TSTP Solution File: DAT023_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT023_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Mon May 20 19:50:51 EDT 2024
% Result : Theorem 13.23s 2.30s
% Output : Refutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 165
% Syntax : Number of formulae : 1004 ( 24 unt; 8 typ; 0 def)
% Number of atoms : 3148 ( 186 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 3504 (1352 ~;1977 |; 29 &)
% ( 135 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 4100 (1187 atm; 818 fun;1637 num; 458 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 138 ( 134 usr; 134 prp; 0-2 aty)
% Number of functors : 16 ( 6 usr; 12 con; 0-2 aty)
% Number of variables : 480 ( 466 !; 14 ?; 480 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: collection ).
tff(func_def_11,type,
sK2: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f47541,plain,
$false,
inference(avatar_sat_refutation,[],[f54,f59,f64,f70,f117,f124,f131,f167,f232,f233,f239,f251,f361,f362,f368,f477,f478,f479,f2042,f2047,f2052,f2053,f3622,f4531,f4535,f4536,f4537,f4542,f4547,f4552,f4557,f4559,f4564,f4569,f4574,f4577,f4582,f4587,f4592,f4594,f4599,f4601,f4610,f4615,f4617,f4619,f4646,f4672,f4716,f4721,f4726,f4732,f4734,f4740,f4742,f4789,f4790,f4826,f4855,f4856,f4915,f4917,f4919,f4921,f4973,f5170,f5288,f5347,f5387,f5415,f5416,f5854,f5856,f5858,f5862,f5968,f7848,f7894,f7895,f10775,f11100,f11120,f11125,f11134,f11135,f11158,f11160,f11161,f11162,f11172,f11177,f11182,f11208,f11393,f11394,f11395,f11806,f11810,f11811,f11815,f11819,f11820,f11821,f11822,f11824,f12335,f12585,f12620,f12625,f12663,f12668,f12670,f12671,f12680,f12681,f12688,f12690,f12697,f12699,f12727,f12756,f12757,f12773,f12774,f13082,f23045,f23050,f23051,f23224,f23225,f23231,f23232,f23237,f23238,f23239,f23384,f23385,f23386,f23523,f23525,f23530,f23831,f23832,f23833,f23939,f23940,f23953,f23954,f23955,f23977,f25057,f25254,f27543,f27598,f27603,f27641,f27642,f27643,f30344,f30345,f30346,f30347,f30348,f31225,f31295,f31337,f31339,f31344,f31563,f31567,f31583,f31659,f31996,f31997,f31998,f31999,f32076,f32077,f32488,f32493,f32516,f32517,f32518,f45175,f45179,f45183,f45188,f45191,f45192,f45195,f45196,f46047,f46069,f46087,f46088,f46140,f46142,f46144,f46147,f46150,f46194,f46199,f46219,f46220,f46271,f46274,f46391,f46825,f46849,f47448,f47457,f47466,f47470,f47478,f47484,f47492,f47497,f47503,f47504,f47517,f47519,f47521,f47525,f47526,f47527,f47528,f47535,f47536,f47538,f47540]) ).
tff(f47540,plain,
( spl3_13
| spl3_8
| spl3_18 ),
inference(avatar_split_clause,[],[f47539,f2039,f164,f358]) ).
tff(f358,plain,
( spl3_13
<=> $less(1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
tff(f164,plain,
( spl3_8
<=> $less(sK2,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
tff(f2039,plain,
( spl3_18
<=> ( 1 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
tff(f47539,plain,
( $less(1,sK2)
| spl3_8
| spl3_18 ),
inference(subsumption_resolution,[],[f439,f2040]) ).
tff(f2040,plain,
( ( 1 != sK2 )
| spl3_18 ),
inference(avatar_component_clause,[],[f2039]) ).
tff(f439,plain,
( $less(1,sK2)
| ( 1 = sK2 )
| spl3_8 ),
inference(resolution,[],[f16,f166]) ).
tff(f166,plain,
( ~ $less(sK2,1)
| spl3_8 ),
inference(avatar_component_clause,[],[f164]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f47538,plain,
( spl3_13
| spl3_8
| spl3_18 ),
inference(avatar_split_clause,[],[f47537,f2039,f164,f358]) ).
tff(f47537,plain,
( $less(1,sK2)
| spl3_8
| spl3_18 ),
inference(subsumption_resolution,[],[f464,f2040]) ).
tff(f464,plain,
( $less(1,sK2)
| ( 1 = sK2 )
| spl3_8 ),
inference(resolution,[],[f16,f166]) ).
tff(f47536,plain,
( spl3_12
| spl3_13
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f951,f128,f358,f355]) ).
tff(f355,plain,
( spl3_12
<=> ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
tff(f128,plain,
( spl3_7
<=> $less(0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
tff(f951,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(2,X0))
| $less(X0,0) )
| ~ spl3_7 ),
inference(evaluation,[],[f934]) ).
tff(f934,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(1,$sum(X0,1)))
| $less(X0,0) )
| ~ spl3_7 ),
inference(resolution,[],[f263,f157]) ).
tff(f157,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,0) ),
inference(resolution,[],[f150,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f150,plain,
! [X0: $int] :
( ~ $less(0,X0)
| ~ $less(X0,1) ),
inference(superposition,[],[f101,f11]) ).
tff(f11,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f101,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f20,f9]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f263,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,sK2)
| $less(-1,$sum(1,X1))
| $less(X1,X0) )
| ~ spl3_7 ),
inference(resolution,[],[f252,f84]) ).
tff(f84,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f18,f9]) ).
tff(f252,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_7 ),
inference(resolution,[],[f223,f87]) ).
tff(f87,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f86]) ).
tff(f86,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f18,f71]) ).
tff(f71,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f13,f19]) ).
tff(f19,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f13,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f223,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,X0)
| $less(X1,sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f215,f15]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f215,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,0) )
| ~ spl3_7 ),
inference(resolution,[],[f15,f130]) ).
tff(f130,plain,
( $less(0,sK2)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f128]) ).
tff(f47535,plain,
( spl3_12
| spl3_13
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f948,f128,f358,f355]) ).
tff(f948,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(2,X0))
| $less(X0,0) )
| ~ spl3_7 ),
inference(evaluation,[],[f937]) ).
tff(f937,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(1,$sum(1,X0)))
| $less(X0,0) )
| ~ spl3_7 ),
inference(resolution,[],[f263,f160]) ).
tff(f160,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,0) ),
inference(resolution,[],[f150,f84]) ).
tff(f47528,plain,
( spl3_13
| spl3_133
| ~ spl3_7
| ~ spl3_71 ),
inference(avatar_split_clause,[],[f13630,f11813,f128,f47523,f358]) ).
tff(f47523,plain,
( spl3_133
<=> ! [X0: $int] :
( $less(X0,1)
| $less(-1,$sum(2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_133])]) ).
tff(f11813,plain,
( spl3_71
<=> ! [X0: $int] :
( $less(X0,1)
| $less(0,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).
tff(f13630,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(2,X0)) )
| ~ spl3_7
| ~ spl3_71 ),
inference(evaluation,[],[f13613]) ).
tff(f13613,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum($sum(X0,1),1)) )
| ~ spl3_7
| ~ spl3_71 ),
inference(resolution,[],[f13493,f260]) ).
tff(f260,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,sK2)
| $less(-1,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_7 ),
inference(resolution,[],[f252,f18]) ).
tff(f13493,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,1) )
| ~ spl3_71 ),
inference(resolution,[],[f11814,f150]) ).
tff(f11814,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,1) )
| ~ spl3_71 ),
inference(avatar_component_clause,[],[f11813]) ).
tff(f47527,plain,
( spl3_13
| spl3_133
| ~ spl3_7
| ~ spl3_71 ),
inference(avatar_split_clause,[],[f13629,f11813,f128,f47523,f358]) ).
tff(f13629,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(2,X0)) )
| ~ spl3_7
| ~ spl3_71 ),
inference(evaluation,[],[f13614]) ).
tff(f13614,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(1,$sum(X0,1))) )
| ~ spl3_7
| ~ spl3_71 ),
inference(resolution,[],[f13493,f263]) ).
tff(f47526,plain,
( spl3_13
| spl3_133
| ~ spl3_7
| ~ spl3_72 ),
inference(avatar_split_clause,[],[f13657,f11817,f128,f47523,f358]) ).
tff(f11817,plain,
( spl3_72
<=> ! [X0: $int] :
( $less(X0,1)
| $less(0,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).
tff(f13657,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(2,X0)) )
| ~ spl3_7
| ~ spl3_72 ),
inference(evaluation,[],[f13640]) ).
tff(f13640,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum($sum(1,X0),1)) )
| ~ spl3_7
| ~ spl3_72 ),
inference(resolution,[],[f13517,f260]) ).
tff(f13517,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,1) )
| ~ spl3_72 ),
inference(resolution,[],[f11818,f150]) ).
tff(f11818,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,1) )
| ~ spl3_72 ),
inference(avatar_component_clause,[],[f11817]) ).
tff(f47525,plain,
( spl3_13
| spl3_133
| ~ spl3_7
| ~ spl3_72 ),
inference(avatar_split_clause,[],[f13656,f11817,f128,f47523,f358]) ).
tff(f13656,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(2,X0)) )
| ~ spl3_7
| ~ spl3_72 ),
inference(evaluation,[],[f13641]) ).
tff(f13641,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(1,sK2)
| $less(-1,$sum(1,$sum(1,X0))) )
| ~ spl3_7
| ~ spl3_72 ),
inference(resolution,[],[f13517,f263]) ).
tff(f47521,plain,
( spl3_13
| spl3_8
| spl3_18 ),
inference(avatar_split_clause,[],[f47520,f2039,f164,f358]) ).
tff(f47520,plain,
( $less(1,sK2)
| spl3_8
| spl3_18 ),
inference(subsumption_resolution,[],[f31685,f2040]) ).
tff(f31685,plain,
( $less(1,sK2)
| ( 1 = sK2 )
| spl3_8 ),
inference(resolution,[],[f166,f16]) ).
tff(f47519,plain,
( spl3_13
| spl3_8
| spl3_18 ),
inference(avatar_split_clause,[],[f47518,f2039,f164,f358]) ).
tff(f47518,plain,
( $less(1,sK2)
| spl3_8
| spl3_18 ),
inference(subsumption_resolution,[],[f31686,f2040]) ).
tff(f31686,plain,
( $less(1,sK2)
| ( 1 = sK2 )
| spl3_8 ),
inference(resolution,[],[f166,f16]) ).
tff(f47517,plain,
( spl3_129
| spl3_132
| ~ spl3_41
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f36663,f5412,f4669,f47514,f47490]) ).
tff(f47490,plain,
( spl3_129
<=> ! [X0: $int] :
( ~ $less(X0,1)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_129])]) ).
tff(f47514,plain,
( spl3_132
<=> $less(sK2,$sum(2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_132])]) ).
tff(f4669,plain,
( spl3_41
<=> $less($sum(1,sK2),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
tff(f5412,plain,
( spl3_53
<=> $less(1,$sum(2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).
tff(f36663,plain,
( ! [X0: $int] :
( $less(sK2,$sum(2,sK2))
| $less(X0,2)
| ~ $less(X0,1) )
| ~ spl3_41
| ~ spl3_53 ),
inference(resolution,[],[f33276,f5931]) ).
tff(f5931,plain,
( ! [X0: $int] :
( $less(X0,$sum(2,sK2))
| ~ $less(X0,1) )
| ~ spl3_53 ),
inference(resolution,[],[f5414,f15]) ).
tff(f5414,plain,
( $less(1,$sum(2,sK2))
| ~ spl3_53 ),
inference(avatar_component_clause,[],[f5412]) ).
tff(f33276,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(sK2,X0)
| $less(X1,2) )
| ~ spl3_41 ),
inference(resolution,[],[f33238,f15]) ).
tff(f33238,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(sK2,X0) )
| ~ spl3_41 ),
inference(resolution,[],[f32029,f84]) ).
tff(f32029,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,sK2))
| $less(X0,2) )
| ~ spl3_41 ),
inference(resolution,[],[f4671,f15]) ).
tff(f4671,plain,
( $less($sum(1,sK2),2)
| ~ spl3_41 ),
inference(avatar_component_clause,[],[f4669]) ).
tff(f47504,plain,
( spl3_129
| spl3_122
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f45374,f4852,f2050,f47460,f47490]) ).
tff(f47460,plain,
( spl3_122
<=> $less($uminus($sum(1,sK2)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_122])]) ).
tff(f2050,plain,
( spl3_20
<=> ! [X0: $int] :
( $less($sum(1,X0),2)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
tff(f4852,plain,
( spl3_49
<=> $less(1,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).
tff(f45374,plain,
( ! [X0: $int] :
( $less($uminus($sum(1,sK2)),0)
| $less(X0,2)
| ~ $less(X0,1) )
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f44665,f5115]) ).
tff(f5115,plain,
( ! [X0: $int] :
( $less(X0,$sum(1,sK2))
| ~ $less(X0,1) )
| ~ spl3_49 ),
inference(resolution,[],[f4854,f15]) ).
tff(f4854,plain,
( $less(1,$sum(1,sK2))
| ~ spl3_49 ),
inference(avatar_component_clause,[],[f4852]) ).
tff(f44665,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less($uminus(X0),0)
| $less(X1,2) )
| ~ spl3_20 ),
inference(superposition,[],[f22973,f19]) ).
tff(f22973,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$uminus(X0))
| $less(X0,0)
| $less(X1,2) )
| ~ spl3_20 ),
inference(resolution,[],[f22964,f15]) ).
tff(f22964,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| $less(X0,0) )
| ~ spl3_20 ),
inference(superposition,[],[f22886,f19]) ).
tff(f22886,plain,
( ! [X0: $int] :
( $less($uminus(X0),0)
| $less(X0,2) )
| ~ spl3_20 ),
inference(resolution,[],[f22884,f87]) ).
tff(f22884,plain,
( ! [X0: $int] :
( ~ $less(-1,$uminus(X0))
| $less(X0,2) )
| ~ spl3_20 ),
inference(superposition,[],[f22813,f19]) ).
tff(f22813,plain,
( ! [X0: $int] :
( $less($uminus(X0),2)
| ~ $less(-1,X0) )
| ~ spl3_20 ),
inference(resolution,[],[f5101,f18808]) ).
tff(f18808,plain,
( ! [X0: $int] :
( ~ $less($sum(-1,X0),0)
| $less(X0,2) )
| ~ spl3_20 ),
inference(evaluation,[],[f18707]) ).
tff(f18707,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less($sum($uminus(1),X0),0) )
| ~ spl3_20 ),
inference(superposition,[],[f2051,f7292]) ).
tff(f7292,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f7229]) ).
tff(f7229,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f10,f13]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f2051,plain,
( ! [X0: $int] :
( $less($sum(1,X0),2)
| ~ $less(X0,0) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f2050]) ).
tff(f5101,plain,
! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ),
inference(superposition,[],[f17,f13]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_145,[]) ).
tff(f47503,plain,
( spl3_129
| spl3_131
| ~ spl3_20
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f45376,f5412,f2050,f47500,f47490]) ).
tff(f47500,plain,
( spl3_131
<=> $less($uminus($sum(2,sK2)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_131])]) ).
tff(f45376,plain,
( ! [X0: $int] :
( $less($uminus($sum(2,sK2)),0)
| $less(X0,2)
| ~ $less(X0,1) )
| ~ spl3_20
| ~ spl3_53 ),
inference(resolution,[],[f44665,f5931]) ).
tff(f47497,plain,
( spl3_130
| spl3_129
| ~ spl3_41
| ~ spl3_118 ),
inference(avatar_split_clause,[],[f46447,f46216,f4669,f47490,f47494]) ).
tff(f47494,plain,
( spl3_130
<=> $less(sK2,$sum(3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_130])]) ).
tff(f46216,plain,
( spl3_118
<=> $less(1,$sum(3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_118])]) ).
tff(f46447,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| $less(sK2,$sum(3,sK2))
| $less(X0,2) )
| ~ spl3_41
| ~ spl3_118 ),
inference(resolution,[],[f46327,f33276]) ).
tff(f46327,plain,
( ! [X0: $int] :
( $less(X0,$sum(3,sK2))
| ~ $less(X0,1) )
| ~ spl3_118 ),
inference(resolution,[],[f46218,f15]) ).
tff(f46218,plain,
( $less(1,$sum(3,sK2))
| ~ spl3_118 ),
inference(avatar_component_clause,[],[f46216]) ).
tff(f47492,plain,
( spl3_128
| spl3_129
| ~ spl3_20
| ~ spl3_118 ),
inference(avatar_split_clause,[],[f46449,f46216,f2050,f47490,f47486]) ).
tff(f47486,plain,
( spl3_128
<=> $less($uminus($sum(3,sK2)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_128])]) ).
tff(f46449,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| $less($uminus($sum(3,sK2)),0)
| $less(X0,2) )
| ~ spl3_20
| ~ spl3_118 ),
inference(resolution,[],[f46327,f44665]) ).
tff(f47484,plain,
( spl3_122
| spl3_127
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f46593,f4852,f2050,f47482,f47460]) ).
tff(f47482,plain,
( spl3_127
<=> ! [X0: $int] :
( $less(1,$sum(X0,1))
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_127])]) ).
tff(f46593,plain,
( ! [X0: $int] :
( $less(1,$sum(X0,1))
| $less($uminus($sum(1,sK2)),0)
| $less(X0,2) )
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f34144,f44665]) ).
tff(f34144,plain,
( ! [X0: $int] :
( $less(1,$sum(X0,1))
| $less(X0,$sum(1,sK2)) )
| ~ spl3_49 ),
inference(resolution,[],[f209,f4854]) ).
tff(f209,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ),
inference(resolution,[],[f15,f18]) ).
tff(f47478,plain,
( spl3_125
| spl3_126
| ~ spl3_7
| ~ spl3_22
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f46761,f4852,f3620,f128,f47476,f47472]) ).
tff(f47472,plain,
( spl3_125
<=> $less($uminus($sum(1,sK2)),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_125])]) ).
tff(f47476,plain,
( spl3_126
<=> ! [X0: $int] :
( $less(X0,sK2)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_126])]) ).
tff(f3620,plain,
( spl3_22
<=> ! [X0: $int] :
( $less(-1,X0)
| $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
tff(f46761,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| $less(-1,X0)
| $less($uminus($sum(1,sK2)),1) )
| ~ spl3_7
| ~ spl3_22
| ~ spl3_49 ),
inference(resolution,[],[f43964,f11708]) ).
tff(f11708,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(-1,X0)
| $less(X1,1) )
| ~ spl3_22 ),
inference(resolution,[],[f3621,f15]) ).
