882]) ).
tff(f1882,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) )
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111 ),
inference(forward_demodulation,[],[f1881,f375]) ).
tff(f1881,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum($sum(X0,fact1(sK6)),X1)) )
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111 ),
inference(forward_demodulation,[],[f1839,f1190]) ).
tff(f1190,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum(X3,$product(X0,$sum(X1,X2))) = $sum($product(X0,X2),$sum(X3,$product(X0,X1))) )
| ~ spl9_49
| ~ spl9_91 ),
inference(superposition,[],[f1084,f469]) ).
tff(f469,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) )
| ~ spl9_49 ),
inference(avatar_component_clause,[],[f468]) ).
tff(f1839,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($sum(X0,fact1(sK6)),X1)) = $sum($product(sK7,X1),$sum(sK7,$product(sK7,X0))) )
| ~ spl9_58
| ~ spl9_111 ),
inference(superposition,[],[f1567,f613]) ).
tff(f1567,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X2),$product(X0,X1)) )
| ~ spl9_111 ),
inference(avatar_component_clause,[],[f1566]) ).
tff(f2544,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$sum($product(sK7,X1),X2)) = $sum($product(sK7,$sum(X0,$sum(fact1(sK6),X1))),X2) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2474,f375]) ).
tff(f2474,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum($sum(X0,fact1(sK6)),X1)),X2) = $sum($sum(sK7,$product(sK7,X0)),$sum($product(sK7,X1),X2)) )
| ~ spl9_58
| ~ spl9_131 ),
inference(superposition,[],[f2423,f613]) ).
tff(f5235,plain,
( spl9_264
| ~ spl9_33
| ~ spl9_235 ),
inference(avatar_split_clause,[],[f4941,f4854,f292,f5233]) ).
tff(f5233,plain,
( spl9_264
<=> ! [X0: $int] :
( ~ $less(X0,sK5)
| $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_264])]) ).
tff(f4941,plain,
( ! [X0: $int] :
( ~ $less(X0,sK5)
| $less(X0,1) )
| ~ spl9_33
| ~ spl9_235 ),
inference(resolution,[],[f4856,f293]) ).
tff(f4856,plain,
( $less(sK5,1)
| ~ spl9_235 ),
inference(avatar_component_clause,[],[f4854]) ).
tff(f5225,plain,
( spl9_263
| ~ spl9_58
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f1927,f1574,f612,f5223]) ).
tff(f5223,plain,
( spl9_263
<=> ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product($sum(X0,fact1(sK6)),X1))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_263])]) ).
tff(f1574,plain,
( spl9_113
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X2,X1),$product(X1,X0))
| $less(X1,0)
| $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_113])]) ).
tff(f1927,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product($sum(X0,fact1(sK6)),X1))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,X1) )
| ~ spl9_58
| ~ spl9_113 ),
inference(superposition,[],[f1575,f613]) ).
tff(f1575,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X2,X1),$product(X1,X0))
| $less(X1,0)
| $less(X2,X0) )
| ~ spl9_113 ),
inference(avatar_component_clause,[],[f1574]) ).
tff(f5215,plain,
( spl9_262
| ~ spl9_58
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1906,f1570,f612,f5213]) ).
tff(f5213,plain,
( spl9_262
<=> ! [X0: $int,X1: $int] :
( ~ $less($product($sum(X0,fact1(sK6)),X1),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_262])]) ).
tff(f1570,plain,
( spl9_112
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X0),$product(X2,X1))
| $less(X1,0)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_112])]) ).
tff(f1906,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product($sum(X0,fact1(sK6)),X1),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,sK7) )
| ~ spl9_58
| ~ spl9_112 ),
inference(superposition,[],[f1571,f613]) ).
tff(f1571,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X0),$product(X2,X1))
| $less(X1,0)
| $less(X0,X2) )
| ~ spl9_112 ),
inference(avatar_component_clause,[],[f1570]) ).
tff(f5208,plain,
( spl9_261
| ~ spl9_58
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1781,f1562,f612,f5206]) ).
tff(f5206,plain,
( spl9_261
<=> ! [X0: $int,X1: $int] : ( $sum($product($sum(X0,fact1(sK6)),X1),$sum(sK7,$product(sK7,X0))) = $product($sum(X0,fact1(sK6)),$sum(X1,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_261])]) ).
tff(f1562,plain,
( spl9_110
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X2,X1)) = $sum($product(X0,X2),$product(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_110])]) ).
tff(f1781,plain,
( ! [X0: $int,X1: $int] : ( $sum($product($sum(X0,fact1(sK6)),X1),$sum(sK7,$product(sK7,X0))) = $product($sum(X0,fact1(sK6)),$sum(X1,sK7)) )
| ~ spl9_58
| ~ spl9_110 ),
inference(superposition,[],[f1563,f613]) ).
tff(f1563,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X2,X1)) = $sum($product(X0,X2),$product(X1,X0)) )
| ~ spl9_110 ),
inference(avatar_component_clause,[],[f1562]) ).
tff(f5202,plain,
( spl9_260
| ~ spl9_58
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1713,f1554,f612,f5200]) ).
tff(f5200,plain,
( spl9_260
<=> ! [X0: $int,X1: $int] : ( $product($sum(X0,fact1(sK6)),$sum(sK7,X1)) = $sum($sum(sK7,$product(sK7,X0)),$product($sum(X0,fact1(sK6)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_260])]) ).
tff(f1554,plain,
( spl9_109
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X1,X0),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_109])]) ).
tff(f1713,plain,
( ! [X0: $int,X1: $int] : ( $product($sum(X0,fact1(sK6)),$sum(sK7,X1)) = $sum($sum(sK7,$product(sK7,X0)),$product($sum(X0,fact1(sK6)),X1)) )
| ~ spl9_58
| ~ spl9_109 ),
inference(superposition,[],[f1555,f613]) ).
tff(f1555,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X1,X0),$product(X0,X2)) )
| ~ spl9_109 ),
inference(avatar_component_clause,[],[f1554]) ).
tff(f5192,plain,
( spl9_259
| ~ spl9_50
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f647,f612,f472,f5190]) ).
tff(f5190,plain,
( spl9_259
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(X0,fact1(sK6))),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_259])]) ).
tff(f472,plain,
( spl9_50
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
tff(f647,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$sum(X0,fact1(sK6))),$sum(sK7,$product(sK7,X0)))
| $less($sum(X0,fact1(sK6)),0)
| $less(X1,sK7) )
| ~ spl9_50
| ~ spl9_58 ),
inference(superposition,[],[f473,f613]) ).
tff(f473,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) )
| ~ spl9_50 ),
inference(avatar_component_clause,[],[f472]) ).
tff(f5182,plain,
( spl9_258
| ~ spl9_50
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f646,f612,f472,f5180]) ).
tff(f5180,plain,
( spl9_258
<=> ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,$sum(X0,fact1(sK6))))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_258])]) ).
tff(f646,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,$sum(X0,fact1(sK6))))
| $less($sum(X0,fact1(sK6)),0)
| $less(sK7,X1) )
| ~ spl9_50
| ~ spl9_58 ),
inference(superposition,[],[f473,f613]) ).
tff(f5159,plain,
( spl9_257
| ~ spl9_26
| ~ spl9_64 ),
inference(avatar_split_clause,[],[f726,f708,f250,f5157]) ).
tff(f5157,plain,
( spl9_257
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_257])]) ).
tff(f726,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl9_26
| ~ spl9_64 ),
inference(superposition,[],[f709,f251]) ).
tff(f5150,plain,
( spl9_256
| ~ spl9_42
| ~ spl9_58
| ~ spl9_126 ),
inference(avatar_split_clause,[],[f2408,f2252,f612,f374,f5148]) ).
tff(f5148,plain,
( spl9_256
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(sK7,$product(sK7,$sum(X1,X0))),$sum(X2,$sum(sK7,$product(sK7,X0))))
| ~ $less($product(sK7,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_256])]) ).
tff(f2252,plain,
( spl9_126
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($product(X0,$sum(X1,X2)),$sum(X3,$product(X0,X2)))
| ~ $less($product(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_126])]) ).
tff(f2408,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(sK7,$product(sK7,$sum(X1,X0))),$sum(X2,$sum(sK7,$product(sK7,X0))))
| ~ $less($product(sK7,X1),X2) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_126 ),
inference(forward_demodulation,[],[f2378,f642]) ).
tff(f2378,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($product(sK7,$sum(X1,$sum(X0,fact1(sK6)))),$sum(X2,$sum(sK7,$product(sK7,X0))))
| ~ $less($product(sK7,X1),X2) )
| ~ spl9_58
| ~ spl9_126 ),
inference(superposition,[],[f2253,f613]) ).
tff(f2253,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($product(X0,$sum(X1,X2)),$sum(X3,$product(X0,X2)))
| ~ $less($product(X0,X1),X3) )
| ~ spl9_126 ),
inference(avatar_component_clause,[],[f2252]) ).
tff(f5141,plain,
( spl9_255
| ~ spl9_42
| ~ spl9_58
| ~ spl9_125 ),
inference(avatar_split_clause,[],[f2309,f2248,f612,f374,f5139]) ).
tff(f5139,plain,
( spl9_255
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(sK7,$product(sK7,X0))),$sum(sK7,$product(sK7,$sum(X2,X0))))
| ~ $less(X1,$product(sK7,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_255])]) ).
tff(f2248,plain,
( spl9_125
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,$product(X0,X2)),$product(X0,$sum(X1,X2)))
| ~ $less(X3,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_125])]) ).
tff(f2309,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(sK7,$product(sK7,X0))),$sum(sK7,$product(sK7,$sum(X2,X0))))
| ~ $less(X1,$product(sK7,X2)) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_125 ),
inference(forward_demodulation,[],[f2268,f642]) ).
tff(f2268,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,$sum(sK7,$product(sK7,X0))),$product(sK7,$sum(X2,$sum(X0,fact1(sK6)))))
| ~ $less(X1,$product(sK7,X2)) )
| ~ spl9_58
| ~ spl9_125 ),
inference(superposition,[],[f2249,f613]) ).
tff(f2249,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$product(X0,X2)),$product(X0,$sum(X1,X2)))
| ~ $less(X3,$product(X0,X1)) )
| ~ spl9_125 ),
inference(avatar_component_clause,[],[f2248]) ).
tff(f5130,plain,
( spl9_62
| spl9_254
| ~ spl9_4
| ~ spl9_7
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f2925,f2881,f162,f143,f5128,f683]) ).
tff(f683,plain,
( spl9_62
<=> $less(fact1(sK6),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_62])]) ).
tff(f5128,plain,
( spl9_254
<=> ! [X0: $int] :
( ( sK7 = $product(X0,fact1(sK6)) )
| $less(sK7,X0)
| $less($product(X0,fact1(sK6)),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_254])]) ).
tff(f143,plain,
( spl9_4
<=> ( fact1(sK5) = $product(sK7,fact1(sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
tff(f162,plain,
( spl9_7
<=> ( fact1(sK5) = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
tff(f2925,plain,
( ! [X0: $int] :
( ( sK7 = $product(X0,fact1(sK6)) )
| $less($product(X0,fact1(sK6)),sK7)
| $less(sK7,X0)
| $less(fact1(sK6),0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_136 ),
inference(forward_demodulation,[],[f2924,f163]) ).
tff(f163,plain,
( ( fact1(sK5) = sK7 )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f162]) ).
tff(f2924,plain,
( ! [X0: $int] :
( $less($product(X0,fact1(sK6)),sK7)
| $less(sK7,X0)
| $less(fact1(sK6),0)
| ( fact1(sK5) = $product(X0,fact1(sK6)) ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_136 ),
inference(forward_demodulation,[],[f2914,f163]) ).
tff(f2914,plain,
( ! [X0: $int] :
( $less($product(X0,fact1(sK6)),fact1(sK5))
| $less(sK7,X0)
| $less(fact1(sK6),0)
| ( fact1(sK5) = $product(X0,fact1(sK6)) ) )
| ~ spl9_4
| ~ spl9_136 ),
inference(superposition,[],[f2882,f145]) ).
tff(f145,plain,
( ( fact1(sK5) = $product(sK7,fact1(sK6)) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f5121,plain,
( spl9_253
| ~ spl9_43
| ~ spl9_57
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f1944,f1574,f595,f382,f5119]) ).
tff(f5119,plain,
( spl9_253
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(fact1(sK6),$product(X0,X1)))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_253])]) ).
tff(f1944,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(fact1(sK6),$product(X0,X1)))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,X1) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_113 ),
inference(forward_demodulation,[],[f1926,f383]) ).
tff(f1926,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product($product(fact1(sK6),X0),X1))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,X1) )
| ~ spl9_57
| ~ spl9_113 ),
inference(superposition,[],[f1575,f596]) ).
tff(f5112,plain,
( spl9_252
| ~ spl9_43
| ~ spl9_57
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1914,f1570,f595,f382,f5110]) ).
tff(f5110,plain,
( spl9_252
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_252])]) ).
tff(f1914,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less(X1,sK7) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_112 ),
inference(forward_demodulation,[],[f1905,f383]) ).
tff(f1905,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product($product(fact1(sK6),X0),X1),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less(X1,sK7) )
| ~ spl9_57
| ~ spl9_112 ),
inference(superposition,[],[f1571,f596]) ).
tff(f4988,plain,
( spl9_251
| ~ spl9_53
| ~ spl9_78
| ~ spl9_250 ),
inference(avatar_split_clause,[],[f4984,f4978,f889,f556,f4986]) ).
tff(f4986,plain,
( spl9_251
<=> ! [X0: $int,X1: $int] : ( $sum($product(X0,X1),X0) = $product(X0,$sum(X1,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_251])]) ).
tff(f889,plain,
( spl9_78
<=> ! [X0: $int] : ( $product(fact1(sK6),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_78])]) ).
tff(f4978,plain,
( spl9_250
<=> ! [X0: $int,X1: $int] : ( $sum($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0)) = $product(fact1(sK6),$product(X0,$sum(X1,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_250])]) ).
tff(f4984,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(X0,X1),X0) = $product(X0,$sum(X1,1)) )
| ~ spl9_53
| ~ spl9_78
| ~ spl9_250 ),
inference(forward_demodulation,[],[f4983,f890]) ).
tff(f890,plain,
( ! [X0: $int] : ( $product(fact1(sK6),X0) = X0 )
| ~ spl9_78 ),
inference(avatar_component_clause,[],[f889]) ).
tff(f4983,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,$sum(X1,1)) = $sum($product(fact1(sK6),$product(X0,X1)),X0) )
| ~ spl9_53
| ~ spl9_78
| ~ spl9_250 ),
inference(evaluation,[],[f4982]) ).
tff(f4982,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,$sum(X1,1)) = $sum($product(fact1(sK6),$product(X0,X1)),$product(1,X0)) )
| ~ spl9_53
| ~ spl9_78
| ~ spl9_250 ),
inference(forward_demodulation,[],[f4981,f558]) ).
tff(f4981,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0)) = $product(X0,$sum(X1,sK7)) )
| ~ spl9_78
| ~ spl9_250 ),
inference(forward_demodulation,[],[f4979,f890]) ).
tff(f4979,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0)) = $product(fact1(sK6),$product(X0,$sum(X1,sK7))) )
| ~ spl9_250 ),
inference(avatar_component_clause,[],[f4978]) ).
tff(f4980,plain,
( spl9_250
| ~ spl9_43
| ~ spl9_57
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1817,f1562,f595,f382,f4978]) ).
tff(f1817,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(fact1(sK6),$product(X0,X1)),$product(sK7,X0)) = $product(fact1(sK6),$product(X0,$sum(X1,sK7))) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1816,f383]) ).
tff(f1816,plain,
( ! [X0: $int,X1: $int] : ( $sum($product($product(fact1(sK6),X0),X1),$product(sK7,X0)) = $product(fact1(sK6),$product(X0,$sum(X1,sK7))) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1780,f383]) ).
tff(f1780,plain,
( ! [X0: $int,X1: $int] : ( $sum($product($product(fact1(sK6),X0),X1),$product(sK7,X0)) = $product($product(fact1(sK6),X0),$sum(X1,sK7)) )
| ~ spl9_57
| ~ spl9_110 ),
inference(superposition,[],[f1563,f596]) ).
tff(f4972,plain,
( spl9_249
| ~ spl9_43
| ~ spl9_57
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1752,f1554,f595,f382,f4970]) ).
tff(f4970,plain,
( spl9_249
<=> ! [X0: $int,X1: $int] : ( $sum($product(sK7,X0),$product(fact1(sK6),$product(X0,X1))) = $product(fact1(sK6),$product(X0,$sum(sK7,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_249])]) ).
tff(f1752,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(sK7,X0),$product(fact1(sK6),$product(X0,X1))) = $product(fact1(sK6),$product(X0,$sum(sK7,X1))) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1751,f383]) ).
tff(f1751,plain,
( ! [X0: $int,X1: $int] : ( $product($product(fact1(sK6),X0),$sum(sK7,X1)) = $sum($product(sK7,X0),$product(fact1(sK6),$product(X0,X1))) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1712,f383]) ).
tff(f1712,plain,
( ! [X0: $int,X1: $int] : ( $product($product(fact1(sK6),X0),$sum(sK7,X1)) = $sum($product(sK7,X0),$product($product(fact1(sK6),X0),X1)) )
| ~ spl9_57
| ~ spl9_109 ),
inference(superposition,[],[f1555,f596]) ).
tff(f4963,plain,
( spl9_248
| ~ spl9_50
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f604,f595,f472,f4961]) ).
tff(f4961,plain,
( spl9_248
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(fact1(sK6),X0)),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_248])]) ).
tff(f604,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(fact1(sK6),X0)),$product(sK7,X0))
| $less($product(fact1(sK6),X0),0)
| $less(X1,sK7) )
| ~ spl9_50
| ~ spl9_57 ),
inference(superposition,[],[f473,f596]) ).
tff(f4954,plain,
( spl9_247
| ~ spl9_50
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f603,f595,f472,f4952]) ).
tff(f4952,plain,
( spl9_247
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,$product(fact1(sK6),X0)))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_247])]) ).
tff(f603,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,$product(fact1(sK6),X0)))
| $less($product(fact1(sK6),X0),0)
| $less(sK7,X1) )
| ~ spl9_50
| ~ spl9_57 ),
inference(superposition,[],[f473,f596]) ).
tff(f4945,plain,
( spl9_246
| ~ spl9_4
| ~ spl9_7
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2867,f2690,f162,f143,f4943]) ).
tff(f4943,plain,
( spl9_246
<=> ! [X0: $int,X1: $int] :
( ( $product(X0,sK7) != $product($product(X0,sK7),X1) )
| ( 0 = $product(X0,sK7) )
| ( fact1(sK6) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_246])]) ).
tff(f2867,plain,
( ! [X0: $int,X1: $int] :
( ( $product(X0,sK7) != $product($product(X0,sK7),X1) )
| ( 0 = $product(X0,sK7) )
| ( fact1(sK6) = X1 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2838,f163]) ).
tff(f2838,plain,
( ! [X0: $int,X1: $int] :
( ( $product(X0,fact1(sK5)) != $product($product(X0,sK7),X1) )
| ( 0 = $product(X0,sK7) )
| ( fact1(sK6) = X1 ) )
| ~ spl9_4
| ~ spl9_135 ),
inference(superposition,[],[f2691,f145]) ).
tff(f4935,plain,
( spl9_59
| spl9_245
| ~ spl9_58
| ~ spl9_114 ),
inference(avatar_split_clause,[],[f1968,f1578,f612,f4933,f616]) ).
tff(f616,plain,
( spl9_59
<=> ( 0 = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_59])]) ).
tff(f4933,plain,
( spl9_245
<=> ! [X0: $int,X1: $int] :
( ( $sum(sK7,$product(sK7,X0)) != $product(X1,sK7) )
| ( $sum(X0,fact1(sK6)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_245])]) ).
tff(f1578,plain,
( spl9_114
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,X0) != $product(X0,X2) )
| ( 0 = X0 )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_114])]) ).
tff(f1968,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(sK7,$product(sK7,X0)) != $product(X1,sK7) )
| ( 0 = sK7 )
| ( $sum(X0,fact1(sK6)) = X1 ) )
| ~ spl9_58
| ~ spl9_114 ),
inference(superposition,[],[f1579,f613]) ).
tff(f1579,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,X0) != $product(X0,X2) )
| ( 0 = X0 )
| ( X1 = X2 ) )
| ~ spl9_114 ),
inference(avatar_component_clause,[],[f1578]) ).
tff(f4927,plain,
( spl9_172
| spl9_244
| ~ spl9_58
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f1938,f1574,f612,f4925,f3922]) ).
tff(f3922,plain,
( spl9_172
<=> $less(sK7,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_172])]) ).
tff(f4925,plain,
( spl9_244
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X1,sK7),$sum(sK7,$product(sK7,X0)))
| $less(X1,$sum(X0,fact1(sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_244])]) ).
tff(f1938,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,sK7),$sum(sK7,$product(sK7,X0)))
| $less(sK7,0)
| $less(X1,$sum(X0,fact1(sK6))) )
| ~ spl9_58
| ~ spl9_113 ),
inference(superposition,[],[f1575,f613]) ).
tff(f4920,plain,
( spl9_172
| spl9_243
| ~ spl9_58
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1895,f1570,f612,f4918,f3922]) ).
tff(f4918,plain,
( spl9_243
<=> ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,sK7))
| $less($sum(X0,fact1(sK6)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_243])]) ).
tff(f1895,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(sK7,$product(sK7,X0)),$product(X1,sK7))
| $less(sK7,0)
| $less($sum(X0,fact1(sK6)),X1) )
| ~ spl9_58
| ~ spl9_112 ),
inference(superposition,[],[f1571,f613]) ).
tff(f4912,plain,
( spl9_242
| ~ spl9_42
| ~ spl9_58
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1809,f1562,f612,f374,f4910]) ).
tff(f4910,plain,
( spl9_242
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) = $sum($sum(sK7,$product(sK7,X0)),$product(X1,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_242])]) ).
tff(f1809,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) = $sum($sum(sK7,$product(sK7,X0)),$product(X1,sK7)) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1770,f375]) ).
tff(f1770,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($sum(X0,fact1(sK6)),X1)) = $sum($sum(sK7,$product(sK7,X0)),$product(X1,sK7)) )
| ~ spl9_58
| ~ spl9_110 ),
inference(superposition,[],[f1563,f613]) ).
tff(f4905,plain,
( spl9_241
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f716,f612,f468,f374,f4903]) ).
tff(f4903,plain,
( spl9_241
<=> ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) = $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_241])]) ).
tff(f716,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) = $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) )
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58 ),
inference(forward_demodulation,[],[f644,f375]) ).
tff(f644,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($sum(X0,fact1(sK6)),X1)) = $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) )
| ~ spl9_49
| ~ spl9_58 ),
inference(superposition,[],[f469,f613]) ).
