TSTP Solution File: DAT097_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:06:01 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 157
% Syntax : Number of formulae : 456 ( 73 unt; 18 typ; 0 def)
% Number of atoms : 1342 ( 331 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1493 ( 589 ~; 699 |; 75 &)
% ( 119 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 1152 ( 198 atm; 255 fun; 166 num; 533 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 29 ( 16 >; 13 *; 0 +; 0 <<)
% Number of predicates : 116 ( 111 usr; 108 prp; 0-2 aty)
% Number of functors : 18 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 851 ( 807 !; 44 ?; 851 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_11,type,
sK2: ( $int * list ) > $int ).
tff(func_def_12,type,
sK3: ( $int * list ) > list ).
tff(func_def_13,type,
sK4: ( $int * list ) > $int ).
tff(func_def_14,type,
sK5: ( $int * list ) > list ).
tff(func_def_15,type,
sK6: ( $int * list ) > $int ).
tff(func_def_16,type,
sK7: ( $int * list ) > list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(pred_def_6,type,
sP0: ( $int * list ) > $o ).
tff(pred_def_7,type,
sP1: ( $int * list ) > $o ).
tff(f1571,plain,
$false,
inference(avatar_sat_refutation,[],[f105,f109,f114,f118,f122,f126,f130,f134,f138,f142,f146,f150,f154,f158,f162,f166,f170,f176,f180,f184,f188,f192,f196,f200,f213,f217,f221,f235,f239,f243,f257,f278,f282,f286,f290,f294,f298,f322,f338,f347,f354,f370,f376,f380,f389,f400,f404,f410,f414,f418,f435,f443,f450,f454,f458,f462,f508,f512,f516,f520,f543,f547,f551,f555,f559,f569,f636,f640,f644,f648,f652,f656,f809,f813,f817,f821,f903,f907,f911,f915,f919,f923,f927,f931,f1035,f1039,f1052,f1056,f1215,f1219,f1223,f1227,f1231,f1288,f1292,f1310,f1355,f1359,f1384,f1396,f1420,f1454,f1458,f1467,f1491,f1527,f1536,f1569]) ).
tff(f1569,plain,
( ~ spl8_7
| ~ spl8_37
| ~ spl8_102 ),
inference(avatar_contradiction_clause,[],[f1568]) ).
tff(f1568,plain,
( $false
| ~ spl8_7
| ~ spl8_37
| ~ spl8_102 ),
inference(evaluation,[],[f1567]) ).
tff(f1567,plain,
( ( 1 = $sum(2,0) )
| ~ spl8_7
| ~ spl8_37
| ~ spl8_102 ),
inference(forward_demodulation,[],[f1566,f129]) ).
tff(f129,plain,
( ! [X0: $int] : ( 0 = count(X0,nil) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f128]) ).
tff(f128,plain,
( spl8_7
<=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f1566,plain,
( ! [X0: $int] : ( 1 = $sum(2,count(X0,nil)) )
| ~ spl8_37
| ~ spl8_102 ),
inference(evaluation,[],[f1542]) ).
tff(f1542,plain,
( ! [X0: $int] : ( 1 = $sum(1,$sum(1,count(X0,nil))) )
| ~ spl8_37
| ~ spl8_102 ),
inference(superposition,[],[f1453,f297]) ).
tff(f297,plain,
( ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) )
| ~ spl8_37 ),
inference(avatar_component_clause,[],[f296]) ).
tff(f296,plain,
( spl8_37
<=> ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
tff(f1453,plain,
( ! [X0: $int,X1: $int] : ( 1 = $sum(1,count(X1,cons(X0,nil))) )
| ~ spl8_102 ),
inference(avatar_component_clause,[],[f1452]) ).
tff(f1452,plain,
( spl8_102
<=> ! [X0: $int,X1: $int] : ( 1 = $sum(1,count(X1,cons(X0,nil))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
tff(f1536,plain,
( spl8_107
| ~ spl8_4
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f482,f452,f116,f1534]) ).
tff(f1534,plain,
( spl8_107
<=> ! [X4: $int,X0: $int,X3: list,X2: $int,X1: list] :
( ~ in(X0,X1)
| in(X2,X3)
| ( count(X0,cons(X4,X1)) = count(X0,append(cons(X4,X1),cons(X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
tff(f116,plain,
( spl8_4
<=> ! [X0: $int,X3: list,X2: list,X1: $int] :
( ( count(X1,X3) = count(X1,append(X3,cons(X0,X2))) )
| in(X0,X2)
| ~ in(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f452,plain,
( spl8_54
<=> ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
tff(f482,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list,X4: $int] :
( ~ in(X0,X1)
| in(X2,X3)
| ( count(X0,cons(X4,X1)) = count(X0,append(cons(X4,X1),cons(X2,X3))) ) )
| ~ spl8_4
| ~ spl8_54 ),
inference(resolution,[],[f453,f117]) ).
tff(f117,plain,
( ! [X2: list,X3: list,X0: $int,X1: $int] :
( ~ in(X1,X3)
| in(X0,X2)
| ( count(X1,X3) = count(X1,append(X3,cons(X0,X2))) ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f453,plain,
( ! [X2: $int,X0: $int,X1: list] :
( in(X0,cons(X2,X1))
| ~ in(X0,X1) )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f452]) ).
tff(f1527,plain,
( spl8_106
| ~ spl8_24
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f391,f387,f198,f1525]) ).
tff(f1525,plain,
( spl8_106
<=> ! [X2: list,X0: $int,X1: $int] :
( ( cons(X1,X2) = cons(sK6(X0,cons(X1,X2)),sK7(X0,cons(X1,X2))) )
| ( cons(X1,X2) = cons(sK4(X0,cons(X1,X2)),sK5(X0,cons(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
tff(f198,plain,
( spl8_24
<=> ! [X2: $int,X0: $int,X3: list] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
tff(f387,plain,
( spl8_45
<=> ! [X0: $int,X1: list] :
( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
tff(f391,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ( cons(X1,X2) = cons(sK6(X0,cons(X1,X2)),sK7(X0,cons(X1,X2))) )
| ( cons(X1,X2) = cons(sK4(X0,cons(X1,X2)),sK5(X0,cons(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl8_24
| ~ spl8_45 ),
inference(resolution,[],[f388,f199]) ).
tff(f199,plain,
( ! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f198]) ).
tff(f388,plain,
( ! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f387]) ).
tff(f1491,plain,
( spl8_105
| ~ spl8_10
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f390,f387,f140,f1489]) ).