tff(f3621,plain,
( ! [X0: $int] :
( $less(-1,X0)
| $less(X0,1) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f3620]) ).
tff(f43964,plain,
( ! [X0: $int] :
( $less($uminus($sum(1,sK2)),X0)
| $less(X0,sK2) )
| ~ spl3_7
| ~ spl3_49 ),
inference(resolution,[],[f22802,f4854]) ).
tff(f22802,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(1,X0)
| $less($uminus(X0),X1)
| $less(X1,sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f5101,f897]) ).
tff(f897,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(1,X1),0)
| $less(X1,X0)
| $less(X0,sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f263,f104]) ).
tff(f104,plain,
! [X0: $int] :
( ~ $less(-1,X0)
| ~ $less(X0,0) ),
inference(evaluation,[],[f103]) ).
tff(f103,plain,
! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) ),
inference(superposition,[],[f20,f71]) ).
tff(f47470,plain,
( spl3_122
| spl3_124
| ~ spl3_7
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f46763,f4852,f2050,f128,f47468,f47460]) ).
tff(f47468,plain,
( spl3_124
<=> ! [X0: $int] :
( $less(X0,sK2)
| $less($uminus(X0),2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_124])]) ).
tff(f46763,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| $less($uminus(X0),2)
| $less($uminus($sum(1,sK2)),0) )
| ~ spl3_7
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f43964,f43921]) ).
tff(f43921,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less($uminus(X0),2)
| $less(X1,0) )
| ~ spl3_20 ),
inference(superposition,[],[f22946,f19]) ).
tff(f22946,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$uminus(X0))
| $less(X0,2)
| $less(X1,0) )
| ~ spl3_20 ),
inference(resolution,[],[f22886,f15]) ).
tff(f47466,plain,
( spl3_122
| spl3_123
| ~ spl3_7
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f46795,f4852,f2050,f128,f47464,f47460]) ).
tff(f47464,plain,
( spl3_123
<=> ! [X0: $int] :
( $less($uminus(X0),sK2)
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_123])]) ).
tff(f46795,plain,
( ! [X0: $int] :
( $less($uminus(X0),sK2)
| $less(X0,2)
| $less($uminus($sum(1,sK2)),0) )
| ~ spl3_7
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f43964,f22946]) ).
tff(f47457,plain,
( ~ spl3_13
| spl3_15
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f47446,f474,f470,f358]) ).
tff(f470,plain,
( spl3_15
<=> ( 2 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
tff(f474,plain,
( spl3_16
<=> $less(sK2,2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
tff(f47446,plain,
( ~ $less(1,sK2)
| spl3_15
| ~ spl3_16 ),
inference(subsumption_resolution,[],[f47445,f471]) ).
tff(f471,plain,
( ( 2 != sK2 )
| spl3_15 ),
inference(avatar_component_clause,[],[f470]) ).
tff(f47445,plain,
( ( 2 = sK2 )
| ~ $less(1,sK2)
| ~ spl3_16 ),
inference(evaluation,[],[f47325]) ).
tff(f47325,plain,
( ( sK2 = $sum(1,1) )
| ~ $less(1,sK2)
| $less($sum(1,1),2)
| ~ spl3_16 ),
inference(resolution,[],[f423,f44391]) ).
tff(f44391,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),sK2)
| $less($sum(X0,1),2) )
| ~ spl3_16 ),
inference(resolution,[],[f7245,f34288]) ).
tff(f34288,plain,
( ! [X0: $int] :
( $less(sK2,$sum(1,X0))
| $less(X0,2) )
| ~ spl3_16 ),
inference(superposition,[],[f34239,f9]) ).
tff(f34239,plain,
( ! [X0: $int] :
( $less(sK2,$sum(X0,1))
| $less(X0,2) )
| ~ spl3_16 ),
inference(resolution,[],[f209,f476]) ).
tff(f476,plain,
( $less(sK2,2)
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f474]) ).
tff(f7245,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ),
inference(superposition,[],[f20,f10]) ).
tff(f423,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,1),X1)
| ( $sum(X0,1) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f20]) ).
tff(f47448,plain,
( ~ spl3_13
| spl3_15
| ~ spl3_16 ),
inference(avatar_contradiction_clause,[],[f47447]) ).
tff(f47447,plain,
( $false
| ~ spl3_13
| spl3_15
| ~ spl3_16 ),
inference(subsumption_resolution,[],[f47446,f360]) ).
tff(f360,plain,
( $less(1,sK2)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f358]) ).
tff(f46849,plain,
( spl3_121
| ~ spl3_60
| ~ spl3_120 ),
inference(avatar_split_clause,[],[f46830,f46822,f10772,f46846]) ).
tff(f46846,plain,
( spl3_121
<=> $less($uminus($sum(1,sK2)),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_121])]) ).
tff(f10772,plain,
( spl3_60
<=> $less(sK2,3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).
tff(f46822,plain,
( spl3_120
<=> $less($uminus($sum(1,sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_120])]) ).
tff(f46830,plain,
( $less($uminus($sum(1,sK2)),3)
| ~ spl3_60
| ~ spl3_120 ),
inference(resolution,[],[f46824,f31723]) ).
tff(f31723,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,3) )
| ~ spl3_60 ),
inference(resolution,[],[f10774,f15]) ).
tff(f10774,plain,
( $less(sK2,3)
| ~ spl3_60 ),
inference(avatar_component_clause,[],[f10772]) ).
tff(f46824,plain,
( $less($uminus($sum(1,sK2)),sK2)
| ~ spl3_120 ),
inference(avatar_component_clause,[],[f46822]) ).
tff(f46825,plain,
( spl3_120
| ~ spl3_7
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f46751,f4852,f128,f46822]) ).
tff(f46751,plain,
( $less($uminus($sum(1,sK2)),sK2)
| ~ spl3_7
| ~ spl3_49 ),
inference(resolution,[],[f43964,f14]) ).
tff(f14,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f46391,plain,
( ~ spl3_119
| ~ spl3_111 ),
inference(avatar_split_clause,[],[f46359,f46044,f46388]) ).
tff(f46388,plain,
( spl3_119
<=> $less($sum(3,sK2),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_119])]) ).
tff(f46044,plain,
( spl3_111
<=> $less(-1,$sum(3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_111])]) ).
tff(f46359,plain,
( ~ $less($sum(3,sK2),-1)
| ~ spl3_111 ),
inference(resolution,[],[f46052,f14]) ).
tff(f46052,plain,
( ! [X0: $int] :
( $less(X0,$sum(3,sK2))
| ~ $less(X0,-1) )
| ~ spl3_111 ),
inference(resolution,[],[f46046,f15]) ).
tff(f46046,plain,
( $less(-1,$sum(3,sK2))
| ~ spl3_111 ),
inference(avatar_component_clause,[],[f46044]) ).
tff(f46274,plain,
( ~ spl3_13
| spl3_92
| ~ spl3_117 ),
inference(avatar_contradiction_clause,[],[f46273]) ).
tff(f46273,plain,
( $false
| ~ spl3_13
| spl3_92
| ~ spl3_117 ),
inference(subsumption_resolution,[],[f46272,f23937]) ).
tff(f23937,plain,
( ~ $less(3,sK2)
| spl3_92 ),
inference(avatar_component_clause,[],[f23936]) ).
tff(f23936,plain,
( spl3_92
<=> $less(3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_92])]) ).
tff(f46272,plain,
( $less(3,sK2)
| ~ spl3_13
| ~ spl3_117 ),
inference(subsumption_resolution,[],[f46263,f360]) ).
tff(f46263,plain,
( ~ $less(1,sK2)
| $less(3,sK2)
| ~ spl3_13
| ~ spl3_117 ),
inference(superposition,[],[f26760,f46214]) ).
tff(f46214,plain,
( ( 1 = $sum(3,sK2) )
| ~ spl3_117 ),
inference(avatar_component_clause,[],[f46212]) ).
tff(f46212,plain,
( spl3_117
<=> ( 1 = $sum(3,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_117])]) ).
tff(f26760,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(X1,X0),X0)
| $less(X1,sK2) )
| ~ spl3_13 ),
inference(superposition,[],[f26627,f9]) ).
tff(f26627,plain,
( ! [X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),X0)
| $less(X1,sK2) )
| ~ spl3_13 ),
inference(evaluation,[],[f26624]) ).
tff(f26624,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,sK2)
| ~ $less($sum($uminus($uminus(X0)),X1),X0) )
| ~ spl3_13 ),
inference(superposition,[],[f26070,f7292]) ).
tff(f26070,plain,
( ! [X0: $int,X1: $int] :
( $less($sum($uminus(X1),X0),sK2)
| ~ $less(X0,X1) )
| ~ spl3_13 ),
inference(superposition,[],[f22863,f9]) ).
tff(f22863,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X0,$uminus(X1)),sK2)
| ~ $less(X0,X1) )
| ~ spl3_13 ),
inference(evaluation,[],[f22833]) ).
tff(f22833,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,$uminus(X1)),sK2)
| $less(0,0) )
| ~ spl3_13 ),
inference(resolution,[],[f5101,f410]) ).
tff(f410,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,sK2)
| $less(0,X1) )
| ~ spl3_13 ),
inference(resolution,[],[f373,f135]) ).
tff(f135,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f84,f11]) ).
tff(f373,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,X0)
| $less(X1,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f370,f15]) ).
tff(f370,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,1) )
| ~ spl3_13 ),
inference(resolution,[],[f360,f15]) ).
tff(f46271,plain,
( ~ spl3_13
| ~ spl3_117 ),
inference(avatar_contradiction_clause,[],[f46270]) ).
tff(f46270,plain,
( $false
| ~ spl3_13
| ~ spl3_117 ),
inference(subsumption_resolution,[],[f46267,f14]) ).
tff(f46267,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_117 ),
inference(evaluation,[],[f46262]) ).
tff(f46262,plain,
( ~ $less(1,3)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_117 ),
inference(superposition,[],[f26627,f46214]) ).
tff(f46220,plain,
( spl3_117
| spl3_118
| spl3_115 ),
inference(avatar_split_clause,[],[f46204,f46191,f46216,f46212]) ).
tff(f46191,plain,
( spl3_115
<=> $less($sum(3,sK2),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_115])]) ).
tff(f46204,plain,
( $less(1,$sum(3,sK2))
| ( 1 = $sum(3,sK2) )
| spl3_115 ),
inference(resolution,[],[f46193,f16]) ).
tff(f46193,plain,
( ~ $less($sum(3,sK2),1)
| spl3_115 ),
inference(avatar_component_clause,[],[f46191]) ).
tff(f46219,plain,
( spl3_117
| spl3_118
| spl3_115 ),
inference(avatar_split_clause,[],[f46203,f46191,f46216,f46212]) ).
tff(f46203,plain,
( $less(1,$sum(3,sK2))
| ( 1 = $sum(3,sK2) )
| spl3_115 ),
inference(resolution,[],[f46193,f16]) ).
tff(f46199,plain,
( spl3_116
| ~ spl3_20
| ~ spl3_114 ),
inference(avatar_split_clause,[],[f46189,f46084,f2050,f46196]) ).
tff(f46196,plain,
( spl3_116
<=> $less($uminus($sum(3,sK2)),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_116])]) ).
tff(f46084,plain,
( spl3_114
<=> $less(0,$sum(3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_114])]) ).
tff(f46189,plain,
( $less($uminus($sum(3,sK2)),2)
| ~ spl3_20
| ~ spl3_114 ),
inference(evaluation,[],[f46187]) ).
tff(f46187,plain,
( $less($uminus($sum(3,sK2)),2)
| $less(0,0)
| ~ spl3_20
| ~ spl3_114 ),
inference(resolution,[],[f46086,f43921]) ).
tff(f46086,plain,
( $less(0,$sum(3,sK2))
| ~ spl3_114 ),
inference(avatar_component_clause,[],[f46084]) ).
tff(f46194,plain,
( ~ spl3_115
| ~ spl3_114 ),
inference(avatar_split_clause,[],[f46175,f46084,f46191]) ).
tff(f46175,plain,
( ~ $less($sum(3,sK2),1)
| ~ spl3_114 ),
inference(resolution,[],[f46086,f150]) ).
tff(f46150,plain,
( ~ spl3_7
| ~ spl3_13
| spl3_92
| ~ spl3_113 ),
inference(avatar_contradiction_clause,[],[f46149]) ).
tff(f46149,plain,
( $false
| ~ spl3_7
| ~ spl3_13
| spl3_92
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46148,f23937]) ).
tff(f46148,plain,
( $less(3,sK2)
| ~ spl3_7
| ~ spl3_13
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46124,f130]) ).
tff(f46124,plain,
( ~ $less(0,sK2)
| $less(3,sK2)
| ~ spl3_13
| ~ spl3_113 ),
inference(superposition,[],[f26760,f46082]) ).
tff(f46082,plain,
( ( 0 = $sum(3,sK2) )
| ~ spl3_113 ),
inference(avatar_component_clause,[],[f46080]) ).
tff(f46080,plain,
( spl3_113
<=> ( 0 = $sum(3,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_113])]) ).
tff(f46147,plain,
( ~ spl3_13
| ~ spl3_113 ),
inference(avatar_contradiction_clause,[],[f46146]) ).
tff(f46146,plain,
( $false
| ~ spl3_13
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46128,f14]) ).
tff(f46128,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_113 ),
inference(evaluation,[],[f46123]) ).
tff(f46123,plain,
( ~ $less(0,3)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_113 ),
inference(superposition,[],[f26627,f46082]) ).
tff(f46144,plain,
( ~ spl3_13
| ~ spl3_21
| spl3_92
| ~ spl3_113 ),
inference(avatar_contradiction_clause,[],[f46143]) ).
tff(f46143,plain,
( $false
| ~ spl3_13
| ~ spl3_21
| spl3_92
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46134,f23937]) ).
tff(f46134,plain,
( $less(3,sK2)
| ~ spl3_13
| ~ spl3_21
| ~ spl3_113 ),
inference(evaluation,[],[f46106]) ).
tff(f46106,plain,
( $less(0,0)
| $less(3,sK2)
| ~ spl3_13
| ~ spl3_21
| ~ spl3_113 ),
inference(superposition,[],[f26973,f46082]) ).
tff(f26973,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,sK2))
| $less(X0,sK2) )
| ~ spl3_13
| ~ spl3_21 ),
inference(resolution,[],[f26760,f3618]) ).
tff(f3618,plain,
( ! [X1: $int] :
( $less(X1,sK2)
| $less(0,X1) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f3617]) ).
tff(f3617,plain,
( spl3_21
<=> ! [X1: $int] :
( $less(X1,sK2)
| $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
tff(f46142,plain,
( ~ spl3_13
| spl3_92
| ~ spl3_113 ),
inference(avatar_contradiction_clause,[],[f46141]) ).
tff(f46141,plain,
( $false
| ~ spl3_13
| spl3_92
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46135,f23937]) ).
tff(f46135,plain,
( $less(3,sK2)
| ~ spl3_13
| ~ spl3_113 ),
inference(evaluation,[],[f46102]) ).
tff(f46102,plain,
( ~ $less(0,1)
| $less(3,sK2)
| ~ spl3_13
| ~ spl3_113 ),
inference(superposition,[],[f26855,f46082]) ).
tff(f26855,plain,
( ! [X0: $int] :
( ~ $less($sum(X0,sK2),1)
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(superposition,[],[f26749,f9]) ).
tff(f26749,plain,
( ! [X0: $int] :
( ~ $less($sum(sK2,X0),1)
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f26627,f370]) ).
tff(f46140,plain,
( ~ spl3_13
| ~ spl3_60
| ~ spl3_113 ),
inference(avatar_contradiction_clause,[],[f46139]) ).
tff(f46139,plain,
( $false
| ~ spl3_13
| ~ spl3_60
| ~ spl3_113 ),
inference(subsumption_resolution,[],[f46136,f14]) ).
tff(f46136,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_60
| ~ spl3_113 ),
inference(evaluation,[],[f46100]) ).
tff(f46100,plain,
( ~ $less(0,1)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_60
| ~ spl3_113 ),
inference(superposition,[],[f33658,f46082]) ).
tff(f33658,plain,
( ! [X0: $int] :
( ~ $less($sum(3,X0),1)
| $less(X0,sK2) )
| ~ spl3_13
| ~ spl3_60 ),
inference(resolution,[],[f26627,f32361]) ).
tff(f32361,plain,
( ! [X0: $int] :
( $less(X0,3)
| ~ $less(X0,1) )
| ~ spl3_13
| ~ spl3_60 ),
inference(resolution,[],[f31723,f31714]) ).
tff(f31714,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,1) )
| ~ spl3_13 ),
inference(resolution,[],[f360,f15]) ).
tff(f46088,plain,
( spl3_113
| spl3_114
| spl3_112 ),
inference(avatar_split_clause,[],[f46072,f46066,f46084,f46080]) ).
tff(f46066,plain,
( spl3_112
<=> $less($sum(3,sK2),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_112])]) ).
tff(f46072,plain,
( $less(0,$sum(3,sK2))
| ( 0 = $sum(3,sK2) )
| spl3_112 ),
inference(resolution,[],[f46068,f16]) ).
tff(f46068,plain,
( ~ $less($sum(3,sK2),0)
| spl3_112 ),
inference(avatar_component_clause,[],[f46066]) ).
tff(f46087,plain,
( spl3_113
| spl3_114
| spl3_112 ),
inference(avatar_split_clause,[],[f46071,f46066,f46084,f46080]) ).
tff(f46071,plain,
( $less(0,$sum(3,sK2))
| ( 0 = $sum(3,sK2) )
| spl3_112 ),
inference(resolution,[],[f46068,f16]) ).
tff(f46069,plain,
( ~ spl3_112
| ~ spl3_111 ),
inference(avatar_split_clause,[],[f46051,f46044,f46066]) ).
tff(f46051,plain,
( ~ $less($sum(3,sK2),0)
| ~ spl3_111 ),
inference(resolution,[],[f46046,f104]) ).
tff(f46047,plain,
( spl3_111
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f46040,f4729,f46044]) ).
tff(f4729,plain,
( spl3_45
<=> $less(-1,$sum(2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).
tff(f46040,plain,
( $less(-1,$sum(3,sK2))
| ~ spl3_45 ),
inference(evaluation,[],[f46006]) ).
tff(f46006,plain,
( $less(-1,$sum($sum(2,sK2),1))
| ~ spl3_45 ),
inference(resolution,[],[f34263,f14]) ).
tff(f34263,plain,
( ! [X0: $int] :
( $less(-1,$sum(X0,1))
| $less(X0,$sum(2,sK2)) )
| ~ spl3_45 ),
inference(resolution,[],[f209,f4731]) ).