tff(f4890,plain,
( spl9_240
| ~ spl9_53
| ~ spl9_148
| ~ spl9_239 ),
inference(avatar_split_clause,[],[f4886,f4881,f3333,f556,f4888]) ).
tff(f4888,plain,
( spl9_240
<=> ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ( $sum(1,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_240])]) ).
tff(f4881,plain,
( spl9_239
<=> ! [X0: $int,X1: $int] :
( ( $sum(sK7,$product(sK7,X0)) != $product(sK7,X1) )
| ( $sum(X0,fact1(sK6)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_239])]) ).
tff(f4886,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(X0,1) = X1 )
| ( $sum(1,X0) != X1 ) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_239 ),
inference(forward_demodulation,[],[f4885,f3335]) ).
tff(f4885,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(1,X0) != X1 )
| ( $sum(X0,fact1(sK6)) = X1 ) )
| ~ spl9_53
| ~ spl9_239 ),
inference(evaluation,[],[f4884]) ).
tff(f4884,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(1,$product(1,X0)) != $product(1,X1) )
| ( $sum(X0,fact1(sK6)) = X1 ) )
| ~ spl9_53
| ~ spl9_239 ),
inference(forward_demodulation,[],[f4882,f558]) ).
tff(f4882,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(sK7,$product(sK7,X0)) != $product(sK7,X1) )
| ( $sum(X0,fact1(sK6)) = X1 ) )
| ~ spl9_239 ),
inference(avatar_component_clause,[],[f4881]) ).
tff(f4883,plain,
( spl9_59
| spl9_239
| ~ spl9_51
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f649,f612,f476,f4881,f616]) ).
tff(f476,plain,
( spl9_51
<=> ! [X2: $int,X0: $int,X3: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
tff(f649,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(sK7,$product(sK7,X0)) != $product(sK7,X1) )
| ( 0 = sK7 )
| ( $sum(X0,fact1(sK6)) = X1 ) )
| ~ spl9_51
| ~ spl9_58 ),
inference(superposition,[],[f477,f613]) ).
tff(f477,plain,
( ! [X2: $int,X3: $int,X0: $int] :
( ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 )
| ( X2 = X3 ) )
| ~ spl9_51 ),
inference(avatar_component_clause,[],[f476]) ).
tff(f4875,plain,
( spl9_238
| ~ spl9_49
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f645,f612,f468,f4873]) ).
tff(f4873,plain,
( spl9_238
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) = $sum($product(sK7,X1),$sum(sK7,$product(sK7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_238])]) ).
tff(f645,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) = $sum($product(sK7,X1),$sum(sK7,$product(sK7,X0))) )
| ~ spl9_49
| ~ spl9_58 ),
inference(superposition,[],[f469,f613]) ).
tff(f4865,plain,
( spl9_62
| spl9_237
| ~ spl9_4
| ~ spl9_7
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f2677,f2430,f162,f143,f4863,f683]) ).
tff(f4863,plain,
( spl9_237
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X0,fact1(sK6)),$product(X1,sK7))
| $less(X0,$product(X1,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_237])]) ).
tff(f2677,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,fact1(sK6)),$product(X1,sK7))
| $less(fact1(sK6),0)
| $less(X0,$product(X1,sK7)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_133 ),
inference(forward_demodulation,[],[f2657,f163]) ).
tff(f2657,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,fact1(sK6)),$product(X1,fact1(sK5)))
| $less(fact1(sK6),0)
| $less(X0,$product(X1,sK7)) )
| ~ spl9_4
| ~ spl9_133 ),
inference(superposition,[],[f2431,f145]) ).
tff(f4861,plain,
( spl9_235
| spl9_236
| ~ spl9_4
| ~ spl9_7
| ~ spl9_34
| ~ spl9_53
| spl9_115 ),
inference(avatar_split_clause,[],[f3480,f1672,f556,f296,f162,f143,f4858,f4854]) ).
tff(f4858,plain,
( spl9_236
<=> ( 1 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_236])]) ).
tff(f296,plain,
( spl9_34
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
tff(f3480,plain,
( ( 1 = sK5 )
| $less(sK5,1)
| ~ spl9_4
| ~ spl9_7
| ~ spl9_34
| ~ spl9_53
| spl9_115 ),
inference(forward_demodulation,[],[f3479,f558]) ).
tff(f3479,plain,
( ( sK5 = sK7 )
| $less(sK5,1)
| ~ spl9_4
| ~ spl9_7
| ~ spl9_34
| ~ spl9_53
| spl9_115 ),
inference(forward_demodulation,[],[f3478,f2946]) ).
tff(f2946,plain,
( ( sK7 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53 ),
inference(forward_demodulation,[],[f2940,f163]) ).
tff(f2940,plain,
( ( fact1(sK5) = fact1(sK6) )
| ~ spl9_4
| ~ spl9_53 ),
inference(evaluation,[],[f929]) ).
tff(f929,plain,
( ( fact1(sK5) = $product(1,fact1(sK6)) )
| ~ spl9_4
| ~ spl9_53 ),
inference(superposition,[],[f145,f558]) ).
tff(f3478,plain,
( $less(sK5,1)
| ( sK5 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_34
| ~ spl9_53
| spl9_115 ),
inference(forward_demodulation,[],[f3477,f558]) ).
tff(f3477,plain,
( $less(sK5,sK7)
| ( sK5 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_34
| ~ spl9_53
| spl9_115 ),
inference(forward_demodulation,[],[f3473,f2946]) ).
tff(f3473,plain,
( $less(sK5,fact1(sK6))
| ( sK5 = fact1(sK6) )
| ~ spl9_34
| spl9_115 ),
inference(resolution,[],[f1673,f297]) ).
tff(f297,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f296]) ).
tff(f1673,plain,
( ~ $less(fact1(sK6),sK5)
| spl9_115 ),
inference(avatar_component_clause,[],[f1672]) ).
tff(f4850,plain,
( spl9_62
| spl9_234
| ~ spl9_4
| ~ spl9_7
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f2625,f2426,f162,f143,f4848,f683]) ).
tff(f4848,plain,
( spl9_234
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X0,sK7),$product(X1,fact1(sK6)))
| $less($product(X0,sK7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_234])]) ).
tff(f2625,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,sK7),$product(X1,fact1(sK6)))
| $less(fact1(sK6),0)
| $less($product(X0,sK7),X1) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_132 ),
inference(forward_demodulation,[],[f2597,f163]) ).
tff(f2597,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,fact1(sK5)),$product(X1,fact1(sK6)))
| $less(fact1(sK6),0)
| $less($product(X0,sK7),X1) )
| ~ spl9_4
| ~ spl9_132 ),
inference(superposition,[],[f2427,f145]) ).
tff(f4843,plain,
( spl9_233
| ~ spl9_42
| ~ spl9_58
| ~ spl9_111 ),
inference(avatar_split_clause,[],[f1872,f1566,f612,f374,f4841]) ).
tff(f4841,plain,
( spl9_233
<=> ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) = $sum(sK7,$product(sK7,$sum(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_233])]) ).
tff(f1872,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) = $sum(sK7,$product(sK7,$sum(X1,X0))) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_111 ),
inference(forward_demodulation,[],[f1828,f642]) ).
tff(f1828,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),$product(sK7,X1)) = $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) )
| ~ spl9_58
| ~ spl9_111 ),
inference(superposition,[],[f1567,f613]) ).
tff(f4835,plain,
( spl9_232
| ~ spl9_42
| ~ spl9_58
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1759,f1554,f612,f374,f4833]) ).
tff(f4833,plain,
( spl9_232
<=> ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X1,X0))) = $sum($product(X1,sK7),$sum(sK7,$product(sK7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_232])]) ).
tff(f1759,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X1,X0))) = $sum($product(X1,sK7),$sum(sK7,$product(sK7,X0))) )
| ~ spl9_42
| ~ spl9_58
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1724,f642]) ).
tff(f1724,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) = $sum($product(X1,sK7),$sum(sK7,$product(sK7,X0))) )
| ~ spl9_58
| ~ spl9_109 ),
inference(superposition,[],[f1555,f613]) ).
tff(f4821,plain,
( ~ spl9_5
| spl9_2
| ~ spl9_230
| spl9_231
| ~ spl9_4
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(avatar_split_clause,[],[f592,f581,f576,f568,f552,f444,f382,f250,f143,f4818,f4814,f133,f148]) ).
tff(f148,plain,
( spl9_5
<=> sP0(sK6,sK5,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
tff(f444,plain,
( spl9_47
<=> ! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
tff(f552,plain,
( spl9_52
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(sK2(X0,X1,X2),X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(sK2(X0,X1,X2))) )
| $less(sK2(X0,X1,X2),0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
tff(f576,plain,
( spl9_55
<=> ( $product(sK7,sK6) = sK1(sK6,sK5,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
tff(f581,plain,
( spl9_56
<=> ( sK2(sK6,sK5,sK7) = $sum(-1,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
tff(f592,plain,
( $less($sum(-1,sK6),0)
| ~ $less($sum(-1,sK6),sK6)
| $less(sK6,0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_4
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(forward_demodulation,[],[f591,f583]) ).
tff(f583,plain,
( ( sK2(sK6,sK5,sK7) = $sum(-1,sK6) )
| ~ spl9_56 ),
inference(avatar_component_clause,[],[f581]) ).
tff(f591,plain,
( ~ $less($sum(-1,sK6),sK6)
| $less(sK6,0)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_4
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(forward_demodulation,[],[f590,f583]) ).
tff(f590,plain,
( $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_4
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(trivial_inequality_removal,[],[f589]) ).
tff(f589,plain,
( ( fact1(sK5) != fact1(sK5) )
| $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_4
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(forward_demodulation,[],[f588,f145]) ).
tff(f588,plain,
( ( fact1(sK5) != $product(sK7,fact1(sK6)) )
| $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_26
| ~ spl9_43
| ~ spl9_47
| ~ spl9_52
| ~ spl9_54
| ~ spl9_55
| ~ spl9_56 ),
inference(forward_demodulation,[],[f587,f574]) ).
tff(f574,plain,
( ( fact1(sK6) = $product(sK6,fact1($sum(-1,sK6))) )
| ~ spl9_26
| ~ spl9_47
| ~ spl9_54 ),
inference(forward_demodulation,[],[f572,f251]) ).
tff(f572,plain,
( ( fact1(sK6) = $product(sK6,fact1($sum(sK6,-1))) )
| ~ spl9_47
| ~ spl9_54 ),
inference(resolution,[],[f570,f445]) ).
tff(f445,plain,
( ! [X0: $int] :
( ~ $less(0,X0)
| ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) ) )
| ~ spl9_47 ),
inference(avatar_component_clause,[],[f444]) ).
tff(f587,plain,
( ( fact1(sK5) != $product(sK7,$product(sK6,fact1($sum(-1,sK6)))) )
| $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_43
| ~ spl9_52
| ~ spl9_55
| ~ spl9_56 ),
inference(forward_demodulation,[],[f586,f583]) ).
tff(f586,plain,
( ( fact1(sK5) != $product(sK7,$product(sK6,fact1(sK2(sK6,sK5,sK7)))) )
| $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_43
| ~ spl9_52
| ~ spl9_55 ),
inference(forward_demodulation,[],[f585,f383]) ).
tff(f585,plain,
( ( fact1(sK5) != $product($product(sK7,sK6),fact1(sK2(sK6,sK5,sK7))) )
| $less(sK6,0)
| ~ $less(sK2(sK6,sK5,sK7),sK6)
| $less(sK2(sK6,sK5,sK7),0)
| ~ sP0(sK6,sK5,sK7)
| ~ spl9_52
| ~ spl9_55 ),
inference(superposition,[],[f553,f578]) ).
tff(f578,plain,
( ( $product(sK7,sK6) = sK1(sK6,sK5,sK7) )
| ~ spl9_55 ),
inference(avatar_component_clause,[],[f576]) ).
tff(f553,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(sK2(X0,X1,X2))) )
| $less(X0,0)
| ~ $less(sK2(X0,X1,X2),X0)
| $less(sK2(X0,X1,X2),0)
| ~ sP0(X0,X1,X2) )
| ~ spl9_52 ),
inference(avatar_component_clause,[],[f552]) ).
tff(f4806,plain,
( spl9_227
| ~ spl9_3
| ~ spl9_21
| ~ spl9_70
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f1038,f964,f759,f227,f138,f4785]) ).
tff(f4785,plain,
( spl9_227
<=> even1(2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_227])]) ).
tff(f1038,plain,
( ~ even1(0)
| even1(2)
| ~ spl9_21
| ~ spl9_70
| ~ spl9_83 ),
inference(forward_demodulation,[],[f1034,f228]) ).
tff(f1034,plain,
( ! [X0: $int] :
( even1(2)
| ~ even1($sum(X0,$uminus(X0))) )
| ~ spl9_70
| ~ spl9_83 ),
inference(superposition,[],[f965,f760]) ).
tff(f4797,plain,
( ~ spl9_229
| ~ spl9_3
| ~ spl9_21
| ~ spl9_67 ),
inference(avatar_split_clause,[],[f749,f736,f227,f138,f4794]) ).
tff(f4794,plain,
( spl9_229
<=> even1(-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_229])]) ).
tff(f749,plain,
( ~ even1(0)
| ~ even1(-1)
| ~ spl9_21
| ~ spl9_67 ),
inference(evaluation,[],[f746]) ).
tff(f746,plain,
( ~ even1(0)
| ~ even1($uminus(1))
| ~ spl9_21
| ~ spl9_67 ),
inference(superposition,[],[f737,f228]) ).
tff(f4792,plain,
( ~ spl9_227
| ~ spl9_228
| ~ spl9_24
| ~ spl9_66 ),
inference(avatar_split_clause,[],[f739,f732,f239,f4789,f4785]) ).
tff(f4789,plain,
( spl9_228
<=> even1(1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_228])]) ).
tff(f239,plain,
( spl9_24
<=> ! [X0: $int] :
( ~ even1($sum(X0,1))
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
tff(f739,plain,
( ~ even1(1)
| ~ even1(2)
| ~ spl9_24
| ~ spl9_66 ),
inference(resolution,[],[f733,f240]) ).
tff(f240,plain,
( ! [X0: $int] :
( ~ even1($sum(X0,1))
| ~ even1(X0) )
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f239]) ).
tff(f4783,plain,
( spl9_226
| ~ spl9_12
| ~ spl9_47
| ~ spl9_64 ),
inference(avatar_split_clause,[],[f730,f708,f444,f188,f4780]) ).
tff(f4780,plain,
( spl9_226
<=> ( 1 = fact1(1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_226])]) ).
tff(f188,plain,
( spl9_12
<=> ( 1 = fact1(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
tff(f730,plain,
( ( 1 = fact1(1) )
| ~ spl9_12
| ~ spl9_47
| ~ spl9_64 ),
inference(forward_demodulation,[],[f729,f190]) ).
tff(f190,plain,
( ( 1 = fact1(0) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f729,plain,
( ( fact1(0) = fact1(1) )
| ~ spl9_47
| ~ spl9_64 ),
inference(evaluation,[],[f724]) ).
tff(f724,plain,
( ( fact1($sum(0,1)) = $product($sum(0,1),fact1($sum($sum(0,1),-1))) )
| ~ spl9_47
| ~ spl9_64 ),
inference(resolution,[],[f709,f445]) ).
tff(f4662,plain,
( spl9_225
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f3147,f2881,f889,f556,f162,f143,f4660]) ).
tff(f4660,plain,
( spl9_225
<=> ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less(X0,$product(X1,X0))
| $less(X0,0)
| ( $product(X1,X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_225])]) ).
tff(f3147,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less(X0,$product(X1,X0))
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(forward_demodulation,[],[f3146,f558]) ).
tff(f3146,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,sK7)
| $less(X0,$product(X1,X0))
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(forward_demodulation,[],[f3044,f2946]) ).
tff(f3044,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,$product(X1,X0))
| $less(X1,fact1(sK6))
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_78
| ~ spl9_136 ),
inference(superposition,[],[f2882,f890]) ).
tff(f4658,plain,
( spl9_224
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(avatar_split_clause,[],[f3145,f2881,f889,f556,f162,f143,f4656]) ).
tff(f4656,plain,
( spl9_224
<=> ! [X0: $int,X1: $int] :
( $less(1,X1)
| $less($product(X1,X0),X0)
| $less(X0,0)
| ( $product(X1,X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_224])]) ).
tff(f3145,plain,
( ! [X0: $int,X1: $int] :
( $less(1,X1)
| $less($product(X1,X0),X0)
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(forward_demodulation,[],[f3144,f558]) ).
tff(f3144,plain,
( ! [X0: $int,X1: $int] :
( $less(sK7,X1)
| $less($product(X1,X0),X0)
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_136 ),
inference(forward_demodulation,[],[f3043,f2946]) ).
tff(f3043,plain,
( ! [X0: $int,X1: $int] :
( $less($product(X1,X0),X0)
| $less(fact1(sK6),X1)
| $less(X0,0)
| ( $product(X1,X0) = X0 ) )
| ~ spl9_78
| ~ spl9_136 ),
inference(superposition,[],[f2882,f890]) ).
tff(f4650,plain,
( spl9_223
| spl9_59
| ~ spl9_4
| ~ spl9_7
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2877,f2690,f162,f143,f616,f4648]) ).
tff(f4648,plain,
( spl9_223
<=> ! [X0: $int,X1: $int] :
( ( $product(sK7,$product(fact1(sK6),X0)) != $product(sK7,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_223])]) ).
tff(f2877,plain,
( ! [X0: $int,X1: $int] :
( ( 0 = sK7 )
| ( $product(sK7,$product(fact1(sK6),X0)) != $product(sK7,X1) )
| ( X0 = X1 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2876,f163]) ).
tff(f2876,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,$product(fact1(sK6),X0)) != $product(sK7,X1) )
| ( 0 = fact1(sK5) )
| ( X0 = X1 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2857,f163]) ).
tff(f2857,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,$product(fact1(sK6),X0)) != $product(fact1(sK5),X1) )
| ( 0 = fact1(sK5) )
| ( X0 = X1 ) )
| ~ spl9_4
| ~ spl9_135 ),
inference(superposition,[],[f2691,f145]) ).
tff(f4646,plain,
( spl9_222
| ~ spl9_53
| ~ spl9_55 ),
inference(avatar_split_clause,[],[f940,f576,f556,f4643]) ).
tff(f4643,plain,
( spl9_222
<=> ( sK6 = sK1(sK6,sK5,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_222])]) ).
tff(f940,plain,
( ( sK6 = sK1(sK6,sK5,1) )
| ~ spl9_53
| ~ spl9_55 ),
inference(evaluation,[],[f931]) ).
tff(f931,plain,
( ( $product(1,sK6) = sK1(sK6,sK5,1) )
| ~ spl9_53
| ~ spl9_55 ),
inference(superposition,[],[f578,f558]) ).
tff(f4637,plain,
( spl9_220
| spl9_221
| ~ spl9_4
| ~ spl9_7
| ~ spl9_57
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f2873,f2690,f595,f162,f143,f4635,f4631]) ).
tff(f4631,plain,
( spl9_220
<=> ( 0 = $product(sK7,fact1(sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_220])]) ).
tff(f4635,plain,
( spl9_221
<=> ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(sK7,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_221])]) ).
tff(f2873,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(sK7,X1) )
| ( 0 = $product(sK7,fact1(sK6)) )
| ( X0 = X1 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_57
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2872,f163]) ).
tff(f2872,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(fact1(sK5),X1) )
| ( 0 = $product(sK7,fact1(sK6)) )
| ( X0 = X1 ) )
| ~ spl9_4
| ~ spl9_57
| ~ spl9_135 ),
inference(forward_demodulation,[],[f2848,f145]) ).
tff(f2848,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product($product(sK7,fact1(sK6)),X1) )
| ( 0 = $product(sK7,fact1(sK6)) )
| ( X0 = X1 ) )
| ~ spl9_57
| ~ spl9_135 ),
inference(superposition,[],[f2691,f596]) ).
tff(f4624,plain,
( spl9_143
| spl9_219
| ~ spl9_26
| spl9_62
| ~ spl9_124 ),
inference(avatar_split_clause,[],[f2331,f2191,f683,f250,f4621,f3223]) ).
tff(f3223,plain,
( spl9_143
<=> ( 0 = fact1(sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_143])]) ).
tff(f4621,plain,
( spl9_219
<=> ( fact1(fact1(sK6)) = $product(fact1(sK6),fact1($sum(-1,fact1(sK6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_219])]) ).
tff(f2191,plain,
( spl9_124
<=> ! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) )
| $less(X0,0)
| ( 0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_124])]) ).
tff(f2331,plain,
( ( fact1(fact1(sK6)) = $product(fact1(sK6),fact1($sum(-1,fact1(sK6)))) )
| ( 0 = fact1(sK6) )
| ~ spl9_26
| spl9_62
| ~ spl9_124 ),
inference(forward_demodulation,[],[f2327,f251]) ).
tff(f2327,plain,
( ( fact1(fact1(sK6)) = $product(fact1(sK6),fact1($sum(fact1(sK6),-1))) )
| ( 0 = fact1(sK6) )
| spl9_62
| ~ spl9_124 ),
inference(resolution,[],[f684,f2192]) ).
tff(f2192,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) )
| ( 0 = X0 ) )
| ~ spl9_124 ),
inference(avatar_component_clause,[],[f2191]) ).
tff(f684,plain,
( ~ $less(fact1(sK6),0)
| spl9_62 ),
inference(avatar_component_clause,[],[f683]) ).
tff(f4615,plain,
( spl9_59
| spl9_218
| ~ spl9_57
| ~ spl9_114 ),
inference(avatar_split_clause,[],[f1967,f1578,f595,f4613,f616]) ).
tff(f4613,plain,
( spl9_218
<=> ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(X1,sK7) )
| ( $product(fact1(sK6),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_218])]) ).
tff(f1967,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(X1,sK7) )
| ( 0 = sK7 )
| ( $product(fact1(sK6),X0) = X1 ) )
| ~ spl9_57
| ~ spl9_114 ),
inference(superposition,[],[f1579,f596]) ).
tff(f4608,plain,
( spl9_172
| spl9_217
| ~ spl9_57
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f1937,f1574,f595,f4606,f3922]) ).
tff(f4606,plain,
( spl9_217
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X1,sK7),$product(sK7,X0))
| $less(X1,$product(fact1(sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_217])]) ).
tff(f1937,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,sK7),$product(sK7,X0))
| $less(sK7,0)
| $less(X1,$product(fact1(sK6),X0)) )
| ~ spl9_57
| ~ spl9_113 ),
inference(superposition,[],[f1575,f596]) ).
tff(f4601,plain,
( spl9_172
| spl9_216
| ~ spl9_57
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1894,f1570,f595,f4599,f3922]) ).