tff(f1489,plain,
( spl8_105
<=> ! [X0: $int,X1: list] :
( ( cons(X0,X1) = cons(sK6(X0,cons(X0,X1)),sK7(X0,cons(X0,X1))) )
| ( cons(X0,X1) = cons(sK4(X0,cons(X0,X1)),sK5(X0,cons(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
tff(f140,plain,
( spl8_10
<=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
tff(f390,plain,
( ! [X0: $int,X1: list] :
( ( cons(X0,X1) = cons(sK6(X0,cons(X0,X1)),sK7(X0,cons(X0,X1))) )
| ( cons(X0,X1) = cons(sK4(X0,cons(X0,X1)),sK5(X0,cons(X0,X1))) ) )
| ~ spl8_10
| ~ spl8_45 ),
inference(resolution,[],[f388,f141]) ).
tff(f141,plain,
( ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5))
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f140]) ).
tff(f1467,plain,
( spl8_104
| ~ spl8_41
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f372,f368,f352,f1465]) ).
tff(f1465,plain,
( spl8_104
<=> ! [X2: $int,X0: $int,X1: list] :
( ( cons(X0,X1) = nil )
| ( cons(X0,X1) = cons(sK2(X2,cons(X0,X1)),sK3(X2,cons(X0,X1))) )
| ~ inRange(X2,X1)
| ~ $less(X0,X2)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
tff(f352,plain,
( spl8_41
<=> ! [X2: $int,X0: $int,X3: list] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
tff(f368,plain,
( spl8_42
<=> ! [X0: $int,X1: list] :
( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
tff(f372,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( cons(X0,X1) = nil )
| ( cons(X0,X1) = cons(sK2(X2,cons(X0,X1)),sK3(X2,cons(X0,X1))) )
| ~ inRange(X2,X1)
| ~ $less(X0,X2)
| $less(X0,0) )
| ~ spl8_41
| ~ spl8_42 ),
inference(resolution,[],[f369,f353]) ).
tff(f353,plain,
( ! [X2: $int,X3: list,X0: $int] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) )
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f352]) ).
tff(f369,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f368]) ).
tff(f1458,plain,
( spl8_103
| ~ spl8_24
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f382,f374,f198,f1456]) ).
tff(f1456,plain,
( spl8_103
<=> ! [X2: list,X0: $int,X1: $int] :
( ( sK6(X0,cons(X1,X2)) = X0 )
| ( cons(X1,X2) = cons(sK4(X0,cons(X1,X2)),sK5(X0,cons(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
tff(f374,plain,
( spl8_43
<=> ! [X0: $int,X1: list] :
( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
tff(f382,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ( sK6(X0,cons(X1,X2)) = X0 )
| ( cons(X1,X2) = cons(sK4(X0,cons(X1,X2)),sK5(X0,cons(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl8_24
| ~ spl8_43 ),
inference(resolution,[],[f375,f199]) ).
tff(f375,plain,
( ! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| ( sK6(X0,X1) = X0 )
| ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f374]) ).
tff(f1454,plain,
( spl8_102
| ~ spl8_7
| ~ spl8_8
| ~ spl8_93 ),
inference(avatar_split_clause,[],[f1345,f1229,f132,f128,f1452]) ).
tff(f132,plain,
( spl8_8
<=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f1229,plain,
( spl8_93
<=> ! [X2: list,X0: $int,X1: $int] : ( $sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
tff(f1345,plain,
( ! [X0: $int,X1: $int] : ( 1 = $sum(1,count(X1,cons(X0,nil))) )
| ~ spl8_7
| ~ spl8_8
| ~ spl8_93 ),
inference(evaluation,[],[f1344]) ).
tff(f1344,plain,
( ! [X0: $int,X1: $int] : ( $sum(1,count(X1,cons(X0,nil))) = $sum(1,0) )
| ~ spl8_7
| ~ spl8_8
| ~ spl8_93 ),
inference(forward_demodulation,[],[f1317,f129]) ).
tff(f1317,plain,
( ! [X0: $int,X1: $int] : ( $sum(1,count(X1,nil)) = $sum(1,count(X1,cons(X0,nil))) )
| ~ spl8_8
| ~ spl8_93 ),
inference(superposition,[],[f1230,f133]) ).
tff(f133,plain,
( ! [X0: list] : ( append(nil,X0) = X0 )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f132]) ).
tff(f1230,plain,
( ! [X2: list,X0: $int,X1: $int] : ( $sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil)))) )
| ~ spl8_93 ),
inference(avatar_component_clause,[],[f1229]) ).
tff(f1420,plain,
( spl8_101
| ~ spl8_10
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f381,f374,f140,f1418]) ).
tff(f1418,plain,
( spl8_101
<=> ! [X0: $int,X1: list] :
( ( sK6(X0,cons(X0,X1)) = X0 )
| ( cons(X0,X1) = cons(sK4(X0,cons(X0,X1)),sK5(X0,cons(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
tff(f381,plain,
( ! [X0: $int,X1: list] :
( ( sK6(X0,cons(X0,X1)) = X0 )
| ( cons(X0,X1) = cons(sK4(X0,cons(X0,X1)),sK5(X0,cons(X0,X1))) ) )
| ~ spl8_10
| ~ spl8_43 ),
inference(resolution,[],[f375,f141]) ).
tff(f1396,plain,
( spl8_100
| ~ spl8_34
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f355,f352,f284,f1394]) ).
tff(f1394,plain,
( spl8_100
<=> ! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| ( nil = cons(X2,X1) )
| $less(sK2(X0,cons(X2,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
tff(f284,plain,
( spl8_34
<=> ! [X0: $int,X1: list] :
( $less(sK2(X0,X1),X0)
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
tff(f355,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| ( nil = cons(X2,X1) )
| $less(sK2(X0,cons(X2,X1)),X0) )
| ~ spl8_34
| ~ spl8_41 ),
inference(resolution,[],[f353,f285]) ).
tff(f285,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| $less(sK2(X0,X1),X0) )
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f284]) ).
tff(f1384,plain,
( spl8_99
| ~ spl8_22
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f383,f378,f190,f1382]) ).
tff(f1382,plain,
( spl8_99
<=> ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| $less(0,count(X0,sK5(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
tff(f190,plain,
( spl8_22
<=> ! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
tff(f378,plain,
( spl8_44
<=> ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
tff(f383,plain,
( ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| $less(0,count(X0,sK5(X0,X1))) )
| ~ spl8_22
| ~ spl8_44 ),
inference(resolution,[],[f379,f191]) ).
tff(f191,plain,
( ! [X0: $int,X1: list] :
( ~ in(X0,X1)
| $less(0,count(X0,X1)) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f379,plain,
( ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f378]) ).
tff(f1359,plain,
( spl8_98
| ~ spl8_36
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f358,f352,f292,f1357]) ).