tff(f4731,plain,
( $less(-1,$sum(2,sK2))
| ~ spl3_45 ),
inference(avatar_component_clause,[],[f4729]) ).
tff(f45196,plain,
( spl3_110
| ~ spl3_20
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f45125,f5412,f2050,f45185]) ).
tff(f45185,plain,
( spl3_110
<=> $less($uminus($sum(2,sK2)),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_110])]) ).
tff(f45125,plain,
( $less($uminus($sum(2,sK2)),2)
| ~ spl3_20
| ~ spl3_53 ),
inference(evaluation,[],[f44806]) ).
tff(f44806,plain,
( $less($uminus($sum(2,sK2)),2)
| $less(1,0)
| ~ spl3_20
| ~ spl3_53 ),
inference(resolution,[],[f43921,f5414]) ).
tff(f45195,plain,
( spl3_107
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f45126,f4852,f2050,f45172]) ).
tff(f45172,plain,
( spl3_107
<=> $less($uminus($sum(1,sK2)),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_107])]) ).
tff(f45126,plain,
( $less($uminus($sum(1,sK2)),2)
| ~ spl3_20
| ~ spl3_49 ),
inference(evaluation,[],[f44805]) ).
tff(f44805,plain,
( $less($uminus($sum(1,sK2)),2)
| $less(1,0)
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f43921,f4854]) ).
tff(f45192,plain,
( spl3_110
| ~ spl3_20
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f45143,f4737,f2050,f45185]) ).
tff(f4737,plain,
( spl3_46
<=> $less(0,$sum(2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).
tff(f45143,plain,
( $less($uminus($sum(2,sK2)),2)
| ~ spl3_20
| ~ spl3_46 ),
inference(evaluation,[],[f44788]) ).
tff(f44788,plain,
( $less($uminus($sum(2,sK2)),2)
| $less(0,0)
| ~ spl3_20
| ~ spl3_46 ),
inference(resolution,[],[f43921,f4739]) ).
tff(f4739,plain,
( $less(0,$sum(2,sK2))
| ~ spl3_46 ),
inference(avatar_component_clause,[],[f4737]) ).
tff(f45191,plain,
( spl3_107
| ~ spl3_20
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f45144,f4723,f2050,f45172]) ).
tff(f4723,plain,
( spl3_44
<=> $less(0,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).
tff(f45144,plain,
( $less($uminus($sum(1,sK2)),2)
| ~ spl3_20
| ~ spl3_44 ),
inference(evaluation,[],[f44787]) ).
tff(f44787,plain,
( $less($uminus($sum(1,sK2)),2)
| $less(0,0)
| ~ spl3_20
| ~ spl3_44 ),
inference(resolution,[],[f43921,f4725]) ).
tff(f4725,plain,
( $less(0,$sum(1,sK2))
| ~ spl3_44 ),
inference(avatar_component_clause,[],[f4723]) ).
tff(f45188,plain,
( spl3_109
| spl3_110
| ~ spl3_20
| ~ spl3_53 ),
inference(avatar_split_clause,[],[f44741,f5412,f2050,f45185,f45181]) ).
tff(f45181,plain,
( spl3_109
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_109])]) ).
tff(f44741,plain,
( ! [X0: $int] :
( $less($uminus($sum(2,sK2)),2)
| $less(X0,0)
| ~ $less(X0,1) )
| ~ spl3_20
| ~ spl3_53 ),
inference(resolution,[],[f43921,f5931]) ).
tff(f45183,plain,
( spl3_109
| spl3_107
| ~ spl3_20
| ~ spl3_49 ),
inference(avatar_split_clause,[],[f44739,f4852,f2050,f45172,f45181]) ).
tff(f44739,plain,
( ! [X0: $int] :
( $less($uminus($sum(1,sK2)),2)
| $less(X0,0)
| ~ $less(X0,1) )
| ~ spl3_20
| ~ spl3_49 ),
inference(resolution,[],[f43921,f5115]) ).
tff(f45179,plain,
( spl3_108
| spl3_107
| ~ spl3_20
| ~ spl3_98 ),
inference(avatar_split_clause,[],[f44737,f27638,f2050,f45172,f45177]) ).
tff(f45177,plain,
( spl3_108
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,-2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_108])]) ).
tff(f27638,plain,
( spl3_98
<=> $less(-2,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_98])]) ).
tff(f44737,plain,
( ! [X0: $int] :
( $less($uminus($sum(1,sK2)),2)
| $less(X0,0)
| ~ $less(X0,-2) )
| ~ spl3_20
| ~ spl3_98 ),
inference(resolution,[],[f43921,f27648]) ).
tff(f27648,plain,
( ! [X0: $int] :
( $less(X0,$sum(1,sK2))
| ~ $less(X0,-2) )
| ~ spl3_98 ),
inference(resolution,[],[f27640,f15]) ).
tff(f27640,plain,
( $less(-2,$sum(1,sK2))
| ~ spl3_98 ),
inference(avatar_component_clause,[],[f27638]) ).
tff(f45175,plain,
( spl3_106
| spl3_107
| ~ spl3_20
| ~ spl3_105 ),
inference(avatar_split_clause,[],[f44736,f32513,f2050,f45172,f45169]) ).
tff(f45169,plain,
( spl3_106
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,-3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_106])]) ).
tff(f32513,plain,
( spl3_105
<=> $less(-3,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_105])]) ).
tff(f44736,plain,
( ! [X0: $int] :
( $less($uminus($sum(1,sK2)),2)
| $less(X0,0)
| ~ $less(X0,-3) )
| ~ spl3_20
| ~ spl3_105 ),
inference(resolution,[],[f43921,f32521]) ).
tff(f32521,plain,
( ! [X0: $int] :
( $less(X0,$sum(1,sK2))
| ~ $less(X0,-3) )
| ~ spl3_105 ),
inference(resolution,[],[f32515,f15]) ).
tff(f32515,plain,
( $less(-3,$sum(1,sK2))
| ~ spl3_105 ),
inference(avatar_component_clause,[],[f32513]) ).
tff(f32518,plain,
( ( $sum(1,sK2) != -3 )
| $less($sum(1,sK2),sK2)
| ~ $less(-3,sK2) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f32517,plain,
( spl3_104
| spl3_105
| spl3_103 ),
inference(avatar_split_clause,[],[f32502,f32490,f32513,f32509]) ).
tff(f32509,plain,
( spl3_104
<=> ( $sum(1,sK2) = -3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_104])]) ).
tff(f32490,plain,
( spl3_103
<=> $less($sum(1,sK2),-3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_103])]) ).
tff(f32502,plain,
( $less(-3,$sum(1,sK2))
| ( $sum(1,sK2) = -3 )
| spl3_103 ),
inference(resolution,[],[f32492,f16]) ).
tff(f32492,plain,
( ~ $less($sum(1,sK2),-3)
| spl3_103 ),
inference(avatar_component_clause,[],[f32490]) ).
tff(f32516,plain,
( spl3_104
| spl3_105
| spl3_103 ),
inference(avatar_split_clause,[],[f32501,f32490,f32513,f32509]) ).
tff(f32501,plain,
( $less(-3,$sum(1,sK2))
| ( $sum(1,sK2) = -3 )
| spl3_103 ),
inference(resolution,[],[f32492,f16]) ).
tff(f32493,plain,
( ~ spl3_103
| spl3_38
| ~ spl3_99 ),
inference(avatar_split_clause,[],[f32478,f30341,f4607,f32490]) ).
tff(f4607,plain,
( spl3_38
<=> $less($sum(1,sK2),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
tff(f30341,plain,
( spl3_99
<=> $less(-3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_99])]) ).
tff(f32478,plain,
( ~ $less($sum(1,sK2),-3)
| spl3_38
| ~ spl3_99 ),
inference(resolution,[],[f31749,f4608]) ).
tff(f4608,plain,
( ~ $less($sum(1,sK2),sK2)
| spl3_38 ),
inference(avatar_component_clause,[],[f4607]) ).
tff(f31749,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,-3) )
| ~ spl3_99 ),
inference(resolution,[],[f30343,f15]) ).
tff(f30343,plain,
( $less(-3,sK2)
| ~ spl3_99 ),
inference(avatar_component_clause,[],[f30341]) ).
tff(f32488,plain,
( ~ spl3_102
| ~ spl3_99 ),
inference(avatar_split_clause,[],[f32469,f30341,f32485]) ).
tff(f32485,plain,
( spl3_102
<=> $less(sK2,-3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_102])]) ).
tff(f32469,plain,
( ~ $less(sK2,-3)
| ~ spl3_99 ),
inference(resolution,[],[f31749,f14]) ).
tff(f32077,plain,
( ~ spl3_101
| spl3_93 ),
inference(avatar_split_clause,[],[f32075,f25054,f31993]) ).
tff(f31993,plain,
( spl3_101
<=> ( -1 = $sum(-2,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_101])]) ).
tff(f25054,plain,
( spl3_93
<=> ( -1 = $sum(sK2,-2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_93])]) ).
tff(f32075,plain,
( ( -1 != $sum(-2,sK2) )
| spl3_93 ),
inference(superposition,[],[f25055,f9]) ).
tff(f25055,plain,
( ( -1 != $sum(sK2,-2) )
| spl3_93 ),
inference(avatar_component_clause,[],[f25054]) ).
tff(f32076,plain,
( ~ spl3_101
| spl3_93 ),
inference(avatar_split_clause,[],[f32074,f25054,f31993]) ).
tff(f32074,plain,
( ( -1 != $sum(-2,sK2) )
| spl3_93 ),
inference(superposition,[],[f25055,f9]) ).
tff(f31999,plain,
( spl3_101
| ~ spl3_93 ),
inference(avatar_split_clause,[],[f31986,f25054,f31993]) ).
tff(f31986,plain,
( ( -1 = $sum(-2,sK2) )
| ~ spl3_93 ),
inference(superposition,[],[f9,f25056]) ).
tff(f25056,plain,
( ( -1 = $sum(sK2,-2) )
| ~ spl3_93 ),
inference(avatar_component_clause,[],[f25054]) ).
tff(f31998,plain,
( spl3_101
| ~ spl3_93 ),
inference(avatar_split_clause,[],[f31985,f25054,f31993]) ).
tff(f31985,plain,
( ( -1 = $sum(-2,sK2) )
| ~ spl3_93 ),
inference(superposition,[],[f9,f25056]) ).
tff(f31997,plain,
( spl3_101
| ~ spl3_93 ),
inference(avatar_split_clause,[],[f31984,f25054,f31993]) ).
tff(f31984,plain,
( ( -1 = $sum(-2,sK2) )
| ~ spl3_93 ),
inference(superposition,[],[f25056,f9]) ).
tff(f31996,plain,
( spl3_101
| ~ spl3_93 ),
inference(avatar_split_clause,[],[f31983,f25054,f31993]) ).
tff(f31983,plain,
( ( -1 = $sum(-2,sK2) )
| ~ spl3_93 ),
inference(superposition,[],[f25056,f9]) ).
tff(f31659,plain,
( ~ spl3_1
| spl3_38
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f31658,f7887,f4607,f51]) ).
tff(f51,plain,
( spl3_1
<=> $less(2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f7887,plain,
( spl3_58
<=> ( 2 = $sum(1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).
tff(f31658,plain,
( ~ $less(2,sK2)
| spl3_38
| ~ spl3_58 ),
inference(forward_demodulation,[],[f4608,f7889]) ).
tff(f7889,plain,
( ( 2 = $sum(1,sK2) )
| ~ spl3_58 ),
inference(avatar_component_clause,[],[f7887]) ).
tff(f31583,plain,
( spl3_62
| ~ spl3_58
| ~ spl3_86 ),
inference(avatar_split_clause,[],[f31582,f23234,f7887,f11117]) ).
tff(f11117,plain,
( spl3_62
<=> $less($uminus(sK2),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).
tff(f23234,plain,
( spl3_86
<=> $less($uminus(sK2),$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_86])]) ).
tff(f31582,plain,
( $less($uminus(sK2),2)
| ~ spl3_58
| ~ spl3_86 ),
inference(forward_demodulation,[],[f23236,f7889]) ).
tff(f23236,plain,
( $less($uminus(sK2),$sum(1,sK2))
| ~ spl3_86 ),
inference(avatar_component_clause,[],[f23234]) ).
tff(f31567,plain,
( ~ spl3_58
| ~ spl3_91 ),
inference(avatar_contradiction_clause,[],[f31566]) ).
tff(f31566,plain,
( $false
| ~ spl3_58
| ~ spl3_91 ),
inference(evaluation,[],[f31565]) ).
tff(f31565,plain,
( ( 2 = $sum(1,3) )
| ~ spl3_58
| ~ spl3_91 ),
inference(forward_demodulation,[],[f7889,f23934]) ).
tff(f23934,plain,
( ( sK2 = 3 )
| ~ spl3_91 ),
inference(avatar_component_clause,[],[f23932]) ).
tff(f23932,plain,
( spl3_91
<=> ( sK2 = 3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_91])]) ).
tff(f31563,plain,
( ~ spl3_73
| ~ spl3_91 ),
inference(avatar_contradiction_clause,[],[f31562]) ).
tff(f31562,plain,
( $false
| ~ spl3_73
| ~ spl3_91 ),
inference(evaluation,[],[f31561]) ).
tff(f31561,plain,
( ( 1 = $sum(2,$uminus(3)) )
| ~ spl3_73
| ~ spl3_91 ),
inference(forward_demodulation,[],[f12334,f23934]) ).
tff(f12334,plain,
( ( 1 = $sum(2,$uminus(sK2)) )
| ~ spl3_73 ),
inference(avatar_component_clause,[],[f12332]) ).
tff(f12332,plain,
( spl3_73
<=> ( 1 = $sum(2,$uminus(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_73])]) ).
tff(f31344,plain,
( spl3_100
| ~ spl3_2
| ~ spl3_91 ),
inference(avatar_split_clause,[],[f30350,f23932,f56,f31341]) ).
tff(f31341,plain,
( spl3_100
<=> in(3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_100])]) ).
tff(f56,plain,
( spl3_2
<=> in(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f30350,plain,
( in(3,sK0)
| ~ spl3_2
| ~ spl3_91 ),
inference(backward_demodulation,[],[f58,f23934]) ).
tff(f58,plain,
( in(sK2,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f31339,plain,
( spl3_1
| ~ spl3_91 ),
inference(avatar_contradiction_clause,[],[f31338]) ).
tff(f31338,plain,
( $false
| spl3_1
| ~ spl3_91 ),
inference(evaluation,[],[f30349]) ).
tff(f30349,plain,
( ~ $less(2,3)
| spl3_1
| ~ spl3_91 ),
inference(backward_demodulation,[],[f53,f23934]) ).
tff(f53,plain,
( ~ $less(2,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f51]) ).
tff(f31337,plain,
( ~ spl3_16
| ~ spl3_91 ),
inference(avatar_contradiction_clause,[],[f31336]) ).
tff(f31336,plain,
( $false
| ~ spl3_16
| ~ spl3_91 ),
inference(evaluation,[],[f30385]) ).
tff(f30385,plain,
( $less(3,2)
| ~ spl3_16
| ~ spl3_91 ),
inference(backward_demodulation,[],[f476,f23934]) ).
tff(f31295,plain,
( spl3_59
| ~ spl3_91 ),
inference(avatar_contradiction_clause,[],[f31294]) ).
tff(f31294,plain,
( $false
| spl3_59
| ~ spl3_91 ),
inference(evaluation,[],[f30640]) ).
tff(f30640,plain,
( ~ $less(2,$sum(1,3))
| spl3_59
| ~ spl3_91 ),
inference(backward_demodulation,[],[f7892,f23934]) ).
tff(f7892,plain,
( ~ $less(2,$sum(1,sK2))
| spl3_59 ),
inference(avatar_component_clause,[],[f7891]) ).
tff(f7891,plain,
( spl3_59
<=> $less(2,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).
tff(f31225,plain,
( ~ spl3_91
| ~ spl3_93 ),
inference(avatar_contradiction_clause,[],[f31224]) ).
tff(f31224,plain,
( $false
| ~ spl3_91
| ~ spl3_93 ),
inference(evaluation,[],[f30867]) ).
tff(f30867,plain,
( ( -1 = $sum(3,-2) )
| ~ spl3_91
| ~ spl3_93 ),
inference(backward_demodulation,[],[f25056,f23934]) ).
tff(f30348,plain,
( spl3_91
| spl3_60
| spl3_92 ),
inference(avatar_split_clause,[],[f24005,f23936,f10772,f23932]) ).
tff(f24005,plain,
( $less(sK2,3)
| ( sK2 = 3 )
| spl3_92 ),
inference(resolution,[],[f23937,f16]) ).
tff(f30347,plain,
( spl3_91
| spl3_60
| spl3_92 ),
inference(avatar_split_clause,[],[f24006,f23936,f10772,f23932]) ).
tff(f24006,plain,
( $less(sK2,3)
| ( sK2 = 3 )
| spl3_92 ),
inference(resolution,[],[f23937,f16]) ).
tff(f30346,plain,
( spl3_58
| spl3_41
| spl3_59 ),
inference(avatar_split_clause,[],[f25209,f7891,f4669,f7887]) ).
tff(f25209,plain,
( $less($sum(1,sK2),2)
| ( 2 = $sum(1,sK2) )
| spl3_59 ),
inference(resolution,[],[f7892,f16]) ).
tff(f30345,plain,
( spl3_58
| spl3_41
| spl3_59 ),
inference(avatar_split_clause,[],[f25210,f7891,f4669,f7887]) ).
tff(f25210,plain,
( $less($sum(1,sK2),2)
| ( 2 = $sum(1,sK2) )
| spl3_59 ),
inference(resolution,[],[f7892,f16]) ).
tff(f30344,plain,
( spl3_99
| ~ spl3_13
| ~ spl3_60 ),
inference(avatar_split_clause,[],[f30334,f10772,f358,f30341]) ).
tff(f30334,plain,
( $less(-3,sK2)
| ~ spl3_13
| ~ spl3_60 ),
inference(evaluation,[],[f30333]) ).
tff(f30333,plain,
( ~ $less(0,1)
| $less($uminus(3),sK2)
| ~ spl3_13
| ~ spl3_60 ),
inference(superposition,[],[f26756,f13]) ).
tff(f26756,plain,
( ! [X0: $int] :
( ~ $less($sum(3,X0),1)
| $less(X0,sK2) )
| ~ spl3_13
| ~ spl3_60 ),
inference(resolution,[],[f26627,f24260]) ).