tff(f4599,plain,
( spl9_216
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,sK7))
| $less($product(fact1(sK6),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_216])]) ).
tff(f1894,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(sK7,X0),$product(X1,sK7))
| $less(sK7,0)
| $less($product(fact1(sK6),X0),X1) )
| ~ spl9_57
| ~ spl9_112 ),
inference(superposition,[],[f1571,f596]) ).
tff(f4594,plain,
( spl9_215
| ~ spl9_42
| ~ spl9_49
| ~ spl9_58
| ~ spl9_91
| ~ spl9_111 ),
inference(avatar_split_clause,[],[f1882,f1566,f1083,f612,f468,f374,f4592]) ).
tff(f4592,plain,
( spl9_215
<=> ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X0,$sum(fact1(sK6),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_215])]) ).
tff(f4580,plain,
( spl9_214
| ~ spl9_53
| ~ spl9_148
| ~ spl9_213 ),
inference(avatar_split_clause,[],[f4576,f4571,f3333,f556,f4578]) ).
tff(f4578,plain,
( spl9_214
<=> ! [X0: $int] :
( ( 0 = $sum(X0,1) )
| ( 0 != $sum(1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_214])]) ).
tff(f4571,plain,
( spl9_213
<=> ! [X0: $int] :
( ( 0 != $sum(sK7,$product(sK7,X0)) )
| ( 0 = $sum(X0,fact1(sK6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_213])]) ).
tff(f4576,plain,
( ! [X0: $int] :
( ( 0 = $sum(X0,1) )
| ( 0 != $sum(1,X0) ) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_213 ),
inference(forward_demodulation,[],[f4575,f3335]) ).
tff(f4575,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,X0) )
| ( 0 = $sum(X0,fact1(sK6)) ) )
| ~ spl9_53
| ~ spl9_213 ),
inference(evaluation,[],[f4574]) ).
tff(f4574,plain,
( ! [X0: $int] :
( ( 0 != $sum(1,$product(1,X0)) )
| ( 0 = $sum(X0,fact1(sK6)) ) )
| ~ spl9_53
| ~ spl9_213 ),
inference(forward_demodulation,[],[f4572,f558]) ).
tff(f4572,plain,
( ! [X0: $int] :
( ( 0 != $sum(sK7,$product(sK7,X0)) )
| ( 0 = $sum(X0,fact1(sK6)) ) )
| ~ spl9_213 ),
inference(avatar_component_clause,[],[f4571]) ).
tff(f4573,plain,
( spl9_59
| spl9_213
| ~ spl9_58
| ~ spl9_96 ),
inference(avatar_split_clause,[],[f1428,f1103,f612,f4571,f616]) ).
tff(f1103,plain,
( spl9_96
<=> ! [X0: $int,X1: $int] :
( ( 0 != $product(X0,X1) )
| ( 0 = X0 )
| ( 0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_96])]) ).
tff(f1428,plain,
( ! [X0: $int] :
( ( 0 != $sum(sK7,$product(sK7,X0)) )
| ( 0 = sK7 )
| ( 0 = $sum(X0,fact1(sK6)) ) )
| ~ spl9_58
| ~ spl9_96 ),
inference(superposition,[],[f1104,f613]) ).
tff(f1104,plain,
( ! [X0: $int,X1: $int] :
( ( 0 != $product(X0,X1) )
| ( 0 = X0 )
| ( 0 = X1 ) )
| ~ spl9_96 ),
inference(avatar_component_clause,[],[f1103]) ).
tff(f4565,plain,
( spl9_212
| ~ spl9_58
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1345,f1091,f612,f4563]) ).
tff(f4563,plain,
( spl9_212
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) = $product(X1,$sum(sK7,$product(sK7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_212])]) ).
tff(f1091,plain,
( spl9_93
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product(X2,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_93])]) ).
tff(f1345,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) = $product(X1,$sum(sK7,$product(sK7,X0))) )
| ~ spl9_58
| ~ spl9_93 ),
inference(superposition,[],[f1092,f613]) ).
tff(f1092,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product(X2,$product(X0,X1)) )
| ~ spl9_93 ),
inference(avatar_component_clause,[],[f1091]) ).
tff(f4555,plain,
( spl9_211
| ~ spl9_58
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1327,f1091,f612,f4553]) ).
tff(f4553,plain,
( spl9_211
<=> ! [X0: $int,X1: $int] : ( $product(X1,$sum(sK7,$product(sK7,X0))) = $product($sum(X0,fact1(sK6)),$product(X1,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_211])]) ).
tff(f1327,plain,
( ! [X0: $int,X1: $int] : ( $product(X1,$sum(sK7,$product(sK7,X0))) = $product($sum(X0,fact1(sK6)),$product(X1,sK7)) )
| ~ spl9_58
| ~ spl9_93 ),
inference(superposition,[],[f1092,f613]) ).
tff(f4549,plain,
( spl9_210
| ~ spl9_58
| ~ spl9_92 ),
inference(avatar_split_clause,[],[f1287,f1087,f612,f4547]) ).
tff(f4547,plain,
( spl9_210
<=> ! [X0: $int,X1: $int] : ( $product($sum(sK7,$product(sK7,X0)),X1) = $product($sum(X0,fact1(sK6)),$product(sK7,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_210])]) ).
tff(f1087,plain,
( spl9_92
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_92])]) ).
tff(f1287,plain,
( ! [X0: $int,X1: $int] : ( $product($sum(sK7,$product(sK7,X0)),X1) = $product($sum(X0,fact1(sK6)),$product(sK7,X1)) )
| ~ spl9_58
| ~ spl9_92 ),
inference(superposition,[],[f1088,f613]) ).
tff(f1088,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X1,X0),X2) )
| ~ spl9_92 ),
inference(avatar_component_clause,[],[f1087]) ).
tff(f4542,plain,
( spl9_209
| ~ spl9_58
| ~ spl9_90 ),
inference(avatar_split_clause,[],[f1171,f1079,f612,f4540]) ).
tff(f4540,plain,
( spl9_209
<=> ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_209])]) ).
tff(f1171,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X1,$sum(X0,fact1(sK6)))) )
| ~ spl9_58
| ~ spl9_90 ),
inference(superposition,[],[f613,f1080]) ).
tff(f4534,plain,
( spl9_208
| ~ spl9_43
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f643,f612,f382,f4532]) ).
tff(f4532,plain,
( spl9_208
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) = $product($sum(sK7,$product(sK7,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_208])]) ).
tff(f643,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product($sum(X0,fact1(sK6)),X1)) = $product($sum(sK7,$product(sK7,X0)),X1) )
| ~ spl9_43
| ~ spl9_58 ),
inference(superposition,[],[f383,f613]) ).
tff(f4527,plain,
( spl9_207
| ~ spl9_42
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f642,f612,f374,f4525]) ).
tff(f4525,plain,
( spl9_207
<=> ! [X0: $int,X1: $int] : ( $sum(sK7,$product(sK7,$sum(X0,X1))) = $product(sK7,$sum(X0,$sum(X1,fact1(sK6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_207])]) ).
tff(f4519,plain,
( spl9_59
| spl9_206
| ~ spl9_51
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f605,f595,f476,f4517,f616]) ).
tff(f4517,plain,
( spl9_206
<=> ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(sK7,X1) )
| ( $product(fact1(sK6),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_206])]) ).
tff(f605,plain,
( ! [X0: $int,X1: $int] :
( ( $product(sK7,X0) != $product(sK7,X1) )
| ( 0 = sK7 )
| ( $product(fact1(sK6),X0) = X1 ) )
| ~ spl9_51
| ~ spl9_57 ),
inference(superposition,[],[f477,f596]) ).
tff(f4376,plain,
( spl9_205
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f3130,f2430,f889,f556,f162,f143,f4374]) ).
tff(f4374,plain,
( spl9_205
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(1,$product(X1,X2))
| ~ $less(X0,$product(X1,$product(X2,X0)))
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_205])]) ).
tff(f3130,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(1,$product(X1,X2))
| ~ $less(X0,$product(X1,$product(X2,X0)))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_133 ),
inference(forward_demodulation,[],[f3129,f558]) ).
tff(f3129,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(sK7,$product(X1,X2))
| ~ $less(X0,$product(X1,$product(X2,X0)))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_133 ),
inference(forward_demodulation,[],[f3038,f2946]) ).
tff(f3038,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,$product(X1,$product(X2,X0)))
| $less(X0,0)
| $less(fact1(sK6),$product(X1,X2)) )
| ~ spl9_78
| ~ spl9_133 ),
inference(superposition,[],[f2431,f890]) ).
tff(f4372,plain,
( spl9_204
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_132 ),
inference(avatar_split_clause,[],[f3125,f2426,f889,f556,f162,f143,f4370]) ).
tff(f4370,plain,
( spl9_204
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($product(X1,X2),1)
| ~ $less($product(X1,$product(X2,X0)),X0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_204])]) ).
tff(f3125,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($product(X1,X2),1)
| ~ $less($product(X1,$product(X2,X0)),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_132 ),
inference(forward_demodulation,[],[f3124,f558]) ).
tff(f3124,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($product(X1,X2),sK7)
| ~ $less($product(X1,$product(X2,X0)),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_132 ),
inference(forward_demodulation,[],[f3036,f2946]) ).
tff(f3036,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X2,X0)),X0)
| $less(X0,0)
| $less($product(X1,X2),fact1(sK6)) )
| ~ spl9_78
| ~ spl9_132 ),
inference(superposition,[],[f2427,f890]) ).
tff(f4251,plain,
( spl9_203
| ~ spl9_53
| ~ spl9_202 ),
inference(avatar_split_clause,[],[f4247,f4243,f556,f4249]) ).
tff(f4249,plain,
( spl9_203
<=> ! [X0: $int,X1: $int] : ( $sum($sum(1,X0),X1) = $sum(1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_203])]) ).
tff(f4243,plain,
( spl9_202
<=> ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),X1) = $sum(sK7,$sum(X1,$product(sK7,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_202])]) ).
tff(f4247,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(1,X0),X1) = $sum(1,$sum(X1,X0)) )
| ~ spl9_53
| ~ spl9_202 ),
inference(evaluation,[],[f4246]) ).
tff(f4246,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(1,$product(1,X0)),X1) = $sum(1,$sum(X1,$product(1,X0))) )
| ~ spl9_53
| ~ spl9_202 ),
inference(forward_demodulation,[],[f4244,f558]) ).
tff(f4244,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),X1) = $sum(sK7,$sum(X1,$product(sK7,X0))) )
| ~ spl9_202 ),
inference(avatar_component_clause,[],[f4243]) ).
tff(f4245,plain,
( spl9_202
| ~ spl9_4
| ~ spl9_7
| ~ spl9_58
| ~ spl9_91
| ~ spl9_131 ),
inference(avatar_split_clause,[],[f2557,f2422,f1083,f612,f162,f143,f4243]) ).
tff(f2557,plain,
( ! [X0: $int,X1: $int] : ( $sum($sum(sK7,$product(sK7,X0)),X1) = $sum(sK7,$sum(X1,$product(sK7,X0))) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_58
| ~ spl9_91
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2556,f613]) ).
tff(f2556,plain,
( ! [X0: $int,X1: $int] : ( $sum(sK7,$sum(X1,$product(sK7,X0))) = $sum($product(sK7,$sum(X0,fact1(sK6))),X1) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_91
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2555,f163]) ).
tff(f2555,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X0,fact1(sK6))),X1) = $sum(fact1(sK5),$sum(X1,$product(sK7,X0))) )
| ~ spl9_4
| ~ spl9_91
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2483,f1084]) ).
tff(f2483,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X0,fact1(sK6))),X1) = $sum($product(sK7,X0),$sum(fact1(sK5),X1)) )
| ~ spl9_4
| ~ spl9_131 ),
inference(superposition,[],[f2423,f145]) ).
tff(f4238,plain,
( spl9_201
| ~ spl9_49
| ~ spl9_57
| ~ spl9_90
| ~ spl9_131 ),
inference(avatar_split_clause,[],[f2543,f2422,f1079,f595,f468,f4236]) ).
tff(f4236,plain,
( spl9_201
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X1,X0)),X2) = $sum($product(sK7,$sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_201])]) ).
tff(f2543,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum(X1,X0)),X2) = $sum($product(sK7,$sum(X0,X1)),X2) )
| ~ spl9_49
| ~ spl9_57
| ~ spl9_90
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2542,f609]) ).
tff(f609,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $product(sK7,$sum(X0,X1)) )
| ~ spl9_49
| ~ spl9_57 ),
inference(forward_demodulation,[],[f601,f469]) ).
tff(f601,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $sum($product(sK7,X0),$product(sK7,X1)) )
| ~ spl9_49
| ~ spl9_57 ),
inference(superposition,[],[f469,f596]) ).
tff(f2542,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum($product(fact1(sK6),X0),X1)),X2) = $sum($product(sK7,$sum(X1,X0)),X2) )
| ~ spl9_49
| ~ spl9_57
| ~ spl9_90
| ~ spl9_131 ),
inference(forward_demodulation,[],[f2473,f1141]) ).
tff(f1141,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,$sum(X1,X2)),X3) = $sum($product(X0,X2),$sum($product(X0,X1),X3)) )
| ~ spl9_49
| ~ spl9_90 ),
inference(superposition,[],[f1080,f469]) ).
tff(f2473,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($product(sK7,$sum($product(fact1(sK6),X0),X1)),X2) = $sum($product(sK7,X0),$sum($product(sK7,X1),X2)) )
| ~ spl9_57
| ~ spl9_131 ),
inference(superposition,[],[f2423,f596]) ).
tff(f4227,plain,
( spl9_200
| ~ spl9_34
| ~ spl9_116 ),
inference(avatar_split_clause,[],[f2333,f1688,f296,f4225]) ).
tff(f4225,plain,
( spl9_200
<=> ! [X0: $int] :
( $less(X0,sK7)
| $less(sK7,$product(X0,fact1(sK6)))
| ( sK7 = $product(X0,fact1(sK6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_200])]) ).
tff(f1688,plain,
( spl9_116
<=> ! [X0: $int] :
( ~ $less($product(X0,fact1(sK6)),sK7)
| $less(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_116])]) ).
tff(f2333,plain,
( ! [X0: $int] :
( $less(X0,sK7)
| $less(sK7,$product(X0,fact1(sK6)))
| ( sK7 = $product(X0,fact1(sK6)) ) )
| ~ spl9_34
| ~ spl9_116 ),
inference(resolution,[],[f1689,f297]) ).
tff(f1689,plain,
( ! [X0: $int] :
( ~ $less($product(X0,fact1(sK6)),sK7)
| $less(X0,sK7) )
| ~ spl9_116 ),
inference(avatar_component_clause,[],[f1688]) ).
tff(f4223,plain,
( spl9_199
| ~ spl9_12
| ~ spl9_47
| ~ spl9_53
| ~ spl9_58
| ~ spl9_64
| ~ spl9_148
| ~ spl9_198 ),
inference(avatar_split_clause,[],[f4218,f4210,f3333,f708,f612,f556,f444,f188,f4220]) ).
tff(f4220,plain,
( spl9_199
<=> ( 2 = fact1(2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_199])]) ).
tff(f4210,plain,
( spl9_198
<=> ( $product(fact1(fact1(sK6)),$sum(1,fact1(sK6))) = fact1($sum(1,fact1(sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_198])]) ).
tff(f4218,plain,
( ( 2 = fact1(2) )
| ~ spl9_12
| ~ spl9_47
| ~ spl9_53
| ~ spl9_58
| ~ spl9_64
| ~ spl9_148
| ~ spl9_198 ),
inference(evaluation,[],[f4217]) ).
tff(f4217,plain,
( ( fact1(2) = $product(1,2) )
| ~ spl9_12
| ~ spl9_47
| ~ spl9_53
| ~ spl9_58
| ~ spl9_64
| ~ spl9_148
| ~ spl9_198 ),
inference(forward_demodulation,[],[f4216,f730]) ).
tff(f4216,plain,
( ( fact1(2) = $product(fact1(1),2) )
| ~ spl9_53
| ~ spl9_58
| ~ spl9_148
| ~ spl9_198 ),
inference(forward_demodulation,[],[f4215,f3335]) ).
tff(f4215,plain,
( ( $product(fact1(fact1(sK6)),2) = fact1(2) )
| ~ spl9_53
| ~ spl9_58
| ~ spl9_198 ),
inference(evaluation,[],[f4214]) ).
tff(f4214,plain,
( ( $product(fact1(fact1(sK6)),$sum(1,1)) = fact1($sum(1,1)) )
| ~ spl9_53
| ~ spl9_58
| ~ spl9_198 ),
inference(forward_demodulation,[],[f4212,f938]) ).
tff(f938,plain,
( ! [X0: $int] : ( $sum(1,X0) = $sum(X0,fact1(sK6)) )
| ~ spl9_53
| ~ spl9_58 ),
inference(evaluation,[],[f934]) ).
tff(f934,plain,
( ! [X0: $int] : ( $product(1,$sum(X0,fact1(sK6))) = $sum(1,$product(1,X0)) )
| ~ spl9_53
| ~ spl9_58 ),
inference(superposition,[],[f613,f558]) ).
tff(f4212,plain,
( ( $product(fact1(fact1(sK6)),$sum(1,fact1(sK6))) = fact1($sum(1,fact1(sK6))) )
| ~ spl9_198 ),
inference(avatar_component_clause,[],[f4210]) ).
tff(f4213,plain,
( spl9_198
| ~ spl9_26
| spl9_62
| ~ spl9_120 ),
inference(avatar_split_clause,[],[f2332,f1984,f683,f250,f4210]) ).
tff(f1984,plain,
( spl9_120
<=> ! [X0: $int] :
( ( fact1($sum(X0,1)) = $product(fact1(X0),$sum(X0,1)) )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_120])]) ).
tff(f2332,plain,
( ( $product(fact1(fact1(sK6)),$sum(1,fact1(sK6))) = fact1($sum(1,fact1(sK6))) )
| ~ spl9_26
| spl9_62
| ~ spl9_120 ),
inference(forward_demodulation,[],[f2328,f251]) ).
tff(f2328,plain,
( ( fact1($sum(fact1(sK6),1)) = $product(fact1(fact1(sK6)),$sum(fact1(sK6),1)) )
| spl9_62
| ~ spl9_120 ),
inference(resolution,[],[f684,f1985]) ).
tff(f1985,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( fact1($sum(X0,1)) = $product(fact1(X0),$sum(X0,1)) ) )
| ~ spl9_120 ),
inference(avatar_component_clause,[],[f1984]) ).
tff(f4205,plain,
( spl9_197
| ~ spl9_49
| ~ spl9_57
| ~ spl9_111 ),
inference(avatar_split_clause,[],[f1880,f1566,f595,f468,f4203]) ).
tff(f4203,plain,
( spl9_197
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $product(sK7,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_197])]) ).
tff(f1880,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $product(sK7,$sum(X1,X0)) )
| ~ spl9_49
| ~ spl9_57
| ~ spl9_111 ),
inference(forward_demodulation,[],[f1838,f469]) ).
tff(f1838,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $sum($product(sK7,X1),$product(sK7,X0)) )
| ~ spl9_57
| ~ spl9_111 ),
inference(superposition,[],[f1567,f596]) ).
tff(f4197,plain,
( spl9_59
| spl9_196
| ~ spl9_57
| ~ spl9_96 ),
inference(avatar_split_clause,[],[f1427,f1103,f595,f4195,f616]) ).
tff(f4195,plain,
( spl9_196
<=> ! [X0: $int] :
( ( 0 != $product(sK7,X0) )
| ( 0 = $product(fact1(sK6),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_196])]) ).
tff(f1427,plain,
( ! [X0: $int] :
( ( 0 != $product(sK7,X0) )
| ( 0 = sK7 )
| ( 0 = $product(fact1(sK6),X0) ) )
| ~ spl9_57
| ~ spl9_96 ),
inference(superposition,[],[f1104,f596]) ).
tff(f4193,plain,
( ~ spl9_195
| spl9_127
| ~ spl9_148 ),
inference(avatar_split_clause,[],[f3962,f3333,f2321,f4190]) ).
tff(f4190,plain,
( spl9_195
<=> $less(1,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_195])]) ).
tff(f2321,plain,
( spl9_127
<=> $less(fact1(sK6),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_127])]) ).
tff(f3962,plain,
( ~ $less(1,sK6)
| spl9_127
| ~ spl9_148 ),
inference(superposition,[],[f2322,f3335]) ).
tff(f2322,plain,
( ~ $less(fact1(sK6),sK6)
| spl9_127 ),
inference(avatar_component_clause,[],[f2321]) ).
tff(f4187,plain,
( spl9_194
| ~ spl9_43
| ~ spl9_57
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1397,f1091,f595,f382,f4185]) ).
tff(f4185,plain,
( spl9_194
<=> ! [X0: $int,X1: $int] : ( $product(X1,$product(sK7,X0)) = $product(sK7,$product(fact1(sK6),$product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_194])]) ).
tff(f1397,plain,
( ! [X0: $int,X1: $int] : ( $product(X1,$product(sK7,X0)) = $product(sK7,$product(fact1(sK6),$product(X0,X1))) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_93 ),
inference(forward_demodulation,[],[f1344,f383]) ).
tff(f1344,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product($product(fact1(sK6),X0),X1)) = $product(X1,$product(sK7,X0)) )
| ~ spl9_57
| ~ spl9_93 ),
inference(superposition,[],[f1092,f596]) ).
tff(f4182,plain,
( spl9_193
| ~ spl9_57
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1381,f1091,f595,f4180]) ).
tff(f4180,plain,
( spl9_193
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product(sK7,$product(X0,$product(X1,fact1(sK6)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_193])]) ).
tff(f1381,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product(sK7,$product(X0,$product(X1,fact1(sK6)))) )
| ~ spl9_57
| ~ spl9_93 ),
inference(superposition,[],[f596,f1092]) ).
tff(f4175,plain,
( spl9_192
| ~ spl9_57
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1365,f1091,f595,f4173]) ).
tff(f4173,plain,
( spl9_192
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product(sK7,$product(X1,$product(fact1(sK6),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_192])]) ).
tff(f1365,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product(sK7,$product(X1,$product(fact1(sK6),X0))) )
| ~ spl9_57
| ~ spl9_93 ),
inference(superposition,[],[f596,f1092]) ).
tff(f4168,plain,
( spl9_191
| ~ spl9_57
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1326,f1091,f595,f4166]) ).
tff(f4166,plain,
( spl9_191
<=> ! [X0: $int,X1: $int] : ( $product(X1,$product(sK7,X0)) = $product($product(fact1(sK6),X0),$product(X1,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_191])]) ).