tff(f1357,plain,
( spl8_98
<=> ! [X0: $int,X3: $int,X2: list,X1: list] :
( sP0(X3,append(cons(X0,X1),X2))
| ~ inRange(X3,append(X1,X2))
| ~ $less(X0,X3)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
tff(f292,plain,
( spl8_36
<=> ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
tff(f358,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( sP0(X3,append(cons(X0,X1),X2))
| ~ inRange(X3,append(X1,X2))
| ~ $less(X0,X3)
| $less(X0,0) )
| ~ spl8_36
| ~ spl8_41 ),
inference(superposition,[],[f353,f293]) ).
tff(f293,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) )
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f292]) ).
tff(f1355,plain,
( spl8_97
| ~ spl8_30
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f357,f352,f241,f1353]) ).
tff(f1353,plain,
( spl8_97
<=> ! [X0: list,X1: $int] :
( sP0(X1,X0)
| ~ inRange(X1,tail(X0))
| ~ $less(head(X0),X1)
| $less(head(X0),0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
tff(f241,plain,
( spl8_30
<=> ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
tff(f357,plain,
( ! [X0: list,X1: $int] :
( sP0(X1,X0)
| ~ inRange(X1,tail(X0))
| ~ $less(head(X0),X1)
| $less(head(X0),0)
| ( nil = X0 ) )
| ~ spl8_30
| ~ spl8_41 ),
inference(superposition,[],[f353,f242]) ).
tff(f242,plain,
( ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f241]) ).
tff(f1310,plain,
( spl8_96
| ~ spl8_16
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f384,f378,f164,f1308]) ).
tff(f1308,plain,
( spl8_96
<=> ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
tff(f164,plain,
( spl8_16
<=> ! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f384,plain,
( ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) )
| ~ spl8_16
| ~ spl8_44 ),
inference(resolution,[],[f379,f165]) ).
tff(f165,plain,
( ! [X0: $int,X1: list] :
( ~ in(X0,X1)
| sP1(X0,X1) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f164]) ).
tff(f1292,plain,
( spl8_95
| ~ spl8_36
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f340,f336,f292,f1290]) ).
tff(f1290,plain,
( spl8_95
<=> ! [X0: $int,X3: $int,X2: list,X1: list] :
( ( count(X3,append(X1,X2)) = count(X3,append(cons(X0,X1),X2)) )
| ( X0 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
tff(f336,plain,
( spl8_39
<=> ! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
tff(f340,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( ( count(X3,append(X1,X2)) = count(X3,append(cons(X0,X1),X2)) )
| ( X0 = X3 ) )
| ~ spl8_36
| ~ spl8_39 ),
inference(superposition,[],[f337,f293]) ).
tff(f337,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f336]) ).
tff(f1288,plain,
( spl8_94
| ~ spl8_26
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f317,f280,f215,f1286]) ).
tff(f1286,plain,
( spl8_94
<=> ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| $less(0,sK2(X1,X0))
| ( 0 = sK2(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
tff(f215,plain,
( spl8_26
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
tff(f280,plain,
( spl8_33
<=> ! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
tff(f317,plain,
( ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| $less(0,sK2(X1,X0))
| ( 0 = sK2(X1,X0) ) )
| ~ spl8_26
| ~ spl8_33 ),
inference(resolution,[],[f281,f216]) ).
tff(f216,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f215]) ).
tff(f281,plain,
( ! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f280]) ).
tff(f1231,plain,
( spl8_93
| ~ spl8_7
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f1048,f925,f128,f1229]) ).
tff(f925,plain,
( spl8_83
<=> ! [X0: $int,X3: list,X2: $int,X1: list] :
( ( $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) )
| $less(0,count(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
tff(f1048,plain,
( ! [X2: list,X0: $int,X1: $int] : ( $sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil)))) )
| ~ spl8_7
| ~ spl8_83 ),
inference(evaluation,[],[f1045]) ).
tff(f1045,plain,
( ! [X2: list,X0: $int,X1: $int] :
( $less(0,0)
| ( $sum(1,count(X1,X2)) = $sum(1,count(X1,append(X2,cons(X0,nil)))) ) )
| ~ spl8_7
| ~ spl8_83 ),
inference(superposition,[],[f926,f129]) ).
tff(f926,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( $less(0,count(X2,X3))
| ( $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) ) )
| ~ spl8_83 ),
inference(avatar_component_clause,[],[f925]) ).
tff(f1227,plain,
( spl8_92
| ~ spl8_22
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f348,f345,f190,f1225]) ).
tff(f1225,plain,
( spl8_92
<=> ! [X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| $less(0,count(X0,sK5(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
tff(f345,plain,
( spl8_40
<=> ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
tff(f348,plain,
( ! [X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| $less(0,count(X0,sK5(X0,X1))) )
| ~ spl8_22
| ~ spl8_40 ),
inference(resolution,[],[f346,f191]) ).
tff(f346,plain,
( ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f345]) ).
tff(f1223,plain,
( spl8_91
| ~ spl8_30
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f339,f336,f241,f1221]) ).
tff(f1221,plain,
( spl8_91
<=> ! [X0: list,X1: $int] :
( ( count(X1,tail(X0)) = count(X1,X0) )
| ( head(X0) = X1 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
tff(f339,plain,
( ! [X0: list,X1: $int] :
( ( count(X1,tail(X0)) = count(X1,X0) )
| ( head(X0) = X1 )
| ( nil = X0 ) )
| ~ spl8_30
| ~ spl8_39 ),
inference(superposition,[],[f337,f242]) ).
tff(f1219,plain,
( spl8_90
| ~ spl8_36
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f333,f296,f292,f1217]) ).
tff(f1217,plain,
( spl8_90
<=> ! [X2: list,X0: $int,X1: list] : ( $sum(1,count(X0,append(X1,X2))) = count(X0,append(cons(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
tff(f333,plain,
( ! [X2: list,X0: $int,X1: list] : ( $sum(1,count(X0,append(X1,X2))) = count(X0,append(cons(X0,X1),X2)) )
| ~ spl8_36
| ~ spl8_37 ),
inference(superposition,[],[f297,f293]) ).
tff(f1215,plain,
( spl8_89
| ~ spl8_30
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f332,f296,f241,f1213]) ).
tff(f1213,plain,
( spl8_89
<=> ! [X0: list] :
( ( $sum(1,count(head(X0),tail(X0))) = count(head(X0),X0) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
tff(f332,plain,
( ! [X0: list] :
( ( $sum(1,count(head(X0),tail(X0))) = count(head(X0),X0) )
| ( nil = X0 ) )
| ~ spl8_30
| ~ spl8_37 ),
inference(superposition,[],[f297,f242]) ).
tff(f1056,plain,
( spl8_88
| ~ spl8_15
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f356,f352,f160,f1054]) ).