tff(f24260,plain,
( ! [X0: $int] :
( $less(X0,3)
| ~ $less(X0,1) )
| ~ spl3_13
| ~ spl3_60 ),
inference(resolution,[],[f23982,f370]) ).
tff(f23982,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,3) )
| ~ spl3_60 ),
inference(resolution,[],[f10774,f15]) ).
tff(f27643,plain,
( ( $sum(1,sK2) != -2 )
| $less($sum(1,sK2),sK2)
| ~ $less(-2,sK2) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f27642,plain,
( spl3_97
| spl3_98
| spl3_96 ),
inference(avatar_split_clause,[],[f27618,f27600,f27638,f27634]) ).
tff(f27634,plain,
( spl3_97
<=> ( $sum(1,sK2) = -2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_97])]) ).
tff(f27600,plain,
( spl3_96
<=> $less($sum(1,sK2),-2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_96])]) ).
tff(f27618,plain,
( $less(-2,$sum(1,sK2))
| ( $sum(1,sK2) = -2 )
| spl3_96 ),
inference(resolution,[],[f27602,f16]) ).
tff(f27602,plain,
( ~ $less($sum(1,sK2),-2)
| spl3_96 ),
inference(avatar_component_clause,[],[f27600]) ).
tff(f27641,plain,
( spl3_97
| spl3_98
| spl3_96 ),
inference(avatar_split_clause,[],[f27617,f27600,f27638,f27634]) ).
tff(f27617,plain,
( $less(-2,$sum(1,sK2))
| ( $sum(1,sK2) = -2 )
| spl3_96 ),
inference(resolution,[],[f27602,f16]) ).
tff(f27603,plain,
( ~ spl3_96
| spl3_38
| ~ spl3_94 ),
inference(avatar_split_clause,[],[f27583,f27540,f4607,f27600]) ).
tff(f27540,plain,
( spl3_94
<=> $less(-2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_94])]) ).
tff(f27583,plain,
( ~ $less($sum(1,sK2),-2)
| spl3_38
| ~ spl3_94 ),
inference(resolution,[],[f27547,f4608]) ).
tff(f27547,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,-2) )
| ~ spl3_94 ),
inference(resolution,[],[f27542,f15]) ).
tff(f27542,plain,
( $less(-2,sK2)
| ~ spl3_94 ),
inference(avatar_component_clause,[],[f27540]) ).
tff(f27598,plain,
( ~ spl3_95
| ~ spl3_94 ),
inference(avatar_split_clause,[],[f27567,f27540,f27595]) ).
tff(f27595,plain,
( spl3_95
<=> $less(sK2,-2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_95])]) ).
tff(f27567,plain,
( ~ $less(sK2,-2)
| ~ spl3_94 ),
inference(resolution,[],[f27547,f14]) ).
tff(f27543,plain,
( spl3_94
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f27533,f474,f358,f27540]) ).
tff(f27533,plain,
( $less(-2,sK2)
| ~ spl3_13
| ~ spl3_16 ),
inference(evaluation,[],[f27532]) ).
tff(f27532,plain,
( ~ $less(0,1)
| $less($uminus(2),sK2)
| ~ spl3_13
| ~ spl3_16 ),
inference(superposition,[],[f26722,f13]) ).
tff(f26722,plain,
( ! [X0: $int] :
( ~ $less($sum(2,X0),1)
| $less(X0,sK2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f26627,f482]) ).
tff(f482,plain,
( ! [X0: $int] :
( $less(X0,2)
| ~ $less(X0,1) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f481,f370]) ).
tff(f481,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,2) )
| ~ spl3_16 ),
inference(resolution,[],[f476,f15]) ).
tff(f25254,plain,
( ~ spl3_79
| ~ spl3_86 ),
inference(avatar_split_clause,[],[f25241,f23234,f12677]) ).
tff(f12677,plain,
( spl3_79
<=> $less(sK2,$uminus(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_79])]) ).
tff(f25241,plain,
( ~ $less(sK2,$uminus(sK2))
| ~ spl3_86 ),
inference(resolution,[],[f23236,f101]) ).
tff(f25057,plain,
( spl3_93
| ~ spl3_73 ),
inference(avatar_split_clause,[],[f25050,f12332,f25054]) ).
tff(f25050,plain,
( ( -1 = $sum(sK2,-2) )
| ~ spl3_73 ),
inference(evaluation,[],[f25020]) ).
tff(f25020,plain,
( ( $uminus(1) = $sum(sK2,$uminus(2)) )
| ~ spl3_73 ),
inference(superposition,[],[f2115,f12334]) ).
tff(f2115,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X1,$uminus(X0))) = $sum(X0,$uminus(X1)) ),
inference(superposition,[],[f12,f19]) ).
tff(f12,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f23977,plain,
( ~ spl3_16
| ~ spl3_92 ),
inference(avatar_contradiction_clause,[],[f23976]) ).
tff(f23976,plain,
( $false
| ~ spl3_16
| ~ spl3_92 ),
inference(evaluation,[],[f23956]) ).
tff(f23956,plain,
( $less(3,2)
| ~ spl3_16
| ~ spl3_92 ),
inference(resolution,[],[f23938,f481]) ).
tff(f23938,plain,
( $less(3,sK2)
| ~ spl3_92 ),
inference(avatar_component_clause,[],[f23936]) ).
tff(f23955,plain,
( ( 0 != sK2 )
| ~ $less(0,sK2)
| $less(sK2,0) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f23954,plain,
( ( 0 != sK2 )
| ( 0 != $uminus(sK2) )
| ( 1 != $sum(2,$uminus(sK2)) )
| ( 1 = $sum(2,sK2) ) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f23953,plain,
( ( 0 != sK2 )
| ( 0 != $uminus(sK2) )
| ~ $less(0,sK2)
| $less(0,$uminus(sK2)) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f23940,plain,
( spl3_91
| spl3_92
| spl3_60 ),
inference(avatar_split_clause,[],[f23915,f10772,f23936,f23932]) ).
tff(f23915,plain,
( $less(3,sK2)
| ( sK2 = 3 )
| spl3_60 ),
inference(resolution,[],[f10773,f16]) ).
tff(f10773,plain,
( ~ $less(sK2,3)
| spl3_60 ),
inference(avatar_component_clause,[],[f10772]) ).
tff(f23939,plain,
( spl3_91
| spl3_92
| spl3_60 ),
inference(avatar_split_clause,[],[f23914,f10772,f23936,f23932]) ).
tff(f23914,plain,
( $less(3,sK2)
| ( sK2 = 3 )
| spl3_60 ),
inference(resolution,[],[f10773,f16]) ).
tff(f23833,plain,
( spl3_58
| spl3_41
| spl3_59 ),
inference(avatar_split_clause,[],[f12501,f7891,f4669,f7887]) ).
tff(f12501,plain,
( $less($sum(1,sK2),2)
| ( 2 = $sum(1,sK2) )
| spl3_59 ),
inference(resolution,[],[f7892,f16]) ).
tff(f23832,plain,
( spl3_58
| spl3_41
| spl3_59 ),
inference(avatar_split_clause,[],[f12502,f7891,f4669,f7887]) ).
tff(f12502,plain,
( $less($sum(1,sK2),2)
| ( 2 = $sum(1,sK2) )
| spl3_59 ),
inference(resolution,[],[f7892,f16]) ).
tff(f23831,plain,
( spl3_90
| ~ spl3_60
| ~ spl3_84 ),
inference(avatar_split_clause,[],[f23798,f23221,f10772,f23828]) ).
tff(f23828,plain,
( spl3_90
<=> $less($sum(1,$uminus(sK2)),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_90])]) ).
tff(f23221,plain,
( spl3_84
<=> $less($sum(1,$uminus(sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_84])]) ).
tff(f23798,plain,
( $less($sum(1,$uminus(sK2)),3)
| ~ spl3_60
| ~ spl3_84 ),
inference(resolution,[],[f23223,f12346]) ).
tff(f12346,plain,
( ! [X0: $int] :
( ~ $less(X0,sK2)
| $less(X0,3) )
| ~ spl3_60 ),
inference(resolution,[],[f10774,f15]) ).
tff(f23223,plain,
( $less($sum(1,$uminus(sK2)),sK2)
| ~ spl3_84 ),
inference(avatar_component_clause,[],[f23221]) ).
tff(f23530,plain,
( spl3_89
| ~ spl3_83 ),
inference(avatar_split_clause,[],[f23489,f23047,f23527]) ).
tff(f23527,plain,
( spl3_89
<=> ( 0 = $sum(-1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_89])]) ).
tff(f23047,plain,
( spl3_83
<=> ( -1 = $uminus(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_83])]) ).
tff(f23489,plain,
( ( 0 = $sum(-1,sK2) )
| ~ spl3_83 ),
inference(superposition,[],[f71,f23049]) ).
tff(f23049,plain,
( ( -1 = $uminus(sK2) )
| ~ spl3_83 ),
inference(avatar_component_clause,[],[f23047]) ).
tff(f23525,plain,
( spl3_18
| ~ spl3_83 ),
inference(avatar_contradiction_clause,[],[f23524]) ).
tff(f23524,plain,
( $false
| spl3_18
| ~ spl3_83 ),
inference(subsumption_resolution,[],[f23499,f2040]) ).
tff(f23499,plain,
( ( 1 = sK2 )
| ~ spl3_83 ),
inference(evaluation,[],[f23488]) ).
tff(f23488,plain,
( ( sK2 = $uminus(-1) )
| ~ spl3_83 ),
inference(superposition,[],[f19,f23049]) ).
tff(f23523,plain,
( spl3_88
| ~ spl3_83 ),
inference(avatar_split_clause,[],[f23487,f23047,f23520]) ).
tff(f23520,plain,
( spl3_88
<=> ( 0 = $sum(sK2,-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_88])]) ).
tff(f23487,plain,
( ( 0 = $sum(sK2,-1) )
| ~ spl3_83 ),
inference(superposition,[],[f13,f23049]) ).
tff(f23386,plain,
( spl3_87
| ~ spl3_82 ),
inference(avatar_split_clause,[],[f23359,f12753,f23381]) ).
tff(f23381,plain,
( spl3_87
<=> ( 0 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_87])]) ).
tff(f12753,plain,
( spl3_82
<=> ( 0 = $uminus(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_82])]) ).
tff(f23359,plain,
( ( 0 = sK2 )
| ~ spl3_82 ),
inference(evaluation,[],[f23344]) ).
tff(f23344,plain,
( ( 0 = $sum(0,sK2) )
| ~ spl3_82 ),
inference(superposition,[],[f71,f12755]) ).
tff(f12755,plain,
( ( 0 = $uminus(sK2) )
| ~ spl3_82 ),
inference(avatar_component_clause,[],[f12753]) ).
tff(f23385,plain,
( spl3_87
| ~ spl3_82 ),
inference(avatar_split_clause,[],[f23360,f12753,f23381]) ).
tff(f23360,plain,
( ( 0 = sK2 )
| ~ spl3_82 ),
inference(evaluation,[],[f23343]) ).
tff(f23343,plain,
( ( sK2 = $uminus(0) )
| ~ spl3_82 ),
inference(superposition,[],[f19,f12755]) ).
tff(f23384,plain,
( spl3_87
| ~ spl3_82 ),
inference(avatar_split_clause,[],[f23361,f12753,f23381]) ).
tff(f23361,plain,
( ( 0 = sK2 )
| ~ spl3_82 ),
inference(evaluation,[],[f23342]) ).
tff(f23342,plain,
( ( 0 = $sum(sK2,0) )
| ~ spl3_82 ),
inference(superposition,[],[f13,f12755]) ).
tff(f23239,plain,
( spl3_82
| spl3_75
| spl3_76 ),
inference(avatar_split_clause,[],[f23104,f12622,f12617,f12753]) ).
tff(f12617,plain,
( spl3_75
<=> $less($uminus(sK2),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_75])]) ).
tff(f12622,plain,
( spl3_76
<=> $less(0,$uminus(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_76])]) ).
tff(f23104,plain,
( $less($uminus(sK2),0)
| ( 0 = $uminus(sK2) )
| spl3_76 ),
inference(resolution,[],[f12623,f16]) ).
tff(f12623,plain,
( ~ $less(0,$uminus(sK2))
| spl3_76 ),
inference(avatar_component_clause,[],[f12622]) ).
tff(f23238,plain,
( spl3_82
| spl3_75
| spl3_76 ),
inference(avatar_split_clause,[],[f23105,f12622,f12617,f12753]) ).
tff(f23105,plain,
( $less($uminus(sK2),0)
| ( 0 = $uminus(sK2) )
| spl3_76 ),
inference(resolution,[],[f12623,f16]) ).
tff(f23237,plain,
( spl3_86
| ~ spl3_49
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f23205,f12665,f4852,f23234]) ).
tff(f12665,plain,
( spl3_77
<=> $less($uminus(sK2),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_77])]) ).
tff(f23205,plain,
( $less($uminus(sK2),$sum(1,sK2))
| ~ spl3_49
| ~ spl3_77 ),
inference(evaluation,[],[f23195]) ).
tff(f23195,plain,
( $less($uminus(sK2),$sum(1,sK2))
| $less(0,-1)
| ~ spl3_49
| ~ spl3_77 ),
inference(resolution,[],[f12666,f7767]) ).
tff(f7767,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(1,sK2))
| $less(0,X1) )
| ~ spl3_49 ),
inference(resolution,[],[f5661,f135]) ).
tff(f5661,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,X0)
| $less(X1,$sum(1,sK2)) )
| ~ spl3_49 ),
inference(resolution,[],[f5115,f15]) ).
tff(f12666,plain,
( $less($uminus(sK2),-1)
| ~ spl3_77 ),
inference(avatar_component_clause,[],[f12665]) ).
tff(f23232,plain,
( spl3_85
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f23206,f12665,f474,f358,f23228]) ).
tff(f23228,plain,
( spl3_85
<=> $less($sum(1,$uminus(sK2)),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_85])]) ).
tff(f23206,plain,
( $less($sum(1,$uminus(sK2)),2)
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(evaluation,[],[f23194]) ).
tff(f23194,plain,
( $less($sum(1,$uminus(sK2)),2)
| $less(-1,-1)
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(resolution,[],[f12666,f1239]) ).
tff(f1239,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less($sum(1,X1),2)
| $less(-1,X0) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f1180,f101]) ).
tff(f1180,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(-1,X0)
| $less(X1,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f1121,f481]) ).
tff(f1121,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,sK2)
| $less(-1,X0) )
| ~ spl3_13 ),
inference(resolution,[],[f1050,f87]) ).
tff(f1050,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
| $less(X1,X0)
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f546,f20]) ).
tff(f546,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,sK2)
| $less(0,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f18]) ).
tff(f23231,plain,
( spl3_85
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f23226,f12665,f474,f358,f23228]) ).
tff(f23226,plain,
( $less($sum(1,$uminus(sK2)),2)
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(forward_demodulation,[],[f23207,f9]) ).
tff(f23207,plain,
( $less($sum($uminus(sK2),1),2)
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(evaluation,[],[f23193]) ).
tff(f23193,plain,
( $less($sum($uminus(sK2),1),2)
| $less(-1,-1)
| ~ spl3_13
| ~ spl3_16
| ~ spl3_77 ),
inference(resolution,[],[f12666,f1238]) ).
tff(f1238,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less($sum(X1,1),2)
| $less(-1,X0) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f1180,f20]) ).
tff(f23225,plain,
( spl3_84
| ~ spl3_13
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f23208,f12665,f358,f23221]) ).
tff(f23208,plain,
( $less($sum(1,$uminus(sK2)),sK2)
| ~ spl3_13
| ~ spl3_77 ),
inference(evaluation,[],[f23191]) ).
tff(f23191,plain,
( $less(-1,-1)
| $less($sum(1,$uminus(sK2)),sK2)
| ~ spl3_13
| ~ spl3_77 ),
inference(resolution,[],[f12666,f1150]) ).
tff(f1150,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(-1,X1)
| $less($sum(1,X0),sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f1121,f101]) ).
tff(f23224,plain,
( spl3_84
| ~ spl3_13
| ~ spl3_77 ),
inference(avatar_split_clause,[],[f23219,f12665,f358,f23221]) ).
tff(f23219,plain,
( $less($sum(1,$uminus(sK2)),sK2)
| ~ spl3_13
| ~ spl3_77 ),
inference(forward_demodulation,[],[f23209,f9]) ).
tff(f23209,plain,
( $less($sum($uminus(sK2),1),sK2)
| ~ spl3_13
| ~ spl3_77 ),
inference(evaluation,[],[f23190]) ).
tff(f23190,plain,
( $less(-1,-1)
| $less($sum($uminus(sK2),1),sK2)
| ~ spl3_13
| ~ spl3_77 ),
inference(resolution,[],[f12666,f1149]) ).
tff(f1149,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(-1,X1)
| $less($sum(X0,1),sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f1121,f20]) ).
tff(f23051,plain,
( spl3_83
| spl3_66
| spl3_77 ),
inference(avatar_split_clause,[],[f13083,f12665,f11155,f23047]) ).
tff(f11155,plain,
( spl3_66
<=> $less(-1,$uminus(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).
tff(f13083,plain,
( $less(-1,$uminus(sK2))
| ( -1 = $uminus(sK2) )
| spl3_77 ),
inference(resolution,[],[f12667,f16]) ).
tff(f12667,plain,
( ~ $less($uminus(sK2),-1)
| spl3_77 ),
inference(avatar_component_clause,[],[f12665]) ).
tff(f23050,plain,
( spl3_83
| spl3_66
| spl3_77 ),
inference(avatar_split_clause,[],[f13084,f12665,f11155,f23047]) ).
tff(f13084,plain,
( $less(-1,$uminus(sK2))
| ( -1 = $uminus(sK2) )
| spl3_77 ),
inference(resolution,[],[f12667,f16]) ).
tff(f23045,plain,
( ~ spl3_7
| ~ spl3_61 ),
inference(avatar_contradiction_clause,[],[f23044]) ).
tff(f23044,plain,
( $false
| ~ spl3_7
| ~ spl3_61 ),
inference(subsumption_resolution,[],[f23019,f14]) ).
tff(f23019,plain,
( $less(sK2,sK2)
| ~ spl3_7
| ~ spl3_61 ),
inference(resolution,[],[f23017,f11098]) ).
tff(f11098,plain,
( $less(1,$uminus(sK2))
| ~ spl3_61 ),
inference(avatar_component_clause,[],[f11097]) ).
tff(f11097,plain,
( spl3_61
<=> $less(1,$uminus(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).
tff(f23017,plain,
( ! [X0: $int] :
( ~ $less(1,$uminus(X0))
| $less(X0,sK2) )
| ~ spl3_7 ),
inference(superposition,[],[f22800,f19]) ).