tff(f1326,plain,
( ! [X0: $int,X1: $int] : ( $product(X1,$product(sK7,X0)) = $product($product(fact1(sK6),X0),$product(X1,sK7)) )
| ~ spl9_57
| ~ spl9_93 ),
inference(superposition,[],[f1092,f596]) ).
tff(f4162,plain,
( spl9_190
| ~ spl9_43
| ~ spl9_57
| ~ spl9_92 ),
inference(avatar_split_clause,[],[f1308,f1087,f595,f382,f4160]) ).
tff(f4160,plain,
( spl9_190
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product($product(fact1(sK6),X0),$product(sK7,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_190])]) ).
tff(f1308,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$product(X0,X1)) = $product($product(fact1(sK6),X0),$product(sK7,X1)) )
| ~ spl9_43
| ~ spl9_57
| ~ spl9_92 ),
inference(forward_demodulation,[],[f1286,f383]) ).
tff(f1286,plain,
( ! [X0: $int,X1: $int] : ( $product($product(sK7,X0),X1) = $product($product(fact1(sK6),X0),$product(sK7,X1)) )
| ~ spl9_57
| ~ spl9_92 ),
inference(superposition,[],[f1088,f596]) ).
tff(f4155,plain,
( spl9_189
| ~ spl9_58
| ~ spl9_60 ),
inference(avatar_split_clause,[],[f719,f620,f612,f4153]) ).
tff(f4153,plain,
( spl9_189
<=> ! [X0: $int] :
( ( sK7 != $sum(sK7,$product(sK7,X0)) )
| ( fact1(sK6) = $sum(X0,fact1(sK6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_189])]) ).
tff(f620,plain,
( spl9_60
<=> ! [X0: $int] :
( ( sK7 != $product(sK7,X0) )
| ( fact1(sK6) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_60])]) ).
tff(f719,plain,
( ! [X0: $int] :
( ( sK7 != $sum(sK7,$product(sK7,X0)) )
| ( fact1(sK6) = $sum(X0,fact1(sK6)) ) )
| ~ spl9_58
| ~ spl9_60 ),
inference(superposition,[],[f621,f613]) ).
tff(f621,plain,
( ! [X0: $int] :
( ( sK7 != $product(sK7,X0) )
| ( fact1(sK6) = X0 ) )
| ~ spl9_60 ),
inference(avatar_component_clause,[],[f620]) ).
tff(f4149,plain,
( spl9_188
| ~ spl9_49
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f610,f595,f468,f4147]) ).
tff(f4147,plain,
( spl9_188
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$product(fact1(sK6),X0))) = $product(sK7,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_188])]) ).
tff(f610,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$product(fact1(sK6),X0))) = $product(sK7,$sum(X1,X0)) )
| ~ spl9_49
| ~ spl9_57 ),
inference(forward_demodulation,[],[f602,f469]) ).
tff(f602,plain,
( ! [X0: $int,X1: $int] : ( $product(sK7,$sum(X1,$product(fact1(sK6),X0))) = $sum($product(sK7,X1),$product(sK7,X0)) )
| ~ spl9_49
| ~ spl9_57 ),
inference(superposition,[],[f469,f596]) ).
tff(f4143,plain,
( spl9_187
| ~ spl9_49
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f609,f595,f468,f4141]) ).
tff(f4141,plain,
( spl9_187
<=> ! [X0: $int,X1: $int] : ( $product(sK7,$sum($product(fact1(sK6),X0),X1)) = $product(sK7,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_187])]) ).
tff(f4135,plain,
( spl9_186
| ~ spl9_43
| ~ spl9_116 ),
inference(avatar_split_clause,[],[f2339,f1688,f382,f4133]) ).
tff(f4133,plain,
( spl9_186
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X0,$product(X1,fact1(sK6))),sK7)
| $less($product(X0,X1),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_186])]) ).
tff(f2339,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,$product(X1,fact1(sK6))),sK7)
| $less($product(X0,X1),sK7) )
| ~ spl9_43
| ~ spl9_116 ),
inference(superposition,[],[f1689,f383]) ).
tff(f4091,plain,
( ~ spl9_185
| spl9_115
| ~ spl9_148 ),
inference(avatar_split_clause,[],[f3960,f3333,f1672,f4088]) ).
tff(f3960,plain,
( ~ $less(1,sK5)
| spl9_115
| ~ spl9_148 ),
inference(superposition,[],[f1673,f3335]) ).
tff(f4086,plain,
( spl9_184
| ~ spl9_53
| ~ spl9_148
| ~ spl9_183 ),
inference(avatar_split_clause,[],[f4082,f4076,f3333,f556,f4084]) ).
tff(f4084,plain,
( spl9_184
<=> ! [X0: $int,X1: $int] :
( $less($product(X0,X1),1)
| ~ $less($product(X1,X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_184])]) ).
tff(f4076,plain,
( spl9_183
<=> ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X0,fact1(sK6))),sK7)
| $less($product(X0,X1),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_183])]) ).
tff(f4082,plain,
( ! [X0: $int,X1: $int] :
( $less($product(X0,X1),1)
| ~ $less($product(X1,X0),1) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_183 ),
inference(forward_demodulation,[],[f4081,f558]) ).
tff(f4081,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,X0),1)
| $less($product(X0,X1),sK7) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_183 ),
inference(evaluation,[],[f4080]) ).
tff(f4080,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X0,1)),1)
| $less($product(X0,X1),sK7) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_183 ),
inference(forward_demodulation,[],[f4079,f3335]) ).
tff(f4079,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X0,fact1(sK6))),1)
| $less($product(X0,X1),sK7) )
| ~ spl9_53
| ~ spl9_183 ),
inference(forward_demodulation,[],[f4077,f558]) ).
tff(f4077,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X0,fact1(sK6))),sK7)
| $less($product(X0,X1),sK7) )
| ~ spl9_183 ),
inference(avatar_component_clause,[],[f4076]) ).
tff(f4078,plain,
( spl9_183
| ~ spl9_92
| ~ spl9_116 ),
inference(avatar_split_clause,[],[f2338,f1688,f1087,f4076]) ).
tff(f2338,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,$product(X0,fact1(sK6))),sK7)
| $less($product(X0,X1),sK7) )
| ~ spl9_92
| ~ spl9_116 ),
inference(superposition,[],[f1689,f1088]) ).
tff(f4072,plain,
( spl9_182
| ~ spl9_4
| ~ spl9_7
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1815,f1562,f162,f143,f4070]) ).
tff(f4070,plain,
( spl9_182
<=> ! [X0: $int] : ( $sum($product(fact1(sK6),X0),sK7) = $product(fact1(sK6),$sum(X0,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_182])]) ).
tff(f1815,plain,
( ! [X0: $int] : ( $sum($product(fact1(sK6),X0),sK7) = $product(fact1(sK6),$sum(X0,sK7)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1779,f163]) ).
tff(f1779,plain,
( ! [X0: $int] : ( $sum($product(fact1(sK6),X0),fact1(sK5)) = $product(fact1(sK6),$sum(X0,sK7)) )
| ~ spl9_4
| ~ spl9_110 ),
inference(superposition,[],[f1563,f145]) ).
tff(f4067,plain,
( spl9_181
| ~ spl9_4
| ~ spl9_7
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1750,f1554,f162,f143,f4065]) ).
tff(f4065,plain,
( spl9_181
<=> ! [X0: $int] : ( $product(fact1(sK6),$sum(sK7,X0)) = $sum(sK7,$product(fact1(sK6),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_181])]) ).
tff(f1750,plain,
( ! [X0: $int] : ( $product(fact1(sK6),$sum(sK7,X0)) = $sum(sK7,$product(fact1(sK6),X0)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1711,f163]) ).
tff(f1711,plain,
( ! [X0: $int] : ( $product(fact1(sK6),$sum(sK7,X0)) = $sum(fact1(sK5),$product(fact1(sK6),X0)) )
| ~ spl9_4
| ~ spl9_109 ),
inference(superposition,[],[f1555,f145]) ).
tff(f4061,plain,
( spl9_180
| ~ spl9_43
| ~ spl9_63 ),
inference(avatar_split_clause,[],[f1684,f687,f382,f4059]) ).
tff(f4059,plain,
( spl9_180
<=> ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X0,$product(X1,fact1(sK6))))
| $less(sK7,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_180])]) ).
tff(f687,plain,
( spl9_63
<=> ! [X0: $int] :
( ~ $less(sK7,$product(X0,fact1(sK6)))
| $less(sK7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_63])]) ).
tff(f1684,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X0,$product(X1,fact1(sK6))))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_43
| ~ spl9_63 ),
inference(superposition,[],[f688,f383]) ).
tff(f688,plain,
( ! [X0: $int] :
( ~ $less(sK7,$product(X0,fact1(sK6)))
| $less(sK7,X0) )
| ~ spl9_63 ),
inference(avatar_component_clause,[],[f687]) ).
tff(f4021,plain,
( spl9_179
| ~ spl9_53
| ~ spl9_148
| ~ spl9_178 ),
inference(avatar_split_clause,[],[f4017,f4011,f3333,f556,f4019]) ).
tff(f4019,plain,
( spl9_179
<=> ! [X0: $int,X1: $int] :
( $less(1,$product(X0,X1))
| ~ $less(1,$product(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_179])]) ).
tff(f4011,plain,
( spl9_178
<=> ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X1,$product(X0,fact1(sK6))))
| $less(sK7,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_178])]) ).
tff(f4017,plain,
( ! [X0: $int,X1: $int] :
( $less(1,$product(X0,X1))
| ~ $less(1,$product(X1,X0)) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_178 ),
inference(forward_demodulation,[],[f4016,f558]) ).
tff(f4016,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(1,$product(X1,X0))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_178 ),
inference(forward_demodulation,[],[f4015,f558]) ).
tff(f4015,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X1,X0))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_148
| ~ spl9_178 ),
inference(evaluation,[],[f4014]) ).
tff(f4014,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X1,$product(X0,1)))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_148
| ~ spl9_178 ),
inference(forward_demodulation,[],[f4012,f3335]) ).
tff(f4012,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X1,$product(X0,fact1(sK6))))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_178 ),
inference(avatar_component_clause,[],[f4011]) ).
tff(f4013,plain,
( spl9_178
| ~ spl9_63
| ~ spl9_92 ),
inference(avatar_split_clause,[],[f1683,f1087,f687,f4011]) ).
tff(f1683,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(sK7,$product(X1,$product(X0,fact1(sK6))))
| $less(sK7,$product(X0,X1)) )
| ~ spl9_63
| ~ spl9_92 ),
inference(superposition,[],[f688,f1088]) ).
tff(f4007,plain,
( spl9_177
| ~ spl9_60
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1382,f1091,f620,f4005]) ).
tff(f4005,plain,
( spl9_177
<=> ! [X0: $int,X1: $int] :
( ( sK7 != $product(X0,$product(X1,sK7)) )
| ( $product(X0,X1) = fact1(sK6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_177])]) ).
tff(f1382,plain,
( ! [X0: $int,X1: $int] :
( ( sK7 != $product(X0,$product(X1,sK7)) )
| ( $product(X0,X1) = fact1(sK6) ) )
| ~ spl9_60
| ~ spl9_93 ),
inference(superposition,[],[f621,f1092]) ).
tff(f3953,plain,
( spl9_176
| ~ spl9_53
| ~ spl9_148
| ~ spl9_175 ),
inference(avatar_split_clause,[],[f3949,f3944,f3333,f556,f3951]) ).
tff(f3951,plain,
( spl9_176
<=> ! [X0: $int,X1: $int] :
( ( 1 = $product(X0,X1) )
| ( 1 != $product(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_176])]) ).
tff(f3944,plain,
( spl9_175
<=> ! [X0: $int,X1: $int] :
( ( sK7 != $product(X1,$product(sK7,X0)) )
| ( $product(X0,X1) = fact1(sK6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_175])]) ).
tff(f3949,plain,
( ! [X0: $int,X1: $int] :
( ( 1 = $product(X0,X1) )
| ( 1 != $product(X1,X0) ) )
| ~ spl9_53
| ~ spl9_148
| ~ spl9_175 ),
inference(forward_demodulation,[],[f3948,f3335]) ).
tff(f3948,plain,
( ! [X0: $int,X1: $int] :
( ( 1 != $product(X1,X0) )
| ( $product(X0,X1) = fact1(sK6) ) )
| ~ spl9_53
| ~ spl9_175 ),
inference(evaluation,[],[f3947]) ).
tff(f3947,plain,
( ! [X0: $int,X1: $int] :
( ( 1 != $product(X1,$product(1,X0)) )
| ( $product(X0,X1) = fact1(sK6) ) )
| ~ spl9_53
| ~ spl9_175 ),
inference(forward_demodulation,[],[f3945,f558]) ).
tff(f3945,plain,
( ! [X0: $int,X1: $int] :
( ( sK7 != $product(X1,$product(sK7,X0)) )
| ( $product(X0,X1) = fact1(sK6) ) )
| ~ spl9_175 ),
inference(avatar_component_clause,[],[f3944]) ).
tff(f3946,plain,
( spl9_175
| ~ spl9_60
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1367,f1091,f620,f3944]) ).
tff(f1367,plain,
( ! [X0: $int,X1: $int] :
( ( sK7 != $product(X1,$product(sK7,X0)) )
| ( $product(X0,X1) = fact1(sK6) ) )
| ~ spl9_60
| ~ spl9_93 ),
inference(superposition,[],[f621,f1092]) ).
tff(f3939,plain,
( spl9_172
| spl9_174
| ~ spl9_4
| ~ spl9_7
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f1946,f1574,f162,f143,f3937,f3922]) ).
tff(f3937,plain,
( spl9_174
<=> ! [X0: $int] :
( ~ $less($product(X0,sK7),sK7)
| $less(X0,fact1(sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_174])]) ).
tff(f1946,plain,
( ! [X0: $int] :
( ~ $less($product(X0,sK7),sK7)
| $less(sK7,0)
| $less(X0,fact1(sK6)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_113 ),
inference(forward_demodulation,[],[f1936,f163]) ).
tff(f1936,plain,
( ! [X0: $int] :
( ~ $less($product(X0,sK7),fact1(sK5))
| $less(sK7,0)
| $less(X0,fact1(sK6)) )
| ~ spl9_4
| ~ spl9_113 ),
inference(superposition,[],[f1575,f145]) ).
tff(f3931,plain,
( ~ spl9_53
| ~ spl9_172 ),
inference(avatar_contradiction_clause,[],[f3930]) ).
tff(f3930,plain,
( $false
| ~ spl9_53
| ~ spl9_172 ),
inference(evaluation,[],[f3929]) ).
tff(f3929,plain,
( $less(1,0)
| ~ spl9_53
| ~ spl9_172 ),
inference(forward_demodulation,[],[f3924,f558]) ).
tff(f3924,plain,
( $less(sK7,0)
| ~ spl9_172 ),
inference(avatar_component_clause,[],[f3922]) ).
tff(f3928,plain,
( spl9_172
| spl9_173
| ~ spl9_4
| ~ spl9_7
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1910,f1570,f162,f143,f3926,f3922]) ).
tff(f3926,plain,
( spl9_173
<=> ! [X0: $int] :
( ~ $less(sK7,$product(X0,sK7))
| $less(fact1(sK6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_173])]) ).
tff(f1910,plain,
( ! [X0: $int] :
( ~ $less(sK7,$product(X0,sK7))
| $less(sK7,0)
| $less(fact1(sK6),X0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_112 ),
inference(forward_demodulation,[],[f1893,f163]) ).
tff(f1893,plain,
( ! [X0: $int] :
( ~ $less(fact1(sK5),$product(X0,sK7))
| $less(sK7,0)
| $less(fact1(sK6),X0) )
| ~ spl9_4
| ~ spl9_112 ),
inference(superposition,[],[f1571,f145]) ).
tff(f3917,plain,
( spl9_171
| ~ spl9_4
| ~ spl9_7
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1807,f1562,f162,f143,f3915]) ).
tff(f3915,plain,
( spl9_171
<=> ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(sK7,$product(X0,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_171])]) ).
tff(f1807,plain,
( ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(sK7,$product(X0,sK7)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1768,f163]) ).
tff(f1768,plain,
( ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(fact1(sK5),$product(X0,sK7)) )
| ~ spl9_4
| ~ spl9_110 ),
inference(superposition,[],[f1563,f145]) ).
tff(f3910,plain,
( spl9_170
| ~ spl9_4
| ~ spl9_7
| ~ spl9_26
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1757,f1554,f250,f162,f143,f3908]) ).
tff(f3908,plain,
( spl9_170
<=> ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum(sK7,$product(X0,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_170])]) ).
tff(f1757,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum(sK7,$product(X0,sK7)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_26
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1756,f251]) ).
tff(f1756,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum($product(X0,sK7),sK7) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1722,f163]) ).
tff(f1722,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum($product(X0,sK7),fact1(sK5)) )
| ~ spl9_4
| ~ spl9_109 ),
inference(superposition,[],[f1555,f145]) ).
tff(f3902,plain,
( spl9_169
| ~ spl9_57
| ~ spl9_60 ),
inference(avatar_split_clause,[],[f718,f620,f595,f3900]) ).
tff(f3900,plain,
( spl9_169
<=> ! [X0: $int] :
( ( sK7 != $product(sK7,X0) )
| ( fact1(sK6) = $product(fact1(sK6),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_169])]) ).
tff(f718,plain,
( ! [X0: $int] :
( ( sK7 != $product(sK7,X0) )
| ( fact1(sK6) = $product(fact1(sK6),X0) ) )
| ~ spl9_57
| ~ spl9_60 ),
inference(superposition,[],[f621,f596]) ).
tff(f3895,plain,
( spl9_61
| ~ spl9_26
| ~ spl9_58 ),
inference(avatar_split_clause,[],[f641,f612,f250,f633]) ).
tff(f633,plain,
( spl9_61
<=> ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(sK7,$product(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_61])]) ).
tff(f641,plain,
( ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(sK7,$product(sK7,X0)) )
| ~ spl9_26
| ~ spl9_58 ),
inference(superposition,[],[f613,f251]) ).
tff(f3548,plain,
( spl9_168
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_114 ),
inference(avatar_split_clause,[],[f3109,f1578,f889,f556,f162,f143,f3546]) ).
tff(f3546,plain,
( spl9_168
<=> ! [X0: $int,X1: $int] :
( ( 1 = X1 )
| ( $product(X0,X1) != X0 )
| ( 0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_168])]) ).
tff(f3109,plain,
( ! [X0: $int,X1: $int] :
( ( 1 = X1 )
| ( $product(X0,X1) != X0 )
| ( 0 = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_114 ),
inference(forward_demodulation,[],[f3108,f558]) ).
tff(f3108,plain,
( ! [X0: $int,X1: $int] :
( ( sK7 = X1 )
| ( $product(X0,X1) != X0 )
| ( 0 = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_114 ),
inference(forward_demodulation,[],[f3029,f2946]) ).
tff(f3029,plain,
( ! [X0: $int,X1: $int] :
( ( $product(X0,X1) != X0 )
| ( 0 = X0 )
| ( fact1(sK6) = X1 ) )
| ~ spl9_78
| ~ spl9_114 ),
inference(superposition,[],[f1579,f890]) ).
tff(f3544,plain,
( spl9_167
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_113 ),
inference(avatar_split_clause,[],[f3107,f1574,f889,f556,f162,f143,f3542]) ).
tff(f3542,plain,
( spl9_167
<=> ! [X0: $int,X1: $int] :
( $less(1,X1)
| ~ $less(X0,$product(X0,X1))
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_167])]) ).
tff(f3107,plain,
( ! [X0: $int,X1: $int] :
( $less(1,X1)
| ~ $less(X0,$product(X0,X1))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_113 ),
inference(forward_demodulation,[],[f3106,f558]) ).
tff(f3106,plain,
( ! [X0: $int,X1: $int] :
( $less(sK7,X1)
| ~ $less(X0,$product(X0,X1))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_113 ),
inference(forward_demodulation,[],[f3028,f2946]) ).
tff(f3028,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$product(X0,X1))
| $less(X0,0)
| $less(fact1(sK6),X1) )
| ~ spl9_78
| ~ spl9_113 ),
inference(superposition,[],[f1575,f890]) ).
tff(f3540,plain,
( spl9_166
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f3102,f1570,f889,f556,f162,f143,f3538]) ).
tff(f3538,plain,
( spl9_166
<=> ! [X0: $int,X1: $int] :
( $less(X1,1)
| ~ $less($product(X0,X1),X0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_166])]) ).
tff(f3102,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| ~ $less($product(X0,X1),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_112 ),
inference(forward_demodulation,[],[f3101,f558]) ).
tff(f3101,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,sK7)
| ~ $less($product(X0,X1),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_112 ),
inference(forward_demodulation,[],[f3026,f2946]) ).
tff(f3026,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X0,X1),X0)
| $less(X0,0)
| $less(X1,fact1(sK6)) )
| ~ spl9_78
| ~ spl9_112 ),
inference(superposition,[],[f1571,f890]) ).
tff(f3536,plain,
( spl9_165
| ~ spl9_53
| ~ spl9_58
| ~ spl9_78
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f3089,f1562,f889,f612,f556,f3534]) ).
tff(f3534,plain,
( spl9_165
<=> ! [X0: $int,X1: $int] : ( $sum($product(X0,X1),X0) = $product(X0,$sum(1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_165])]) ).
tff(f3089,plain,
( ! [X0: $int,X1: $int] : ( $sum($product(X0,X1),X0) = $product(X0,$sum(1,X1)) )
| ~ spl9_53
| ~ spl9_58
| ~ spl9_78
| ~ spl9_110 ),
inference(forward_demodulation,[],[f3021,f938]) ).
tff(f3021,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,$sum(X1,fact1(sK6))) = $sum($product(X0,X1),X0) )
| ~ spl9_78
| ~ spl9_110 ),
inference(superposition,[],[f1563,f890]) ).
tff(f3532,plain,
( spl9_164
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f3086,f1554,f889,f556,f162,f143,f3530]) ).
tff(f3086,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$product(X0,X1)) = $product(X0,$sum(1,X1)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_109 ),
inference(forward_demodulation,[],[f3085,f558]) ).
tff(f3085,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,$sum(sK7,X1)) = $sum(X0,$product(X0,X1)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_78
| ~ spl9_109 ),
inference(forward_demodulation,[],[f3019,f2946]) ).
tff(f3019,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,$sum(fact1(sK6),X1)) = $sum(X0,$product(X0,X1)) )
| ~ spl9_78
| ~ spl9_109 ),
inference(superposition,[],[f1555,f890]) ).
tff(f3527,plain,
( spl9_163
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f2946,f556,f162,f143,f3524]) ).
tff(f3524,plain,
( spl9_163
<=> ( sK7 = fact1(sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_163])]) ).
tff(f3522,plain,
( spl9_162
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(avatar_split_clause,[],[f3072,f889,f556,f472,f162,f143,f3520]) ).