tff(f1054,plain,
( spl8_88
<=> ! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| inRange(X0,cons(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
tff(f160,plain,
( spl8_15
<=> ! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
tff(f356,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| inRange(X0,cons(X2,X1)) )
| ~ spl8_15
| ~ spl8_41 ),
inference(resolution,[],[f353,f161]) ).
tff(f161,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| inRange(X0,X1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f160]) ).
tff(f1052,plain,
( spl8_87
| ~ spl8_29
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f309,f276,f237,f1050]) ).
tff(f1050,plain,
( spl8_87
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
tff(f237,plain,
( spl8_29
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
tff(f276,plain,
( spl8_32
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
tff(f309,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl8_29
| ~ spl8_32 ),
inference(superposition,[],[f238,f277]) ).
tff(f277,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f276]) ).
tff(f238,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f237]) ).
tff(f1039,plain,
( spl8_86
| ~ spl8_29
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f308,f276,f237,f1037]) ).
tff(f1037,plain,
( spl8_86
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
tff(f308,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl8_29
| ~ spl8_32 ),
inference(superposition,[],[f238,f277]) ).
tff(f1035,plain,
( spl8_85
| ~ spl8_28
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f302,f276,f233,f1033]) ).
tff(f1033,plain,
( spl8_85
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
tff(f233,plain,
( spl8_28
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
tff(f302,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl8_28
| ~ spl8_32 ),
inference(superposition,[],[f277,f234]) ).
tff(f234,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl8_28 ),
inference(avatar_component_clause,[],[f233]) ).
tff(f931,plain,
( spl8_84
| ~ spl8_16
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f349,f345,f164,f929]) ).
tff(f929,plain,
( spl8_84
<=> ! [X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
tff(f349,plain,
( ! [X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) )
| ~ spl8_16
| ~ spl8_40 ),
inference(resolution,[],[f346,f165]) ).
tff(f927,plain,
( spl8_83
| ~ spl8_22
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f444,f402,f190,f925]) ).
tff(f402,plain,
( spl8_47
<=> ! [X0: $int,X3: list,X2: $int,X1: list] :
( ( $sum(1,count(X2,append(X3,cons(X0,X1)))) = $sum(1,count(X2,X3)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
tff(f444,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) )
| $less(0,count(X2,X3)) )
| ~ spl8_22
| ~ spl8_47 ),
inference(resolution,[],[f403,f191]) ).
tff(f403,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( in(X0,X1)
| ( $sum(1,count(X2,append(X3,cons(X0,X1)))) = $sum(1,count(X2,X3)) ) )
| ~ spl8_47 ),
inference(avatar_component_clause,[],[f402]) ).
tff(f923,plain,
( spl8_82
| ~ spl8_23
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f343,f336,f194,f921]) ).
tff(f921,plain,
( spl8_82
<=> ! [X2: list,X0: $int,X1: $int] :
( ~ $less(0,count(X0,X2))
| in(X0,cons(X1,X2))
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
tff(f194,plain,
( spl8_23
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
tff(f343,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ~ $less(0,count(X0,X2))
| in(X0,cons(X1,X2))
| ( X0 = X1 ) )
| ~ spl8_23
| ~ spl8_39 ),
inference(superposition,[],[f195,f337]) ).
tff(f195,plain,
( ! [X0: $int,X1: list] :
( ~ $less(0,count(X0,X1))
| in(X0,X1) )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f919,plain,
( spl8_81
| ~ spl8_27
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f326,f292,f219,f917]) ).
tff(f917,plain,
( spl8_81
<=> ! [X2: list,X0: $int,X1: list] : ( $sum(1,length(append(X1,X2))) = length(append(cons(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
tff(f219,plain,
( spl8_27
<=> ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
tff(f326,plain,
( ! [X2: list,X0: $int,X1: list] : ( $sum(1,length(append(X1,X2))) = length(append(cons(X0,X1),X2)) )
| ~ spl8_27
| ~ spl8_36 ),
inference(superposition,[],[f220,f293]) ).
tff(f220,plain,
( ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) )
| ~ spl8_27 ),
inference(avatar_component_clause,[],[f219]) ).
tff(f915,plain,
( spl8_80
| ~ spl8_28
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f268,f237,f233,f913]) ).
tff(f913,plain,
( spl8_80
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
tff(f268,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl8_28
| ~ spl8_29 ),
inference(superposition,[],[f238,f234]) ).
tff(f911,plain,
( spl8_79
| ~ spl8_28
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f264,f237,f233,f909]) ).
tff(f909,plain,
( spl8_79
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
tff(f264,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl8_28
| ~ spl8_29 ),
inference(superposition,[],[f238,f234]) ).
tff(f907,plain,
( spl8_78
| ~ spl8_25
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f260,f237,f211,f905]) ).
tff(f905,plain,
( spl8_78
<=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
tff(f211,plain,
( spl8_25
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f260,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl8_25
| ~ spl8_29 ),
inference(resolution,[],[f238,f212]) ).
tff(f212,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f211]) ).
tff(f903,plain,
( spl8_77
| ~ spl8_21
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f224,f215,f186,f901]) ).
tff(f901,plain,
( spl8_77
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
tff(f186,plain,
( spl8_21
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
tff(f224,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl8_21
| ~ spl8_26 ),
inference(resolution,[],[f216,f187]) ).
tff(f187,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f186]) ).
tff(f821,plain,
( spl8_76
| ~ spl8_24
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f327,f292,f198,f819]) ).
tff(f819,plain,
( spl8_76
<=> ! [X0: $int,X3: $int,X2: list,X1: list] :
( sP1(X3,append(cons(X0,X1),X2))
| ~ in(X3,append(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
tff(f327,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( sP1(X3,append(cons(X0,X1),X2))
| ~ in(X3,append(X1,X2)) )
| ~ spl8_24
| ~ spl8_36 ),
inference(superposition,[],[f199,f293]) ).
tff(f817,plain,
( spl8_75
| ~ spl8_20
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f313,f276,f182,f815]) ).
tff(f815,plain,
( spl8_75
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
tff(f182,plain,
( spl8_20
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f313,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl8_20
| ~ spl8_32 ),
inference(superposition,[],[f183,f277]) ).
tff(f183,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f182]) ).
tff(f813,plain,
( spl8_74
| ~ spl8_21
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f312,f276,f186,f811]) ).
tff(f811,plain,
( spl8_74
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
tff(f312,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl8_21
| ~ spl8_32 ),
inference(superposition,[],[f187,f277]) ).
tff(f809,plain,
( spl8_73
| ~ spl8_25
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f225,f215,f211,f807]) ).
tff(f807,plain,
( spl8_73
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
tff(f225,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl8_25
| ~ spl8_26 ),
inference(resolution,[],[f216,f212]) ).
