TSTP Solution File: DAT085_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT085_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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:04:01 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 166
% Syntax : Number of formulae : 494 ( 73 unt; 18 typ; 0 def)
% Number of atoms : 1423 ( 363 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1615 ( 668 ~; 741 |; 67 &)
% ( 128 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 1183 ( 214 atm; 259 fun; 167 num; 543 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 29 ( 16 >; 13 *; 0 +; 0 <<)
% Number of predicates : 125 ( 120 usr; 117 prp; 0-2 aty)
% Number of functors : 18 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 873 ( 829 !; 44 ?; 873 :)
% 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(f1611,plain,
$false,
inference(avatar_sat_refutation,[],[f103,f108,f112,f117,f123,f127,f131,f135,f139,f143,f147,f151,f155,f159,f163,f168,f172,f176,f182,f186,f190,f194,f198,f202,f206,f219,f223,f227,f244,f248,f252,f256,f287,f291,f295,f299,f303,f307,f346,f355,f361,f365,f373,f379,f383,f391,f402,f406,f420,f424,f428,f443,f447,f451,f455,f459,f463,f510,f514,f518,f541,f545,f549,f553,f557,f561,f566,f632,f636,f640,f644,f648,f652,f807,f811,f815,f822,f888,f892,f896,f900,f904,f913,f917,f1032,f1036,f1040,f1044,f1048,f1207,f1211,f1215,f1266,f1272,f1276,f1293,f1303,f1321,f1325,f1343,f1367,f1374,f1378,f1529,f1533,f1537,f1556,f1560,f1564,f1569,f1575,f1579,f1583,f1600,f1604,f1608,f1610]) ).
tff(f1610,plain,
( ~ spl8_2
| ~ spl8_110 ),
inference(avatar_contradiction_clause,[],[f1609]) ).
tff(f1609,plain,
( $false
| ~ spl8_2
| ~ spl8_110 ),
inference(resolution,[],[f1568,f107]) ).
tff(f107,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f106]) ).
tff(f106,plain,
( spl8_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f1568,plain,
( ! [X0: $int,X1: $int] : $less(X0,X1)
| ~ spl8_110 ),
inference(avatar_component_clause,[],[f1567]) ).
tff(f1567,plain,
( spl8_110
<=> ! [X0: $int,X1: $int] : $less(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).
tff(f1608,plain,
( spl8_116
| ~ spl8_30
| ~ spl8_75 ),
inference(avatar_split_clause,[],[f836,f809,f246,f1606]) ).
tff(f1606,plain,
( spl8_116
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,$sum(X1,1)))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).
tff(f246,plain,
( spl8_30
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
tff(f809,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(f836,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum(X0,X1),$sum(X2,$sum(X1,1)))
| ~ $less(X2,X0) )
| ~ spl8_30
| ~ spl8_75 ),
inference(resolution,[],[f810,f247]) ).
tff(f247,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f246]) ).
tff(f810,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl8_75 ),
inference(avatar_component_clause,[],[f809]) ).
tff(f1604,plain,
( spl8_115
| ~ spl8_32
| ~ spl8_67 ),
inference(avatar_split_clause,[],[f622,f564,f254,f1602]) ).
tff(f1602,plain,
( spl8_115
<=> ! [X0: list,X1: list] :
( ( append(tail(X0),X1) = tail(append(X0,X1)) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_115])]) ).
tff(f254,plain,
( spl8_32
<=> ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
tff(f564,plain,
( spl8_67
<=> ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
tff(f622,plain,
( ! [X0: list,X1: list] :
( ( append(tail(X0),X1) = tail(append(X0,X1)) )
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_67 ),
inference(superposition,[],[f565,f255]) ).
tff(f255,plain,
( ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f254]) ).
tff(f565,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) )
| ~ spl8_67 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f1600,plain,
( spl8_114
| ~ spl8_37
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f484,f453,f301,f1598]) ).
tff(f1598,plain,
( spl8_114
<=> ! [X0: $int,X3: $int,X2: list,X1: list] :
( in(X3,append(cons(X0,X1),X2))
| ~ in(X3,append(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_114])]) ).
tff(f301,plain,
( spl8_37
<=> ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
tff(f453,plain,
( spl8_55
<=> ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
tff(f484,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( in(X3,append(cons(X0,X1),X2))
| ~ in(X3,append(X1,X2)) )
| ~ spl8_37
| ~ spl8_55 ),
inference(superposition,[],[f454,f302]) ).
tff(f302,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) )
| ~ spl8_37 ),
inference(avatar_component_clause,[],[f301]) ).
tff(f454,plain,
( ! [X2: $int,X0: $int,X1: list] :
( in(X0,cons(X2,X1))
| ~ in(X0,X1) )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f453]) ).
tff(f1583,plain,
( spl8_113
| ~ spl8_37
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f439,f426,f301,f1581]) ).
tff(f1581,plain,
( spl8_113
<=> ! [X2: list,X0: $int,X1: list,X3: list] : ( nil != append(append(cons(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).
tff(f426,plain,
( spl8_51
<=> ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
tff(f439,plain,
( ! [X2: list,X3: list,X0: $int,X1: list] : ( nil != append(append(cons(X0,X1),X2),X3) )
| ~ spl8_37
| ~ spl8_51 ),
inference(superposition,[],[f427,f302]) ).
tff(f427,plain,
( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f426]) ).
tff(f1579,plain,
( spl8_112
| ~ spl8_37
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f437,f422,f301,f1577]) ).
tff(f1577,plain,
( spl8_112
<=> ! [X0: $int,X3: list,X2: list,X1: list] : sP1(X0,append(append(cons(X0,X1),X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).
tff(f422,plain,
( spl8_50
<=> ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
tff(f437,plain,
( ! [X2: list,X3: list,X0: $int,X1: list] : sP1(X0,append(append(cons(X0,X1),X2),X3))
| ~ spl8_37
| ~ spl8_50 ),
inference(superposition,[],[f423,f302]) ).
tff(f423,plain,
( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
| ~ spl8_50 ),
inference(avatar_component_clause,[],[f422]) ).
tff(f1575,plain,
( spl8_111
| ~ spl8_32
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f436,f422,f254,f1573]) ).
tff(f1573,plain,
( spl8_111
<=> ! [X0: list,X1: list] :
( sP1(head(X0),append(X0,X1))
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).
tff(f436,plain,
( ! [X0: list,X1: list] :
( sP1(head(X0),append(X0,X1))
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_50 ),
inference(superposition,[],[f423,f255]) ).
