TSTP Solution File: DAT091_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT091_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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:05:59 EDT 2024
% Result : Theorem 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 136
% Syntax : Number of formulae : 379 ( 74 unt; 18 typ; 0 def)
% Number of atoms : 996 ( 273 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1070 ( 435 ~; 459 |; 67 &)
% ( 98 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 784 ( 143 atm; 149 fun; 97 num; 395 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 29 ( 16 >; 13 *; 0 +; 0 <<)
% Number of predicates : 95 ( 90 usr; 87 prp; 0-2 aty)
% Number of functors : 17 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 657 ( 613 !; 44 ?; 657 :)
% 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(f958,plain,
$false,
inference(avatar_sat_refutation,[],[f103,f108,f112,f117,f121,f125,f129,f133,f137,f141,f147,f151,f155,f159,f163,f167,f171,f175,f181,f186,f190,f194,f198,f202,f213,f218,f222,f226,f240,f244,f248,f280,f284,f288,f292,f296,f300,f322,f343,f355,f361,f365,f373,f379,f383,f391,f397,f412,f423,f437,f441,f445,f453,f464,f468,f472,f476,f480,f591,f595,f599,f630,f634,f641,f645,f649,f653,f658,f732,f734,f743,f758,f762,f766,f872,f878,f898,f905,f909,f913,f917,f935,f939,f943,f951,f955,f957]) ).
tff(f957,plain,
( ~ spl8_2
| ~ spl8_81 ),
inference(avatar_contradiction_clause,[],[f956]) ).
tff(f956,plain,
( $false
| ~ spl8_2
| ~ spl8_81 ),
inference(resolution,[],[f916,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(f916,plain,
( ! [X0: $int,X1: $int] : $less(X0,X1)
| ~ spl8_81 ),
inference(avatar_component_clause,[],[f915]) ).
tff(f915,plain,
( spl8_81
<=> ! [X0: $int,X1: $int] : $less(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
tff(f955,plain,
( spl8_86
| ~ spl8_36
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f458,f439,f294,f953]) ).
tff(f953,plain,
( spl8_86
<=> ! [X0: $int,X3: list,X2: list,X1: list] : sP1(X0,append(append(cons(X0,X1),X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
tff(f294,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(f439,plain,
( spl8_51
<=> ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
tff(f458,plain,
( ! [X2: list,X3: list,X0: $int,X1: list] : sP1(X0,append(append(cons(X0,X1),X2),X3))
| ~ spl8_36
| ~ spl8_51 ),
inference(superposition,[],[f440,f295]) ).
tff(f295,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(cons(X0,X1),X2) = cons(X0,append(X1,X2)) )
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f294]) ).
tff(f440,plain,
( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f439]) ).
tff(f951,plain,
( spl8_85
| ~ spl8_31
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f457,f439,f246,f949]) ).
tff(f949,plain,
( spl8_85
<=> ! [X0: list,X1: list] :
( sP1(head(X0),append(X0,X1))
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
tff(f246,plain,
( spl8_31
<=> ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
tff(f457,plain,
( ! [X0: list,X1: list] :
( sP1(head(X0),append(X0,X1))
| ( nil = X0 ) )
| ~ spl8_31
| ~ spl8_51 ),
inference(superposition,[],[f440,f247]) ).
tff(f247,plain,
( ! [X0: list] :
( ( cons(head(X0),tail(X0)) = X0 )
| ( nil = X0 ) )
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f246]) ).
tff(f943,plain,
( spl8_84
| ~ spl8_55
| ~ spl8_63 ),
inference(avatar_split_clause,[],[f679,f632,f466,f941]) ).
tff(f941,plain,
( spl8_84
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
tff(f466,plain,
( spl8_55
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
tff(f632,plain,
( spl8_63
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
tff(f679,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) )
| ~ spl8_55
| ~ spl8_63 ),
inference(resolution,[],[f633,f467]) ).
tff(f467,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f466]) ).