tff(f656,plain,
( spl8_72
| ~ spl8_14
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f324,f288,f156,f654]) ).
tff(f654,plain,
( spl8_72
<=> ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
tff(f156,plain,
( spl8_14
<=> ! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f288,plain,
( spl8_35
<=> ! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
tff(f324,plain,
( ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) )
| ~ spl8_14
| ~ spl8_35 ),
inference(resolution,[],[f289,f157]) ).
tff(f157,plain,
( ! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| sP0(X0,X1) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f156]) ).
tff(f289,plain,
( ! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f288]) ).
tff(f652,plain,
( spl8_71
| ~ spl8_18
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f394,f320,f174,f650]) ).
tff(f650,plain,
( spl8_71
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
tff(f174,plain,
( spl8_18
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f320,plain,
( spl8_38
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
tff(f394,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl8_18
| ~ spl8_38 ),
inference(superposition,[],[f321,f175]) ).
tff(f175,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f321,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f320]) ).
tff(f648,plain,
( spl8_70
| ~ spl8_18
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f305,f276,f174,f646]) ).
tff(f646,plain,
( spl8_70
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
tff(f305,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl8_18
| ~ spl8_32 ),
inference(superposition,[],[f277,f175]) ).
tff(f644,plain,
( spl8_69
| ~ spl8_18
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f300,f276,f174,f642]) ).
tff(f642,plain,
( spl8_69
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
tff(f300,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl8_18
| ~ spl8_32 ),
inference(superposition,[],[f277,f175]) ).
tff(f640,plain,
( spl8_68
| ~ spl8_27
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f271,f241,f219,f638]) ).
tff(f638,plain,
( spl8_68
<=> ! [X0: list] :
( ( $sum(1,length(tail(X0))) = length(X0) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
tff(f271,plain,
( ! [X0: list] :
( ( $sum(1,length(tail(X0))) = length(X0) )
| ( nil = X0 ) )
| ~ spl8_27
| ~ spl8_30 ),
inference(superposition,[],[f220,f242]) ).
tff(f636,plain,
( spl8_67
| ~ spl8_20
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f222,f211,f182,f634]) ).
tff(f634,plain,
( spl8_67
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
tff(f222,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl8_20
| ~ spl8_25 ),
inference(resolution,[],[f212,f183]) ).
tff(f569,plain,
( spl8_66
| ~ spl8_12
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f329,f292,f148,f567]) ).
tff(f567,plain,
( spl8_66
<=> ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
tff(f148,plain,
( spl8_12
<=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f329,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) )
| ~ spl8_12
| ~ spl8_36 ),
inference(superposition,[],[f149,f293]) ).
tff(f149,plain,
( ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f148]) ).
tff(f559,plain,
( spl8_65
| ~ spl8_11
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f304,f276,f144,f557]) ).
tff(f557,plain,
( spl8_65
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
tff(f144,plain,
( spl8_11
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f304,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl8_11
| ~ spl8_32 ),
inference(superposition,[],[f277,f145]) ).
tff(f145,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f555,plain,
( spl8_64
| ~ spl8_24
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f272,f241,f198,f553]) ).
tff(f553,plain,
( spl8_64
<=> ! [X0: list,X1: $int] :
( sP1(X1,X0)
| ~ in(X1,tail(X0))
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
tff(f272,plain,
( ! [X0: list,X1: $int] :
( sP1(X1,X0)
| ~ in(X1,tail(X0))
| ( nil = X0 ) )
| ~ spl8_24
| ~ spl8_30 ),
inference(superposition,[],[f199,f242]) ).
tff(f551,plain,
( spl8_63
| ~ spl8_18
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f266,f237,f174,f549]) ).
tff(f549,plain,
( spl8_63
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
tff(f266,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl8_18
| ~ spl8_29 ),
inference(superposition,[],[f238,f175]) ).
tff(f547,plain,
( spl8_62
| ~ spl8_18
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f262,f237,f174,f545]) ).
tff(f545,plain,
( spl8_62
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
tff(f262,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl8_18
| ~ spl8_29 ),
inference(superposition,[],[f238,f175]) ).
tff(f543,plain,
( spl8_61
| ~ spl8_18
| ~ spl8_28 ),
inference(avatar_split_clause,[],[f245,f233,f174,f541]) ).
tff(f541,plain,
( spl8_61
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
tff(f245,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl8_18
| ~ spl8_28 ),
inference(superposition,[],[f234,f175]) ).
tff(f520,plain,
( spl8_60
| ~ spl8_8
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f325,f292,f132,f518]) ).
tff(f518,plain,
( spl8_60
<=> ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
tff(f325,plain,
( ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) )
| ~ spl8_8
| ~ spl8_36 ),
inference(superposition,[],[f293,f133]) ).
tff(f516,plain,
( spl8_59
| ~ spl8_11
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f265,f237,f144,f514]) ).
tff(f514,plain,
( spl8_59
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
tff(f265,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl8_11
| ~ spl8_29 ),
inference(superposition,[],[f238,f145]) ).
tff(f512,plain,
( spl8_58
| ~ spl8_16
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f445,f402,f164,f510]) ).
tff(f510,plain,
( spl8_58
<=> ! [X0: $int,X3: list,X2: $int,X1: list] :
( ( $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) )
| sP1(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
tff(f445,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( $sum(1,count(X0,X1)) = $sum(1,count(X0,append(X1,cons(X2,X3)))) )
| sP1(X2,X3) )
| ~ spl8_16
| ~ spl8_47 ),
inference(resolution,[],[f403,f165]) ).
tff(f508,plain,
( spl8_57
| ~ spl8_11
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f261,f237,f144,f506]) ).
tff(f506,plain,
( spl8_57
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
tff(f261,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl8_11
| ~ spl8_29 ),
inference(superposition,[],[f238,f145]) ).
tff(f462,plain,
( spl8_56
| ~ spl8_13
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f328,f292,f152,f460]) ).
tff(f460,plain,
( spl8_56
<=> ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
tff(f152,plain,
( spl8_13
<=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f328,plain,
( ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 )
| ~ spl8_13
| ~ spl8_36 ),
inference(superposition,[],[f153,f293]) ).
tff(f153,plain,
( ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f152]) ).
tff(f458,plain,
( spl8_55
| ~ spl8_11
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f314,f276,f144,f456]) ).
tff(f456,plain,
( spl8_55
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
tff(f314,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl8_11
| ~ spl8_32 ),
inference(evaluation,[],[f299]) ).
tff(f299,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl8_11
| ~ spl8_32 ),
inference(superposition,[],[f277,f145]) ).
tff(f454,plain,
( spl8_54
| ~ spl8_17
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f208,f198,f168,f452]) ).