tff(f1569,plain,
( spl8_110
| ~ spl8_48
| ~ spl8_98 ),
inference(avatar_split_clause,[],[f1424,f1319,f404,f1567]) ).
tff(f404,plain,
( spl8_48
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
tff(f1319,plain,
( spl8_98
<=> ! [X2: $int,X0: $int] : ( X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
tff(f1424,plain,
( ! [X0: $int,X1: $int] : $less(X0,X1)
| ~ spl8_48
| ~ spl8_98 ),
inference(superposition,[],[f405,f1320]) ).
tff(f1320,plain,
( ! [X2: $int,X0: $int] : ( X0 = X2 )
| ~ spl8_98 ),
inference(avatar_component_clause,[],[f1319]) ).
tff(f405,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f404]) ).
tff(f1564,plain,
( spl8_109
| ~ spl8_54
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f584,f543,f449,f1562]) ).
tff(f1562,plain,
( spl8_109
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).
tff(f449,plain,
( spl8_54
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
tff(f543,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(f584,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) )
| ~ spl8_54
| ~ spl8_62 ),
inference(resolution,[],[f544,f450]) ).
tff(f450,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f449]) ).
tff(f544,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl8_62 ),
inference(avatar_component_clause,[],[f543]) ).
tff(f1560,plain,
( spl8_108
| ~ spl8_30
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f476,f449,f246,f1558]) ).
tff(f1558,plain,
( spl8_108
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).
tff(f476,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) )
| ~ spl8_30
| ~ spl8_54 ),
inference(resolution,[],[f450,f247]) ).
tff(f1556,plain,
( spl8_107
| ~ spl8_32
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f438,f426,f254,f1554]) ).
tff(f1554,plain,
( spl8_107
<=> ! [X0: list,X1: list] :
( ( nil != append(X0,X1) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
tff(f438,plain,
( ! [X0: list,X1: list] :
( ( nil != append(X0,X1) )
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_51 ),
inference(superposition,[],[f427,f255]) ).
tff(f1537,plain,
( spl8_106
| ~ spl8_54
| ~ spl8_58 ),
inference(avatar_split_clause,[],[f519,f508,f449,f1535]) ).
tff(f1535,plain,
( spl8_106
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
tff(f508,plain,
( spl8_58
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
tff(f519,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl8_54
| ~ spl8_58 ),
inference(resolution,[],[f509,f450]) ).
tff(f509,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl8_58 ),
inference(avatar_component_clause,[],[f508]) ).
tff(f1533,plain,
( spl8_105
| ~ spl8_37
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f410,f400,f301,f1531]) ).
tff(f1531,plain,
( spl8_105
<=> ! [X2: list,X0: $int,X1: list] : in(X0,append(cons(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
tff(f400,plain,
( spl8_47
<=> ! [X0: $int,X1: list] : in(X0,cons(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
tff(f410,plain,
( ! [X2: list,X0: $int,X1: list] : in(X0,append(cons(X0,X1),X2))
| ~ spl8_37
| ~ spl8_47 ),
inference(superposition,[],[f401,f302]) ).
tff(f401,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_47 ),
inference(avatar_component_clause,[],[f400]) ).
tff(f1529,plain,
( spl8_104
| ~ spl8_32
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f409,f400,f254,f1527]) ).
tff(f1527,plain,
( spl8_104
<=> ! [X0: list] :
( in(head(X0),X0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
tff(f409,plain,
( ! [X0: list] :
( in(head(X0),X0)
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_47 ),
inference(superposition,[],[f401,f255]) ).
tff(f1378,plain,
( spl8_103
| ~ spl8_41
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f665,f634,f359,f1376]) ).
tff(f1376,plain,
( spl8_103
<=> ! [X2: $int,X0: list,X1: list] :
( ( length(X0) != length(X1) )
| ( cons(X2,tail(X0)) = X1 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
tff(f359,plain,
( spl8_41
<=> ! [X2: list,X0: $int,X1: list] :
( ( $sum(1,length(X1)) != length(X2) )
| ( cons(X0,X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
tff(f634,plain,
( spl8_69
<=> ! [X0: list] :
( ( length(X0) = $sum(1,length(tail(X0))) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
tff(f665,plain,
( ! [X2: $int,X0: list,X1: list] :
( ( length(X0) != length(X1) )
| ( cons(X2,tail(X0)) = X1 )
| ( nil = X0 ) )
| ~ spl8_41
| ~ spl8_69 ),
inference(superposition,[],[f360,f635]) ).
tff(f635,plain,
( ! [X0: list] :
( ( length(X0) = $sum(1,length(tail(X0))) )
| ( nil = X0 ) )
| ~ spl8_69 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f360,plain,
( ! [X2: list,X0: $int,X1: list] :
( ( $sum(1,length(X1)) != length(X2) )
| ( cons(X0,X1) = X2 ) )
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f359]) ).
tff(f1374,plain,
( spl8_102
| ~ spl8_28
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f397,f359,f225,f1372]) ).
tff(f1372,plain,
( spl8_102
<=> ! [X2: list,X0: $int,X1: list,X3: $int] :
( ( length(X2) != $sum(2,length(X1)) )
| ( cons(X3,cons(X0,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
tff(f225,plain,
( spl8_28
<=> ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
tff(f397,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( ( length(X2) != $sum(2,length(X1)) )
| ( cons(X3,cons(X0,X1)) = X2 ) )
| ~ spl8_28
| ~ spl8_41 ),
inference(evaluation,[],[f395]) ).
tff(f395,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( ( length(X2) != $sum(1,$sum(1,length(X1))) )
| ( cons(X3,cons(X0,X1)) = X2 ) )
| ~ spl8_28
| ~ spl8_41 ),
inference(superposition,[],[f360,f226]) ).
tff(f226,plain,
( ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) )
| ~ spl8_28 ),
inference(avatar_component_clause,[],[f225]) ).
tff(f1367,plain,
( spl8_101
| ~ spl8_25
| ~ spl8_46 ),
inference(avatar_split_clause,[],[f393,f389,f204,f1365]) ).
tff(f1365,plain,
( spl8_101
<=> ! [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_101])]) ).
tff(f204,plain,
( spl8_25
<=> ! [X2: $int,X0: $int,X3: list] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f389,plain,
( spl8_46
<=> ! [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_46])]) ).
tff(f393,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_25
| ~ spl8_46 ),
inference(resolution,[],[f390,f205]) ).