tff(f22800,plain,
( ! [X0: $int] :
( $less($uminus(X0),sK2)
| ~ $less(1,X0) )
| ~ spl3_7 ),
inference(resolution,[],[f5101,f283]) ).
tff(f283,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),0)
| $less(X0,sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f262,f104]) ).
tff(f262,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,X0))
| $less(X0,sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f252,f88]) ).
tff(f88,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f83,f9]) ).
tff(f83,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f18,f14]) ).
tff(f13082,plain,
( ~ spl3_77
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f13064,f11155,f12665]) ).
tff(f13064,plain,
( ~ $less($uminus(sK2),-1)
| ~ spl3_66 ),
inference(resolution,[],[f12714,f14]) ).
tff(f12714,plain,
( ! [X0: $int] :
( $less(X0,$uminus(sK2))
| ~ $less(X0,-1) )
| ~ spl3_66 ),
inference(resolution,[],[f11157,f15]) ).
tff(f11157,plain,
( $less(-1,$uminus(sK2))
| ~ spl3_66 ),
inference(avatar_component_clause,[],[f11155]) ).
tff(f12774,plain,
( ~ spl3_65
| ~ spl3_76 ),
inference(avatar_split_clause,[],[f12758,f12622,f11131]) ).
tff(f11131,plain,
( spl3_65
<=> $less($uminus(sK2),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).
tff(f12758,plain,
( ~ $less($uminus(sK2),1)
| ~ spl3_76 ),
inference(resolution,[],[f12624,f150]) ).
tff(f12624,plain,
( $less(0,$uminus(sK2))
| ~ spl3_76 ),
inference(avatar_component_clause,[],[f12622]) ).
tff(f12773,plain,
( ~ spl3_65
| ~ spl3_76 ),
inference(avatar_contradiction_clause,[],[f12772]) ).
tff(f12772,plain,
( $false
| ~ spl3_65
| ~ spl3_76 ),
inference(subsumption_resolution,[],[f12758,f11133]) ).
tff(f11133,plain,
( $less($uminus(sK2),1)
| ~ spl3_65 ),
inference(avatar_component_clause,[],[f11131]) ).
tff(f12757,plain,
( spl3_82
| spl3_76
| spl3_75 ),
inference(avatar_split_clause,[],[f12741,f12617,f12622,f12753]) ).
tff(f12741,plain,
( $less(0,$uminus(sK2))
| ( 0 = $uminus(sK2) )
| spl3_75 ),
inference(resolution,[],[f12619,f16]) ).
tff(f12619,plain,
( ~ $less($uminus(sK2),0)
| spl3_75 ),
inference(avatar_component_clause,[],[f12617]) ).
tff(f12756,plain,
( spl3_82
| spl3_76
| spl3_75 ),
inference(avatar_split_clause,[],[f12740,f12617,f12622,f12753]) ).
tff(f12740,plain,
( $less(0,$uminus(sK2))
| ( 0 = $uminus(sK2) )
| spl3_75 ),
inference(resolution,[],[f12619,f16]) ).
tff(f12727,plain,
( ~ spl3_75
| ~ spl3_66 ),
inference(avatar_split_clause,[],[f12713,f11155,f12617]) ).
tff(f12713,plain,
( ~ $less($uminus(sK2),0)
| ~ spl3_66 ),
inference(resolution,[],[f11157,f104]) ).
tff(f12699,plain,
( spl3_81
| ~ spl3_13
| spl3_63 ),
inference(avatar_split_clause,[],[f12698,f11122,f358,f12694]) ).
tff(f12694,plain,
( spl3_81
<=> $less(0,$sum(1,$uminus(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_81])]) ).
tff(f11122,plain,
( spl3_63
<=> $less($uminus(sK2),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).
tff(f12698,plain,
( $less(0,$sum(1,$uminus(sK2)))
| ~ spl3_13
| spl3_63 ),
inference(subsumption_resolution,[],[f12657,f14]) ).
tff(f12657,plain,
( $less(sK2,sK2)
| $less(0,$sum(1,$uminus(sK2)))
| ~ spl3_13
| spl3_63 ),
inference(resolution,[],[f11123,f549]) ).
tff(f549,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,sK2)
| $less(0,$sum(1,X1))
| $less(X1,X0) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f84]) ).
tff(f11123,plain,
( ~ $less($uminus(sK2),sK2)
| spl3_63 ),
inference(avatar_component_clause,[],[f11122]) ).
tff(f12697,plain,
( spl3_81
| ~ spl3_13
| spl3_63 ),
inference(avatar_split_clause,[],[f12692,f11122,f358,f12694]) ).
tff(f12692,plain,
( $less(0,$sum(1,$uminus(sK2)))
| ~ spl3_13
| spl3_63 ),
inference(forward_demodulation,[],[f12691,f9]) ).
tff(f12691,plain,
( $less(0,$sum($uminus(sK2),1))
| ~ spl3_13
| spl3_63 ),
inference(subsumption_resolution,[],[f12656,f14]) ).
tff(f12656,plain,
( $less(sK2,sK2)
| $less(0,$sum($uminus(sK2),1))
| ~ spl3_13
| spl3_63 ),
inference(resolution,[],[f11123,f546]) ).
tff(f12690,plain,
( spl3_80
| ~ spl3_7
| spl3_63 ),
inference(avatar_split_clause,[],[f12689,f11122,f128,f12685]) ).
tff(f12685,plain,
( spl3_80
<=> $less(-1,$sum(1,$uminus(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_80])]) ).
tff(f12689,plain,
( $less(-1,$sum(1,$uminus(sK2)))
| ~ spl3_7
| spl3_63 ),
inference(subsumption_resolution,[],[f12654,f14]) ).
tff(f12654,plain,
( $less(sK2,sK2)
| $less(-1,$sum(1,$uminus(sK2)))
| ~ spl3_7
| spl3_63 ),
inference(resolution,[],[f11123,f263]) ).
tff(f12688,plain,
( spl3_80
| ~ spl3_7
| spl3_63 ),
inference(avatar_split_clause,[],[f12683,f11122,f128,f12685]) ).
tff(f12683,plain,
( $less(-1,$sum(1,$uminus(sK2)))
| ~ spl3_7
| spl3_63 ),
inference(forward_demodulation,[],[f12682,f9]) ).
tff(f12682,plain,
( $less(-1,$sum($uminus(sK2),1))
| ~ spl3_7
| spl3_63 ),
inference(subsumption_resolution,[],[f12653,f14]) ).
tff(f12653,plain,
( $less(sK2,sK2)
| $less(-1,$sum($uminus(sK2),1))
| ~ spl3_7
| spl3_63 ),
inference(resolution,[],[f11123,f260]) ).
tff(f12681,plain,
( spl3_78
| spl3_79
| spl3_63 ),
inference(avatar_split_clause,[],[f12652,f11122,f12677,f12673]) ).
tff(f12673,plain,
( spl3_78
<=> ( sK2 = $uminus(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_78])]) ).
tff(f12652,plain,
( $less(sK2,$uminus(sK2))
| ( sK2 = $uminus(sK2) )
| spl3_63 ),
inference(resolution,[],[f11123,f16]) ).
tff(f12680,plain,
( spl3_78
| spl3_79
| spl3_63 ),
inference(avatar_split_clause,[],[f12651,f11122,f12677,f12673]) ).
tff(f12651,plain,
( $less(sK2,$uminus(sK2))
| ( sK2 = $uminus(sK2) )
| spl3_63 ),
inference(resolution,[],[f11123,f16]) ).
tff(f12671,plain,
( spl3_76
| ~ spl3_21
| spl3_63 ),
inference(avatar_split_clause,[],[f12650,f11122,f3617,f12622]) ).
tff(f12650,plain,
( $less(0,$uminus(sK2))
| ~ spl3_21
| spl3_63 ),
inference(resolution,[],[f11123,f3618]) ).
tff(f12670,plain,
( ~ spl3_13
| spl3_63
| ~ spl3_65 ),
inference(avatar_contradiction_clause,[],[f12669]) ).
tff(f12669,plain,
( $false
| ~ spl3_13
| spl3_63
| ~ spl3_65 ),
inference(subsumption_resolution,[],[f12645,f11133]) ).
tff(f12645,plain,
( ~ $less($uminus(sK2),1)
| ~ spl3_13
| spl3_63 ),
inference(resolution,[],[f11123,f370]) ).
tff(f12668,plain,
( ~ spl3_77
| ~ spl3_10
| spl3_63 ),
inference(avatar_split_clause,[],[f12642,f11122,f236,f12665]) ).
tff(f236,plain,
( spl3_10
<=> $less(-1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
tff(f12642,plain,
( ~ $less($uminus(sK2),-1)
| ~ spl3_10
| spl3_63 ),
inference(resolution,[],[f11123,f241]) ).
tff(f241,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,-1) )
| ~ spl3_10 ),
inference(resolution,[],[f238,f15]) ).
tff(f238,plain,
( $less(-1,sK2)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f236]) ).
tff(f12663,plain,
( ~ spl3_75
| ~ spl3_7
| spl3_63 ),
inference(avatar_split_clause,[],[f12641,f11122,f128,f12617]) ).
tff(f12641,plain,
( ~ $less($uminus(sK2),0)
| ~ spl3_7
| spl3_63 ),
inference(resolution,[],[f11123,f215]) ).
tff(f12625,plain,
( spl3_76
| spl3_65 ),
inference(avatar_split_clause,[],[f12603,f11131,f12622]) ).
tff(f12603,plain,
( $less(0,$uminus(sK2))
| spl3_65 ),
inference(resolution,[],[f11132,f135]) ).
tff(f11132,plain,
( ~ $less($uminus(sK2),1)
| spl3_65 ),
inference(avatar_component_clause,[],[f11131]) ).
tff(f12620,plain,
( ~ spl3_75
| ~ spl3_22
| spl3_65 ),
inference(avatar_split_clause,[],[f12601,f11131,f3620,f12617]) ).
tff(f12601,plain,
( ~ $less($uminus(sK2),0)
| ~ spl3_22
| spl3_65 ),
inference(resolution,[],[f11132,f11651]) ).
tff(f11651,plain,
( ! [X0: $int] :
( $less(X0,1)
| ~ $less(X0,0) )
| ~ spl3_22 ),
inference(resolution,[],[f3621,f104]) ).
tff(f12585,plain,
( spl3_74
| ~ spl3_60
| ~ spl3_63 ),
inference(avatar_split_clause,[],[f12569,f11122,f10772,f12582]) ).
tff(f12582,plain,
( spl3_74
<=> $less($uminus(sK2),3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_74])]) ).
tff(f12569,plain,
( $less($uminus(sK2),3)
| ~ spl3_60
| ~ spl3_63 ),
inference(resolution,[],[f12346,f11124]) ).
tff(f11124,plain,
( $less($uminus(sK2),sK2)
| ~ spl3_63 ),
inference(avatar_component_clause,[],[f11122]) ).
tff(f12335,plain,
( spl3_73
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f12329,f7887,f12332]) ).
tff(f12329,plain,
( ( 1 = $sum(2,$uminus(sK2)) )
| ~ spl3_58 ),
inference(evaluation,[],[f12273]) ).
tff(f12273,plain,
( ( $sum(1,0) = $sum(2,$uminus(sK2)) )
| ~ spl3_58 ),
inference(superposition,[],[f11495,f13]) ).
tff(f11495,plain,
( ! [X0: $int] : ( $sum(2,X0) = $sum(1,$sum(sK2,X0)) )
| ~ spl3_58 ),
inference(superposition,[],[f10,f7889]) ).
tff(f11824,plain,
( spl3_62
| spl3_8
| ~ spl3_58
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11823,f11131,f7887,f164,f11117]) ).
tff(f11823,plain,
( $less($uminus(sK2),2)
| spl3_8
| ~ spl3_58
| ~ spl3_65 ),
inference(subsumption_resolution,[],[f11796,f166]) ).
tff(f11796,plain,
( $less(sK2,1)
| $less($uminus(sK2),2)
| ~ spl3_58
| ~ spl3_65 ),
inference(resolution,[],[f11197,f11452]) ).
tff(f11452,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(sK2,X0) )
| ~ spl3_58 ),
inference(superposition,[],[f84,f7889]) ).
tff(f11197,plain,
( ! [X0: $int] :
( ~ $less(X0,$uminus(sK2))
| $less(X0,1) )
| ~ spl3_65 ),
inference(resolution,[],[f11133,f15]) ).
tff(f11822,plain,
( spl3_62
| spl3_70
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11790,f11131,f474,f358,f11808,f11117]) ).
tff(f11808,plain,
( spl3_70
<=> ! [X0: $int] :
( $less(X0,1)
| $less(-1,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).
tff(f11790,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less(-1,$sum(1,X0))
| $less($uminus(sK2),2) )
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(resolution,[],[f11197,f854]) ).
tff(f854,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,X0))
| $less(X1,2)
| $less(X0,X1) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f619,f84]) ).
tff(f619,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(-1,X0)
| $less(X1,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f575,f15]) ).
tff(f575,plain,
( ! [X0: $int] :
( $less(-1,X0)
| $less(X0,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f573,f481]) ).
tff(f573,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| $less(-1,X0) )
| ~ spl3_13 ),
inference(evaluation,[],[f541]) ).
tff(f541,plain,
( ! [X0: $int] :
( $less(X0,sK2)
| $less(0,0)
| $less(-1,X0) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f87]) ).
tff(f11821,plain,
( spl3_62
| spl3_72
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11789,f11131,f474,f358,f11817,f11117]) ).
tff(f11789,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),2)
| $less(0,$sum(1,X0)) )
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(resolution,[],[f11197,f756]) ).
tff(f756,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,2)
| $less(0,$sum(1,X1))
| $less(X1,X0) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f707,f84]) ).
tff(f707,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,2)
| $less(0,X1) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f501,f135]) ).
tff(f501,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,X0)
| $less(X1,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f482,f15]) ).
tff(f11820,plain,
( spl3_62
| spl3_71
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11788,f11131,f474,f358,f11813,f11117]) ).
tff(f11788,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),2)
| $less(0,$sum(X0,1)) )
| ~ spl3_13
| ~ spl3_16
| ~ spl3_65 ),
inference(resolution,[],[f11197,f753]) ).
tff(f753,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,2)
| $less(0,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f707,f18]) ).
tff(f11819,plain,
( spl3_63
| spl3_72
| ~ spl3_13
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11787,f11131,f358,f11817,f11122]) ).
tff(f11787,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),sK2)
| $less(0,$sum(1,X0)) )
| ~ spl3_13
| ~ spl3_65 ),
inference(resolution,[],[f11197,f549]) ).
tff(f11815,plain,
( spl3_63
| spl3_71
| ~ spl3_13
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11786,f11131,f358,f11813,f11122]) ).
tff(f11786,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),sK2)
| $less(0,$sum(X0,1)) )
| ~ spl3_13
| ~ spl3_65 ),
inference(resolution,[],[f11197,f546]) ).
tff(f11811,plain,
( spl3_62
| spl3_69
| ~ spl3_7
| ~ spl3_16
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11785,f11131,f474,f128,f11804,f11117]) ).
tff(f11804,plain,
( spl3_69
<=> ! [X0: $int] :
( $less(X0,1)
| $less(-1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).
tff(f11785,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_7
| ~ spl3_16
| ~ spl3_65 ),
inference(resolution,[],[f11197,f483]) ).
tff(f483,plain,
( ! [X0: $int,X1: $int] :
( $less(X0,2)
| $less(-1,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_7
| ~ spl3_16 ),
inference(resolution,[],[f481,f260]) ).
tff(f11810,plain,
( spl3_63
| spl3_70
| ~ spl3_7
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11784,f11131,f128,f11808,f11122]) ).
tff(f11784,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),sK2)
| $less(-1,$sum(1,X0)) )
| ~ spl3_7
| ~ spl3_65 ),
inference(resolution,[],[f11197,f263]) ).
tff(f11806,plain,
( spl3_63
| spl3_69
| ~ spl3_7
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11783,f11131,f128,f11804,f11122]) ).
tff(f11783,plain,
( ! [X0: $int] :
( $less(X0,1)
| $less($uminus(sK2),sK2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_7
| ~ spl3_65 ),
inference(resolution,[],[f11197,f260]) ).
tff(f11395,plain,
( spl3_58
| spl3_59
| spl3_41 ),
inference(avatar_split_clause,[],[f11297,f4669,f7891,f7887]) ).
tff(f11297,plain,
( $less(2,$sum(1,sK2))
| ( 2 = $sum(1,sK2) )
| spl3_41 ),
inference(resolution,[],[f4670,f16]) ).
tff(f4670,plain,
( ~ $less($sum(1,sK2),2)
| spl3_41 ),
inference(avatar_component_clause,[],[f4669]) ).
tff(f11394,plain,
( spl3_58
| spl3_59
| spl3_41 ),
inference(avatar_split_clause,[],[f11298,f4669,f7891,f7887]) ).
tff(f11298,plain,
( $less(2,$sum(1,sK2))
| ( 2 = $sum(1,sK2) )
| spl3_41 ),
inference(resolution,[],[f4670,f16]) ).
tff(f11393,plain,
( ~ spl3_16
| ~ spl3_59 ),
inference(avatar_contradiction_clause,[],[f11392]) ).
tff(f11392,plain,
( $false
| ~ spl3_16
| ~ spl3_59 ),
inference(subsumption_resolution,[],[f11373,f476]) ).
tff(f11373,plain,
( ~ $less(sK2,2)
| ~ spl3_59 ),
inference(resolution,[],[f7893,f101]) ).
tff(f7893,plain,
( $less(2,$sum(1,sK2))
| ~ spl3_59 ),
inference(avatar_component_clause,[],[f7891]) ).
tff(f11208,plain,
( spl3_63
| spl3_22
| ~ spl3_13
| ~ spl3_65 ),
inference(avatar_split_clause,[],[f11205,f11131,f358,f3620,f11122]) ).
tff(f11205,plain,
( ! [X0: $int] :
( $less(-1,X0)
| $less(X0,1)
| $less($uminus(sK2),sK2) )
| ~ spl3_13
| ~ spl3_65 ),
inference(resolution,[],[f11133,f1186]) ).
tff(f1186,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X1)
| $less(-1,X0)
| $less(X0,X1)
| $less(X2,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f1121,f15]) ).
tff(f11182,plain,
( spl3_68
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f11169,f11127,f11179]) ).
tff(f11179,plain,
( spl3_68
<=> ( sK2 = -1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).
tff(f11127,plain,
( spl3_64
<=> ( 1 = $uminus(sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).
tff(f11169,plain,
( ( sK2 = -1 )
| ~ spl3_64 ),
inference(evaluation,[],[f11168]) ).