tff(f168,plain,
( spl8_17
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
tff(f208,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) )
| ~ spl8_17
| ~ spl8_24 ),
inference(resolution,[],[f199,f169]) ).
tff(f169,plain,
( ! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| in(X0,X1) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f168]) ).
tff(f450,plain,
( spl8_53
| ~ spl8_18
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f205,f186,f174,f448]) ).
tff(f448,plain,
( spl8_53
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
tff(f205,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl8_18
| ~ spl8_21 ),
inference(superposition,[],[f187,f175]) ).
tff(f443,plain,
( spl8_52
| ~ spl8_18
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f202,f182,f174,f441]) ).
tff(f441,plain,
( spl8_52
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
tff(f202,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl8_18
| ~ spl8_20 ),
inference(superposition,[],[f183,f175]) ).
tff(f435,plain,
( spl8_51
| ~ spl8_4
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f385,f378,f116,f433]) ).
tff(f433,plain,
( spl8_51
<=> ! [X0: $int,X3: list,X2: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| in(X2,X3)
| ( count(X0,sK5(X0,X1)) = count(X0,append(sK5(X0,X1),cons(X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
tff(f385,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| in(X2,X3)
| ( count(X0,sK5(X0,X1)) = count(X0,append(sK5(X0,X1),cons(X2,X3))) ) )
| ~ spl8_4
| ~ spl8_44 ),
inference(resolution,[],[f379,f117]) ).
tff(f418,plain,
( spl8_50
| ~ spl8_9
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f331,f292,f136,f416]) ).
tff(f416,plain,
( spl8_50
<=> ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
tff(f136,plain,
( spl8_9
<=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f331,plain,
( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
| ~ spl8_9
| ~ spl8_36 ),
inference(superposition,[],[f137,f293]) ).
tff(f137,plain,
( ! [X0: $int,X1: list] : ( cons(X0,X1) != nil )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f136]) ).
tff(f414,plain,
( spl8_49
| ~ spl8_10
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f330,f292,f140,f412]) ).
tff(f412,plain,
( spl8_49
<=> ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
tff(f330,plain,
( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
| ~ spl8_10
| ~ spl8_36 ),
inference(superposition,[],[f141,f293]) ).
tff(f410,plain,
( spl8_48
| ~ spl8_10
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f273,f241,f140,f408]) ).
tff(f408,plain,
( spl8_48
<=> ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
tff(f273,plain,
( ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) )
| ~ spl8_10
| ~ spl8_30 ),
inference(superposition,[],[f141,f242]) ).
tff(f404,plain,
( spl8_47
| ~ spl8_4
| ~ spl8_31
| ~ spl8_36
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f366,f296,f292,f255,f116,f402]) ).
tff(f255,plain,
( spl8_31
<=> ! [X0: $int,X1: list] : in(X0,cons(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
tff(f366,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( $sum(1,count(X2,append(X3,cons(X0,X1)))) = $sum(1,count(X2,X3)) )
| in(X0,X1) )
| ~ spl8_4
| ~ spl8_31
| ~ spl8_36
| ~ spl8_37 ),
inference(forward_demodulation,[],[f365,f297]) ).
tff(f365,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( count(X2,cons(X2,X3)) = $sum(1,count(X2,append(X3,cons(X0,X1)))) )
| in(X0,X1) )
| ~ spl8_4
| ~ spl8_31
| ~ spl8_36
| ~ spl8_37 ),
inference(forward_demodulation,[],[f361,f333]) ).
tff(f361,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( in(X0,X1)
| ( count(X2,cons(X2,X3)) = count(X2,append(cons(X2,X3),cons(X0,X1))) ) )
| ~ spl8_4
| ~ spl8_31 ),
inference(resolution,[],[f256,f117]) ).
tff(f256,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f255]) ).
tff(f400,plain,
( spl8_46
| ~ spl8_4
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f350,f345,f116,f398]) ).
tff(f398,plain,
( spl8_46
<=> ! [X0: $int,X3: list,X2: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| in(X2,X3)
| ( count(X0,sK5(X0,X1)) = count(X0,append(sK5(X0,X1),cons(X2,X3))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
tff(f350,plain,
( ! [X2: $int,X3: list,X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| in(X2,X3)
| ( count(X0,sK5(X0,X1)) = count(X0,append(sK5(X0,X1),cons(X2,X3))) ) )
| ~ spl8_4
| ~ spl8_40 ),
inference(resolution,[],[f346,f117]) ).
tff(f389,plain,
spl8_45,
inference(avatar_split_clause,[],[f83,f387]) ).
tff(f83,plain,
! [X0: $int,X1: list] :
( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ( in(X0,sK5(X0,X1))
& ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
| ( ( sK6(X0,X1) = X0 )
& ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f59,f61,f60]) ).
tff(f60,plain,
! [X0: $int,X1: list] :
( ? [X6: $int,X7: list] :
( in(X0,X7)
& ( cons(X6,X7) = X1 ) )
=> ( in(X0,sK5(X0,X1))
& ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f61,plain,
! [X0: $int,X1: list] :
( ? [X8: $int,X9: list] :
( ( X0 = X8 )
& ( cons(X8,X9) = X1 ) )
=> ( ( sK6(X0,X1) = X0 )
& ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f59,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X6: $int,X7: list] :
( in(X0,X7)
& ( cons(X6,X7) = X1 ) )
| ? [X8: $int,X9: list] :
( ( X0 = X8 )
& ( cons(X8,X9) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f58]) ).
tff(f58,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f57]) ).
tff(f57,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f380,plain,
spl8_44,
inference(avatar_split_clause,[],[f85,f378]) ).
tff(f85,plain,
! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f376,plain,
spl8_43,
inference(avatar_split_clause,[],[f84,f374]) ).
tff(f84,plain,
! [X0: $int,X1: list] :
( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f370,plain,
spl8_42,
inference(avatar_split_clause,[],[f73,f368]) ).
tff(f73,plain,
! [X0: $int,X1: list] :
( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ( inRange(X0,sK3(X0,X1))
& $less(sK2(X0,X1),X0)
& ~ $less(sK2(X0,X1),0)
& ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f52,f53]) ).
tff(f53,plain,
! [X0: $int,X1: list] :
( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
=> ( inRange(X0,sK3(X0,X1))
& $less(sK2(X0,X1),X0)
& ~ $less(sK2(X0,X1),0)
& ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f52,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f51]) ).
tff(f51,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f50]) ).
tff(f50,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f354,plain,
spl8_41,
inference(avatar_split_clause,[],[f95,f352]) ).
tff(f95,plain,
! [X2: $int,X3: list,X0: $int] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(equality_resolution,[],[f78]) ).