tff(f205,plain,
( ! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) )
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f204]) ).
tff(f390,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_46 ),
inference(avatar_component_clause,[],[f389]) ).
tff(f1343,plain,
( spl8_100
| ~ spl8_11
| ~ spl8_46 ),
inference(avatar_split_clause,[],[f392,f389,f145,f1341]) ).
tff(f1341,plain,
( spl8_100
<=> ! [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_100])]) ).
tff(f145,plain,
( spl8_11
<=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f392,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_11
| ~ spl8_46 ),
inference(resolution,[],[f390,f146]) ).
tff(f146,plain,
( ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5))
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f145]) ).
tff(f1325,plain,
( spl8_99
| ~ spl8_42
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f375,f371,f363,f1323]) ).
tff(f1323,plain,
( spl8_99
<=> ! [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_99])]) ).
tff(f363,plain,
( spl8_42
<=> ! [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_42])]) ).
tff(f371,plain,
( spl8_43
<=> ! [X0: $int,X1: list] :
( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
tff(f375,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_42
| ~ spl8_43 ),
inference(resolution,[],[f372,f364]) ).
tff(f364,plain,
( ! [X2: $int,X3: list,X0: $int] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) )
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f363]) ).
tff(f372,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f371]) ).
tff(f1321,plain,
( spl8_98
| ~ spl8_7
| ~ spl8_38
| ~ spl8_39
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f1262,f1034,f344,f305,f129,f1319]) ).
tff(f129,plain,
( spl8_7
<=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f305,plain,
( spl8_38
<=> ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
tff(f344,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(f1034,plain,
( spl8_86
<=> ! [X0: $int,X1: $int] : ( cons(X0,nil) = cons(X1,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
tff(f1262,plain,
( ! [X2: $int,X0: $int] : ( X0 = X2 )
| ~ spl8_7
| ~ spl8_38
| ~ spl8_39
| ~ spl8_86 ),
inference(evaluation,[],[f1261]) ).
tff(f1261,plain,
( ! [X2: $int,X0: $int] :
( ( 0 = 1 )
| ( X0 = X2 ) )
| ~ spl8_7
| ~ spl8_38
| ~ spl8_39
| ~ spl8_86 ),
inference(forward_demodulation,[],[f1260,f130]) ).
tff(f130,plain,
( ! [X0: $int] : ( 0 = count(X0,nil) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f129]) ).
tff(f1260,plain,
( ! [X2: $int,X0: $int] :
( ( 1 = count(X2,nil) )
| ( X0 = X2 ) )
| ~ spl8_7
| ~ spl8_38
| ~ spl8_39
| ~ spl8_86 ),
inference(forward_demodulation,[],[f1228,f1259]) ).
tff(f1259,plain,
( ! [X0: $int,X1: $int] : ( 1 = count(X0,cons(X1,nil)) )
| ~ spl8_7
| ~ spl8_38
| ~ spl8_86 ),
inference(evaluation,[],[f1258]) ).
tff(f1258,plain,
( ! [X0: $int,X1: $int] : ( $sum(1,0) = count(X0,cons(X1,nil)) )
| ~ spl8_7
| ~ spl8_38
| ~ spl8_86 ),
inference(forward_demodulation,[],[f1227,f130]) ).
tff(f1227,plain,
( ! [X0: $int,X1: $int] : ( $sum(1,count(X0,nil)) = count(X0,cons(X1,nil)) )
| ~ spl8_38
| ~ spl8_86 ),
inference(superposition,[],[f306,f1035]) ).
tff(f1035,plain,
( ! [X0: $int,X1: $int] : ( cons(X0,nil) = cons(X1,nil) )
| ~ spl8_86 ),
inference(avatar_component_clause,[],[f1034]) ).
tff(f306,plain,
( ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f305]) ).
tff(f1228,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ( count(X2,nil) = count(X2,cons(X1,nil)) )
| ( X0 = X2 ) )
| ~ spl8_39
| ~ spl8_86 ),
inference(superposition,[],[f345,f1035]) ).
tff(f345,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f344]) ).
tff(f1303,plain,
( spl8_97
| ~ spl8_35
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f366,f363,f293,f1301]) ).
tff(f1301,plain,
( spl8_97
<=> ! [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_97])]) ).
tff(f293,plain,
( spl8_35
<=> ! [X0: $int,X1: list] :
( $less(sK2(X0,X1),X0)
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
tff(f366,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_35
| ~ spl8_42 ),
inference(resolution,[],[f364,f294]) ).
tff(f294,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| $less(sK2(X0,X1),X0) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f293]) ).
tff(f1293,plain,
( spl8_96
| ~ spl8_23
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f386,f381,f196,f1291]) ).
tff(f1291,plain,
( spl8_96
<=> ! [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_96])]) ).
tff(f196,plain,
( spl8_23
<=> ! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
tff(f381,plain,
( spl8_45
<=> ! [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_45])]) ).
tff(f386,plain,
( ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| $less(0,count(X0,sK5(X0,X1))) )
| ~ spl8_23
| ~ spl8_45 ),
inference(resolution,[],[f382,f197]) ).
tff(f197,plain,
( ! [X0: $int,X1: list] :
( ~ in(X0,X1)
| $less(0,count(X0,X1)) )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f196]) ).
tff(f382,plain,
( ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f381]) ).
tff(f1276,plain,
( spl8_95
| ~ spl8_37
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f369,f363,f301,f1274]) ).
tff(f1274,plain,
( spl8_95
<=> ! [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_95])]) ).
tff(f369,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_37
| ~ spl8_42 ),
inference(superposition,[],[f364,f302]) ).
tff(f1272,plain,
( spl8_94
| ~ spl8_32
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f368,f363,f254,f1270]) ).
tff(f1270,plain,
( spl8_94
<=> ! [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_94])]) ).
tff(f368,plain,
( ! [X0: list,X1: $int] :
( sP0(X1,X0)
| ~ inRange(X1,tail(X0))
| ~ $less(head(X0),X1)
| $less(head(X0),0)
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_42 ),
inference(superposition,[],[f364,f255]) ).
tff(f1266,plain,
( spl8_93
| ~ spl8_17
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f387,f381,f170,f1264]) ).
tff(f1264,plain,
( spl8_93
<=> ! [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_93])]) ).
tff(f170,plain,
( spl8_17
<=> ! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
tff(f387,plain,
( ! [X0: $int,X1: list] :
( ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) )
| ~ spl8_17
| ~ spl8_45 ),
inference(resolution,[],[f382,f171]) ).