tff(f11168,plain,
( ( sK2 = $uminus(1) )
| ~ spl3_64 ),
inference(superposition,[],[f19,f11129]) ).
tff(f11129,plain,
( ( 1 = $uminus(sK2) )
| ~ spl3_64 ),
inference(avatar_component_clause,[],[f11127]) ).
tff(f11177,plain,
( spl3_67
| ~ spl3_64 ),
inference(avatar_split_clause,[],[f11167,f11127,f11174]) ).
tff(f11174,plain,
( spl3_67
<=> ( 0 = $sum(sK2,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).
tff(f11167,plain,
( ( 0 = $sum(sK2,1) )
| ~ spl3_64 ),
inference(superposition,[],[f13,f11129]) ).
tff(f11172,plain,
( spl3_47
| ~ spl3_64 ),
inference(avatar_contradiction_clause,[],[f11171]) ).
tff(f11171,plain,
( $false
| spl3_47
| ~ spl3_64 ),
inference(subsumption_resolution,[],[f11166,f4787]) ).
tff(f4787,plain,
( ( 0 != $sum(1,sK2) )
| spl3_47 ),
inference(avatar_component_clause,[],[f4786]) ).
tff(f4786,plain,
( spl3_47
<=> ( 0 = $sum(1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).
tff(f11166,plain,
( ( 0 = $sum(1,sK2) )
| ~ spl3_64 ),
inference(superposition,[],[f71,f11129]) ).
tff(f11162,plain,
( spl3_66
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f11149,f11097,f474,f358,f11155]) ).
tff(f11149,plain,
( $less(-1,$uminus(sK2))
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(evaluation,[],[f11146]) ).
tff(f11146,plain,
( $less($sum(1,1),2)
| $less(-1,$uminus(sK2))
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(resolution,[],[f11098,f1239]) ).
tff(f11161,plain,
( spl3_66
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f11150,f11097,f474,f358,f11155]) ).
tff(f11150,plain,
( $less(-1,$uminus(sK2))
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(evaluation,[],[f11145]) ).
tff(f11145,plain,
( $less($sum(1,1),2)
| $less(-1,$uminus(sK2))
| ~ spl3_13
| ~ spl3_16
| ~ spl3_61 ),
inference(resolution,[],[f11098,f1238]) ).
tff(f11160,plain,
( spl3_66
| spl3_1
| ~ spl3_13
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f11159,f11097,f358,f51,f11155]) ).
tff(f11159,plain,
( $less(-1,$uminus(sK2))
| spl3_1
| ~ spl3_13
| ~ spl3_61 ),
inference(subsumption_resolution,[],[f11151,f53]) ).
tff(f11151,plain,
( $less(-1,$uminus(sK2))
| $less(2,sK2)
| ~ spl3_13
| ~ spl3_61 ),
inference(evaluation,[],[f11143]) ).
tff(f11143,plain,
( $less(-1,$uminus(sK2))
| $less($sum(1,1),sK2)
| ~ spl3_13
| ~ spl3_61 ),
inference(resolution,[],[f11098,f1150]) ).
tff(f11158,plain,
( spl3_66
| spl3_1
| ~ spl3_13
| ~ spl3_61 ),
inference(avatar_split_clause,[],[f11153,f11097,f358,f51,f11155]) ).
tff(f11153,plain,
( $less(-1,$uminus(sK2))
| spl3_1
| ~ spl3_13
| ~ spl3_61 ),
inference(subsumption_resolution,[],[f11152,f53]) ).
tff(f11152,plain,
( $less(-1,$uminus(sK2))
| $less(2,sK2)
| ~ spl3_13
| ~ spl3_61 ),
inference(evaluation,[],[f11142]) ).
tff(f11142,plain,
( $less(-1,$uminus(sK2))
| $less($sum(1,1),sK2)
| ~ spl3_13
| ~ spl3_61 ),
inference(resolution,[],[f11098,f1149]) ).
tff(f11135,plain,
( spl3_64
| spl3_65
| spl3_61 ),
inference(avatar_split_clause,[],[f11104,f11097,f11131,f11127]) ).
tff(f11104,plain,
( $less($uminus(sK2),1)
| ( 1 = $uminus(sK2) )
| spl3_61 ),
inference(resolution,[],[f11099,f16]) ).
tff(f11099,plain,
( ~ $less(1,$uminus(sK2))
| spl3_61 ),
inference(avatar_component_clause,[],[f11097]) ).
tff(f11134,plain,
( spl3_64
| spl3_65
| spl3_61 ),
inference(avatar_split_clause,[],[f11103,f11097,f11131,f11127]) ).
tff(f11103,plain,
( $less($uminus(sK2),1)
| ( 1 = $uminus(sK2) )
| spl3_61 ),
inference(resolution,[],[f11099,f16]) ).
tff(f11125,plain,
( spl3_63
| ~ spl3_56
| spl3_61 ),
inference(avatar_split_clause,[],[f11102,f11097,f7843,f11122]) ).
tff(f7843,plain,
( spl3_56
<=> ! [X1: $int] :
( $less(1,X1)
| $less(X1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).
tff(f11102,plain,
( $less($uminus(sK2),sK2)
| ~ spl3_56
| spl3_61 ),
inference(resolution,[],[f11099,f7844]) ).
tff(f7844,plain,
( ! [X1: $int] :
( $less(1,X1)
| $less(X1,sK2) )
| ~ spl3_56 ),
inference(avatar_component_clause,[],[f7843]) ).
tff(f11120,plain,
( spl3_62
| ~ spl3_16
| ~ spl3_56
| spl3_61 ),
inference(avatar_split_clause,[],[f11101,f11097,f7843,f474,f11117]) ).
tff(f11101,plain,
( $less($uminus(sK2),2)
| ~ spl3_16
| ~ spl3_56
| spl3_61 ),
inference(resolution,[],[f11099,f7966]) ).
tff(f7966,plain,
( ! [X0: $int] :
( $less(1,X0)
| $less(X0,2) )
| ~ spl3_16
| ~ spl3_56 ),
inference(resolution,[],[f7844,f481]) ).
tff(f11100,plain,
( ~ spl3_61
| ~ spl3_58 ),
inference(avatar_split_clause,[],[f11084,f7887,f11097]) ).
tff(f11084,plain,
( ~ $less(1,$uminus(sK2))
| ~ spl3_58 ),
inference(evaluation,[],[f11083]) ).
tff(f11083,plain,
( $less(2,0)
| ~ $less(1,$uminus(sK2))
| ~ spl3_58 ),
inference(superposition,[],[f10878,f71]) ).
tff(f10878,plain,
( ! [X0: $int] :
( $less(2,$sum(X0,sK2))
| ~ $less(1,X0) )
| ~ spl3_58 ),
inference(superposition,[],[f17,f7889]) ).
tff(f10775,plain,
( spl3_60
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f10765,f4669,f10772]) ).
tff(f10765,plain,
( $less(sK2,3)
| ~ spl3_41 ),
inference(evaluation,[],[f10759]) ).
tff(f10759,plain,
( $less(sK2,$sum(1,2))
| $less(2,2)
| ~ spl3_41 ),
inference(factoring,[],[f8357]) ).
tff(f8357,plain,
( ! [X0: $int,X1: $int] :
( $less(sK2,$sum(1,X0))
| $less(X1,2)
| $less(X0,X1) )
| ~ spl3_41 ),
inference(resolution,[],[f8141,f84]) ).
tff(f8141,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(sK2,X0)
| $less(X1,2) )
| ~ spl3_41 ),
inference(resolution,[],[f8097,f15]) ).
tff(f8097,plain,
( ! [X0: $int] :
( $less(X0,2)
| $less(sK2,X0) )
| ~ spl3_41 ),
inference(resolution,[],[f7896,f84]) ).
tff(f7896,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,sK2))
| $less(X0,2) )
| ~ spl3_41 ),
inference(resolution,[],[f4671,f15]) ).
tff(f7895,plain,
( spl3_58
| spl3_59
| spl3_41 ),
inference(avatar_split_clause,[],[f7863,f4669,f7891,f7887]) ).
tff(f7863,plain,
( $less(2,$sum(1,sK2))
| ( 2 = $sum(1,sK2) )
| spl3_41 ),
inference(resolution,[],[f4670,f16]) ).
tff(f7894,plain,
( spl3_58
| spl3_59
| spl3_41 ),
inference(avatar_split_clause,[],[f7862,f4669,f7891,f7887]) ).
tff(f7862,plain,
( $less(2,$sum(1,sK2))
| ( 2 = $sum(1,sK2) )
| spl3_41 ),
inference(resolution,[],[f4670,f16]) ).
tff(f7848,plain,
( spl3_56
| spl3_57
| ~ spl3_13
| ~ spl3_41 ),
inference(avatar_split_clause,[],[f7828,f4669,f358,f7846,f7843]) ).
tff(f7846,plain,
( spl3_57
<=> ! [X0: $int] :
( ~ $less(X0,$sum(-1,sK2))
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).
tff(f7828,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(-1,sK2))
| $less(X0,2)
| $less(1,X1)
| $less(X1,sK2) )
| ~ spl3_13
| ~ spl3_41 ),
inference(resolution,[],[f5737,f1121]) ).
tff(f5737,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X0,sK2))
| $less(X1,2) )
| ~ spl3_41 ),
inference(resolution,[],[f5514,f15]) ).
tff(f5514,plain,
( ! [X0: $int] :
( $less($sum(X0,sK2),2)
| ~ $less(X0,1) )
| ~ spl3_41 ),
inference(resolution,[],[f4791,f17]) ).
tff(f4791,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,sK2))
| $less(X0,2) )
| ~ spl3_41 ),
inference(resolution,[],[f4671,f15]) ).
tff(f5968,plain,
( ~ spl3_55
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f5947,f4729,f5965]) ).
tff(f5965,plain,
( spl3_55
<=> $less($sum(2,sK2),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).
tff(f5947,plain,
( ~ $less($sum(2,sK2),-1)
| ~ spl3_45 ),
inference(resolution,[],[f5328,f14]) ).
tff(f5328,plain,
( ! [X0: $int] :
( $less(X0,$sum(2,sK2))
| ~ $less(X0,-1) )
| ~ spl3_45 ),
inference(resolution,[],[f4731,f15]) ).
tff(f5862,plain,
( spl3_22
| spl3_54
| ~ spl3_13
| ~ spl3_52 ),
inference(avatar_split_clause,[],[f5841,f5408,f358,f5860,f3620]) ).
tff(f5860,plain,
( spl3_54
<=> ! [X0: $int] :
( ~ $less(X0,2)
| $less($sum(X0,sK2),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).
tff(f5408,plain,
( spl3_52
<=> ( 1 = $sum(2,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).
tff(f5841,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,2)
| $less(-1,X1)
| $less(X1,1)
| $less($sum(X0,sK2),sK2) )
| ~ spl3_13
| ~ spl3_52 ),
inference(resolution,[],[f5423,f1186]) ).
tff(f5423,plain,
( ! [X0: $int] :
( $less($sum(X0,sK2),1)
| ~ $less(X0,2) )
| ~ spl3_52 ),
inference(superposition,[],[f17,f5410]) ).
tff(f5410,plain,
( ( 1 = $sum(2,sK2) )
| ~ spl3_52 ),
inference(avatar_component_clause,[],[f5408]) ).
tff(f5858,plain,
( spl3_9
| ~ spl3_52 ),
inference(avatar_contradiction_clause,[],[f5857]) ).
tff(f5857,plain,
( $false
| spl3_9
| ~ spl3_52 ),
inference(subsumption_resolution,[],[f5848,f231]) ).
tff(f231,plain,
( ~ $less(sK2,0)
| spl3_9 ),
inference(avatar_component_clause,[],[f229]) ).
tff(f229,plain,
( spl3_9
<=> $less(sK2,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
tff(f5848,plain,
( $less(sK2,0)
| ~ spl3_52 ),
inference(evaluation,[],[f5827]) ).
tff(f5827,plain,
( ~ $less(1,2)
| $less(sK2,0)
| ~ spl3_52 ),
inference(resolution,[],[f5423,f160]) ).
tff(f5856,plain,
( ~ spl3_13
| ~ spl3_52 ),
inference(avatar_contradiction_clause,[],[f5855]) ).
tff(f5855,plain,
( $false
| ~ spl3_13
| ~ spl3_52 ),
inference(subsumption_resolution,[],[f5849,f14]) ).
tff(f5849,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_52 ),
inference(evaluation,[],[f5826]) ).
tff(f5826,plain,
( ~ $less(1,2)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_52 ),
inference(resolution,[],[f5423,f633]) ).
tff(f633,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f548,f150]) ).
tff(f548,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f88]) ).
tff(f5854,plain,
( spl3_43
| ~ spl3_52 ),
inference(avatar_contradiction_clause,[],[f5853]) ).
tff(f5853,plain,
( $false
| spl3_43
| ~ spl3_52 ),
inference(evaluation,[],[f5822]) ).
tff(f5822,plain,
( ~ $less(1,2)
| spl3_43
| ~ spl3_52 ),
inference(resolution,[],[f5423,f4720]) ).
tff(f4720,plain,
( ~ $less($sum(1,sK2),1)
| spl3_43 ),
inference(avatar_component_clause,[],[f4718]) ).
tff(f4718,plain,
( spl3_43
<=> $less($sum(1,sK2),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).
tff(f5416,plain,
( spl3_52
| spl3_53
| spl3_51 ),
inference(avatar_split_clause,[],[f5390,f5384,f5412,f5408]) ).
tff(f5384,plain,
( spl3_51
<=> $less($sum(2,sK2),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).
tff(f5390,plain,
( $less(1,$sum(2,sK2))
| ( 1 = $sum(2,sK2) )
| spl3_51 ),
inference(resolution,[],[f5386,f16]) ).
tff(f5386,plain,
( ~ $less($sum(2,sK2),1)
| spl3_51 ),
inference(avatar_component_clause,[],[f5384]) ).
tff(f5415,plain,
( spl3_52
| spl3_53
| spl3_51 ),
inference(avatar_split_clause,[],[f5389,f5384,f5412,f5408]) ).
tff(f5389,plain,
( $less(1,$sum(2,sK2))
| ( 1 = $sum(2,sK2) )
| spl3_51 ),
inference(resolution,[],[f5386,f16]) ).
tff(f5387,plain,
( ~ spl3_51
| ~ spl3_46 ),
inference(avatar_split_clause,[],[f5367,f4737,f5384]) ).
tff(f5367,plain,
( ~ $less($sum(2,sK2),1)
| ~ spl3_46 ),
inference(resolution,[],[f4739,f150]) ).
tff(f5347,plain,
( ~ spl3_50
| ~ spl3_45 ),
inference(avatar_split_clause,[],[f5327,f4729,f5344]) ).
tff(f5344,plain,
( spl3_50
<=> $less($sum(2,sK2),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).
tff(f5327,plain,
( ~ $less($sum(2,sK2),0)
| ~ spl3_45 ),
inference(resolution,[],[f4731,f104]) ).
tff(f5288,plain,
~ spl3_38,
inference(avatar_contradiction_clause,[],[f5287]) ).
tff(f5287,plain,
( $false
| ~ spl3_38 ),
inference(subsumption_resolution,[],[f5244,f14]) ).
tff(f5244,plain,
( $less(sK2,sK2)
| ~ spl3_38 ),
inference(resolution,[],[f4745,f88]) ).
tff(f4745,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,sK2))
| $less(X0,sK2) )
| ~ spl3_38 ),
inference(resolution,[],[f4609,f15]) ).
tff(f4609,plain,
( $less($sum(1,sK2),sK2)
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f4607]) ).
tff(f5170,plain,
( ~ spl3_42
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f5154,f365,f4713]) ).
tff(f4713,plain,
( spl3_42
<=> $less($sum(1,sK2),-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
tff(f365,plain,
( spl3_14
<=> $less(-1,$sum(1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
tff(f5154,plain,
( ~ $less($sum(1,sK2),-1)
| ~ spl3_14 ),
inference(resolution,[],[f4624,f14]) ).
tff(f4624,plain,
( ! [X0: $int] :
( $less(X0,$sum(1,sK2))
| ~ $less(X0,-1) )
| ~ spl3_14 ),
inference(resolution,[],[f367,f15]) ).
tff(f367,plain,
( $less(-1,$sum(1,sK2))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f365]) ).
tff(f4973,plain,
( spl3_8
| ~ spl3_48 ),
inference(avatar_contradiction_clause,[],[f4972]) ).
tff(f4972,plain,
( $false
| spl3_8
| ~ spl3_48 ),
inference(subsumption_resolution,[],[f4934,f166]) ).
tff(f4934,plain,
( $less(sK2,1)
| ~ spl3_48 ),
inference(superposition,[],[f88,f4850]) ).
tff(f4850,plain,
( ( 1 = $sum(1,sK2) )
| ~ spl3_48 ),
inference(avatar_component_clause,[],[f4848]) ).
tff(f4848,plain,
( spl3_48
<=> ( 1 = $sum(1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).
tff(f4921,plain,
( ~ spl3_13
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f4920]) ).
tff(f4920,plain,
( $false
| ~ spl3_13
| ~ spl3_47 ),
inference(subsumption_resolution,[],[f4909,f14]) ).
tff(f4909,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_47 ),
inference(evaluation,[],[f4884]) ).
tff(f4884,plain,
( ~ $less(0,1)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_47 ),
inference(superposition,[],[f633,f4788]) ).
tff(f4788,plain,
( ( 0 = $sum(1,sK2) )
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f4786]) ).
tff(f4919,plain,
( ~ spl3_13
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f4918]) ).
tff(f4918,plain,
( $false
| ~ spl3_13
| ~ spl3_47 ),
inference(subsumption_resolution,[],[f4911,f14]) ).
tff(f4911,plain,
( $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_47 ),
inference(evaluation,[],[f4880]) ).
tff(f4880,plain,
( $less(0,0)
| $less(sK2,sK2)
| ~ spl3_13
| ~ spl3_47 ),
inference(superposition,[],[f548,f4788]) ).
tff(f4917,plain,
( spl3_9
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f4916]) ).
tff(f4916,plain,
( $false
| spl3_9
| ~ spl3_47 ),
inference(subsumption_resolution,[],[f4912,f231]) ).
tff(f4912,plain,
( $less(sK2,0)
| ~ spl3_47 ),
inference(evaluation,[],[f4873]) ).
tff(f4873,plain,
( ~ $less(0,1)
| $less(sK2,0)
| ~ spl3_47 ),
inference(superposition,[],[f160,f4788]) ).
tff(f4915,plain,
( spl3_9
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f4914]) ).