tff(f3520,plain,
( spl9_162
<=> ! [X0: $int,X1: $int] :
( $less(X1,1)
| ~ $less($product(X1,X0),X0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_162])]) ).
tff(f3072,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| ~ $less($product(X1,X0),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(forward_demodulation,[],[f3071,f558]) ).
tff(f3071,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,sK7)
| ~ $less($product(X1,X0),X0)
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(forward_demodulation,[],[f3012,f2946]) ).
tff(f3012,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($product(X1,X0),X0)
| $less(X0,0)
| $less(X1,fact1(sK6)) )
| ~ spl9_50
| ~ spl9_78 ),
inference(superposition,[],[f473,f890]) ).
tff(f3518,plain,
( spl9_161
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(avatar_split_clause,[],[f3070,f889,f556,f472,f162,f143,f3516]) ).
tff(f3516,plain,
( spl9_161
<=> ! [X0: $int,X1: $int] :
( $less(1,X1)
| ~ $less(X0,$product(X1,X0))
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_161])]) ).
tff(f3070,plain,
( ! [X0: $int,X1: $int] :
( $less(1,X1)
| ~ $less(X0,$product(X1,X0))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(forward_demodulation,[],[f3069,f558]) ).
tff(f3069,plain,
( ! [X0: $int,X1: $int] :
( $less(sK7,X1)
| ~ $less(X0,$product(X1,X0))
| $less(X0,0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50
| ~ spl9_53
| ~ spl9_78 ),
inference(forward_demodulation,[],[f3011,f2946]) ).
tff(f3011,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$product(X1,X0))
| $less(X0,0)
| $less(fact1(sK6),X1) )
| ~ spl9_50
| ~ spl9_78 ),
inference(superposition,[],[f473,f890]) ).
tff(f3514,plain,
( spl9_160
| ~ spl9_78
| ~ spl9_159 ),
inference(avatar_split_clause,[],[f3509,f3505,f889,f3511]) ).
tff(f3511,plain,
( spl9_160
<=> ( $sum(1,sK6) = fact1($sum(1,sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_160])]) ).
tff(f3505,plain,
( spl9_159
<=> ( $product(fact1(sK6),$sum(1,sK6)) = fact1($sum(1,sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_159])]) ).
tff(f3509,plain,
( ( $sum(1,sK6) = fact1($sum(1,sK6)) )
| ~ spl9_78
| ~ spl9_159 ),
inference(forward_demodulation,[],[f3507,f890]) ).
tff(f3507,plain,
( ( $product(fact1(sK6),$sum(1,sK6)) = fact1($sum(1,sK6)) )
| ~ spl9_159 ),
inference(avatar_component_clause,[],[f3505]) ).
tff(f3508,plain,
( spl9_159
| spl9_2
| ~ spl9_26
| ~ spl9_120 ),
inference(avatar_split_clause,[],[f2169,f1984,f250,f133,f3505]) ).
tff(f2169,plain,
( ( $product(fact1(sK6),$sum(1,sK6)) = fact1($sum(1,sK6)) )
| spl9_2
| ~ spl9_26
| ~ spl9_120 ),
inference(forward_demodulation,[],[f2159,f251]) ).
tff(f2159,plain,
( ( fact1($sum(sK6,1)) = $product(fact1(sK6),$sum(sK6,1)) )
| spl9_2
| ~ spl9_120 ),
inference(resolution,[],[f1985,f135]) ).
tff(f3501,plain,
( spl9_143
| spl9_59
| ~ spl9_158
| ~ spl9_4
| ~ spl9_96 ),
inference(avatar_split_clause,[],[f1426,f1103,f143,f3498,f616,f3223]) ).
tff(f3498,plain,
( spl9_158
<=> ( 0 = fact1(sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_158])]) ).
tff(f1426,plain,
( ( 0 != fact1(sK5) )
| ( 0 = sK7 )
| ( 0 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_96 ),
inference(superposition,[],[f1104,f145]) ).
tff(f3496,plain,
( spl9_157
| ~ spl9_53
| ~ spl9_156 ),
inference(avatar_split_clause,[],[f3491,f3486,f556,f3493]) ).
tff(f3493,plain,
( spl9_157
<=> ( $sum(1,sK5) = fact1($sum(1,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_157])]) ).
tff(f3486,plain,
( spl9_156
<=> ( fact1($sum(1,sK5)) = $product(sK7,$sum(1,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_156])]) ).
tff(f3491,plain,
( ( $sum(1,sK5) = fact1($sum(1,sK5)) )
| ~ spl9_53
| ~ spl9_156 ),
inference(evaluation,[],[f3490]) ).
tff(f3490,plain,
( ( fact1($sum(1,sK5)) = $product(1,$sum(1,sK5)) )
| ~ spl9_53
| ~ spl9_156 ),
inference(forward_demodulation,[],[f3488,f558]) ).
tff(f3488,plain,
( ( fact1($sum(1,sK5)) = $product(sK7,$sum(1,sK5)) )
| ~ spl9_156 ),
inference(avatar_component_clause,[],[f3486]) ).
tff(f3489,plain,
( spl9_156
| spl9_1
| ~ spl9_7
| ~ spl9_26
| ~ spl9_120 ),
inference(avatar_split_clause,[],[f2168,f1984,f250,f162,f128,f3486]) ).
tff(f2168,plain,
( ( fact1($sum(1,sK5)) = $product(sK7,$sum(1,sK5)) )
| spl9_1
| ~ spl9_7
| ~ spl9_26
| ~ spl9_120 ),
inference(forward_demodulation,[],[f2167,f163]) ).
tff(f2167,plain,
( ( $product(fact1(sK5),$sum(1,sK5)) = fact1($sum(1,sK5)) )
| spl9_1
| ~ spl9_26
| ~ spl9_120 ),
inference(forward_demodulation,[],[f2158,f251]) ).
tff(f2158,plain,
( ( fact1($sum(sK5,1)) = $product(fact1(sK5),$sum(sK5,1)) )
| spl9_1
| ~ spl9_120 ),
inference(resolution,[],[f1985,f130]) ).
tff(f3469,plain,
( spl9_155
| ~ spl9_4
| ~ spl9_7
| ~ spl9_93 ),
inference(avatar_split_clause,[],[f1396,f1091,f162,f143,f3467]) ).
tff(f3467,plain,
( spl9_155
<=> ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_155])]) ).
tff(f1396,plain,
( ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(X0,sK7) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_93 ),
inference(forward_demodulation,[],[f1343,f163]) ).
tff(f1343,plain,
( ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(X0,fact1(sK5)) )
| ~ spl9_4
| ~ spl9_93 ),
inference(superposition,[],[f1092,f145]) ).
tff(f3463,plain,
( spl9_154
| ~ spl9_27
| ~ spl9_57 ),
inference(avatar_split_clause,[],[f598,f595,f254,f3461]) ).
tff(f3461,plain,
( spl9_154
<=> ! [X0: $int] : ( $product(sK7,X0) = $product(sK7,$product(X0,fact1(sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_154])]) ).
tff(f254,plain,
( spl9_27
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
tff(f598,plain,
( ! [X0: $int] : ( $product(sK7,X0) = $product(sK7,$product(X0,fact1(sK6))) )
| ~ spl9_27
| ~ spl9_57 ),
inference(superposition,[],[f596,f255]) ).
tff(f255,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f254]) ).
tff(f3415,plain,
( spl9_153
| ~ spl9_27
| ~ spl9_116 ),
inference(avatar_split_clause,[],[f2335,f1688,f254,f3413]) ).
tff(f3413,plain,
( spl9_153
<=> ! [X0: $int] :
( ~ $less($product(fact1(sK6),X0),sK7)
| $less(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_153])]) ).
tff(f2335,plain,
( ! [X0: $int] :
( ~ $less($product(fact1(sK6),X0),sK7)
| $less(X0,sK7) )
| ~ spl9_27
| ~ spl9_116 ),
inference(superposition,[],[f1689,f255]) ).
tff(f3410,plain,
( spl9_152
| ~ spl9_27
| ~ spl9_63 ),
inference(avatar_split_clause,[],[f1680,f687,f254,f3408]) ).
tff(f3408,plain,
( spl9_152
<=> ! [X0: $int] :
( ~ $less(sK7,$product(fact1(sK6),X0))
| $less(sK7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_152])]) ).
tff(f1680,plain,
( ! [X0: $int] :
( ~ $less(sK7,$product(fact1(sK6),X0))
| $less(sK7,X0) )
| ~ spl9_27
| ~ spl9_63 ),
inference(superposition,[],[f688,f255]) ).
tff(f3406,plain,
( spl9_151
| ~ spl9_37
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f1455,f1430,f320,f3404]) ).
tff(f3404,plain,
( spl9_151
<=> ! [X0: $int] :
( ( sK5 = X0 )
| $less(X0,sK5)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_151])]) ).
tff(f1430,plain,
( spl9_97
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_97])]) ).
tff(f1455,plain,
( ! [X0: $int] :
( ( sK5 = X0 )
| $less(X0,sK5)
| $less(0,X0) )
| ~ spl9_37
| ~ spl9_97 ),
inference(resolution,[],[f1431,f322]) ).
tff(f1431,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| ( X0 = X1 )
| $less(X1,X0)
| $less(X2,X1) )
| ~ spl9_97 ),
inference(avatar_component_clause,[],[f1430]) ).
tff(f3402,plain,
( spl9_150
| ~ spl9_54
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f1454,f1430,f568,f3400]) ).
tff(f3400,plain,
( spl9_150
<=> ! [X0: $int] :
( ( sK6 = X0 )
| $less(X0,sK6)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_150])]) ).
tff(f1454,plain,
( ! [X0: $int] :
( ( sK6 = X0 )
| $less(X0,sK6)
| $less(0,X0) )
| ~ spl9_54
| ~ spl9_97 ),
inference(resolution,[],[f1431,f570]) ).
tff(f3396,plain,
( spl9_149
| ~ spl9_27
| ~ spl9_60 ),
inference(avatar_split_clause,[],[f721,f620,f254,f3394]) ).
tff(f3394,plain,
( spl9_149
<=> ! [X0: $int] :
( ( sK7 != $product(X0,sK7) )
| ( fact1(sK6) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_149])]) ).
tff(f721,plain,
( ! [X0: $int] :
( ( sK7 != $product(X0,sK7) )
| ( fact1(sK6) = X0 ) )
| ~ spl9_27
| ~ spl9_60 ),
inference(superposition,[],[f621,f255]) ).
tff(f3336,plain,
( spl9_148
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f943,f556,f162,f143,f3333]) ).
tff(f943,plain,
( ( 1 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53 ),
inference(forward_demodulation,[],[f942,f558]) ).
tff(f942,plain,
( ( sK7 = fact1(sK6) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53 ),
inference(forward_demodulation,[],[f941,f163]) ).
tff(f941,plain,
( ( fact1(sK5) = fact1(sK6) )
| ~ spl9_4
| ~ spl9_53 ),
inference(evaluation,[],[f929]) ).
tff(f3331,plain,
( spl9_147
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_146 ),
inference(avatar_split_clause,[],[f3326,f3321,f556,f162,f143,f3328]) ).
tff(f3328,plain,
( spl9_147
<=> ( 1 = $product(sK6,fact1($sum(-1,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_147])]) ).
tff(f3321,plain,
( spl9_146
<=> ( fact1(sK6) = $product(sK6,fact1($sum(-1,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_146])]) ).
tff(f3326,plain,
( ( 1 = $product(sK6,fact1($sum(-1,sK6))) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_146 ),
inference(forward_demodulation,[],[f3325,f558]) ).
tff(f3325,plain,
( ( sK7 = $product(sK6,fact1($sum(-1,sK6))) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_53
| ~ spl9_146 ),
inference(forward_demodulation,[],[f3323,f2946]) ).
tff(f3323,plain,
( ( fact1(sK6) = $product(sK6,fact1($sum(-1,sK6))) )
| ~ spl9_146 ),
inference(avatar_component_clause,[],[f3321]) ).
tff(f3324,plain,
( spl9_146
| ~ spl9_26
| ~ spl9_47
| ~ spl9_54 ),
inference(avatar_split_clause,[],[f574,f568,f444,f250,f3321]) ).
tff(f3237,plain,
( spl9_145
| ~ spl9_53
| ~ spl9_138 ),
inference(avatar_split_clause,[],[f3170,f2927,f556,f3234]) ).
tff(f3234,plain,
( spl9_145
<=> ( 1 = $product(sK5,fact1($sum(-1,sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_145])]) ).
tff(f2927,plain,
( spl9_138
<=> ( sK7 = $product(sK5,fact1($sum(-1,sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_138])]) ).
tff(f3170,plain,
( ( 1 = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_53
| ~ spl9_138 ),
inference(forward_demodulation,[],[f2929,f558]) ).
tff(f2929,plain,
( ( sK7 = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_138 ),
inference(avatar_component_clause,[],[f2927]) ).
tff(f3230,plain,
( spl9_143
| spl9_144
| ~ spl9_34
| spl9_62 ),
inference(avatar_split_clause,[],[f1676,f683,f296,f3227,f3223]) ).
tff(f3227,plain,
( spl9_144
<=> $less(0,fact1(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_144])]) ).
tff(f1676,plain,
( $less(0,fact1(sK6))
| ( 0 = fact1(sK6) )
| ~ spl9_34
| spl9_62 ),
inference(resolution,[],[f684,f297]) ).
tff(f3221,plain,
( spl9_142
| ~ spl9_37
| ~ spl9_86 ),
inference(avatar_split_clause,[],[f1112,f1063,f320,f3219]) ).
tff(f3219,plain,
( spl9_142
<=> ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_142])]) ).
tff(f1063,plain,
( spl9_86
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_86])]) ).
tff(f1112,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,sK5) )
| ~ spl9_37
| ~ spl9_86 ),
inference(resolution,[],[f1064,f322]) ).
tff(f1064,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl9_86 ),
inference(avatar_component_clause,[],[f1063]) ).
tff(f3217,plain,
( spl9_141
| ~ spl9_54
| ~ spl9_86 ),
inference(avatar_split_clause,[],[f1111,f1063,f568,f3215]) ).
tff(f3215,plain,
( spl9_141
<=> ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_141])]) ).
tff(f1111,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,sK6) )
| ~ spl9_54
| ~ spl9_86 ),
inference(resolution,[],[f1064,f570]) ).
tff(f3213,plain,
( spl9_140
| ~ spl9_5
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f930,f556,f148,f3210]) ).
tff(f3210,plain,
( spl9_140
<=> sP0(sK6,sK5,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_140])]) ).
tff(f930,plain,
( sP0(sK6,sK5,1)
| ~ spl9_5
| ~ spl9_53 ),
inference(superposition,[],[f150,f558]) ).
tff(f150,plain,
( sP0(sK6,sK5,sK7)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f148]) ).
tff(f3168,plain,
( spl9_139
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f2956,f556,f476,f316,f188,f162,f143,f3166]) ).
tff(f3166,plain,
( spl9_139
<=> ! [X0: $int] :
( ( 1 = X0 )
| ( fact1(sK5) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_139])]) ).
tff(f316,plain,
( spl9_36
<=> ( 0 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
tff(f2956,plain,
( ! [X0: $int] :
( ( 1 = X0 )
| ( fact1(sK5) != X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51
| ~ spl9_53 ),
inference(forward_demodulation,[],[f2955,f558]) ).
tff(f2955,plain,
( ! [X0: $int] :
( ( sK7 = X0 )
| ( fact1(sK5) != X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51
| ~ spl9_53 ),
inference(forward_demodulation,[],[f869,f2946]) ).
tff(f869,plain,
( ! [X0: $int] :
( ( fact1(sK5) != X0 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51
| ~ spl9_53 ),
inference(evaluation,[],[f868]) ).
tff(f868,plain,
( ! [X0: $int] :
( ( 0 = 1 )
| ( fact1(sK5) != X0 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51
| ~ spl9_53 ),
inference(forward_demodulation,[],[f865,f558]) ).
tff(f865,plain,
( ! [X0: $int] :
( ( fact1(sK5) != X0 )
| ( 0 = sK7 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51 ),
inference(evaluation,[],[f541]) ).
tff(f541,plain,
( ! [X0: $int] :
( ( fact1(sK5) != $product(1,X0) )
| ( 0 = sK7 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_51 ),
inference(forward_demodulation,[],[f530,f380]) ).
tff(f380,plain,
( ( 1 = sK7 )
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36 ),
inference(forward_demodulation,[],[f378,f190]) ).
tff(f378,plain,
( ( fact1(0) = sK7 )
| ~ spl9_7
| ~ spl9_36 ),
inference(superposition,[],[f163,f318]) ).
tff(f318,plain,
( ( 0 = sK5 )
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f316]) ).
tff(f530,plain,
( ! [X0: $int] :
( ( fact1(sK5) != $product(sK7,X0) )
| ( 0 = sK7 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_51 ),
inference(superposition,[],[f477,f145]) ).
tff(f2930,plain,
( spl9_138
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47 ),
inference(avatar_split_clause,[],[f1047,f444,f320,f250,f162,f2927]) ).
tff(f1047,plain,
( ( sK7 = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47 ),
inference(forward_demodulation,[],[f898,f163]) ).
tff(f898,plain,
( ( fact1(sK5) = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47 ),
inference(forward_demodulation,[],[f896,f251]) ).
tff(f896,plain,
( ( fact1(sK5) = $product(sK5,fact1($sum(sK5,-1))) )
| ~ spl9_37
| ~ spl9_47 ),
inference(resolution,[],[f322,f445]) ).
tff(f2887,plain,
( spl9_137
| ~ spl9_33
| ~ spl9_115 ),
inference(avatar_split_clause,[],[f1949,f1672,f292,f2885]) ).
tff(f2885,plain,
( spl9_137
<=> ! [X0: $int] :
( ~ $less(X0,fact1(sK6))
| $less(X0,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_137])]) ).
tff(f1949,plain,
( ! [X0: $int] :
( ~ $less(X0,fact1(sK6))
| $less(X0,sK5) )
| ~ spl9_33
| ~ spl9_115 ),
inference(resolution,[],[f1674,f293]) ).
tff(f2883,plain,
( spl9_136
| ~ spl9_34
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f508,f472,f296,f2881]) ).
tff(f508,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,X2)
| $less($product(X2,X0),$product(X1,X0))
| ( $product(X1,X0) = $product(X2,X0) ) )
| ~ spl9_34
| ~ spl9_50 ),
inference(resolution,[],[f473,f297]) ).
tff(f2692,plain,
( spl9_135
| ~ spl9_43
| ~ spl9_51 ),
inference(avatar_split_clause,[],[f534,f476,f382,f2690]) ).
tff(f534,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( $product(X0,$product(X1,X2)) != $product($product(X0,X1),X3) )
| ( 0 = $product(X0,X1) )
| ( X2 = X3 ) )
| ~ spl9_43
| ~ spl9_51 ),
inference(superposition,[],[f477,f383]) ).
tff(f2688,plain,
( spl9_134
| ~ spl9_43
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f501,f468,f382,f2686]) ).
tff(f501,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,$product(X1,X2)),$product(X0,$product(X1,X3))) = $product(X0,$product(X1,$sum(X2,X3))) )
| ~ spl9_43
| ~ spl9_49 ),
inference(forward_demodulation,[],[f500,f383]) ).
tff(f500,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $product($product(X0,X1),$sum(X2,X3)) = $sum($product(X0,$product(X1,X2)),$product(X0,$product(X1,X3))) )
| ~ spl9_43
| ~ spl9_49 ),
inference(forward_demodulation,[],[f483,f383]) ).
tff(f483,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $product($product(X0,X1),$sum(X2,X3)) = $sum($product(X0,$product(X1,X2)),$product($product(X0,X1),X3)) )
| ~ spl9_43
| ~ spl9_49 ),
inference(superposition,[],[f469,f383]) ).
tff(f2432,plain,
( spl9_133
| ~ spl9_43
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f519,f472,f382,f2430]) ).
tff(f519,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($product(X3,X2),$product(X0,$product(X1,X2)))
| $less(X2,0)
| $less(X3,$product(X0,X1)) )
| ~ spl9_43
| ~ spl9_50 ),
inference(superposition,[],[f473,f383]) ).
tff(f2428,plain,
( spl9_132
| ~ spl9_43
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f514,f472,f382,f2426]) ).
tff(f514,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less($product(X0,$product(X1,X2)),$product(X3,X2))
| $less(X2,0)
| $less($product(X0,X1),X3) )
| ~ spl9_43
| ~ spl9_50 ),
inference(superposition,[],[f473,f383]) ).
tff(f2424,plain,
( spl9_131
| ~ spl9_42
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f491,f468,f374,f2422]) ).
tff(f491,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] : ( $sum($product(X0,X1),$sum($product(X0,X2),X3)) = $sum($product(X0,$sum(X1,X2)),X3) )
| ~ spl9_42
| ~ spl9_49 ),
inference(superposition,[],[f375,f469]) ).
tff(f2420,plain,
( spl9_130
| ~ spl9_32
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f438,f390,f282,f2418]) ).
tff(f2418,plain,
( spl9_130
<=> ! [X0: $int] :
( ( 0 = sK8(X0) )
| ( sK8(X0) = $sum(2,sK8(sK8(X0))) )
| ( 0 = X0 )
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_130])]) ).
tff(f282,plain,
( spl9_32
<=> ! [X0: $int] :
( even1(sK8(X0))
| ( 0 = X0 )
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
tff(f390,plain,
( spl9_45
<=> ! [X0: $int] :
( ( $sum(2,sK8(X0)) = X0 )
| ( 0 = X0 )
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
tff(f438,plain,
( ! [X0: $int] :
( ( 0 = sK8(X0) )
| ( sK8(X0) = $sum(2,sK8(sK8(X0))) )
| ( 0 = X0 )
| ~ even1(X0) )
| ~ spl9_32
| ~ spl9_45 ),
inference(resolution,[],[f391,f283]) ).
tff(f283,plain,
( ! [X0: $int] :
( even1(sK8(X0))
| ( 0 = X0 )
| ~ even1(X0) )
| ~ spl9_32 ),
inference(avatar_component_clause,[],[f282]) ).
tff(f391,plain,
( ! [X0: $int] :
( ~ even1(X0)
| ( 0 = X0 )
| ( $sum(2,sK8(X0)) = X0 ) )
| ~ spl9_45 ),
inference(avatar_component_clause,[],[f390]) ).
tff(f2416,plain,
( spl9_129
| ~ spl9_23
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f437,f390,f235,f2414]) ).
tff(f235,plain,
( spl9_23
<=> ! [X0: $int] :
( even1($sum(X0,2))
| ~ even1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
tff(f437,plain,
( ! [X0: $int] :
( ( 0 = $sum(X0,2) )
| ( $sum(X0,2) = $sum(2,sK8($sum(X0,2))) )
| ~ even1(X0) )
| ~ spl9_23
| ~ spl9_45 ),
inference(resolution,[],[f391,f236]) ).