tff(f171,plain,
( ! [X0: $int,X1: list] :
( ~ in(X0,X1)
| sP1(X0,X1) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f170]) ).
tff(f1215,plain,
( spl8_92
| ~ spl8_32
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f347,f344,f254,f1213]) ).
tff(f1213,plain,
( spl8_92
<=> ! [X0: list,X1: $int] :
( ( count(X1,tail(X0)) = count(X1,X0) )
| ( head(X0) = X1 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
tff(f347,plain,
( ! [X0: list,X1: $int] :
( ( count(X1,tail(X0)) = count(X1,X0) )
| ( head(X0) = X1 )
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_39 ),
inference(superposition,[],[f345,f255]) ).
tff(f1211,plain,
( spl8_91
| ~ spl8_37
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f341,f305,f301,f1209]) ).
tff(f1209,plain,
( spl8_91
<=> ! [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_91])]) ).
tff(f341,plain,
( ! [X2: list,X0: $int,X1: list] : ( $sum(1,count(X0,append(X1,X2))) = count(X0,append(cons(X0,X1),X2)) )
| ~ spl8_37
| ~ spl8_38 ),
inference(superposition,[],[f306,f302]) ).
tff(f1207,plain,
( spl8_90
| ~ spl8_32
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f340,f305,f254,f1205]) ).
tff(f1205,plain,
( spl8_90
<=> ! [X0: list] :
( ( $sum(1,count(head(X0),tail(X0))) = count(head(X0),X0) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
tff(f340,plain,
( ! [X0: list] :
( ( $sum(1,count(head(X0),tail(X0))) = count(head(X0),X0) )
| ( nil = X0 ) )
| ~ spl8_32
| ~ spl8_38 ),
inference(superposition,[],[f306,f255]) ).
tff(f1048,plain,
( spl8_89
| ~ spl8_16
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f367,f363,f166,f1046]) ).
tff(f1046,plain,
( spl8_89
<=> ! [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_89])]) ).
tff(f166,plain,
( spl8_16
<=> ! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f367,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| inRange(X0,cons(X2,X1)) )
| ~ spl8_16
| ~ spl8_42 ),
inference(resolution,[],[f364,f167]) ).
tff(f167,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| inRange(X0,X1) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f166]) ).
tff(f1044,plain,
( spl8_88
| ~ spl8_30
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f321,f285,f246,f1042]) ).
tff(f1042,plain,
( spl8_88
<=> ! [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_88])]) ).
tff(f285,plain,
( spl8_33
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
tff(f321,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl8_30
| ~ spl8_33 ),
inference(superposition,[],[f247,f286]) ).
tff(f286,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f285]) ).
tff(f1040,plain,
( spl8_87
| ~ spl8_30
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f320,f285,f246,f1038]) ).
tff(f1038,plain,
( spl8_87
<=> ! [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_87])]) ).
tff(f320,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl8_30
| ~ spl8_33 ),
inference(superposition,[],[f247,f286]) ).
tff(f1036,plain,
( spl8_86
| ~ spl8_4
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f909,f642,f114,f1034]) ).
tff(f114,plain,
( spl8_4
<=> ( 0 = length(nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f642,plain,
( spl8_71
<=> ! [X2: $int,X0: $int,X1: list] :
( ( 1 != $sum(1,length(X1)) )
| ( cons(X0,X1) = cons(X2,nil) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
tff(f909,plain,
( ! [X0: $int,X1: $int] : ( cons(X0,nil) = cons(X1,nil) )
| ~ spl8_4
| ~ spl8_71 ),
inference(evaluation,[],[f905]) ).
tff(f905,plain,
( ! [X0: $int,X1: $int] :
( ( 1 != $sum(1,0) )
| ( cons(X0,nil) = cons(X1,nil) ) )
| ~ spl8_4
| ~ spl8_71 ),
inference(superposition,[],[f643,f116]) ).
tff(f116,plain,
( ( 0 = length(nil) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f114]) ).
tff(f643,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( 1 != $sum(1,length(X1)) )
| ( cons(X0,X1) = cons(X2,nil) ) )
| ~ spl8_71 ),
inference(avatar_component_clause,[],[f642]) ).
tff(f1032,plain,
( spl8_85
| ~ spl8_29
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f314,f285,f242,f1030]) ).
tff(f1030,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(f242,plain,
( spl8_29
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
tff(f314,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl8_29
| ~ spl8_33 ),
inference(superposition,[],[f286,f243]) ).
tff(f243,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f242]) ).
tff(f917,plain,
( spl8_84
| ~ spl8_17
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f357,f353,f170,f915]) ).
tff(f915,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(f353,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(f357,plain,
( ! [X0: $int,X1: list] :
( ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1)
| sP1(X0,sK5(X0,X1)) )
| ~ spl8_17
| ~ spl8_40 ),
inference(resolution,[],[f354,f171]) ).
tff(f354,plain,
( ! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f353]) ).
tff(f913,plain,
( spl8_83
| ~ spl8_24
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f351,f344,f200,f911]) ).
tff(f911,plain,
( spl8_83
<=> ! [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_83])]) ).
tff(f200,plain,
( spl8_24
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
tff(f351,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ~ $less(0,count(X0,X2))
| in(X0,cons(X1,X2))
| ( X0 = X1 ) )
| ~ spl8_24
| ~ spl8_39 ),
inference(superposition,[],[f201,f345]) ).
tff(f201,plain,
( ! [X0: $int,X1: list] :
( ~ $less(0,count(X0,X1))
| in(X0,X1) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f200]) ).
tff(f904,plain,
( spl8_82
| ~ spl8_28
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f334,f301,f225,f902]) ).
tff(f902,plain,
( spl8_82
<=> ! [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_82])]) ).
tff(f334,plain,
( ! [X2: list,X0: $int,X1: list] : ( $sum(1,length(append(X1,X2))) = length(append(cons(X0,X1),X2)) )
| ~ spl8_28
| ~ spl8_37 ),
inference(superposition,[],[f226,f302]) ).
tff(f900,plain,
( spl8_81
| ~ spl8_29
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f277,f246,f242,f898]) ).
tff(f898,plain,
( spl8_81
<=> ! [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_81])]) ).
tff(f277,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl8_29
| ~ spl8_30 ),
inference(superposition,[],[f247,f243]) ).
tff(f896,plain,
( spl8_80
| ~ spl8_29
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f273,f246,f242,f894]) ).