tff(f4914,plain,
( $false
| spl3_9
| ~ spl3_47 ),
inference(subsumption_resolution,[],[f4868,f231]) ).
tff(f4868,plain,
( $less(sK2,0)
| ~ spl3_47 ),
inference(superposition,[],[f88,f4788]) ).
tff(f4856,plain,
( spl3_48
| spl3_49
| spl3_43 ),
inference(avatar_split_clause,[],[f4830,f4718,f4852,f4848]) ).
tff(f4830,plain,
( $less(1,$sum(1,sK2))
| ( 1 = $sum(1,sK2) )
| spl3_43 ),
inference(resolution,[],[f4720,f16]) ).
tff(f4855,plain,
( spl3_48
| spl3_49
| spl3_43 ),
inference(avatar_split_clause,[],[f4829,f4718,f4852,f4848]) ).
tff(f4829,plain,
( $less(1,$sum(1,sK2))
| ( 1 = $sum(1,sK2) )
| spl3_43 ),
inference(resolution,[],[f4720,f16]) ).
tff(f4826,plain,
( ~ spl3_43
| ~ spl3_44 ),
inference(avatar_split_clause,[],[f4805,f4723,f4718]) ).
tff(f4805,plain,
( ~ $less($sum(1,sK2),1)
| ~ spl3_44 ),
inference(resolution,[],[f4725,f150]) ).
tff(f4790,plain,
( spl3_47
| spl3_44
| spl3_40 ),
inference(avatar_split_clause,[],[f4768,f4643,f4723,f4786]) ).
tff(f4643,plain,
( spl3_40
<=> $less($sum(1,sK2),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
tff(f4768,plain,
( $less(0,$sum(1,sK2))
| ( 0 = $sum(1,sK2) )
| spl3_40 ),
inference(resolution,[],[f4645,f16]) ).
tff(f4645,plain,
( ~ $less($sum(1,sK2),0)
| spl3_40 ),
inference(avatar_component_clause,[],[f4643]) ).
tff(f4789,plain,
( spl3_47
| spl3_44
| spl3_40 ),
inference(avatar_split_clause,[],[f4767,f4643,f4723,f4786]) ).
tff(f4767,plain,
( $less(0,$sum(1,sK2))
| ( 0 = $sum(1,sK2) )
| spl3_40 ),
inference(resolution,[],[f4645,f16]) ).
tff(f4742,plain,
( spl3_46
| ~ spl3_13
| spl3_38 ),
inference(avatar_split_clause,[],[f4741,f4607,f358,f4737]) ).
tff(f4741,plain,
( $less(0,$sum(2,sK2))
| ~ spl3_13
| spl3_38 ),
inference(subsumption_resolution,[],[f4706,f14]) ).
tff(f4706,plain,
( $less(sK2,sK2)
| $less(0,$sum(2,sK2))
| ~ spl3_13
| spl3_38 ),
inference(evaluation,[],[f4696]) ).
tff(f4696,plain,
( $less(sK2,sK2)
| $less(0,$sum(1,$sum(1,sK2)))
| ~ spl3_13
| spl3_38 ),
inference(resolution,[],[f4608,f549]) ).
tff(f4740,plain,
( spl3_46
| ~ spl3_13
| spl3_38 ),
inference(avatar_split_clause,[],[f4735,f4607,f358,f4737]) ).
tff(f4735,plain,
( $less(0,$sum(2,sK2))
| ~ spl3_13
| spl3_38 ),
inference(subsumption_resolution,[],[f4707,f14]) ).
tff(f4707,plain,
( $less(sK2,sK2)
| $less(0,$sum(2,sK2))
| ~ spl3_13
| spl3_38 ),
inference(evaluation,[],[f4695]) ).
tff(f4695,plain,
( $less(sK2,sK2)
| $less(0,$sum($sum(1,sK2),1))
| ~ spl3_13
| spl3_38 ),
inference(resolution,[],[f4608,f546]) ).
tff(f4734,plain,
( spl3_45
| ~ spl3_7
| spl3_38 ),
inference(avatar_split_clause,[],[f4733,f4607,f128,f4729]) ).
tff(f4733,plain,
( $less(-1,$sum(2,sK2))
| ~ spl3_7
| spl3_38 ),
inference(subsumption_resolution,[],[f4709,f14]) ).
tff(f4709,plain,
( $less(sK2,sK2)
| $less(-1,$sum(2,sK2))
| ~ spl3_7
| spl3_38 ),
inference(evaluation,[],[f4692]) ).
tff(f4692,plain,
( $less(sK2,sK2)
| $less(-1,$sum(1,$sum(1,sK2)))
| ~ spl3_7
| spl3_38 ),
inference(resolution,[],[f4608,f263]) ).
tff(f4732,plain,
( spl3_45
| ~ spl3_7
| spl3_38 ),
inference(avatar_split_clause,[],[f4727,f4607,f128,f4729]) ).
tff(f4727,plain,
( $less(-1,$sum(2,sK2))
| ~ spl3_7
| spl3_38 ),
inference(subsumption_resolution,[],[f4710,f14]) ).
tff(f4710,plain,
( $less(sK2,sK2)
| $less(-1,$sum(2,sK2))
| ~ spl3_7
| spl3_38 ),
inference(evaluation,[],[f4691]) ).
tff(f4691,plain,
( $less(sK2,sK2)
| $less(-1,$sum($sum(1,sK2),1))
| ~ spl3_7
| spl3_38 ),
inference(resolution,[],[f4608,f260]) ).
tff(f4726,plain,
( spl3_44
| ~ spl3_21
| spl3_38 ),
inference(avatar_split_clause,[],[f4688,f4607,f3617,f4723]) ).
tff(f4688,plain,
( $less(0,$sum(1,sK2))
| ~ spl3_21
| spl3_38 ),
inference(resolution,[],[f4608,f3618]) ).
tff(f4721,plain,
( ~ spl3_43
| ~ spl3_13
| spl3_38 ),
inference(avatar_split_clause,[],[f4681,f4607,f358,f4718]) ).
tff(f4681,plain,
( ~ $less($sum(1,sK2),1)
| ~ spl3_13
| spl3_38 ),
inference(resolution,[],[f4608,f370]) ).
tff(f4716,plain,
( ~ spl3_42
| ~ spl3_10
| spl3_38 ),
inference(avatar_split_clause,[],[f4678,f4607,f236,f4713]) ).
tff(f4678,plain,
( ~ $less($sum(1,sK2),-1)
| ~ spl3_10
| spl3_38 ),
inference(resolution,[],[f4608,f241]) ).
tff(f4672,plain,
( spl3_41
| ~ spl3_16
| ~ spl3_38 ),
inference(avatar_split_clause,[],[f4648,f4607,f474,f4669]) ).
tff(f4648,plain,
( $less($sum(1,sK2),2)
| ~ spl3_16
| ~ spl3_38 ),
inference(resolution,[],[f4609,f481]) ).
tff(f4646,plain,
( ~ spl3_40
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f4620,f365,f4643]) ).
tff(f4620,plain,
( ~ $less($sum(1,sK2),0)
| ~ spl3_14 ),
inference(resolution,[],[f367,f104]) ).
tff(f4619,plain,
( spl3_37
| spl3_38
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4618,f474,f128,f4607,f4604]) ).
tff(f4604,plain,
( spl3_37
<=> ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less(X0,2)
| ( sK2 = $sum(1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
tff(f4618,plain,
( ! [X0: $int] :
( $less($sum(1,sK2),sK2)
| $less(-1,$sum(2,X0))
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f4491,f9]) ).
tff(f4491,plain,
( ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(sK2,1),sK2)
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(evaluation,[],[f4462]) ).
tff(f4462,plain,
( ! [X0: $int] :
( $less(-1,$sum($sum(1,X0),1))
| $less($sum(sK2,1),sK2)
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(resolution,[],[f326,f1981]) ).
tff(f1981,plain,
( ! [X0: $int] :
( $less(sK2,$sum(1,X0))
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_16 ),
inference(resolution,[],[f522,f88]) ).
tff(f522,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ( sK2 = X0 )
| $less(sK2,X0)
| $less(X1,2) )
| ~ spl3_16 ),
inference(resolution,[],[f486,f15]) ).
tff(f486,plain,
( ! [X0: $int] :
( $less(sK2,X0)
| $less(X0,2)
| ( sK2 = X0 ) )
| ~ spl3_16 ),
inference(resolution,[],[f481,f16]) ).
tff(f326,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(-1,$sum(X1,1))
| $less($sum(X0,1),sK2) )
| ~ spl3_7 ),
inference(resolution,[],[f260,f20]) ).
tff(f4617,plain,
( spl3_39
| spl3_38
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4616,f474,f128,f4607,f4613]) ).
tff(f4613,plain,
( spl3_39
<=> ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less(X0,2)
| ( $sum(X0,1) = sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
tff(f4616,plain,
( ! [X0: $int] :
( $less($sum(1,sK2),sK2)
| $less(-1,$sum(2,X0))
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f4492,f9]) ).
tff(f4492,plain,
( ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(sK2,1),sK2)
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(evaluation,[],[f4461]) ).
tff(f4461,plain,
( ! [X0: $int] :
( $less(-1,$sum($sum(1,X0),1))
| $less($sum(sK2,1),sK2)
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(resolution,[],[f326,f4268]) ).
tff(f4268,plain,
( ! [X0: $int] :
( $less(sK2,$sum(1,X0))
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_16 ),
inference(superposition,[],[f1980,f9]) ).
tff(f1980,plain,
( ! [X0: $int] :
( $less(sK2,$sum(X0,1))
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_16 ),
inference(resolution,[],[f522,f83]) ).
tff(f4615,plain,
( spl3_39
| spl3_38
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4611,f474,f128,f4607,f4613]) ).
tff(f4611,plain,
( ! [X0: $int] :
( $less($sum(1,sK2),sK2)
| $less(-1,$sum(2,X0))
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f4493,f9]) ).
tff(f4493,plain,
( ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(sK2,1),sK2)
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(evaluation,[],[f4460]) ).
tff(f4460,plain,
( ! [X0: $int] :
( $less(-1,$sum($sum(X0,1),1))
| $less($sum(sK2,1),sK2)
| ( $sum(X0,1) = sK2 )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(resolution,[],[f326,f1980]) ).
tff(f4610,plain,
( spl3_37
| spl3_38
| ~ spl3_7
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4602,f474,f128,f4607,f4604]) ).
tff(f4602,plain,
( ! [X0: $int] :
( $less($sum(1,sK2),sK2)
| $less(-1,$sum(2,X0))
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(forward_demodulation,[],[f4494,f9]) ).
tff(f4494,plain,
( ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(sK2,1),sK2)
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(evaluation,[],[f4459]) ).
tff(f4459,plain,
( ! [X0: $int] :
( $less(-1,$sum($sum(X0,1),1))
| $less($sum(sK2,1),sK2)
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_7
| ~ spl3_16 ),
inference(resolution,[],[f326,f4293]) ).
tff(f4293,plain,
( ! [X0: $int] :
( $less(sK2,$sum(X0,1))
| ( sK2 = $sum(1,X0) )
| $less(X0,2) )
| ~ spl3_16 ),
inference(superposition,[],[f1981,f9]) ).
tff(f4601,plain,
( spl3_35
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4600,f358,f128,f365,f4590]) ).
tff(f4590,plain,
( spl3_35
<=> ! [X0: $int] :
( $less($sum(2,X0),sK2)
| ~ $less(X0,-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
tff(f4600,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4495,f9]) ).
tff(f4495,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4456]) ).
tff(f4456,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(1,X0),1),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f570]) ).
tff(f570,plain,
( ! [X0: $int] :
( $less($sum(1,X0),sK2)
| ~ $less(X0,-1) )
| ~ spl3_13 ),
inference(evaluation,[],[f559]) ).
tff(f559,plain,
( ! [X0: $int] :
( $less($sum(1,X0),sK2)
| $less(0,0)
| ~ $less(X0,-1) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f148]) ).
tff(f148,plain,
! [X0: $int] :
( $less($sum(1,X0),0)
| ~ $less(X0,-1) ),
inference(resolution,[],[f101,f87]) ).
tff(f4599,plain,
( spl3_36
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4595,f358,f128,f365,f4597]) ).
tff(f4597,plain,
( spl3_36
<=> ! [X0: $int] :
( $less($sum(2,X0),sK2)
| $less(-1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
tff(f4595,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4496,f9]) ).
tff(f4496,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4455]) ).
tff(f4455,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(1,X0),1),sK2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1776]) ).
tff(f1776,plain,
( ! [X0: $int] :
( $less($sum(1,X0),sK2)
| $less(-1,$sum(X0,1)) )
| ~ spl3_13 ),
inference(resolution,[],[f1150,f83]) ).
tff(f4594,plain,
( spl3_33
| spl3_14
| ~ spl3_7
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f4593,f3617,f128,f365,f4580]) ).
tff(f4580,plain,
( spl3_33
<=> ! [X0: $int] :
( $less($sum(2,X0),sK2)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
tff(f4593,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(forward_demodulation,[],[f4497,f9]) ).
tff(f4497,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(evaluation,[],[f4454]) ).
tff(f4454,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(1,X0),1),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(resolution,[],[f326,f3671]) ).
tff(f3671,plain,
( ! [X0: $int] :
( $less($sum(1,X0),sK2)
| ~ $less(X0,0) )
| ~ spl3_21 ),
inference(resolution,[],[f3618,f101]) ).
tff(f4592,plain,
( spl3_35
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4588,f358,f128,f365,f4590]) ).
tff(f4588,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4498,f9]) ).
tff(f4498,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4446]) ).
tff(f4446,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(X0,1),1),sK2)
| ~ $less(X0,-1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f571]) ).
tff(f571,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| ~ $less(X0,-1) )
| ~ spl3_13 ),
inference(evaluation,[],[f557]) ).
tff(f557,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| $less(0,0)
| ~ $less(X0,-1) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f100]) ).
tff(f100,plain,
! [X0: $int] :
( $less($sum(X0,1),0)
| ~ $less(X0,-1) ),
inference(resolution,[],[f20,f87]) ).
tff(f4587,plain,
( spl3_34
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4583,f358,f128,f365,f4585]) ).
tff(f4585,plain,
( spl3_34
<=> ! [X0: $int] :
( $less($sum(2,X0),sK2)
| $less(-1,$sum(1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
tff(f4583,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| $less(-1,$sum(1,X0)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4499,f9]) ).
tff(f4499,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| $less(-1,$sum(1,X0)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4445]) ).
tff(f4445,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(X0,1),1),sK2)
| $less(-1,$sum(1,X0)) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1679]) ).
tff(f1679,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| $less(-1,$sum(1,X0)) )
| ~ spl3_13 ),
inference(resolution,[],[f1149,f88]) ).
tff(f4582,plain,
( spl3_33
| spl3_14
| ~ spl3_7
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f4578,f3617,f128,f365,f4580]) ).
tff(f4578,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(2,X0),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(forward_demodulation,[],[f4500,f9]) ).
tff(f4500,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(2,X0),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(evaluation,[],[f4444]) ).
tff(f4444,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum($sum(X0,1),1),sK2)
| ~ $less(X0,0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(resolution,[],[f326,f3668]) ).
tff(f3668,plain,
( ! [X0: $int] :
( $less($sum(X0,1),sK2)
| ~ $less(X0,0) )
| ~ spl3_21 ),
inference(resolution,[],[f3618,f20]) ).
tff(f4577,plain,
( spl3_14
| spl3_1
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4576,f358,f128,f51,f365]) ).
tff(f4576,plain,
( $less(-1,$sum(1,sK2))
| spl3_1
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4575,f9]) ).
tff(f4575,plain,
( $less(-1,$sum(sK2,1))
| spl3_1
| ~ spl3_7
| ~ spl3_13 ),
inference(subsumption_resolution,[],[f4502,f53]) ).
tff(f4502,plain,
( $less(-1,$sum(sK2,1))
| $less(2,sK2)
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4435]) ).
tff(f4435,plain,
( $less(-1,$sum(sK2,1))
| $less($sum(1,1),sK2)
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f360]) ).
tff(f4574,plain,
( spl3_32
| spl3_14
| ~ spl3_7
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f4570,f3617,f128,f365,f4572]) ).
tff(f4572,plain,
( spl3_32
<=> ! [X0: $int] :
( $less($sum(X0,1),sK2)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
tff(f4570,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(0,X0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(forward_demodulation,[],[f4420,f9]) ).
tff(f4420,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(0,X0) )
| ~ spl3_7
| ~ spl3_21 ),
inference(resolution,[],[f326,f3618]) ).
tff(f4569,plain,
( spl3_31
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4565,f358,f128,f365,f4567]) ).
tff(f4567,plain,
( spl3_31
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,1),sK2)
| ( 0 = X1 )
| $less(0,X1)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
tff(f4565,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(0,X1)
| $less(X1,X0)
| ( 0 = X1 ) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4419,f9]) ).
tff(f4419,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(0,X1)
| $less(X1,X0)
| ( 0 = X1 ) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1124]) ).
tff(f1124,plain,
( ! [X0: $int,X1: $int] :
( $less(0,X0)
| $less(X1,sK2)
| $less(X0,X1)
| ( 0 = X0 ) )
| ~ spl3_13 ),
inference(resolution,[],[f1050,f16]) ).
tff(f4564,plain,
( spl3_30
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4560,f358,f128,f365,f4562]) ).
tff(f4562,plain,
( spl3_30
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,1),sK2)
| $less(-1,X1)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
tff(f4560,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(X1,X0)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4418,f9]) ).
tff(f4418,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(X1,X0)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1121]) ).
tff(f4559,plain,
( spl3_23
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4558,f358,f128,f365,f4526]) ).
tff(f4526,plain,
( spl3_23
<=> ! [X1: $int] :
( $less($sum(X1,1),sK2)
| $less(-1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
tff(f4558,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(-1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4417,f9]) ).
tff(f4417,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(-1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f573]) ).
tff(f4557,plain,
( spl3_29
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4553,f358,f128,f365,f4555]) ).
tff(f4555,plain,
( spl3_29
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,1),sK2)
| $less(0,$sum(1,X1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
tff(f4553,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(0,$sum(1,X1))
| $less(X1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4416,f9]) ).
tff(f4416,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(0,$sum(1,X1))
| $less(X1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f549]) ).
tff(f4552,plain,
( spl3_28
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4548,f358,f128,f365,f4550]) ).
tff(f4550,plain,
( spl3_28
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,1),sK2)
| $less(0,$sum(X1,1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
tff(f4548,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(0,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4415,f9]) ).
tff(f4415,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(0,$sum(X1,1))
| $less(X1,X0) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f546]) ).