tff(f236,plain,
( ! [X0: $int] :
( even1($sum(X0,2))
| ~ even1(X0) )
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f235]) ).
tff(f2412,plain,
( spl9_128
| ~ spl9_28
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f435,f386,f258,f2410]) ).
tff(f2410,plain,
( spl9_128
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool1] : ( match_bool1(ref(X0),X1,X2,X3) = mk_ref(X0,contents(X0,match_bool1(ref(X0),X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_128])]) ).
tff(f258,plain,
( spl9_28
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool1] : sort1(X0,match_bool1(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
tff(f386,plain,
( spl9_44
<=> ! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort1(ref(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
tff(f435,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: bool1] : ( match_bool1(ref(X0),X1,X2,X3) = mk_ref(X0,contents(X0,match_bool1(ref(X0),X1,X2,X3))) )
| ~ spl9_28
| ~ spl9_44 ),
inference(resolution,[],[f387,f259]) ).
tff(f259,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: bool1] : sort1(X0,match_bool1(X0,X1,X2,X3))
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f258]) ).
tff(f387,plain,
( ! [X0: ty,X1: uni] :
( ~ sort1(ref(X0),X1)
| ( mk_ref(X0,contents(X0,X1)) = X1 ) )
| ~ spl9_44 ),
inference(avatar_component_clause,[],[f386]) ).
tff(f2324,plain,
( spl9_127
| ~ spl9_62
| ~ spl9_102 ),
inference(avatar_split_clause,[],[f2181,f1471,f683,f2321]) ).
tff(f1471,plain,
( spl9_102
<=> ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_102])]) ).
tff(f2181,plain,
( $less(fact1(sK6),sK6)
| ~ spl9_62
| ~ spl9_102 ),
inference(resolution,[],[f1472,f685]) ).
tff(f685,plain,
( $less(fact1(sK6),0)
| ~ spl9_62 ),
inference(avatar_component_clause,[],[f683]) ).
tff(f1472,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK6) )
| ~ spl9_102 ),
inference(avatar_component_clause,[],[f1471]) ).
tff(f2254,plain,
( spl9_126
| ~ spl9_38
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f493,f468,f325,f2252]) ).
tff(f493,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($product(X0,$sum(X1,X2)),$sum(X3,$product(X0,X2)))
| ~ $less($product(X0,X1),X3) )
| ~ spl9_38
| ~ spl9_49 ),
inference(superposition,[],[f326,f469]) ).
tff(f2250,plain,
( spl9_125
| ~ spl9_38
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f492,f468,f325,f2248]) ).
tff(f492,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,$product(X0,X2)),$product(X0,$sum(X1,X2)))
| ~ $less(X3,$product(X0,X1)) )
| ~ spl9_38
| ~ spl9_49 ),
inference(superposition,[],[f326,f469]) ).
tff(f2193,plain,
( spl9_124
| ~ spl9_34
| ~ spl9_47 ),
inference(avatar_split_clause,[],[f459,f444,f296,f2191]) ).
tff(f459,plain,
( ! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) )
| $less(X0,0)
| ( 0 = X0 ) )
| ~ spl9_34
| ~ spl9_47 ),
inference(resolution,[],[f445,f297]) ).
tff(f2189,plain,
( spl9_123
| ~ spl9_28
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f371,f337,f258,f2187]) ).
tff(f2187,plain,
( spl9_123
<=> ! [X4: uni,X0: ty,X3: uni,X2: uni,X1: bool1] : ( match_bool1(X0,X1,X2,X3) = match_bool1(X0,true1,match_bool1(X0,X1,X2,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_123])]) ).
tff(f337,plain,
( spl9_41
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool1(X0,true1,X1,X2) = X1 )
| ~ sort1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
tff(f371,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: bool1,X4: uni] : ( match_bool1(X0,X1,X2,X3) = match_bool1(X0,true1,match_bool1(X0,X1,X2,X3),X4) )
| ~ spl9_28
| ~ spl9_41 ),
inference(resolution,[],[f338,f259]) ).
tff(f338,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ sort1(X0,X1)
| ( match_bool1(X0,true1,X1,X2) = X1 ) )
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f337]) ).
tff(f2185,plain,
( spl9_122
| ~ spl9_28
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f367,f333,f258,f2183]) ).
tff(f2183,plain,
( spl9_122
<=> ! [X4: uni,X0: ty,X3: uni,X2: bool1,X1: uni] : ( match_bool1(X0,X2,X3,X4) = match_bool1(X0,false1,X1,match_bool1(X0,X2,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_122])]) ).
tff(f333,plain,
( spl9_40
<=> ! [X2: uni,X0: ty,X1: uni] :
( ( match_bool1(X0,false1,X1,X2) = X2 )
| ~ sort1(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
tff(f367,plain,
( ! [X2: bool1,X3: uni,X0: ty,X1: uni,X4: uni] : ( match_bool1(X0,X2,X3,X4) = match_bool1(X0,false1,X1,match_bool1(X0,X2,X3,X4)) )
| ~ spl9_28
| ~ spl9_40 ),
inference(resolution,[],[f334,f259]) ).
tff(f334,plain,
( ! [X2: uni,X0: ty,X1: uni] :
( ~ sort1(X0,X2)
| ( match_bool1(X0,false1,X1,X2) = X2 ) )
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f333]) ).
tff(f2175,plain,
( spl9_121
| ~ spl9_28
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f363,f329,f258,f2173]) ).
tff(f2173,plain,
( spl9_121
<=> ! [X0: ty,X3: uni,X2: uni,X1: bool1] : ( match_bool1(X0,X1,X2,X3) = contents(X0,mk_ref(X0,match_bool1(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_121])]) ).
tff(f329,plain,
( spl9_39
<=> ! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
tff(f363,plain,
( ! [X2: uni,X3: uni,X0: ty,X1: bool1] : ( match_bool1(X0,X1,X2,X3) = contents(X0,mk_ref(X0,match_bool1(X0,X1,X2,X3))) )
| ~ spl9_28
| ~ spl9_39 ),
inference(resolution,[],[f330,f259]) ).
tff(f330,plain,
( ! [X0: ty,X1: uni] :
( ~ sort1(X0,X1)
| ( contents(X0,mk_ref(X0,X1)) = X1 ) )
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f329]) ).
tff(f1986,plain,
( spl9_120
| ~ spl9_27
| ~ spl9_29
| ~ spl9_47 ),
inference(avatar_split_clause,[],[f462,f444,f270,f254,f1984]) ).
tff(f270,plain,
( spl9_29
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
tff(f462,plain,
( ! [X0: $int] :
( ( fact1($sum(X0,1)) = $product(fact1(X0),$sum(X0,1)) )
| $less(X0,0) )
| ~ spl9_27
| ~ spl9_29
| ~ spl9_47 ),
inference(forward_demodulation,[],[f461,f255]) ).
tff(f461,plain,
( ! [X0: $int] :
( ( fact1($sum(X0,1)) = $product($sum(X0,1),fact1(X0)) )
| $less(X0,0) )
| ~ spl9_29
| ~ spl9_47 ),
inference(evaluation,[],[f458]) ).
tff(f458,plain,
( ! [X0: $int] :
( ( fact1($sum(X0,1)) = $product($sum(X0,1),fact1($sum($sum(X0,1),-1))) )
| $less(X0,0) )
| ~ spl9_29
| ~ spl9_47 ),
inference(resolution,[],[f445,f271]) ).
tff(f271,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f270]) ).
tff(f1982,plain,
( spl9_119
| ~ spl9_38
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f402,f374,f325,f1980]) ).
tff(f402,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl9_38
| ~ spl9_42 ),
inference(superposition,[],[f326,f375]) ).
tff(f1978,plain,
( spl9_118
| ~ spl9_38
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f401,f374,f325,f1976]) ).
tff(f401,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl9_38
| ~ spl9_42 ),
inference(superposition,[],[f326,f375]) ).
tff(f1974,plain,
( spl9_117
| ~ spl9_35
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f396,f374,f312,f1972]) ).
tff(f396,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl9_35
| ~ spl9_42 ),
inference(superposition,[],[f375,f313]) ).
tff(f1690,plain,
( spl9_62
| spl9_116
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f526,f472,f162,f143,f1688,f683]) ).
tff(f526,plain,
( ! [X0: $int] :
( ~ $less($product(X0,fact1(sK6)),sK7)
| $less(fact1(sK6),0)
| $less(X0,sK7) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50 ),
inference(forward_demodulation,[],[f515,f163]) ).
tff(f515,plain,
( ! [X0: $int] :
( ~ $less($product(X0,fact1(sK6)),fact1(sK5))
| $less(fact1(sK6),0)
| $less(X0,sK7) )
| ~ spl9_4
| ~ spl9_50 ),
inference(superposition,[],[f473,f145]) ).
tff(f1675,plain,
( spl9_115
| ~ spl9_62
| ~ spl9_77 ),
inference(avatar_split_clause,[],[f1560,f858,f683,f1672]) ).
tff(f858,plain,
( spl9_77
<=> ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_77])]) ).
tff(f1560,plain,
( $less(fact1(sK6),sK5)
| ~ spl9_62
| ~ spl9_77 ),
inference(resolution,[],[f859,f685]) ).
tff(f859,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK5) )
| ~ spl9_77 ),
inference(avatar_component_clause,[],[f858]) ).
tff(f1580,plain,
( spl9_114
| ~ spl9_27
| ~ spl9_51 ),
inference(avatar_split_clause,[],[f532,f476,f254,f1578]) ).
tff(f532,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X1,X0) != $product(X0,X2) )
| ( 0 = X0 )
| ( X1 = X2 ) )
| ~ spl9_27
| ~ spl9_51 ),
inference(superposition,[],[f477,f255]) ).
tff(f1576,plain,
( spl9_113
| ~ spl9_27
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f517,f472,f254,f1574]) ).
tff(f517,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X2,X1),$product(X1,X0))
| $less(X1,0)
| $less(X2,X0) )
| ~ spl9_27
| ~ spl9_50 ),
inference(superposition,[],[f473,f255]) ).
tff(f1572,plain,
( spl9_112
| ~ spl9_27
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f512,f472,f254,f1570]) ).
tff(f512,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X0),$product(X2,X1))
| $less(X1,0)
| $less(X0,X2) )
| ~ spl9_27
| ~ spl9_50 ),
inference(superposition,[],[f473,f255]) ).
tff(f1568,plain,
( spl9_111
| ~ spl9_26
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f489,f468,f250,f1566]) ).
tff(f489,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X2),$product(X0,X1)) )
| ~ spl9_26
| ~ spl9_49 ),
inference(superposition,[],[f469,f251]) ).
tff(f1564,plain,
( spl9_110
| ~ spl9_27
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f486,f468,f254,f1562]) ).
tff(f486,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X2,X1)) = $sum($product(X0,X2),$product(X1,X0)) )
| ~ spl9_27
| ~ spl9_49 ),
inference(superposition,[],[f469,f255]) ).
tff(f1556,plain,
( spl9_109
| ~ spl9_27
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f481,f468,f254,f1554]) ).
tff(f481,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X1,X0),$product(X0,X2)) )
| ~ spl9_27
| ~ spl9_49 ),
inference(superposition,[],[f469,f255]) ).
tff(f1552,plain,
( spl9_108
| ~ spl9_20
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f434,f386,f223,f1550]) ).
tff(f1550,plain,
( spl9_108
<=> ! [X0: ty,X1: uni] : ( contents(ref(X0),X1) = mk_ref(X0,contents(X0,contents(ref(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_108])]) ).
tff(f223,plain,
( spl9_20
<=> ! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
tff(f434,plain,
( ! [X0: ty,X1: uni] : ( contents(ref(X0),X1) = mk_ref(X0,contents(X0,contents(ref(X0),X1))) )
| ~ spl9_20
| ~ spl9_44 ),
inference(resolution,[],[f387,f224]) ).
tff(f224,plain,
( ! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1))
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f223]) ).
tff(f1548,plain,
( spl9_107
| ~ spl9_25
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f364,f329,f243,f1546]) ).
tff(f1546,plain,
( spl9_107
<=> ! [X0: ty,X1: uni] : ( mk_ref(X0,X1) = contents(ref(X0),mk_ref(ref(X0),mk_ref(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_107])]) ).
tff(f243,plain,
( spl9_25
<=> ! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
tff(f364,plain,
( ! [X0: ty,X1: uni] : ( mk_ref(X0,X1) = contents(ref(X0),mk_ref(ref(X0),mk_ref(X0,X1))) )
| ~ spl9_25
| ~ spl9_39 ),
inference(resolution,[],[f330,f244]) ).
tff(f244,plain,
( ! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1))
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f243]) ).
tff(f1544,plain,
( spl9_106
| ~ spl9_35
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f360,f325,f312,f1542]) ).
tff(f1542,plain,
( spl9_106
<=> ! [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,[spl9_106])]) ).
tff(f360,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl9_35
| ~ spl9_38 ),
inference(superposition,[],[f326,f313]) ).
tff(f1540,plain,
( spl9_105
| ~ spl9_35
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f356,f325,f312,f1538]) ).
tff(f1538,plain,
( spl9_105
<=> ! [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,[spl9_105])]) ).
tff(f356,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl9_35
| ~ spl9_38 ),
inference(superposition,[],[f326,f313]) ).
tff(f1536,plain,
( spl9_104
| ~ spl9_33
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f352,f325,f292,f1534]) ).
tff(f1534,plain,
( spl9_104
<=> ! [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,[spl9_104])]) ).
tff(f352,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl9_33
| ~ spl9_38 ),
inference(resolution,[],[f326,f293]) ).
tff(f1532,plain,
( spl9_103
| ~ spl9_31
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f304,f296,f278,f1530]) ).
tff(f1530,plain,
( spl9_103
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_103])]) ).
tff(f278,plain,
( spl9_31
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
tff(f304,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl9_31
| ~ spl9_34 ),
inference(resolution,[],[f297,f279]) ).
tff(f279,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl9_31 ),
inference(avatar_component_clause,[],[f278]) ).
tff(f1473,plain,
( spl9_102
| ~ spl9_33
| ~ spl9_54 ),
inference(avatar_split_clause,[],[f573,f568,f292,f1471]) ).
tff(f573,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK6) )
| ~ spl9_33
| ~ spl9_54 ),
inference(resolution,[],[f570,f293]) ).
tff(f1448,plain,
( spl9_101
| ~ spl9_29
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f407,f374,f270,f1446]) ).
tff(f407,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl9_29
| ~ spl9_42 ),
inference(superposition,[],[f271,f375]) ).
tff(f1444,plain,
( spl9_100
| ~ spl9_31
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f406,f374,f278,f1442]) ).
tff(f406,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl9_31
| ~ spl9_42 ),
inference(superposition,[],[f279,f375]) ).
tff(f1440,plain,
( spl9_99
| ~ spl9_25
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f372,f337,f243,f1438]) ).
tff(f1438,plain,
( spl9_99
<=> ! [X2: uni,X0: ty,X1: uni] : ( mk_ref(X0,X1) = match_bool1(ref(X0),true1,mk_ref(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_99])]) ).
tff(f372,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( mk_ref(X0,X1) = match_bool1(ref(X0),true1,mk_ref(X0,X1),X2) )
| ~ spl9_25
| ~ spl9_41 ),
inference(resolution,[],[f338,f244]) ).
tff(f1436,plain,
( spl9_98
| ~ spl9_25
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f368,f333,f243,f1434]) ).
tff(f1434,plain,
( spl9_98
<=> ! [X2: uni,X0: ty,X1: uni] : ( mk_ref(X0,X2) = match_bool1(ref(X0),false1,X1,mk_ref(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_98])]) ).
tff(f368,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( mk_ref(X0,X2) = match_bool1(ref(X0),false1,X1,mk_ref(X0,X2)) )
| ~ spl9_25
| ~ spl9_40 ),
inference(resolution,[],[f334,f244]) ).
tff(f1432,plain,
( spl9_97
| ~ spl9_33
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f301,f296,f292,f1430]) ).
tff(f301,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl9_33
| ~ spl9_34 ),
inference(resolution,[],[f297,f293]) ).
tff(f1105,plain,
( spl9_96
| ~ spl9_19
| ~ spl9_51 ),
inference(avatar_split_clause,[],[f531,f476,f219,f1103]) ).
tff(f219,plain,
( spl9_19
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
tff(f531,plain,
( ! [X0: $int,X1: $int] :
( ( 0 != $product(X0,X1) )
| ( 0 = X0 )
| ( 0 = X1 ) )
| ~ spl9_19
| ~ spl9_51 ),
inference(superposition,[],[f477,f220]) ).
tff(f220,plain,
( ! [X0: $int] : ( 0 = $product(X0,0) )
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f219]) ).
tff(f1101,plain,
( spl9_95
| ~ spl9_14
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f433,f386,f197,f1099]) ).
tff(f1099,plain,
( spl9_95
<=> ! [X0: ty] : ( witness1(ref(X0)) = mk_ref(X0,contents(X0,witness1(ref(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_95])]) ).
tff(f197,plain,
( spl9_14
<=> ! [X0: ty] : sort1(X0,witness1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
tff(f433,plain,
( ! [X0: ty] : ( witness1(ref(X0)) = mk_ref(X0,contents(X0,witness1(ref(X0)))) )
| ~ spl9_14
| ~ spl9_44 ),
inference(resolution,[],[f387,f198]) ).
tff(f198,plain,
( ! [X0: ty] : sort1(X0,witness1(X0))
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f197]) ).
tff(f1097,plain,
( spl9_94
| ~ spl9_25
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f432,f386,f243,f1095]) ).
tff(f1095,plain,
( spl9_94
<=> ! [X0: ty,X1: uni] : ( mk_ref(X0,X1) = mk_ref(X0,contents(X0,mk_ref(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_94])]) ).
tff(f432,plain,
( ! [X0: ty,X1: uni] : ( mk_ref(X0,X1) = mk_ref(X0,contents(X0,mk_ref(X0,X1))) )
| ~ spl9_25
| ~ spl9_44 ),
inference(resolution,[],[f387,f244]) ).
tff(f1093,plain,
( spl9_93
| ~ spl9_27
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f419,f382,f254,f1091]) ).
tff(f419,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product(X2,$product(X0,X1)) )
| ~ spl9_27
| ~ spl9_43 ),
inference(superposition,[],[f383,f255]) ).
tff(f1089,plain,
( spl9_92
| ~ spl9_27
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f415,f382,f254,f1087]) ).
tff(f415,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X1,X0),X2) )
| ~ spl9_27
| ~ spl9_43 ),
inference(superposition,[],[f383,f255]) ).
tff(f1085,plain,
( spl9_91
| ~ spl9_26
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f399,f374,f250,f1083]) ).
tff(f399,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl9_26
| ~ spl9_42 ),
inference(superposition,[],[f375,f251]) ).
tff(f1081,plain,
( spl9_90
| ~ spl9_26
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f394,f374,f250,f1079]) ).
tff(f394,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl9_26
| ~ spl9_42 ),
inference(superposition,[],[f375,f251]) ).
tff(f1077,plain,
( spl9_89
| ~ spl9_20
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f370,f337,f223,f1075]) ).
tff(f1075,plain,
( spl9_89
<=> ! [X2: uni,X0: ty,X1: uni] : ( contents(X0,X1) = match_bool1(X0,true1,contents(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_89])]) ).
tff(f370,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( contents(X0,X1) = match_bool1(X0,true1,contents(X0,X1),X2) )
| ~ spl9_20
| ~ spl9_41 ),
inference(resolution,[],[f338,f224]) ).
tff(f1073,plain,
( spl9_88
| ~ spl9_20
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f366,f333,f223,f1071]) ).
tff(f1071,plain,
( spl9_88
<=> ! [X2: uni,X0: ty,X1: uni] : ( contents(X0,X2) = match_bool1(X0,false1,X1,contents(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_88])]) ).
tff(f366,plain,
( ! [X2: uni,X0: ty,X1: uni] : ( contents(X0,X2) = match_bool1(X0,false1,X1,contents(X0,X2)) )
| ~ spl9_20
| ~ spl9_40 ),
inference(resolution,[],[f334,f224]) ).
tff(f1069,plain,
( spl9_87
| ~ spl9_20
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f362,f329,f223,f1067]) ).
tff(f1067,plain,
( spl9_87
<=> ! [X0: ty,X1: uni] : ( contents(X0,X1) = contents(X0,mk_ref(X0,contents(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_87])]) ).
tff(f362,plain,
( ! [X0: ty,X1: uni] : ( contents(X0,X1) = contents(X0,mk_ref(X0,contents(X0,X1))) )
| ~ spl9_20
| ~ spl9_39 ),
inference(resolution,[],[f330,f224]) ).
tff(f1065,plain,
( spl9_86
| ~ spl9_29
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f299,f292,f270,f1063]) ).
tff(f299,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl9_29
| ~ spl9_33 ),
inference(resolution,[],[f293,f271]) ).
tff(f1046,plain,
( spl9_85
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f893,f556,f444,f320,f250,f162,f1043]) ).
tff(f1043,plain,
( spl9_85
<=> ( 1 = fact1(sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_85])]) ).
tff(f893,plain,
( ( 1 = fact1(sK5) )
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47
| ~ spl9_53 ),
inference(forward_demodulation,[],[f565,f892]) ).
tff(f892,plain,
( ( 1 = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47
| ~ spl9_53 ),
inference(forward_demodulation,[],[f566,f558]) ).
tff(f566,plain,
( ( sK7 = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_7
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47 ),
inference(forward_demodulation,[],[f565,f163]) ).
tff(f565,plain,
( ( fact1(sK5) = $product(sK5,fact1($sum(-1,sK5))) )
| ~ spl9_26
| ~ spl9_37
| ~ spl9_47 ),
inference(forward_demodulation,[],[f563,f251]) ).
tff(f563,plain,
( ( fact1(sK5) = $product(sK5,fact1($sum(sK5,-1))) )
| ~ spl9_37
| ~ spl9_47 ),
inference(resolution,[],[f322,f445]) ).
tff(f970,plain,
( spl9_84
| ~ spl9_24
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f408,f374,f239,f968]) ).
tff(f408,plain,
( ! [X0: $int,X1: $int] :
( ~ even1($sum(X0,$sum(X1,1)))
| ~ even1($sum(X0,X1)) )
| ~ spl9_24
| ~ spl9_42 ),
inference(superposition,[],[f240,f375]) ).
tff(f966,plain,
( spl9_83
| ~ spl9_23
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f405,f374,f235,f964]) ).
tff(f405,plain,
( ! [X0: $int,X1: $int] :
( even1($sum(X0,$sum(X1,2)))
| ~ even1($sum(X0,X1)) )
| ~ spl9_23
| ~ spl9_42 ),
inference(superposition,[],[f236,f375]) ).