tff(f894,plain,
( spl8_80
<=> ! [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_80])]) ).
tff(f273,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl8_29
| ~ spl8_30 ),
inference(superposition,[],[f247,f243]) ).
tff(f892,plain,
( spl8_79
| ~ spl8_26
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f269,f246,f217,f890]) ).
tff(f890,plain,
( spl8_79
<=> ! [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_79])]) ).
tff(f217,plain,
( spl8_26
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
tff(f269,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl8_26
| ~ spl8_30 ),
inference(resolution,[],[f247,f218]) ).
tff(f218,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f217]) ).
tff(f888,plain,
( spl8_78
| ~ spl8_22
| ~ spl8_27 ),
inference(avatar_split_clause,[],[f230,f221,f192,f886]) ).
tff(f886,plain,
( spl8_78
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
tff(f192,plain,
( spl8_22
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
tff(f221,plain,
( spl8_27
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
tff(f230,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl8_22
| ~ spl8_27 ),
inference(resolution,[],[f222,f193]) ).
tff(f193,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f192]) ).
tff(f222,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl8_27 ),
inference(avatar_component_clause,[],[f221]) ).
tff(f822,plain,
( spl8_77
| ~ spl8_25
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f335,f301,f204,f820]) ).
tff(f820,plain,
( spl8_77
<=> ! [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_77])]) ).
tff(f335,plain,
( ! [X2: list,X3: $int,X0: $int,X1: list] :
( sP1(X3,append(cons(X0,X1),X2))
| ~ in(X3,append(X1,X2)) )
| ~ spl8_25
| ~ spl8_37 ),
inference(superposition,[],[f205,f302]) ).
tff(f815,plain,
( spl8_76
| ~ spl8_21
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f325,f285,f188,f813]) ).
tff(f813,plain,
( spl8_76
<=> ! [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_76])]) ).
tff(f188,plain,
( spl8_21
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
tff(f325,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl8_21
| ~ spl8_33 ),
inference(superposition,[],[f189,f286]) ).
tff(f189,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f811,plain,
( spl8_75
| ~ spl8_22
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f324,f285,f192,f809]) ).
tff(f324,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl8_22
| ~ spl8_33 ),
inference(superposition,[],[f193,f286]) ).
tff(f807,plain,
( spl8_74
| ~ spl8_26
| ~ spl8_27 ),
inference(avatar_split_clause,[],[f231,f221,f217,f805]) ).
tff(f805,plain,
( spl8_74
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
tff(f231,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl8_26
| ~ spl8_27 ),
inference(resolution,[],[f222,f218]) ).
tff(f652,plain,
( spl8_73
| ~ spl8_15
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f332,f297,f161,f650]) ).
tff(f650,plain,
( spl8_73
<=> ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
tff(f161,plain,
( spl8_15
<=> ! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
tff(f297,plain,
( spl8_36
<=> ! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
tff(f332,plain,
( ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) )
| ~ spl8_15
| ~ spl8_36 ),
inference(resolution,[],[f298,f162]) ).
tff(f162,plain,
( ! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| sP0(X0,X1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f161]) ).
tff(f298,plain,
( ! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) )
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f297]) ).
tff(f648,plain,
( spl8_72
| ~ spl8_20
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f317,f285,f184,f646]) ).
tff(f646,plain,
( spl8_72
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
tff(f184,plain,
( spl8_20
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f317,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl8_20
| ~ spl8_33 ),
inference(superposition,[],[f286,f185]) ).
tff(f185,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f644,plain,
( spl8_71
| ~ spl8_28
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f506,f441,f225,f642]) ).
tff(f441,plain,
( spl8_52
<=> ! [X0: list,X1: $int] :
( ( 1 != length(X0) )
| ( cons(X1,nil) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
tff(f506,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( 1 != $sum(1,length(X1)) )
| ( cons(X0,X1) = cons(X2,nil) ) )
| ~ spl8_28
| ~ spl8_52 ),
inference(superposition,[],[f442,f226]) ).
tff(f442,plain,
( ! [X0: list,X1: $int] :
( ( 1 != length(X0) )
| ( cons(X1,nil) = X0 ) )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f441]) ).
tff(f640,plain,
( spl8_70
| ~ spl8_20
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f312,f285,f184,f638]) ).
tff(f638,plain,
( spl8_70
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
tff(f312,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl8_20
| ~ spl8_33 ),
inference(superposition,[],[f286,f185]) ).
tff(f636,plain,
( spl8_69
| ~ spl8_28
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f280,f254,f225,f634]) ).
tff(f280,plain,
( ! [X0: list] :
( ( length(X0) = $sum(1,length(tail(X0))) )
| ( nil = X0 ) )
| ~ spl8_28
| ~ spl8_32 ),
inference(superposition,[],[f226,f255]) ).
tff(f632,plain,
( spl8_68
| ~ spl8_21
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f228,f217,f188,f630]) ).
tff(f630,plain,
( spl8_68
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
tff(f228,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl8_21
| ~ spl8_26 ),
inference(resolution,[],[f218,f189]) ).
tff(f566,plain,
( spl8_67
| ~ spl8_13
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f337,f301,f153,f564]) ).
tff(f153,plain,
( spl8_13
<=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f337,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) )
| ~ spl8_13
| ~ spl8_37 ),
inference(superposition,[],[f154,f302]) ).
tff(f154,plain,
( ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f561,plain,
( spl8_66
| ~ spl8_12
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f316,f285,f149,f559]) ).
tff(f559,plain,
( spl8_66
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
tff(f149,plain,
( spl8_12
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f316,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl8_12
| ~ spl8_33 ),
inference(superposition,[],[f286,f150]) ).
tff(f150,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f557,plain,
( spl8_65
| ~ spl8_28
| ~ spl8_31 ),
inference(avatar_split_clause,[],[f310,f250,f225,f555]) ).
tff(f555,plain,
( spl8_65
<=> ! [X2: $int,X0: $int,X1: list] :
( ( 0 != $sum(2,length(X1)) )
| ( nil = cons(X2,cons(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
tff(f250,plain,
( spl8_31
<=> ! [X0: $int,X1: list] :
( ( 0 != $sum(1,length(X1)) )
| ( cons(X0,X1) = nil ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
tff(f310,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( 0 != $sum(2,length(X1)) )
| ( nil = cons(X2,cons(X0,X1)) ) )
| ~ spl8_28
| ~ spl8_31 ),
inference(evaluation,[],[f309]) ).