tff(f78,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f347,plain,
spl8_40,
inference(avatar_split_clause,[],[f86,f345]) ).
tff(f86,plain,
! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f338,plain,
spl8_39,
inference(avatar_split_clause,[],[f92,f336]) ).
tff(f92,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: $int,X1: $int,X2: list] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $int,X3: $int,X4: list,X5: $int] :
( ( X0 != X3 )
=> ( count(X0,cons(X3,X4)) = count(X0,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_3) ).
tff(f322,plain,
( spl8_38
| ~ spl8_1
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f201,f182,f103,f320]) ).
tff(f103,plain,
( spl8_1
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f201,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_1
| ~ spl8_20 ),
inference(resolution,[],[f183,f104]) ).
tff(f104,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f103]) ).
tff(f298,plain,
spl8_37,
inference(avatar_split_clause,[],[f101,f296]) ).
tff(f101,plain,
! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ),
inference(forward_demodulation,[],[f100,f19]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f100,plain,
! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(count(X1,X2),1) ),
inference(equality_resolution,[],[f93]) ).
tff(f93,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: $int,X1: $int,X2: list] :
( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 = X1 )
=> ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $int,X3: $int,X4: list,X5: $int] :
( ( X0 = X3 )
=> ( count(X0,cons(X3,X4)) = $sum(count(X0,X4),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_4) ).
tff(f294,plain,
spl8_36,
inference(avatar_split_clause,[],[f91,f292]) ).
tff(f91,plain,
! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: $int,X1: list,X2: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X6: $int,X0: list,X1: list] : ( append(cons(X6,X0),X1) = cons(X6,append(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_7) ).
tff(f290,plain,
spl8_35,
inference(avatar_split_clause,[],[f76,f288]) ).
tff(f76,plain,
! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f286,plain,
spl8_34,
inference(avatar_split_clause,[],[f75,f284]) ).
tff(f75,plain,
! [X0: $int,X1: list] :
( $less(sK2(X0,X1),X0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f282,plain,
spl8_33,
inference(avatar_split_clause,[],[f74,f280]) ).
tff(f74,plain,
! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f278,plain,
spl8_32,
inference(avatar_split_clause,[],[f20,f276]) ).
tff(f20,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f257,plain,
( spl8_31
| ~ spl8_10
| ~ spl8_17 ),
inference(avatar_split_clause,[],[f172,f168,f140,f255]) ).
tff(f172,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_10
| ~ spl8_17 ),
inference(resolution,[],[f169,f141]) ).
tff(f243,plain,
spl8_30,
inference(avatar_split_clause,[],[f68,f241]) ).
tff(f68,plain,
! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X1: list] :
( ( cons(head(X1),tail(X1)) = X1 )
| ( nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
tff(f239,plain,
spl8_29,
inference(avatar_split_clause,[],[f27,f237]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f235,plain,
spl8_28,
inference(avatar_split_clause,[],[f22,f233]) ).
tff(f22,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f221,plain,
spl8_27,
inference(avatar_split_clause,[],[f72,f219]) ).
tff(f72,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X3: $int,X4: list] : ( length(cons(X3,X4)) = $sum(1,length(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1) ).
tff(f217,plain,
spl8_26,
inference(avatar_split_clause,[],[f26,f215]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f213,plain,
spl8_25,
inference(avatar_split_clause,[],[f25,f211]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f200,plain,
spl8_24,
inference(avatar_split_clause,[],[f97,f198]) ).
tff(f97,plain,
! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ),
inference(equality_resolution,[],[f88]) ).
tff(f88,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f62]) ).
tff(f196,plain,
spl8_23,
inference(avatar_split_clause,[],[f82,f194]) ).
tff(f82,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ $less(0,count(X0,X1)) )
& ( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $less(0,count(X0,X1)) ),
inference(rectify,[],[f18]) ).
tff(f18,plain,
! [X5: $int,X1: list] :
( in(X5,X1)
<=> $less(0,count(X5,X1)) ),
inference(theory_normalization,[],[f14]) ).
tff(f14,axiom,
! [X5: $int,X1: list] :
( in(X5,X1)
<=> $greater(count(X5,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).
tff(f192,plain,
spl8_22,
inference(avatar_split_clause,[],[f81,f190]) ).
tff(f81,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tff(f188,plain,
spl8_21,
inference(avatar_split_clause,[],[f30,f186]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f184,plain,
spl8_20,
inference(avatar_split_clause,[],[f28,f182]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f180,plain,
( spl8_19
| ~ spl8_2
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f171,f160,f107,f178]) ).
tff(f178,plain,
( spl8_19
<=> ! [X0: $int] : inRange(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f107,plain,
( spl8_2
<=> ! [X0: $int] : sP0(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f171,plain,
( ! [X0: $int] : inRange(X0,nil)
| ~ spl8_2
| ~ spl8_15 ),
inference(resolution,[],[f161,f108]) ).
tff(f108,plain,
( ! [X0: $int] : sP0(X0,nil)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f107]) ).
tff(f176,plain,
spl8_18,
inference(avatar_split_clause,[],[f19,f174]) ).
tff(f170,plain,
spl8_17,
inference(avatar_split_clause,[],[f90,f168]) ).
tff(f90,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f38,f48]) ).
tff(f38,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X2: $int,X1: list] :
( in(X2,X1)
<=> ( ? [X3: $int,X4: list] :
( in(X2,X4)
& ( cons(X3,X4) = X1 ) )
| ? [X3: $int,X4: list] :
( ( X2 = X3 )
& ( cons(X3,X4) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).
tff(f166,plain,
spl8_16,
inference(avatar_split_clause,[],[f89,f164]) ).
tff(f89,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tff(f162,plain,
spl8_15,
inference(avatar_split_clause,[],[f80,f160]) ).
tff(f80,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f36,f46]) ).
tff(f36,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,plain,
! [X5: $int,X1: list] :
( inRange(X5,X1)
<=> ( ? [X0: $int,X4: list] :
( inRange(X5,X4)
& $less(X0,X5)
& ~ $less(X0,0)
& ( cons(X0,X4) = X1 ) )
| ( nil = X1 ) ) ),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
! [X5: $int,X1: list] :
( inRange(X5,X1)
<=> ( ? [X0: $int,X4: list] :
( inRange(X5,X4)
& $less(X0,X5)
& $lesseq(0,X0)
& ( cons(X0,X4) = X1 ) )
| ( nil = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(f158,plain,
spl8_14,
inference(avatar_split_clause,[],[f79,f156]) ).
tff(f79,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tff(f154,plain,
spl8_13,
inference(avatar_split_clause,[],[f71,f152]) ).
tff(f71,plain,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
tff(f150,plain,
spl8_12,
inference(avatar_split_clause,[],[f70,f148]) ).