tff(f961,plain,
( spl9_82
| ~ spl9_21
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f398,f374,f227,f959]) ).
tff(f959,plain,
( spl9_82
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_82])]) ).
tff(f398,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl9_21
| ~ spl9_42 ),
inference(superposition,[],[f375,f228]) ).
tff(f957,plain,
( spl9_81
| ~ spl9_26
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f358,f325,f250,f955]) ).
tff(f358,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl9_26
| ~ spl9_38 ),
inference(superposition,[],[f326,f251]) ).
tff(f953,plain,
( spl9_80
| ~ spl9_26
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f354,f325,f250,f951]) ).
tff(f354,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl9_26
| ~ spl9_38 ),
inference(superposition,[],[f326,f251]) ).
tff(f949,plain,
( spl9_79
| ~ spl9_26
| ~ spl9_35 ),
inference(avatar_split_clause,[],[f341,f312,f250,f947]) ).
tff(f341,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl9_26
| ~ spl9_35 ),
inference(superposition,[],[f313,f251]) ).
tff(f891,plain,
( spl9_78
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f426,f382,f316,f188,f162,f143,f889]) ).
tff(f426,plain,
( ! [X0: $int] : ( $product(fact1(sK6),X0) = X0 )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_43 ),
inference(evaluation,[],[f425]) ).
tff(f425,plain,
( ! [X0: $int] : ( $product(1,$product(fact1(sK6),X0)) = $product(1,X0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36
| ~ spl9_43 ),
inference(forward_demodulation,[],[f424,f380]) ).
tff(f424,plain,
( ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(sK7,X0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_43 ),
inference(forward_demodulation,[],[f413,f163]) ).
tff(f413,plain,
( ! [X0: $int] : ( $product(sK7,$product(fact1(sK6),X0)) = $product(fact1(sK5),X0) )
| ~ spl9_4
| ~ spl9_43 ),
inference(superposition,[],[f383,f145]) ).
tff(f860,plain,
( spl9_77
| ~ spl9_33
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f564,f320,f292,f858]) ).
tff(f564,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| $less(X0,sK5) )
| ~ spl9_33
| ~ spl9_37 ),
inference(resolution,[],[f322,f293]) ).
tff(f824,plain,
( spl9_76
| ~ spl9_14
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f369,f337,f197,f822]) ).
tff(f822,plain,
( spl9_76
<=> ! [X0: ty,X1: uni] : ( witness1(X0) = match_bool1(X0,true1,witness1(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_76])]) ).
tff(f369,plain,
( ! [X0: ty,X1: uni] : ( witness1(X0) = match_bool1(X0,true1,witness1(X0),X1) )
| ~ spl9_14
| ~ spl9_41 ),
inference(resolution,[],[f338,f198]) ).
tff(f820,plain,
( spl9_75
| ~ spl9_14
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f365,f333,f197,f818]) ).
tff(f818,plain,
( spl9_75
<=> ! [X0: ty,X1: uni] : ( witness1(X0) = match_bool1(X0,false1,X1,witness1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_75])]) ).
tff(f365,plain,
( ! [X0: ty,X1: uni] : ( witness1(X0) = match_bool1(X0,false1,X1,witness1(X0)) )
| ~ spl9_14
| ~ spl9_40 ),
inference(resolution,[],[f334,f198]) ).
tff(f816,plain,
( spl9_74
| ~ spl9_14
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f361,f329,f197,f814]) ).
tff(f814,plain,
( spl9_74
<=> ! [X0: ty] : ( witness1(X0) = contents(X0,mk_ref(X0,witness1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_74])]) ).
tff(f361,plain,
( ! [X0: ty] : ( witness1(X0) = contents(X0,mk_ref(X0,witness1(X0))) )
| ~ spl9_14
| ~ spl9_39 ),
inference(resolution,[],[f330,f198]) ).
tff(f812,plain,
( spl9_73
| ~ spl9_21
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f357,f325,f227,f810]) ).
tff(f357,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl9_21
| ~ spl9_38 ),
inference(superposition,[],[f326,f228]) ).
tff(f808,plain,
( spl9_72
| ~ spl9_21
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f353,f325,f227,f806]) ).
tff(f353,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl9_21
| ~ spl9_38 ),
inference(superposition,[],[f326,f228]) ).
tff(f804,plain,
( spl9_71
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f246,f231,f802]) ).
tff(f802,plain,
( spl9_71
<=> ! [X0: bool1,X1: bool1] :
( ( X0 = X1 )
| ( true1 = X1 )
| ( true1 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_71])]) ).
tff(f231,plain,
( spl9_22
<=> ! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
tff(f246,plain,
( ! [X0: bool1,X1: bool1] :
( ( X0 = X1 )
| ( true1 = X1 )
| ( true1 = X0 ) )
| ~ spl9_22 ),
inference(superposition,[],[f232,f232]) ).
tff(f232,plain,
( ! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) )
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f231]) ).
tff(f761,plain,
( spl9_70
| ~ spl9_21
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f410,f374,f227,f759]) ).
tff(f410,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl9_21
| ~ spl9_42 ),
inference(evaluation,[],[f393]) ).
tff(f393,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl9_21
| ~ spl9_42 ),
inference(superposition,[],[f375,f228]) ).
tff(f757,plain,
( spl9_69
| ~ spl9_26
| ~ spl9_31 ),
inference(avatar_split_clause,[],[f289,f278,f250,f755]) ).
tff(f289,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl9_26
| ~ spl9_31 ),
inference(superposition,[],[f279,f251]) ).
tff(f753,plain,
( spl9_68
| ~ spl9_26
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f286,f270,f250,f751]) ).
tff(f286,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl9_26
| ~ spl9_29 ),
inference(superposition,[],[f271,f251]) ).
tff(f738,plain,
( spl9_67
| ~ spl9_24
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f262,f250,f239,f736]) ).
tff(f262,plain,
( ! [X0: $int] :
( ~ even1($sum(1,X0))
| ~ even1(X0) )
| ~ spl9_24
| ~ spl9_26 ),
inference(superposition,[],[f240,f251]) ).
tff(f734,plain,
( spl9_66
| ~ spl9_23
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f261,f250,f235,f732]) ).
tff(f261,plain,
( ! [X0: $int] :
( even1($sum(2,X0))
| ~ even1(X0) )
| ~ spl9_23
| ~ spl9_26 ),
inference(superposition,[],[f236,f251]) ).
tff(f715,plain,
( spl9_65
| ~ spl9_5
| ~ spl9_59 ),
inference(avatar_split_clause,[],[f624,f616,f148,f712]) ).
tff(f712,plain,
( spl9_65
<=> sP0(sK6,sK5,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_65])]) ).
tff(f624,plain,
( sP0(sK6,sK5,0)
| ~ spl9_5
| ~ spl9_59 ),
inference(superposition,[],[f150,f618]) ).
tff(f618,plain,
( ( 0 = sK7 )
| ~ spl9_59 ),
inference(avatar_component_clause,[],[f616]) ).
tff(f710,plain,
( spl9_64
| ~ spl9_9
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f285,f270,f174,f708]) ).
tff(f174,plain,
( spl9_9
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
tff(f285,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl9_9
| ~ spl9_29 ),
inference(resolution,[],[f271,f175]) ).
tff(f175,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f689,plain,
( spl9_62
| spl9_63
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50 ),
inference(avatar_split_clause,[],[f522,f472,f162,f143,f687,f683]) ).
tff(f522,plain,
( ! [X0: $int] :
( ~ $less(sK7,$product(X0,fact1(sK6)))
| $less(fact1(sK6),0)
| $less(sK7,X0) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_50 ),
inference(forward_demodulation,[],[f510,f163]) ).
tff(f510,plain,
( ! [X0: $int] :
( ~ $less(fact1(sK5),$product(X0,fact1(sK6)))
| $less(fact1(sK6),0)
| $less(sK7,X0) )
| ~ spl9_4
| ~ spl9_50 ),
inference(superposition,[],[f473,f145]) ).
tff(f635,plain,
( spl9_61
| ~ spl9_4
| ~ spl9_7
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f562,f468,f162,f143,f633]) ).
tff(f562,plain,
( ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(sK7,$product(sK7,X0)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_49 ),
inference(forward_demodulation,[],[f479,f163]) ).
tff(f479,plain,
( ! [X0: $int] : ( $product(sK7,$sum(fact1(sK6),X0)) = $sum(fact1(sK5),$product(sK7,X0)) )
| ~ spl9_4
| ~ spl9_49 ),
inference(superposition,[],[f469,f145]) ).
tff(f622,plain,
( spl9_59
| spl9_60
| ~ spl9_4
| ~ spl9_7
| ~ spl9_51 ),
inference(avatar_split_clause,[],[f560,f476,f162,f143,f620,f616]) ).
tff(f560,plain,
( ! [X0: $int] :
( ( sK7 != $product(sK7,X0) )
| ( 0 = sK7 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_51 ),
inference(forward_demodulation,[],[f535,f163]) ).
tff(f535,plain,
( ! [X0: $int] :
( ( fact1(sK5) != $product(sK7,X0) )
| ( 0 = sK7 )
| ( fact1(sK6) = X0 ) )
| ~ spl9_4
| ~ spl9_51 ),
inference(superposition,[],[f477,f145]) ).
tff(f614,plain,
( spl9_58
| ~ spl9_4
| ~ spl9_7
| ~ spl9_26
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f503,f468,f250,f162,f143,f612]) ).
tff(f503,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum(sK7,$product(sK7,X0)) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_26
| ~ spl9_49 ),
inference(forward_demodulation,[],[f502,f251]) ).
tff(f502,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum($product(sK7,X0),sK7) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_49 ),
inference(forward_demodulation,[],[f484,f163]) ).
tff(f484,plain,
( ! [X0: $int] : ( $product(sK7,$sum(X0,fact1(sK6))) = $sum($product(sK7,X0),fact1(sK5)) )
| ~ spl9_4
| ~ spl9_49 ),
inference(superposition,[],[f469,f145]) ).
tff(f597,plain,
( spl9_57
| ~ spl9_4
| ~ spl9_7
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f424,f382,f162,f143,f595]) ).
tff(f584,plain,
( spl9_56
| ~ spl9_5
| ~ spl9_26
| ~ spl9_48 ),
inference(avatar_split_clause,[],[f464,f448,f250,f148,f581]) ).
tff(f448,plain,
( spl9_48
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( sK2(X0,X1,X2) = $sum(X0,-1) )
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
tff(f464,plain,
( ( sK2(sK6,sK5,sK7) = $sum(-1,sK6) )
| ~ spl9_5
| ~ spl9_26
| ~ spl9_48 ),
inference(forward_demodulation,[],[f463,f251]) ).
tff(f463,plain,
( ( sK2(sK6,sK5,sK7) = $sum(sK6,-1) )
| ~ spl9_5
| ~ spl9_48 ),
inference(resolution,[],[f449,f150]) ).
tff(f449,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ sP0(X0,X1,X2)
| ( sK2(X0,X1,X2) = $sum(X0,-1) ) )
| ~ spl9_48 ),
inference(avatar_component_clause,[],[f448]) ).
tff(f579,plain,
( spl9_55
| ~ spl9_5
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f454,f440,f148,f576]) ).
tff(f440,plain,
( spl9_46
<=> ! [X2: $int,X0: $int,X1: $int] :
( ( $product(X2,X0) = sK1(X0,X1,X2) )
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
tff(f454,plain,
( ( $product(sK7,sK6) = sK1(sK6,sK5,sK7) )
| ~ spl9_5
| ~ spl9_46 ),
inference(resolution,[],[f441,f150]) ).
tff(f441,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ sP0(X0,X1,X2)
| ( $product(X2,X0) = sK1(X0,X1,X2) ) )
| ~ spl9_46 ),
inference(avatar_component_clause,[],[f440]) ).
tff(f571,plain,
( spl9_6
| spl9_54
| spl9_2
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f303,f296,f133,f568,f152]) ).
tff(f152,plain,
( spl9_6
<=> ( 0 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
tff(f303,plain,
( $less(0,sK6)
| ( 0 = sK6 )
| spl9_2
| ~ spl9_34 ),
inference(resolution,[],[f297,f135]) ).
tff(f559,plain,
( spl9_53
| ~ spl9_7
| ~ spl9_12
| ~ spl9_36 ),
inference(avatar_split_clause,[],[f380,f316,f188,f162,f556]) ).
tff(f554,plain,
spl9_52,
inference(avatar_split_clause,[],[f86,f552]) ).
tff(f86,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(sK2(X0,X1,X2),X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(sK2(X0,X1,X2))) )
| $less(sK2(X0,X1,X2),0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tff(f75,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ( ~ $less(sK2(X0,X1,X2),X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(sK2(X0,X1,X2))) )
| $less(sK2(X0,X1,X2),0) )
& ( $sum(X0,$uminus(1)) = sK2(X0,X1,X2) )
& ( $product(X2,X0) = sK1(X0,X1,X2) )
& ( 0 != X0 ) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f72,f74,f73]) ).
tff(f73,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X3: $int] :
( ? [X4: $int] :
( ( ~ $less(X4,X0)
| $less(X0,0)
| ( fact1(X1) != $product(X3,fact1(X4)) )
| $less(X4,0) )
& ( $sum(X0,$uminus(1)) = X4 ) )
& ( $product(X2,X0) = X3 ) )
=> ( ? [X4: $int] :
( ( ~ $less(X4,X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(X4)) )
| $less(X4,0) )
& ( $sum(X0,$uminus(1)) = X4 ) )
& ( $product(X2,X0) = sK1(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f74,plain,
! [X0: $int,X1: $int,X2: $int] :
( ? [X4: $int] :
( ( ~ $less(X4,X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(X4)) )
| $less(X4,0) )
& ( $sum(X0,$uminus(1)) = X4 ) )
=> ( ( ~ $less(sK2(X0,X1,X2),X0)
| $less(X0,0)
| ( fact1(X1) != $product(sK1(X0,X1,X2),fact1(sK2(X0,X1,X2))) )
| $less(sK2(X0,X1,X2),0) )
& ( $sum(X0,$uminus(1)) = sK2(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f72,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ? [X3: $int] :
( ? [X4: $int] :
( ( ~ $less(X4,X0)
| $less(X0,0)
| ( fact1(X1) != $product(X3,fact1(X4)) )
| $less(X4,0) )
& ( $sum(X0,$uminus(1)) = X4 ) )
& ( $product(X2,X0) = X3 ) )
& ( 0 != X0 ) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f71]) ).
tff(f71,plain,
! [X3: $int,X0: $int,X4: $int] :
( ( ? [X5: $int] :
( ? [X6: $int] :
( ( ~ $less(X6,X3)
| $less(X3,0)
| ( fact1(X0) != $product(X5,fact1(X6)) )
| $less(X6,0) )
& ( $sum(X3,$uminus(1)) = X6 ) )
& ( $product(X4,X3) = X5 ) )
& ( 0 != X3 ) )
| ~ sP0(X3,X0,X4) ),
inference(nnf_transformation,[],[f69]) ).
tff(f69,plain,
! [X3: $int,X0: $int,X4: $int] :
( ( ? [X5: $int] :
( ? [X6: $int] :
( ( ~ $less(X6,X3)
| $less(X3,0)
| ( fact1(X0) != $product(X5,fact1(X6)) )
| $less(X6,0) )
& ( $sum(X3,$uminus(1)) = X6 ) )
& ( $product(X4,X3) = X5 ) )
& ( 0 != X3 ) )
| ~ sP0(X3,X0,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f478,plain,
spl9_51,
inference(avatar_split_clause,[],[f118,f476]) ).
tff(f118,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f40]) ).
tff(f40,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_151,[]) ).
tff(f474,plain,
spl9_50,
inference(avatar_split_clause,[],[f109,f472]) ).
tff(f109,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(flattening,[],[f65]) ).
tff(f65,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less($product(X1,X2),$product(X0,X2))
| $less(X2,0)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X1,X0)
=> ( ~ $less(X2,0)
=> ~ $less($product(X1,X2),$product(X0,X2)) ) ),
inference(rectify,[],[f23]) ).
tff(f23,plain,
! [X1: $int,X7: $int,X4: $int] :
( ~ $less(X7,X1)
=> ( ~ $less(X4,0)
=> ~ $less($product(X7,X4),$product(X1,X4)) ) ),
inference(theory_normalization,[],[f8]) ).
tff(f8,axiom,
! [X1: $int,X7: $int,X4: $int] :
( $lesseq(X1,X7)
=> ( $lesseq(0,X4)
=> $lesseq($product(X1,X4),$product(X7,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatOrderMult) ).
tff(f470,plain,
spl9_49,
inference(avatar_split_clause,[],[f39,f468]) ).
tff(f39,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f450,plain,
spl9_48,
inference(avatar_split_clause,[],[f125,f448]) ).
tff(f125,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( sK2(X0,X1,X2) = $sum(X0,-1) )
| ~ sP0(X0,X1,X2) ),
inference(evaluation,[],[f85]) ).
tff(f85,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( $sum(X0,$uminus(1)) = sK2(X0,X1,X2) )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tff(f446,plain,
spl9_47,
inference(avatar_split_clause,[],[f120,f444]) ).
tff(f120,plain,
! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,-1))) )
| ~ $less(0,X0) ),
inference(evaluation,[],[f104]) ).
tff(f104,plain,
! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1)))) )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $int] :
( ( fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1)))) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: $int] :
( $less(0,X0)
=> ( fact1(X0) = $product(X0,fact1($sum(X0,$uminus(1)))) ) ),
inference(rectify,[],[f22]) ).
tff(f22,plain,
! [X8: $int] :
( $less(0,X8)
=> ( fact1(X8) = $product(X8,fact1($sum(X8,$uminus(1)))) ) ),
inference(theory_normalization,[],[f18]) ).
tff(f18,axiom,
! [X8: $int] :
( $less(0,X8)
=> ( fact1(X8) = $product(X8,fact1($difference(X8,1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n) ).
tff(f442,plain,
spl9_46,
inference(avatar_split_clause,[],[f84,f440]) ).
tff(f84,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( $product(X2,X0) = sK1(X0,X1,X2) )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tff(f392,plain,
spl9_45,
inference(avatar_split_clause,[],[f126,f390]) ).
tff(f126,plain,
! [X0: $int] :
( ( $sum(2,sK8(X0)) = X0 )
| ( 0 = X0 )
| ~ even1(X0) ),
inference(forward_demodulation,[],[f102,f24]) ).
tff(f24,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f102,plain,
! [X0: $int] :
( ( $sum(sK8(X0),2) = X0 )
| ( 0 = X0 )
| ~ even1(X0) ),
inference(cnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0: $int] :
( ( ( $sum(sK8(X0),2) = X0 )
& even1(sK8(X0)) )
| ( 0 = X0 )
| ~ even1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f60,f81]) ).
tff(f81,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( $sum(X1,2) = X0 )
& even1(X1) )
=> ( ( $sum(sK8(X0),2) = X0 )
& even1(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f60,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( $sum(X1,2) = X0 )
& even1(X1) )
| ( 0 = X0 )
| ~ even1(X0) ),
inference(flattening,[],[f59]) ).
tff(f59,plain,
! [X0: $int] :
( ? [X1: $int] :
( ( $sum(X1,2) = X0 )
& even1(X1) )
| ( 0 = X0 )
| ~ even1(X0) ),
inference(ennf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int] :
( even1(X0)
=> ( ? [X1: $int] :
( ( $sum(X1,2) = X0 )
& even1(X1) )
| ( 0 = X0 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X4: $int] :
( even1(X4)
=> ( ? [X1: $int] :
( ( $sum(X1,2) = X4 )
& even1(X1) )
| ( 0 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_inversion) ).
tff(f388,plain,
spl9_44,
inference(avatar_split_clause,[],[f108,f386]) ).
tff(f108,plain,
! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort1(ref(X0),X1) ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0: ty,X1: uni] :
( ( mk_ref(X0,contents(X0,X1)) = X1 )
| ~ sort1(ref(X0),X1) ),
inference(ennf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: ty,X1: uni] :
( sort1(ref(X0),X1)
=> ( mk_ref(X0,contents(X0,X1)) = X1 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: ty,X6: uni] :
( sort1(ref(X0),X6)
=> ( mk_ref(X0,contents(X0,X6)) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ref_inversion1) ).
tff(f384,plain,
spl9_43,
inference(avatar_split_clause,[],[f36,f382]) ).
tff(f36,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f376,plain,
spl9_42,
inference(avatar_split_clause,[],[f25,f374]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f339,plain,
spl9_41,
inference(avatar_split_clause,[],[f111,f337]) ).
tff(f111,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool1(X0,true1,X1,X2) = X1 )
| ~ sort1(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tff(f68,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool1(X0,true1,X1,X2) = X1 )
| ~ sort1(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort1(X0,X1)
=> ( match_bool1(X0,true1,X1,X2) = X1 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort1(X0,X4)
=> ( match_bool1(X0,true1,X4,X5) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',match_bool_True) ).
tff(f335,plain,
spl9_40,
inference(avatar_split_clause,[],[f110,f333]) ).
tff(f110,plain,
! [X2: uni,X0: ty,X1: uni] :
( ( match_bool1(X0,false1,X1,X2) = X2 )
| ~ sort1(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
tff(f67,plain,
! [X0: ty,X1: uni,X2: uni] :
( ( match_bool1(X0,false1,X1,X2) = X2 )
| ~ sort1(X0,X2) ),
inference(ennf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: ty,X1: uni,X2: uni] :
( sort1(X0,X2)
=> ( match_bool1(X0,false1,X1,X2) = X2 ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: ty,X4: uni,X5: uni] :
( sort1(X0,X5)
=> ( match_bool1(X0,false1,X4,X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',match_bool_False) ).
tff(f331,plain,
spl9_39,
inference(avatar_split_clause,[],[f107,f329]) ).
tff(f107,plain,
! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort1(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: ty,X1: uni] :
( ( contents(X0,mk_ref(X0,X1)) = X1 )
| ~ sort1(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: ty,X1: uni] :
( sort1(X0,X1)
=> ( contents(X0,mk_ref(X0,X1)) = X1 ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: ty,X6: uni] :
( sort1(X0,X6)
=> ( contents(X0,mk_ref(X0,X6)) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contents_def1) ).
tff(f327,plain,
spl9_38,
inference(avatar_split_clause,[],[f32,f325]) ).
tff(f32,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f323,plain,
( spl9_36
| spl9_37
| spl9_1
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f302,f296,f128,f320,f316]) ).
tff(f302,plain,
( $less(0,sK5)
| ( 0 = sK5 )
| spl9_1
| ~ spl9_34 ),
inference(resolution,[],[f297,f130]) ).
tff(f314,plain,
spl9_35,
inference(avatar_split_clause,[],[f27,f312]) ).