tff(f309,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( 0 != $sum(1,$sum(1,length(X1))) )
| ( nil = cons(X2,cons(X0,X1)) ) )
| ~ spl8_28
| ~ spl8_31 ),
inference(superposition,[],[f251,f226]) ).
tff(f251,plain,
( ! [X0: $int,X1: list] :
( ( 0 != $sum(1,length(X1)) )
| ( cons(X0,X1) = nil ) )
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f250]) ).
tff(f553,plain,
( spl8_64
| ~ spl8_25
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f281,f254,f204,f551]) ).
tff(f551,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(f281,plain,
( ! [X0: list,X1: $int] :
( sP1(X1,X0)
| ~ in(X1,tail(X0))
| ( nil = X0 ) )
| ~ spl8_25
| ~ spl8_32 ),
inference(superposition,[],[f205,f255]) ).
tff(f549,plain,
( spl8_63
| ~ spl8_20
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f275,f246,f184,f547]) ).
tff(f547,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(f275,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl8_20
| ~ spl8_30 ),
inference(superposition,[],[f247,f185]) ).
tff(f545,plain,
( spl8_62
| ~ spl8_20
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f271,f246,f184,f543]) ).
tff(f271,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl8_20
| ~ spl8_30 ),
inference(superposition,[],[f247,f185]) ).
tff(f541,plain,
( spl8_61
| ~ spl8_20
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f258,f242,f184,f539]) ).
tff(f539,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(f258,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl8_20
| ~ spl8_29 ),
inference(superposition,[],[f243,f185]) ).
tff(f518,plain,
( spl8_60
| ~ spl8_8
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f333,f301,f133,f516]) ).
tff(f516,plain,
( spl8_60
<=> ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
tff(f133,plain,
( spl8_8
<=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f333,plain,
( ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) )
| ~ spl8_8
| ~ spl8_37 ),
inference(superposition,[],[f302,f134]) ).
tff(f134,plain,
( ! [X0: list] : ( append(nil,X0) = X0 )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f514,plain,
( spl8_59
| ~ spl8_12
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f274,f246,f149,f512]) ).
tff(f512,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(f274,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl8_12
| ~ spl8_30 ),
inference(superposition,[],[f247,f150]) ).
tff(f510,plain,
( spl8_58
| ~ spl8_12
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f270,f246,f149,f508]) ).
tff(f270,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl8_12
| ~ spl8_30 ),
inference(superposition,[],[f247,f150]) ).
tff(f463,plain,
( spl8_57
| ~ spl8_14
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f336,f301,f157,f461]) ).
tff(f461,plain,
( spl8_57
<=> ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
tff(f157,plain,
( spl8_14
<=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f336,plain,
( ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 )
| ~ spl8_14
| ~ spl8_37 ),
inference(superposition,[],[f158,f302]) ).
tff(f158,plain,
( ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f459,plain,
( spl8_56
| ~ spl8_12
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f326,f285,f149,f457]) ).
tff(f457,plain,
( spl8_56
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
tff(f326,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl8_12
| ~ spl8_33 ),
inference(evaluation,[],[f311]) ).
tff(f311,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl8_12
| ~ spl8_33 ),
inference(superposition,[],[f286,f150]) ).
tff(f455,plain,
( spl8_55
| ~ spl8_18
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f215,f204,f174,f453]) ).
tff(f174,plain,
( spl8_18
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f215,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) )
| ~ spl8_18
| ~ spl8_25 ),
inference(resolution,[],[f205,f175]) ).
tff(f175,plain,
( ! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| in(X0,X1) )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f451,plain,
( spl8_54
| ~ spl8_20
| ~ spl8_22 ),
inference(avatar_split_clause,[],[f211,f192,f184,f449]) ).
tff(f211,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl8_20
| ~ spl8_22 ),
inference(superposition,[],[f193,f185]) ).
tff(f447,plain,
( spl8_53
| ~ spl8_20
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f208,f188,f184,f445]) ).
tff(f445,plain,
( spl8_53
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
tff(f208,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl8_20
| ~ spl8_21 ),
inference(superposition,[],[f189,f185]) ).
tff(f443,plain,
( spl8_52
| ~ spl8_4
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f398,f359,f114,f441]) ).
tff(f398,plain,
( ! [X0: list,X1: $int] :
( ( 1 != length(X0) )
| ( cons(X1,nil) = X0 ) )
| ~ spl8_4
| ~ spl8_41 ),
inference(evaluation,[],[f394]) ).
tff(f394,plain,
( ! [X0: list,X1: $int] :
( ( length(X0) != $sum(1,0) )
| ( cons(X1,nil) = X0 ) )
| ~ spl8_4
| ~ spl8_41 ),
inference(superposition,[],[f360,f116]) ).
tff(f428,plain,
( spl8_51
| ~ spl8_10
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f339,f301,f141,f426]) ).
tff(f141,plain,
( spl8_10
<=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
tff(f339,plain,
( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
| ~ spl8_10
| ~ spl8_37 ),
inference(superposition,[],[f142,f302]) ).
tff(f142,plain,
( ! [X0: $int,X1: list] : ( cons(X0,X1) != nil )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f141]) ).
tff(f424,plain,
( spl8_50
| ~ spl8_11
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f338,f301,f145,f422]) ).
tff(f338,plain,
( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
| ~ spl8_11
| ~ spl8_37 ),
inference(superposition,[],[f146,f302]) ).
tff(f420,plain,
( spl8_49
| ~ spl8_11
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f282,f254,f145,f418]) ).
tff(f418,plain,
( spl8_49
<=> ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
tff(f282,plain,
( ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) )
| ~ spl8_11
| ~ spl8_32 ),
inference(superposition,[],[f146,f255]) ).
tff(f406,plain,
( spl8_48
| ~ spl8_2
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f207,f188,f106,f404]) ).
tff(f207,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_2
| ~ spl8_21 ),
inference(resolution,[],[f189,f107]) ).
tff(f402,plain,
( spl8_47
| ~ spl8_11
| ~ spl8_18 ),
inference(avatar_split_clause,[],[f178,f174,f145,f400]) ).
tff(f178,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_11
| ~ spl8_18 ),
inference(resolution,[],[f175,f146]) ).
tff(f391,plain,
spl8_46,
inference(avatar_split_clause,[],[f82,f389]) ).
tff(f82,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,[],[f61]) ).
tff(f61,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])],[f58,f60,f59]) ).