tff(f4547,plain,
( spl3_27
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4543,f358,f128,f365,f4545]) ).
tff(f4545,plain,
( spl3_27
<=> ! [X0: $int,X1: $int] :
( $less($sum(X0,1),sK2)
| ( X0 = X1 )
| $less(0,X1)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
tff(f4543,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| $less(0,X1)
| $less(X1,X0)
| ( X0 = X1 ) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4414,f9]) ).
tff(f4414,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| $less(0,X1)
| $less(X1,X0)
| ( X0 = X1 ) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f538]) ).
tff(f538,plain,
( ! [X0: $int,X1: $int] :
( $less(0,X1)
| $less(X0,sK2)
| $less(X1,X0)
| ( X0 = X1 ) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f16]) ).
tff(f4542,plain,
( spl3_26
| spl3_14
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4538,f358,f128,f365,f4540]) ).
tff(f4540,plain,
( spl3_26
<=> ! [X0: $int] :
( $less($sum(X0,1),sK2)
| ~ $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
tff(f4538,plain,
( ! [X0: $int] :
( $less(-1,$sum(1,sK2))
| $less($sum(X0,1),sK2)
| ~ $less(X0,1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(forward_demodulation,[],[f4413,f9]) ).
tff(f4413,plain,
( ! [X0: $int] :
( $less(-1,$sum(sK2,1))
| $less($sum(X0,1),sK2)
| ~ $less(X0,1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f370]) ).
tff(f4537,plain,
( spl3_23
| spl3_25
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4518,f358,f128,f4533,f4526]) ).
tff(f4533,plain,
( spl3_25
<=> ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
tff(f4518,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(X1,1),sK2)
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4407]) ).
tff(f4407,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum($sum(1,X0),1))
| $less($sum(X1,1),sK2)
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1528]) ).
tff(f1528,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_13 ),
inference(resolution,[],[f638,f87]) ).
tff(f638,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
| $less(X0,sK2)
| $less(X1,$sum(1,X0)) )
| ~ spl3_13 ),
inference(resolution,[],[f548,f15]) ).
tff(f4536,plain,
( spl3_23
| spl3_24
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4519,f474,f358,f128,f4529,f4526]) ).
tff(f4529,plain,
( spl3_24
<=> ! [X0: $int] :
( $less(-1,$sum(2,X0))
| $less(X0,2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
tff(f4519,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(X1,1),sK2)
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(evaluation,[],[f4406]) ).
tff(f4406,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum($sum(1,X0),1))
| $less($sum(X1,1),sK2)
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f326,f3112]) ).
tff(f3112,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f806,f87]) ).
tff(f806,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
| $less(X0,2)
| $less(X1,$sum(1,X0)) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f755,f15]) ).
tff(f755,plain,
( ! [X0: $int] :
( $less(0,$sum(1,X0))
| $less(X0,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f707,f88]) ).
tff(f4535,plain,
( spl3_23
| spl3_25
| ~ spl3_7
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f4523,f358,f128,f4533,f4526]) ).
tff(f4523,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(X1,1),sK2)
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(evaluation,[],[f4402]) ).
tff(f4402,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum($sum(X0,1),1))
| $less($sum(X1,1),sK2)
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13 ),
inference(resolution,[],[f326,f1508]) ).
tff(f1508,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,sK2)
| $less(-1,X1) )
| ~ spl3_13 ),
inference(resolution,[],[f628,f87]) ).
tff(f628,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
| $less(X0,sK2)
| $less(X1,$sum(X0,1)) )
| ~ spl3_13 ),
inference(resolution,[],[f547,f15]) ).
tff(f547,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,sK2) )
| ~ spl3_13 ),
inference(resolution,[],[f410,f83]) ).
tff(f4531,plain,
( spl3_23
| spl3_24
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4524,f474,f358,f128,f4529,f4526]) ).
tff(f4524,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum(2,X0))
| $less($sum(X1,1),sK2)
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(evaluation,[],[f4401]) ).
tff(f4401,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,$sum($sum(X0,1),1))
| $less($sum(X1,1),sK2)
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_7
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f326,f3084]) ).
tff(f3084,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,2)
| $less(-1,X1) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f796,f87]) ).
tff(f796,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
| $less(X0,2)
| $less(X1,$sum(X0,1)) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f754,f15]) ).
tff(f754,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,1))
| $less(X0,2) )
| ~ spl3_13
| ~ spl3_16 ),
inference(resolution,[],[f707,f83]) ).
tff(f3622,plain,
( spl3_21
| spl3_22
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f3575,f358,f3620,f3617]) ).
tff(f3575,plain,
( ! [X0: $int,X1: $int] :
( $less(-1,X0)
| $less(X1,sK2)
| $less(0,X1)
| $less(X0,1) )
| ~ spl3_13 ),
inference(resolution,[],[f1141,f135]) ).
tff(f1141,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X1)
| $less(-1,X1)
| $less(X0,sK2)
| $less(X2,X0) )
| ~ spl3_13 ),
inference(resolution,[],[f1121,f15]) ).
tff(f2053,plain,
( ( 1 != sK2 )
| ~ in(sK2,sK0)
| in(1,sK0) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f2052,plain,
( spl3_20
| spl3_18
| spl3_8
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f2048,f474,f164,f2039,f2050]) ).
tff(f2048,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less($sum(1,X0),2)
| ~ $less(X0,0) )
| spl3_8
| ~ spl3_16 ),
inference(subsumption_resolution,[],[f2011,f166]) ).
tff(f2011,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less(sK2,1)
| $less($sum(1,X0),2)
| ~ $less(X0,0) )
| ~ spl3_16 ),
inference(resolution,[],[f522,f149]) ).
tff(f149,plain,
! [X0: $int] :
( $less($sum(1,X0),1)
| ~ $less(X0,0) ),
inference(resolution,[],[f101,f135]) ).
tff(f2047,plain,
( spl3_19
| spl3_18
| spl3_8
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f2043,f474,f164,f2039,f2045]) ).
tff(f2045,plain,
( spl3_19
<=> ! [X0: $int] :
( $less($sum(X0,1),2)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
tff(f2043,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less($sum(X0,1),2)
| ~ $less(X0,0) )
| spl3_8
| ~ spl3_16 ),
inference(subsumption_resolution,[],[f2005,f166]) ).
tff(f2005,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less(sK2,1)
| $less($sum(X0,1),2)
| ~ $less(X0,0) )
| ~ spl3_16 ),
inference(resolution,[],[f522,f143]) ).
tff(f143,plain,
! [X0: $int] :
( $less($sum(X0,1),1)
| ~ $less(X0,0) ),
inference(resolution,[],[f135,f20]) ).
tff(f2042,plain,
( spl3_17
| spl3_18
| spl3_8
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f2034,f474,f164,f2039,f2036]) ).
tff(f2036,plain,
( spl3_17
<=> ! [X0: $int] :
( $less(X0,2)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
tff(f2034,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less(X0,2)
| $less(0,X0) )
| spl3_8
| ~ spl3_16 ),
inference(subsumption_resolution,[],[f1970,f166]) ).
tff(f1970,plain,
( ! [X0: $int] :
( ( 1 = sK2 )
| $less(sK2,1)
| $less(X0,2)
| $less(0,X0) )
| ~ spl3_16 ),
inference(resolution,[],[f522,f135]) ).
tff(f479,plain,
( ( 2 != sK2 )
| ~ in(sK2,sK0)
| in(2,sK0) ),
introduced(theory_tautology_sat_conflict,[]) ).
tff(f478,plain,
( spl3_15
| spl3_16
| spl3_1 ),
inference(avatar_split_clause,[],[f456,f51,f474,f470]) ).
tff(f456,plain,
( $less(sK2,2)
| ( 2 = sK2 )
| spl3_1 ),
inference(resolution,[],[f16,f53]) ).
tff(f477,plain,
( spl3_15
| spl3_16
| spl3_1 ),
inference(avatar_split_clause,[],[f431,f51,f474,f470]) ).
tff(f431,plain,
( $less(sK2,2)
| ( 2 = sK2 )
| spl3_1 ),
inference(resolution,[],[f16,f53]) ).
tff(f368,plain,
( spl3_13
| spl3_14
| ~ spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f363,f164,f128,f365,f358]) ).
tff(f363,plain,
( $less(-1,$sum(1,sK2))
| $less(1,sK2)
| ~ spl3_7
| spl3_8 ),
inference(forward_demodulation,[],[f339,f9]) ).
tff(f339,plain,
( $less(1,sK2)
| $less(-1,$sum(sK2,1))
| ~ spl3_7
| spl3_8 ),
inference(resolution,[],[f260,f166]) ).
tff(f362,plain,
( spl3_12
| spl3_13
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f348,f128,f358,f355]) ).
tff(f348,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(2,X0))
| $less(X0,0) )
| ~ spl3_7 ),
inference(evaluation,[],[f338]) ).
tff(f338,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum($sum(1,X0),1))
| $less(X0,0) )
| ~ spl3_7 ),
inference(resolution,[],[f260,f160]) ).
tff(f361,plain,
( spl3_12
| spl3_13
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f349,f128,f358,f355]) ).
tff(f349,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum(2,X0))
| $less(X0,0) )
| ~ spl3_7 ),
inference(evaluation,[],[f337]) ).
tff(f337,plain,
( ! [X0: $int] :
( $less(1,sK2)
| $less(-1,$sum($sum(X0,1),1))
| $less(X0,0) )
| ~ spl3_7 ),
inference(resolution,[],[f260,f157]) ).
tff(f251,plain,
( ~ spl3_11
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f242,f236,f248]) ).
tff(f248,plain,
( spl3_11
<=> $less(sK2,-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
tff(f242,plain,
( ~ $less(sK2,-1)
| ~ spl3_10 ),
inference(resolution,[],[f241,f14]) ).
tff(f239,plain,
( spl3_10
| spl3_9 ),
inference(avatar_split_clause,[],[f234,f229,f236]) ).
tff(f234,plain,
( $less(-1,sK2)
| spl3_9 ),
inference(resolution,[],[f231,f87]) ).
tff(f233,plain,
( ~ spl3_9
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f227,f128,f229]) ).
tff(f227,plain,
( ~ $less(sK2,0)
| ~ spl3_7 ),
inference(evaluation,[],[f226]) ).
tff(f226,plain,
( ~ $less(-1,0)
| ~ $less(sK2,0)
| ~ spl3_7 ),
inference(resolution,[],[f215,f104]) ).
tff(f232,plain,
( ~ spl3_9
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f222,f128,f229]) ).
tff(f222,plain,
( ~ $less(sK2,0)
| ~ spl3_7 ),
inference(resolution,[],[f215,f14]) ).
tff(f167,plain,
( ~ spl3_8
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f155,f128,f164]) ).
tff(f155,plain,
( ~ $less(sK2,1)
| ~ spl3_7 ),
inference(resolution,[],[f150,f130]) ).
tff(f131,plain,
( spl3_7
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f126,f61,f56,f128]) ).
tff(f61,plain,
( spl3_3
<=> ( sK0 = remove(4,remove(1,remove(2,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
tff(f126,plain,
( $less(0,sK2)
| ~ spl3_2
| ~ spl3_3 ),
inference(resolution,[],[f125,f58]) ).
tff(f125,plain,
( ! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,X0) )
| ~ spl3_3 ),
inference(resolution,[],[f119,f35]) ).
tff(f35,plain,
! [X3: $int] :
( ~ in(X3,sK1)
| $less(0,X3) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
( ~ $less(2,sK2)
& in(sK2,sK0)
& ( sK0 = remove(4,remove(1,remove(2,sK1))) )
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28]) ).
tff(f28,plain,
( ? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(2,X2)
& in(X2,X0) )
& ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,X1) ) )
=> ( ? [X2: $int] :
( ~ $less(2,X2)
& in(X2,sK0) )
& ( sK0 = remove(4,remove(1,remove(2,sK1))) )
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
( ? [X2: $int] :
( ~ $less(2,X2)
& in(X2,sK0) )
=> ( ~ $less(2,sK2)
& in(sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(2,X2)
& in(X2,X0) )
& ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,X1) ) ),
inference(rectify,[],[f26]) ).
tff(f26,plain,
? [X0: collection,X1: collection] :
( ? [X3: $int] :
( ~ $less(2,X3)
& in(X3,X0) )
& ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) ) ),
inference(flattening,[],[f25]) ).
tff(f25,plain,
? [X0: collection,X1: collection] :
( ? [X3: $int] :
( ~ $less(2,X3)
& in(X3,X0) )
& ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection] :
( ( ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $less(2,X3) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection] :
( ( ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greater(X3,2) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X0: collection,X1: collection] :
( ( ( remove(4,remove(1,remove(2,X1))) = X0 )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greater(X3,2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f119,plain,
( ! [X0: $int] :
( in(X0,sK1)
| ~ in(X0,sK0) )
| ~ spl3_3 ),
inference(resolution,[],[f112,f43]) ).
tff(f43,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f112,plain,
( ! [X0: $int] :
( in(X0,remove(2,sK1))
| ~ in(X0,sK0) )
| ~ spl3_3 ),
inference(resolution,[],[f110,f43]) ).
tff(f110,plain,
( ! [X0: $int] :
( in(X0,remove(1,remove(2,sK1)))
| ~ in(X0,sK0) )
| ~ spl3_3 ),
inference(superposition,[],[f43,f63]) ).
tff(f63,plain,
( ( sK0 = remove(4,remove(1,remove(2,sK1))) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f124,plain,
( ~ spl3_6
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f118,f61,f121]) ).
tff(f121,plain,
( spl3_6
<=> in(2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
tff(f118,plain,
( ~ in(2,sK0)
| ~ spl3_3 ),
inference(resolution,[],[f112,f40]) ).
tff(f40,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f117,plain,
( ~ spl3_5
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f111,f61,f114]) ).
tff(f114,plain,
( spl3_5
<=> in(1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
tff(f111,plain,
( ~ in(1,sK0)
| ~ spl3_3 ),
inference(resolution,[],[f110,f40]) ).
tff(f70,plain,
( ~ spl3_4
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f65,f61,f67]) ).
tff(f67,plain,
( spl3_4
<=> in(4,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
tff(f65,plain,
( ~ in(4,sK0)
| ~ spl3_3 ),
inference(superposition,[],[f40,f63]) ).
tff(f64,plain,
spl3_3,
inference(avatar_split_clause,[],[f36,f61]) ).
tff(f36,plain,
sK0 = remove(4,remove(1,remove(2,sK1))),
inference(cnf_transformation,[],[f30]) ).
tff(f59,plain,
spl3_2,
inference(avatar_split_clause,[],[f37,f56]) ).
tff(f37,plain,
in(sK2,sK0),
inference(cnf_transformation,[],[f30]) ).
tff(f54,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f38,f51]) ).
tff(f38,plain,
~ $less(2,sK2),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.16 % Problem : DAT023_1 : TPTP v8.2.0. Released v5.0.0.
% 0.17/0.19 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.19/0.41 % Computer : n013.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8042.1875MB
% 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Sun May 19 23:43:08 EDT 2024
% 0.19/0.42 % CPUTime :
% 0.19/0.42 % (7059)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.44 % (7061)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.44 % (7065)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)
% 0.19/0.44 % (7062)WARNING: value z3 for option sas not known
% 0.19/0.44 % (7064)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)
% 0.19/0.44 % (7061)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.44 % (7061)Terminated due to inappropriate strategy.
% 0.19/0.44 % (7061)------------------------------
% 0.19/0.44 % (7061)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.44 % (7061)Termination reason: Inappropriate
% 0.19/0.44
% 0.19/0.44 % (7061)Memory used [KB]: 746
% 0.19/0.44 % (7061)Time elapsed: 0.002 s
% 0.19/0.44 % (7061)Instructions burned: 2 (million)
% 0.19/0.44 % (7063)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.44 % (7061)------------------------------
% 0.19/0.44 % (7061)------------------------------
% 0.19/0.44 % (7062)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)
% 0.19/0.44 % (7063)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.44 % (7063)Terminated due to inappropriate strategy.
% 0.19/0.44 % (7063)------------------------------
% 0.19/0.44 % (7063)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.44 % (7063)Termination reason: Inappropriate
% 0.19/0.44
% 0.19/0.44 % (7063)Memory used [KB]: 746
% 0.19/0.44 % (7063)Time elapsed: 0.003 s
% 0.19/0.44 % (7063)Instructions burned: 2 (million)
% 0.19/0.44 % (7063)------------------------------
% 0.19/0.44 % (7063)------------------------------
% 0.19/0.44 % (7060)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.44 % (7060)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.44 % (7060)Terminated due to inappropriate strategy.
% 0.19/0.44 % (7060)------------------------------
% 0.19/0.44 % (7060)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.44 % (7060)Termination reason: Inappropriate
% 0.19/0.44
% 0.19/0.44 % (7060)Memory used [KB]: 746
% 0.19/0.44 % (7060)Time elapsed: 0.003 s
% 0.19/0.44 % (7060)Instructions burned: 2 (million)
% 0.19/0.44 % (7060)------------------------------
% 0.19/0.44 % (7060)------------------------------
% 0.19/0.45 % (7066)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)
% 0.19/0.46 % (7067)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.46 % (7067)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.46 % (7067)Terminated due to inappropriate strategy.
% 0.19/0.46 % (7067)------------------------------
% 0.19/0.46 % (7067)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.46 % (7067)Termination reason: Inappropriate
% 0.19/0.46
% 0.19/0.46 % (7067)Memory used [KB]: 745
% 0.19/0.46 % (7067)Time elapsed: 0.003 s
% 0.19/0.46 % (7067)Instructions burned: 2 (million)
% 0.19/0.46 % (7067)------------------------------
% 0.19/0.46 % (7067)------------------------------
% 0.19/0.46 % (7068)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)
% 0.19/0.46 % (7069)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)
% 0.28/0.48 % (7070)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)
% 13.23/2.29 % (7070)First to succeed.
% 13.23/2.30 % (7070)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7059"
% 13.23/2.30 % (7070)Refutation found. Thanks to Tanya!
% 13.23/2.30 % SZS status Theorem for theBenchmark
% 13.23/2.30 % SZS output start Proof for theBenchmark
% See solution above
% 13.23/2.31 % (7070)------------------------------
% 13.23/2.31 % (7070)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 13.23/2.31 % (7070)Termination reason: Refutation
% 13.23/2.31
% 13.23/2.31 % (7070)Memory used [KB]: 9679
% 13.23/2.31 % (7070)Time elapsed: 1.824 s
% 13.23/2.31 % (7070)Instructions burned: 3613 (million)
% 13.23/2.31 % (7059)Success in time 1.874 s
%------------------------------------------------------------------------------