tff(f70,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
tff(f146,plain,
spl8_11,
inference(avatar_split_clause,[],[f23,f144]) ).
tff(f23,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f142,plain,
spl8_10,
inference(avatar_split_clause,[],[f99,f140]) ).
tff(f99,plain,
! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
inference(equality_resolution,[],[f98]) ).
tff(f98,plain,
! [X1: list,X4: $int,X5: list] :
( sP1(X4,X1)
| ( cons(X4,X5) != X1 ) ),
inference(equality_resolution,[],[f87]) ).
tff(f87,plain,
! [X0: $int,X1: list,X4: $int,X5: list] :
( sP1(X0,X1)
| ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ),
inference(cnf_transformation,[],[f62]) ).
tff(f138,plain,
spl8_9,
inference(avatar_split_clause,[],[f69,f136]) ).
tff(f69,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
tff(f134,plain,
spl8_8,
inference(avatar_split_clause,[],[f67,f132]) ).
tff(f67,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X1: list] : ( append(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_6) ).
tff(f130,plain,
spl8_7,
inference(avatar_split_clause,[],[f66,f128]) ).
tff(f66,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: $int] : ( 0 = count(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f126,plain,
spl8_6,
inference(avatar_split_clause,[],[f29,f124]) ).
tff(f124,plain,
( spl8_6
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
tff(f29,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f122,plain,
spl8_5,
inference(avatar_split_clause,[],[f21,f120]) ).
tff(f120,plain,
( spl8_5
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
tff(f21,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f118,plain,
spl8_4,
inference(avatar_split_clause,[],[f94,f116]) ).
tff(f94,plain,
! [X2: list,X3: list,X0: $int,X1: $int] :
( ( count(X1,X3) = count(X1,append(X3,cons(X0,X2))) )
| in(X0,X2)
| ~ in(X1,X3) ),
inference(equality_resolution,[],[f64]) ).
tff(f64,plain,
! [X2: list,X3: list,X0: $int,X1: $int,X4: list] :
( ( count(X1,X3) = count(X1,X4) )
| ( append(X3,cons(X0,X2)) != X4 )
| in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
( ( count(X1,X3) = count(X1,X4) )
| ( append(X3,cons(X0,X2)) != X4 )
| in(X0,X2)
| ~ in(X1,X3) ),
inference(flattening,[],[f42]) ).
tff(f42,plain,
! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
( ( count(X1,X3) = count(X1,X4) )
| ( append(X3,cons(X0,X2)) != X4 )
| in(X0,X2)
| ~ in(X1,X3) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
( ( ( append(X3,cons(X0,X2)) = X4 )
& ~ in(X0,X2)
& in(X1,X3) )
=> ( count(X1,X3) = count(X1,X4) ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
~ ~ ! [X0: $int,X1: $int,X2: list,X3: list,X4: list] :
( ( ( append(X3,cons(X0,X2)) = X4 )
& ~ in(X0,X2)
& in(X1,X3) )
=> ( count(X1,X3) = count(X1,X4) ) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ~ ! [X7: $int,X5: $int,X0: list,X1: list,X8: list] :
( ( ( append(X1,cons(X7,X0)) = X8 )
& ~ in(X7,X0)
& in(X5,X1) )
=> ( count(X5,X1) = count(X5,X8) ) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
~ ! [X7: $int,X5: $int,X0: list,X1: list,X8: list] :
( ( ( append(X1,cons(X7,X0)) = X8 )
& ~ in(X7,X0)
& in(X5,X1) )
=> ( count(X5,X1) = count(X5,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f114,plain,
spl8_3,
inference(avatar_split_clause,[],[f65,f111]) ).
tff(f111,plain,
( spl8_3
<=> ( 0 = length(nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f65,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
0 = length(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(f109,plain,
spl8_2,
inference(avatar_split_clause,[],[f96,f107]) ).
tff(f96,plain,
! [X0: $int] : sP0(X0,nil),
inference(equality_resolution,[],[f77]) ).
tff(f77,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f105,plain,
spl8_1,
inference(avatar_split_clause,[],[f24,f103]) ).
tff(f24,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT097_1 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 13:19:36 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (11734)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (11735)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (11735)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (11735)Terminated due to inappropriate strategy.
% 0.14/0.38 % (11735)------------------------------
% 0.14/0.38 % (11735)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (11735)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (11735)Memory used [KB]: 803
% 0.14/0.38 % (11735)Time elapsed: 0.003 s
% 0.14/0.38 % (11735)Instructions burned: 3 (million)
% 0.14/0.38 % (11735)------------------------------
% 0.14/0.38 % (11735)------------------------------
% 0.14/0.39 % (11737)WARNING: value z3 for option sas not known
% 0.14/0.39 % (11736)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (11738)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (11739)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (11737)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (11741)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (11742)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39 % (11736)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (11736)Terminated due to inappropriate strategy.
% 0.14/0.39 % (11736)------------------------------
% 0.14/0.39 % (11736)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (11736)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (11738)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (11736)Memory used [KB]: 804
% 0.14/0.39 % (11738)Terminated due to inappropriate strategy.
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11738)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (11738)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (11738)Memory used [KB]: 803
% 0.14/0.39 % (11738)Time elapsed: 0.005 s
% 0.14/0.39 % (11738)Instructions burned: 3 (million)
% 0.14/0.39 % (11736)Time elapsed: 0.005 s
% 0.14/0.39 % (11736)Instructions burned: 3 (million)
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11738)------------------------------
% 0.14/0.39 % (11736)------------------------------
% 0.14/0.39 % (11736)------------------------------
% 0.14/0.40 % (11743)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (11743)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (11743)Terminated due to inappropriate strategy.
% 0.14/0.40 % (11743)------------------------------
% 0.14/0.40 % (11743)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (11743)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (11743)Memory used [KB]: 804
% 0.14/0.40 % (11743)Time elapsed: 0.004 s
% 0.14/0.40 % (11743)Instructions burned: 3 (million)
% 0.14/0.40 % (11743)------------------------------
% 0.14/0.40 % (11743)------------------------------
% 0.21/0.42 % (11744)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.42 % (11745)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.43 % (11746)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)
% 0.21/0.46 % (11739)First to succeed.
% 0.21/0.46 % (11739)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11734"
% 0.21/0.46 % (11739)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (11739)------------------------------
% 0.21/0.46 % (11739)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46 % (11739)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (11739)Memory used [KB]: 1768
% 0.21/0.46 % (11739)Time elapsed: 0.076 s
% 0.21/0.46 % (11739)Instructions burned: 133 (million)
% 0.21/0.46 % (11734)Success in time 0.1 s
%------------------------------------------------------------------------------