tff(f59,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(f60,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(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 ) ) ) )
& ( ? [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,[],[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(flattening,[],[f56]) ).
tff(f56,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,[],[f47]) ).
tff(f47,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(f383,plain,
spl8_45,
inference(avatar_split_clause,[],[f84,f381]) ).
tff(f84,plain,
! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f379,plain,
spl8_44,
inference(avatar_split_clause,[],[f83,f377]) ).
tff(f377,plain,
( spl8_44
<=> ! [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_44])]) ).
tff(f83,plain,
! [X0: $int,X1: list] :
( ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f373,plain,
spl8_43,
inference(avatar_split_clause,[],[f72,f371]) ).
tff(f72,plain,
! [X0: $int,X1: list] :
( ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 )
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,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])],[f51,f52]) ).
tff(f52,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(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 ) ) )
& ( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[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(flattening,[],[f49]) ).
tff(f49,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,[],[f45]) ).
tff(f45,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(f365,plain,
spl8_42,
inference(avatar_split_clause,[],[f93,f363]) ).
tff(f93,plain,
! [X2: $int,X3: list,X0: $int] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(equality_resolution,[],[f77]) ).
tff(f77,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,[],[f53]) ).
tff(f361,plain,
( spl8_41
| ~ spl8_1
| ~ spl8_28 ),
inference(avatar_split_clause,[],[f239,f225,f101,f359]) ).
tff(f101,plain,
( spl8_1
<=> ! [X0: list,X1: list] :
( ( X0 = X1 )
| ( length(X0) != length(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f239,plain,
( ! [X2: list,X0: $int,X1: list] :
( ( $sum(1,length(X1)) != length(X2) )
| ( cons(X0,X1) = X2 ) )
| ~ spl8_1
| ~ spl8_28 ),
inference(superposition,[],[f102,f226]) ).
tff(f102,plain,
( ! [X0: list,X1: list] :
( ( length(X0) != length(X1) )
| ( X0 = X1 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f101]) ).
tff(f355,plain,
spl8_40,
inference(avatar_split_clause,[],[f85,f353]) ).
tff(f85,plain,
! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f346,plain,
spl8_39,
inference(avatar_split_clause,[],[f91,f344]) ).
tff(f91,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,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/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(f307,plain,
spl8_38,
inference(avatar_split_clause,[],[f99,f305]) ).
tff(f99,plain,
! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) ),
inference(forward_demodulation,[],[f98,f19]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f98,plain,
! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(count(X1,X2),1) ),
inference(equality_resolution,[],[f92]) ).
tff(f92,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,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/sandbox/benchmark/theBenchmark.p',a_4) ).
tff(f303,plain,
spl8_37,
inference(avatar_split_clause,[],[f90,f301]) ).
tff(f90,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/sandbox/benchmark/theBenchmark.p',l_7) ).
tff(f299,plain,
spl8_36,
inference(avatar_split_clause,[],[f75,f297]) ).
tff(f75,plain,
! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f295,plain,
spl8_35,
inference(avatar_split_clause,[],[f74,f293]) ).
tff(f74,plain,
! [X0: $int,X1: list] :
( $less(sK2(X0,X1),X0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f291,plain,
spl8_34,
inference(avatar_split_clause,[],[f73,f289]) ).
tff(f289,plain,
( spl8_34
<=> ! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
tff(f73,plain,
! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f287,plain,
spl8_33,
inference(avatar_split_clause,[],[f20,f285]) ).
tff(f20,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f256,plain,
spl8_32,
inference(avatar_split_clause,[],[f67,f254]) ).
tff(f67,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/sandbox/benchmark/theBenchmark.p',l3) ).
tff(f252,plain,
( spl8_31
| ~ spl8_9
| ~ spl8_28 ),
inference(avatar_split_clause,[],[f238,f225,f137,f250]) ).
tff(f137,plain,
( spl8_9
<=> ! [X0: list] :
( ( 0 != length(X0) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f238,plain,
( ! [X0: $int,X1: list] :
( ( 0 != $sum(1,length(X1)) )
| ( cons(X0,X1) = nil ) )
| ~ spl8_9
| ~ spl8_28 ),
inference(superposition,[],[f138,f226]) ).
tff(f138,plain,
( ! [X0: list] :
( ( 0 != length(X0) )
| ( nil = X0 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f137]) ).
tff(f248,plain,
spl8_30,
inference(avatar_split_clause,[],[f27,f246]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f244,plain,
spl8_29,
inference(avatar_split_clause,[],[f22,f242]) ).
tff(f22,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f227,plain,
spl8_28,
inference(avatar_split_clause,[],[f71,f225]) ).
tff(f71,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/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(f223,plain,
spl8_27,
inference(avatar_split_clause,[],[f26,f221]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f219,plain,
spl8_26,
inference(avatar_split_clause,[],[f25,f217]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f206,plain,
spl8_25,
inference(avatar_split_clause,[],[f95,f204]) ).
tff(f95,plain,
! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ),
inference(equality_resolution,[],[f87]) ).
tff(f87,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f61]) ).
tff(f202,plain,
spl8_24,
inference(avatar_split_clause,[],[f81,f200]) ).
tff(f81,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,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/sandbox/benchmark/theBenchmark.p',a_8) ).
tff(f198,plain,
spl8_23,
inference(avatar_split_clause,[],[f80,f196]) ).
tff(f80,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tff(f194,plain,
spl8_22,
inference(avatar_split_clause,[],[f30,f192]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f190,plain,
spl8_21,
inference(avatar_split_clause,[],[f28,f188]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f186,plain,
spl8_20,
inference(avatar_split_clause,[],[f19,f184]) ).
tff(f182,plain,
( spl8_19
| ~ spl8_3
| ~ spl8_16 ),
inference(avatar_split_clause,[],[f177,f166,f110,f180]) ).
tff(f180,plain,
( spl8_19
<=> ! [X0: $int] : inRange(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f110,plain,
( spl8_3
<=> ! [X0: $int] : sP0(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f177,plain,
( ! [X0: $int] : inRange(X0,nil)
| ~ spl8_3
| ~ spl8_16 ),
inference(resolution,[],[f167,f111]) ).
tff(f111,plain,
( ! [X0: $int] : sP0(X0,nil)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f110]) ).
tff(f176,plain,
spl8_18,
inference(avatar_split_clause,[],[f89,f174]) ).
tff(f89,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f38,f47]) ).