tff(f27,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f298,plain,
spl9_34,
inference(avatar_split_clause,[],[f31,f296]) ).
tff(f31,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f294,plain,
spl9_33,
inference(avatar_split_clause,[],[f30,f292]) ).
tff(f30,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f284,plain,
spl9_32,
inference(avatar_split_clause,[],[f101,f282]) ).
tff(f101,plain,
! [X0: $int] :
( even1(sK8(X0))
| ( 0 = X0 )
| ~ even1(X0) ),
inference(cnf_transformation,[],[f82]) ).
tff(f280,plain,
spl9_31,
inference(avatar_split_clause,[],[f41,f278]) ).
tff(f41,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f276,plain,
( spl9_30
| ~ spl9_19
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f265,f254,f219,f274]) ).
tff(f274,plain,
( spl9_30
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
tff(f265,plain,
( ! [X0: $int] : ( 0 = $product(0,X0) )
| ~ spl9_19
| ~ spl9_27 ),
inference(superposition,[],[f255,f220]) ).
tff(f272,plain,
spl9_29,
inference(avatar_split_clause,[],[f33,f270]) ).
tff(f33,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f260,plain,
spl9_28,
inference(avatar_split_clause,[],[f112,f258]) ).
tff(f112,plain,
! [X2: uni,X3: uni,X0: ty,X1: bool1] : sort1(X0,match_bool1(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: ty,X1: bool1,X2: uni,X3: uni] : sort1(X0,match_bool1(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',match_bool_sort1) ).
tff(f256,plain,
spl9_27,
inference(avatar_split_clause,[],[f35,f254]) ).
tff(f35,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f252,plain,
spl9_26,
inference(avatar_split_clause,[],[f24,f250]) ).
tff(f245,plain,
spl9_25,
inference(avatar_split_clause,[],[f106,f243]) ).
tff(f106,plain,
! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: ty,X1: uni] : sort1(ref(X0),mk_ref(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mk_ref_sort1) ).
tff(f241,plain,
spl9_24,
inference(avatar_split_clause,[],[f103,f239]) ).
tff(f103,plain,
! [X0: $int] :
( ~ even1($sum(X0,1))
| ~ even1(X0) ),
inference(cnf_transformation,[],[f61]) ).
tff(f61,plain,
! [X0: $int] :
( ~ even1($sum(X0,1))
| ~ even1(X0) ),
inference(ennf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: $int] :
( even1(X0)
=> ~ even1($sum(X0,1)) ),
inference(flattening,[],[f48]) ).
tff(f48,plain,
! [X0: $int] :
( even1(X0)
=> ~ even1($sum(X0,1)) ),
inference(true_and_false_elimination,[],[f47]) ).
tff(f47,plain,
! [X0: $int] :
( even1(X0)
=> ( even1($sum(X0,1))
=> $false ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X1: $int] :
( even1(X1)
=> ( even1($sum(X1,1))
=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_not_odd) ).
tff(f237,plain,
spl9_23,
inference(avatar_split_clause,[],[f100,f235]) ).
tff(f100,plain,
! [X0: $int] :
( even1($sum(X0,2))
| ~ even1(X0) ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: $int] :
( even1($sum(X0,2))
| ~ even1(X0) ),
inference(ennf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: $int] :
( even1(X0)
=> even1($sum(X0,2)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X1: $int] :
( even1(X1)
=> even1($sum(X1,2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_odd) ).
tff(f233,plain,
spl9_22,
inference(avatar_split_clause,[],[f99,f231]) ).
tff(f99,plain,
! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: bool1] :
( ( false1 = X0 )
| ( true1 = X0 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X6: bool1] :
( ( false1 = X6 )
| ( true1 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bool_inversion) ).
tff(f229,plain,
spl9_21,
inference(avatar_split_clause,[],[f28,f227]) ).
tff(f28,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f225,plain,
spl9_20,
inference(avatar_split_clause,[],[f105,f223]) ).
tff(f105,plain,
! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: ty,X1: uni] : sort1(X0,contents(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contents_sort1) ).
tff(f221,plain,
spl9_19,
inference(avatar_split_clause,[],[f38,f219]) ).
tff(f38,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f217,plain,
spl9_18,
inference(avatar_split_clause,[],[f37,f215]) ).
tff(f215,plain,
( spl9_18
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
tff(f37,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f213,plain,
spl9_17,
inference(avatar_split_clause,[],[f34,f211]) ).
tff(f211,plain,
( spl9_17
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
tff(f34,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f209,plain,
spl9_16,
inference(avatar_split_clause,[],[f26,f207]) ).
tff(f207,plain,
( spl9_16
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
tff(f26,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f205,plain,
( ~ spl9_8
| ~ spl9_15 ),
inference(avatar_contradiction_clause,[],[f204]) ).
tff(f204,plain,
( $false
| ~ spl9_8
| ~ spl9_15 ),
inference(resolution,[],[f202,f171]) ).
tff(f171,plain,
( sP0(0,sK5,sK7)
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f169]) ).
tff(f169,plain,
( spl9_8
<=> sP0(0,sK5,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
tff(f202,plain,
( ! [X2: $int,X1: $int] : ~ sP0(0,X1,X2)
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f201]) ).
tff(f201,plain,
( spl9_15
<=> ! [X2: $int,X1: $int] : ~ sP0(0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
tff(f203,plain,
spl9_15,
inference(avatar_split_clause,[],[f119,f201]) ).
tff(f119,plain,
! [X2: $int,X1: $int] : ~ sP0(0,X1,X2),
inference(equality_resolution,[],[f83]) ).
tff(f83,plain,
! [X2: $int,X0: $int,X1: $int] :
( ( 0 != X0 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tff(f199,plain,
spl9_14,
inference(avatar_split_clause,[],[f98,f197]) ).
tff(f98,plain,
! [X0: ty] : sort1(X0,witness1(X0)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: ty] : sort1(X0,witness1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',witness_sort1) ).
tff(f195,plain,
( spl9_13
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f186,f183,f193]) ).
tff(f193,plain,
( spl9_13
<=> ! [X0: tuple02,X1: tuple02] : ( X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
tff(f183,plain,
( spl9_11
<=> ! [X0: tuple02] : ( tuple03 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
tff(f186,plain,
( ! [X0: tuple02,X1: tuple02] : ( X0 = X1 )
| ~ spl9_11 ),
inference(superposition,[],[f184,f184]) ).
tff(f184,plain,
( ! [X0: tuple02] : ( tuple03 = X0 )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f183]) ).
tff(f191,plain,
spl9_12,
inference(avatar_split_clause,[],[f96,f188]) ).
tff(f96,plain,
1 = fact1(0),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
1 = fact1(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0) ).
tff(f185,plain,
spl9_11,
inference(avatar_split_clause,[],[f97,f183]) ).
tff(f97,plain,
! [X0: tuple02] : ( tuple03 = X0 ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: tuple02] : ( tuple03 = X0 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X6: tuple02] : ( tuple03 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuple0_inversion) ).
tff(f181,plain,
~ spl9_10,
inference(avatar_split_clause,[],[f95,f178]) ).
tff(f178,plain,
( spl9_10
<=> ( true1 = false1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
tff(f95,plain,
true1 != false1,
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
true1 != false1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_False) ).
tff(f176,plain,
spl9_9,
inference(avatar_split_clause,[],[f29,f174]) ).
tff(f29,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f172,plain,
( spl9_8
| ~ spl9_5
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f167,f152,f148,f169]) ).
tff(f167,plain,
( sP0(0,sK5,sK7)
| ~ spl9_5
| ~ spl9_6 ),
inference(forward_demodulation,[],[f150,f154]) ).
tff(f154,plain,
( ( 0 = sK6 )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f152]) ).
tff(f166,plain,
( spl9_7
| ~ spl9_4
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f160,f152,f143,f162]) ).
tff(f160,plain,
( ( fact1(sK5) = sK7 )
| ~ spl9_4
| ~ spl9_6 ),
inference(evaluation,[],[f159]) ).
tff(f159,plain,
( ( fact1(sK5) = $product(sK7,1) )
| ~ spl9_4
| ~ spl9_6 ),
inference(forward_demodulation,[],[f157,f96]) ).
tff(f157,plain,
( ( fact1(sK5) = $product(sK7,fact1(0)) )
| ~ spl9_4
| ~ spl9_6 ),
inference(superposition,[],[f145,f154]) ).
tff(f165,plain,
( spl9_1
| spl9_5
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f124,f162,f148,f128]) ).
tff(f124,plain,
( ( fact1(sK5) != sK7 )
| sP0(sK6,sK5,sK7)
| $less(sK5,0) ),
inference(evaluation,[],[f113]) ).
tff(f113,plain,
( ( fact1(sK5) != sK7 )
| sP0(sK6,sK5,sK7)
| ( fact1(sK5) != $product(1,fact1(sK5)) )
| $less(sK5,0) ),
inference(definition_unfolding,[],[f93,f89,f89,f89,f88]) ).
tff(f88,plain,
1 = sK4,
inference(cnf_transformation,[],[f80]) ).
tff(f80,plain,
( ( ( ( ( ( fact1(sK3) != sK7 )
& ( 0 = sK6 ) )
| sP0(sK6,sK3,sK7) )
& ( fact1(sK3) = $product(sK7,fact1(sK6)) )
& ~ $less(sK6,0) )
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) )
& ( sK3 = sK5 )
& ( 1 = sK4 )
& ~ $less(sK3,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f70,f79,f78,f77,f76]) ).
tff(f76,plain,
( ? [X0: $int] :
( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X3: $int,X4: $int] :
( ( ( ( fact1(X0) != X4 )
& ( 0 = X3 ) )
| sP0(X3,X0,X4) )
& ( fact1(X0) = $product(X4,fact1(X3)) )
& ~ $less(X3,0) )
| ( fact1(X0) != $product(X1,fact1(X2)) )
| $less(X2,0) )
& ( X0 = X2 ) )
& ( 1 = X1 ) )
& ~ $less(X0,0) )
=> ( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
| ( $product(X1,fact1(X2)) != fact1(sK3) )
| $less(X2,0) )
& ( sK3 = X2 ) )
& ( 1 = X1 ) )
& ~ $less(sK3,0) ) ),
introduced(choice_axiom,[]) ).
tff(f77,plain,
( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
| ( $product(X1,fact1(X2)) != fact1(sK3) )
| $less(X2,0) )
& ( sK3 = X2 ) )
& ( 1 = X1 ) )
=> ( ? [X2: $int] :
( ( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
| ( fact1(sK3) != $product(sK4,fact1(X2)) )
| $less(X2,0) )
& ( sK3 = X2 ) )
& ( 1 = sK4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f78,plain,
( ? [X2: $int] :
( ( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
| ( fact1(sK3) != $product(sK4,fact1(X2)) )
| $less(X2,0) )
& ( sK3 = X2 ) )
=> ( ( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) )
& ( sK3 = sK5 ) ) ),
introduced(choice_axiom,[]) ).
tff(f79,plain,
( ? [X4: $int,X3: $int] :
( ( ( ( fact1(sK3) != X4 )
& ( 0 = X3 ) )
| sP0(X3,sK3,X4) )
& ( $product(X4,fact1(X3)) = fact1(sK3) )
& ~ $less(X3,0) )
=> ( ( ( ( fact1(sK3) != sK7 )
& ( 0 = sK6 ) )
| sP0(sK6,sK3,sK7) )
& ( fact1(sK3) = $product(sK7,fact1(sK6)) )
& ~ $less(sK6,0) ) ),
introduced(choice_axiom,[]) ).
tff(f70,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X3: $int,X4: $int] :
( ( ( ( fact1(X0) != X4 )
& ( 0 = X3 ) )
| sP0(X3,X0,X4) )
& ( fact1(X0) = $product(X4,fact1(X3)) )
& ~ $less(X3,0) )
| ( fact1(X0) != $product(X1,fact1(X2)) )
| $less(X2,0) )
& ( X0 = X2 ) )
& ( 1 = X1 ) )
& ~ $less(X0,0) ),
inference(definition_folding,[],[f57,f69]) ).
tff(f57,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X3: $int,X4: $int] :
( ( ( ( fact1(X0) != X4 )
& ( 0 = X3 ) )
| ( ? [X5: $int] :
( ? [X6: $int] :
( ( ~ $less(X6,X3)
| $less(X3,0)
| ( fact1(X0) != $product(X5,fact1(X6)) )
| $less(X6,0) )
& ( $sum(X3,$uminus(1)) = X6 ) )
& ( $product(X4,X3) = X5 ) )
& ( 0 != X3 ) ) )
& ( fact1(X0) = $product(X4,fact1(X3)) )
& ~ $less(X3,0) )
| ( fact1(X0) != $product(X1,fact1(X2)) )
| $less(X2,0) )
& ( X0 = X2 ) )
& ( 1 = X1 ) )
& ~ $less(X0,0) ),
inference(flattening,[],[f56]) ).
tff(f56,plain,
? [X0: $int] :
( ? [X1: $int] :
( ? [X2: $int] :
( ( ? [X3: $int,X4: $int] :
( ( ( ( fact1(X0) != X4 )
& ( 0 = X3 ) )
| ( ? [X5: $int] :
( ? [X6: $int] :
( ( ~ $less(X6,X3)
| $less(X3,0)
| ( fact1(X0) != $product(X5,fact1(X6)) )
| $less(X6,0) )
& ( $sum(X3,$uminus(1)) = X6 ) )
& ( $product(X4,X3) = X5 ) )
& ( 0 != X3 ) ) )
& ( fact1(X0) = $product(X4,fact1(X3)) )
& ~ $less(X3,0) )
| ( fact1(X0) != $product(X1,fact1(X2)) )
| $less(X2,0) )
& ( X0 = X2 ) )
& ( 1 = X1 ) )
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f42]) ).
tff(f42,plain,
~ ! [X0: $int] :
( ~ $less(X0,0)
=> ! [X1: $int] :
( ( 1 = X1 )
=> ! [X2: $int] :
( ( X0 = X2 )
=> ( ! [X3: $int,X4: $int] :
( ( ( fact1(X0) = $product(X4,fact1(X3)) )
& ~ $less(X3,0) )
=> ( ( ( 0 = X3 )
=> ( fact1(X0) = X4 ) )
& ( ( 0 != X3 )
=> ! [X5: $int] :
( ( $product(X4,X3) = X5 )
=> ! [X6: $int] :
( ( $sum(X3,$uminus(1)) = X6 )
=> ( $less(X6,X3)
& ~ $less(X3,0)
& ( fact1(X0) = $product(X5,fact1(X6)) )
& ~ $less(X6,0) ) ) ) ) ) )
& ( fact1(X0) = $product(X1,fact1(X2)) )
& ~ $less(X2,0) ) ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,plain,
~ ! [X1: $int] :
( ~ $less(X1,0)
=> ! [X7: $int] :
( ( 1 = X7 )
=> ! [X4: $int] :
( ( X1 = X4 )
=> ( ! [X5: $int,X9: $int] :
( ( ( fact1(X1) = $product(X9,fact1(X5)) )
& ~ $less(X5,0) )
=> ( ( ( 0 = X5 )
=> ( fact1(X1) = X9 ) )
& ( ( 0 != X5 )
=> ! [X10: $int] :
( ( $product(X9,X5) = X10 )
=> ! [X11: $int] :
( ( $sum(X5,$uminus(1)) = X11 )
=> ( $less(X11,X5)
& ~ $less(X5,0)
& ( fact1(X1) = $product(X10,fact1(X11)) )
& ~ $less(X11,0) ) ) ) ) ) )
& ( $product(X7,fact1(X4)) = fact1(X1) )
& ~ $less(X4,0) ) ) ) ),
inference(theory_normalization,[],[f20]) ).
tff(f20,negated_conjecture,
~ ! [X1: $int] :
( $lesseq(0,X1)
=> ! [X7: $int] :
( ( 1 = X7 )
=> ! [X4: $int] :
( ( X1 = X4 )
=> ( ! [X5: $int,X9: $int] :
( ( ( fact1(X1) = $product(X9,fact1(X5)) )
& $lesseq(0,X5) )
=> ( ( ( 0 = X5 )
=> ( fact1(X1) = X9 ) )
& ( ( 0 != X5 )
=> ! [X10: $int] :
( ( $product(X9,X5) = X10 )
=> ! [X11: $int] :
( ( $difference(X5,1) = X11 )
=> ( $less(X11,X5)
& $lesseq(0,X5)
& ( fact1(X1) = $product(X10,fact1(X11)) )
& $lesseq(0,X11) ) ) ) ) ) )
& ( $product(X7,fact1(X4)) = fact1(X1) )
& $lesseq(0,X4) ) ) ) ),
inference(negated_conjecture,[],[f19]) ).
tff(f19,conjecture,
! [X1: $int] :
( $lesseq(0,X1)
=> ! [X7: $int] :
( ( 1 = X7 )
=> ! [X4: $int] :
( ( X1 = X4 )
=> ( ! [X5: $int,X9: $int] :
( ( ( fact1(X1) = $product(X9,fact1(X5)) )
& $lesseq(0,X5) )
=> ( ( ( 0 = X5 )
=> ( fact1(X1) = X9 ) )
& ( ( 0 != X5 )
=> ! [X10: $int] :
( ( $product(X9,X5) = X10 )
=> ! [X11: $int] :
( ( $difference(X5,1) = X11 )
=> ( $less(X11,X5)
& $lesseq(0,X5)
& ( fact1(X1) = $product(X10,fact1(X11)) )
& $lesseq(0,X11) ) ) ) ) ) )
& ( $product(X7,fact1(X4)) = fact1(X1) )
& $lesseq(0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_factorial) ).
tff(f89,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f80]) ).
tff(f93,plain,
( ( fact1(sK3) != sK7 )
| sP0(sK6,sK3,sK7)
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f155,plain,
( spl9_1
| spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f123,f152,f148,f128]) ).
tff(f123,plain,
( ( 0 = sK6 )
| sP0(sK6,sK5,sK7)
| $less(sK5,0) ),
inference(evaluation,[],[f114]) ).
tff(f114,plain,
( ( 0 = sK6 )
| sP0(sK6,sK5,sK7)
| ( fact1(sK5) != $product(1,fact1(sK5)) )
| $less(sK5,0) ),
inference(definition_unfolding,[],[f92,f89,f89,f88]) ).
tff(f92,plain,
( ( 0 = sK6 )
| sP0(sK6,sK3,sK7)
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f146,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f122,f143,f128]) ).
tff(f122,plain,
( ( fact1(sK5) = $product(sK7,fact1(sK6)) )
| $less(sK5,0) ),
inference(evaluation,[],[f115]) ).
tff(f115,plain,
( ( fact1(sK5) = $product(sK7,fact1(sK6)) )
| ( fact1(sK5) != $product(1,fact1(sK5)) )
| $less(sK5,0) ),
inference(definition_unfolding,[],[f91,f89,f89,f88]) ).
tff(f91,plain,
( ( fact1(sK3) = $product(sK7,fact1(sK6)) )
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f141,plain,
spl9_3,
inference(avatar_split_clause,[],[f94,f138]) ).
tff(f94,plain,
even1(0),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
even1(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_0) ).
tff(f136,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f121,f133,f128]) ).
tff(f121,plain,
( ~ $less(sK6,0)
| $less(sK5,0) ),
inference(evaluation,[],[f116]) ).
tff(f116,plain,
( ~ $less(sK6,0)
| ( fact1(sK5) != $product(1,fact1(sK5)) )
| $less(sK5,0) ),
inference(definition_unfolding,[],[f90,f89,f88]) ).
tff(f90,plain,
( ~ $less(sK6,0)
| ( fact1(sK3) != $product(sK4,fact1(sK5)) )
| $less(sK5,0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f131,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f117,f128]) ).
tff(f117,plain,
~ $less(sK5,0),
inference(definition_unfolding,[],[f87,f89]) ).
tff(f87,plain,
~ $less(sK3,0),
inference(cnf_transformation,[],[f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW642_2 : TPTP v8.2.0. Released v6.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 18:59:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (23364)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (23369)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)
% 0.14/0.37 % (23367)WARNING: value z3 for option sas not known
% 0.14/0.38 % (23365)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (23368)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (23366)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 % (23367)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 % (23370)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 % (23371)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 % (23365)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (23365)Terminated due to inappropriate strategy.
% 0.14/0.38 % (23365)------------------------------
% 0.14/0.38 % (23365)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (23365)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (23365)Memory used [KB]: 810
% 0.14/0.38 % (23365)Time elapsed: 0.003 s
% 0.14/0.38 % (23365)Instructions burned: 4 (million)
% 0.14/0.38 % (23366)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (23366)Terminated due to inappropriate strategy.
% 0.14/0.38 % (23366)------------------------------
% 0.14/0.38 % (23366)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (23366)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (23366)Memory used [KB]: 810
% 0.14/0.38 % (23366)Time elapsed: 0.004 s
% 0.14/0.38 % (23366)Instructions burned: 4 (million)
% 0.14/0.38 % (23368)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (23368)Terminated due to inappropriate strategy.
% 0.14/0.38 % (23368)------------------------------
% 0.14/0.38 % (23368)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (23368)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (23368)Memory used [KB]: 811
% 0.14/0.38 % (23368)Time elapsed: 0.004 s
% 0.14/0.38 % (23368)Instructions burned: 4 (million)
% 0.14/0.38 % (23365)------------------------------
% 0.14/0.38 % (23365)------------------------------
% 0.14/0.38 % (23366)------------------------------
% 0.14/0.38 % (23366)------------------------------
% 0.14/0.38 % (23368)------------------------------
% 0.14/0.38 % (23368)------------------------------
% 0.21/0.39 % (23372)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.39 % (23373)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)
% 0.21/0.39 % (23374)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)
% 0.21/0.40 % (23372)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (23372)Terminated due to inappropriate strategy.
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.40 % (23372)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40 % (23372)Termination reason: Inappropriate
% 0.21/0.40
% 0.21/0.40 % (23372)Memory used [KB]: 810
% 0.21/0.40 % (23372)Time elapsed: 0.003 s
% 0.21/0.40 % (23372)Instructions burned: 4 (million)
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.41 % (23375)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)
% 1.43/0.59 % (23369)First to succeed.
% 1.43/0.60 % (23369)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23364"
% 1.43/0.60 % (23369)Refutation found. Thanks to Tanya!
% 1.43/0.60 % SZS status Theorem for theBenchmark
% 1.43/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.43/0.61 % (23369)------------------------------
% 1.43/0.61 % (23369)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.43/0.61 % (23369)Termination reason: Refutation
% 1.43/0.61
% 1.43/0.61 % (23369)Memory used [KB]: 4495
% 1.43/0.61 % (23369)Time elapsed: 0.227 s
% 1.43/0.61 % (23369)Instructions burned: 570 (million)
% 1.43/0.61 % (23364)Success in time 0.234 s
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