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/sandbox/benchmark/theBenchmark.p',in_conv) ).
tff(f172,plain,
spl8_17,
inference(avatar_split_clause,[],[f88,f170]) ).
tff(f88,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f168,plain,
spl8_16,
inference(avatar_split_clause,[],[f79,f166]) ).
tff(f79,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f36,f45]) ).
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/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f163,plain,
spl8_15,
inference(avatar_split_clause,[],[f78,f161]) ).
tff(f78,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f159,plain,
spl8_14,
inference(avatar_split_clause,[],[f70,f157]) ).
tff(f70,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/sandbox/benchmark/theBenchmark.p',l1) ).
tff(f155,plain,
spl8_13,
inference(avatar_split_clause,[],[f69,f153]) ).
tff(f69,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/sandbox/benchmark/theBenchmark.p',l2) ).
tff(f151,plain,
spl8_12,
inference(avatar_split_clause,[],[f23,f149]) ).
tff(f23,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f147,plain,
spl8_11,
inference(avatar_split_clause,[],[f97,f145]) ).
tff(f97,plain,
! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
inference(equality_resolution,[],[f96]) ).
tff(f96,plain,
! [X1: list,X4: $int,X5: list] :
( sP1(X4,X1)
| ( cons(X4,X5) != X1 ) ),
inference(equality_resolution,[],[f86]) ).
tff(f86,plain,
! [X0: $int,X1: list,X4: $int,X5: list] :
( sP1(X0,X1)
| ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ),
inference(cnf_transformation,[],[f61]) ).
tff(f143,plain,
spl8_10,
inference(avatar_split_clause,[],[f68,f141]) ).
tff(f68,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/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f139,plain,
( spl8_9
| ~ spl8_1
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f118,f114,f101,f137]) ).
tff(f118,plain,
( ! [X0: list] :
( ( 0 != length(X0) )
| ( nil = X0 ) )
| ~ spl8_1
| ~ spl8_4 ),
inference(superposition,[],[f102,f116]) ).
tff(f135,plain,
spl8_8,
inference(avatar_split_clause,[],[f66,f133]) ).
tff(f66,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/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f131,plain,
spl8_7,
inference(avatar_split_clause,[],[f65,f129]) ).
tff(f65,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: $int] : ( 0 = count(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f127,plain,
spl8_6,
inference(avatar_split_clause,[],[f29,f125]) ).
tff(f125,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(f123,plain,
spl8_5,
inference(avatar_split_clause,[],[f21,f121]) ).
tff(f121,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(f117,plain,
spl8_4,
inference(avatar_split_clause,[],[f64,f114]) ).
tff(f64,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
0 = length(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f112,plain,
spl8_3,
inference(avatar_split_clause,[],[f94,f110]) ).
tff(f94,plain,
! [X0: $int] : sP0(X0,nil),
inference(equality_resolution,[],[f76]) ).
tff(f76,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f53]) ).
tff(f108,plain,
spl8_2,
inference(avatar_split_clause,[],[f24,f106]) ).
tff(f24,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f103,plain,
spl8_1,
inference(avatar_split_clause,[],[f63,f101]) ).
tff(f63,plain,
! [X0: list,X1: list] :
( ( X0 = X1 )
| ( length(X0) != length(X1) ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: list,X1: list] :
( ( X0 = X1 )
| ( length(X0) != length(X1) ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: list,X1: list] :
( ( length(X0) = length(X1) )
=> ( X0 = X1 ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
~ ~ ! [X0: list,X1: list] :
( ( length(X0) = length(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ~ ! [X7: list,X8: list] :
( ( length(X7) = length(X8) )
=> ( X7 = X8 ) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
~ ! [X7: list,X8: list] :
( ( length(X7) = length(X8) )
=> ( X7 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT085_1 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n007.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 : Mon Apr 29 22:01:02 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (13791)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (13796)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (13794)WARNING: value z3 for option sas not known
% 0.14/0.38 % (13793)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (13797)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (13795)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (13794)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (13798)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (13792)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (13793)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (13793)Terminated due to inappropriate strategy.
% 0.14/0.38 % (13793)------------------------------
% 0.14/0.38 % (13793)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (13793)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (13793)Memory used [KB]: 803
% 0.14/0.38 % (13793)Time elapsed: 0.003 s
% 0.14/0.38 % (13793)Instructions burned: 3 (million)
% 0.14/0.38 % (13793)------------------------------
% 0.14/0.38 % (13793)------------------------------
% 0.14/0.38 % (13795)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (13795)Terminated due to inappropriate strategy.
% 0.14/0.38 % (13795)------------------------------
% 0.14/0.38 % (13795)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (13795)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (13795)Memory used [KB]: 803
% 0.14/0.38 % (13795)Time elapsed: 0.003 s
% 0.14/0.38 % (13795)Instructions burned: 3 (million)
% 0.14/0.38 % (13795)------------------------------
% 0.14/0.38 % (13795)------------------------------
% 0.14/0.38 % (13792)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (13792)Terminated due to inappropriate strategy.
% 0.14/0.38 % (13792)------------------------------
% 0.14/0.38 % (13792)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (13792)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (13792)Memory used [KB]: 803
% 0.14/0.38 % (13792)Time elapsed: 0.003 s
% 0.14/0.38 % (13792)Instructions burned: 3 (million)
% 0.14/0.38 % (13792)------------------------------
% 0.14/0.38 % (13792)------------------------------
% 0.14/0.40 % (13799)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (13801)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)
% 0.14/0.40 % (13800)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)
% 0.14/0.40 % (13799)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (13799)Terminated due to inappropriate strategy.
% 0.14/0.40 % (13799)------------------------------
% 0.14/0.40 % (13799)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40 % (13799)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (13799)Memory used [KB]: 803
% 0.14/0.40 % (13799)Time elapsed: 0.004 s
% 0.14/0.40 % (13799)Instructions burned: 3 (million)
% 0.14/0.40 % (13799)------------------------------
% 0.14/0.40 % (13799)------------------------------
% 0.22/0.43 % (13796)First to succeed.
% 0.22/0.43 % (13796)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (13796)------------------------------
% 0.22/0.44 % (13796)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.44 % (13796)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (13796)Memory used [KB]: 1622
% 0.22/0.44 % (13796)Time elapsed: 0.063 s
% 0.22/0.44 % (13796)Instructions burned: 125 (million)
% 0.22/0.44 % (13796)------------------------------
% 0.22/0.44 % (13796)------------------------------
% 0.22/0.44 % (13791)Success in time 0.08 s
%------------------------------------------------------------------------------