tff(f633,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl8_63 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f939,plain,
( spl8_83
| ~ spl8_30
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f493,f466,f242,f937]) ).
tff(f937,plain,
( spl8_83
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
tff(f242,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(f493,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) )
| ~ spl8_30
| ~ spl8_55 ),
inference(resolution,[],[f467,f243]) ).
tff(f243,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f242]) ).
tff(f935,plain,
( spl8_82
| ~ spl8_31
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f459,f443,f246,f933]) ).
tff(f933,plain,
( spl8_82
<=> ! [X0: list,X1: list] :
( ( nil != append(X0,X1) )
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
tff(f443,plain,
( spl8_52
<=> ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
tff(f459,plain,
( ! [X0: list,X1: list] :
( ( nil != append(X0,X1) )
| ( nil = X0 ) )
| ~ spl8_31
| ~ spl8_52 ),
inference(superposition,[],[f444,f247]) ).
tff(f444,plain,
( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f443]) ).
tff(f917,plain,
( spl8_81
| ~ spl8_49
| ~ spl8_64 ),
inference(avatar_split_clause,[],[f799,f636,f421,f915]) ).
tff(f421,plain,
( spl8_49
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
tff(f636,plain,
( spl8_64
<=> ! [X2: $int,X0: $int] : ( X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
tff(f799,plain,
( ! [X0: $int,X1: $int] : $less(X0,X1)
| ~ spl8_49
| ~ spl8_64 ),
inference(superposition,[],[f422,f637]) ).
tff(f637,plain,
( ! [X2: $int,X0: $int] : ( X0 = X2 )
| ~ spl8_64 ),
inference(avatar_component_clause,[],[f636]) ).
tff(f422,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f421]) ).
tff(f913,plain,
( spl8_80
| ~ spl8_55
| ~ spl8_59 ),
inference(avatar_split_clause,[],[f600,f589,f466,f911]) ).
tff(f911,plain,
( spl8_80
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
tff(f589,plain,
( spl8_59
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
tff(f600,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl8_55
| ~ spl8_59 ),
inference(resolution,[],[f590,f467]) ).
tff(f590,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl8_59 ),
inference(avatar_component_clause,[],[f589]) ).
tff(f909,plain,
( spl8_79
| ~ spl8_36
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f427,f320,f294,f907]) ).
tff(f907,plain,
( spl8_79
<=> ! [X2: list,X0: $int,X1: list] : in(X0,append(cons(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
tff(f320,plain,
( spl8_38
<=> ! [X0: $int,X1: list] : in(X0,cons(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
tff(f427,plain,
( ! [X2: list,X0: $int,X1: list] : in(X0,append(cons(X0,X1),X2))
| ~ spl8_36
| ~ spl8_38 ),
inference(superposition,[],[f321,f295]) ).
tff(f321,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f320]) ).
tff(f905,plain,
( spl8_78
| ~ spl8_31
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f426,f320,f246,f903]) ).
tff(f903,plain,
( spl8_78
<=> ! [X0: list] :
( in(head(X0),X0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
tff(f426,plain,
( ! [X0: list] :
( in(head(X0),X0)
| ( nil = X0 ) )
| ~ spl8_31
| ~ spl8_38 ),
inference(superposition,[],[f321,f247]) ).
tff(f898,plain,
( spl8_77
| ~ spl8_24
| ~ spl8_46 ),
inference(avatar_split_clause,[],[f393,f389,f200,f896]) ).
tff(f896,plain,
( spl8_77
<=> ! [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_77])]) ).
tff(f200,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(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_24
| ~ spl8_46 ),
inference(resolution,[],[f390,f201]) ).
tff(f201,plain,
( ! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f200]) ).
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(f878,plain,
( spl8_76
| ~ spl8_10
| ~ spl8_46 ),
inference(avatar_split_clause,[],[f392,f389,f139,f876]) ).
tff(f876,plain,
( spl8_76
<=> ! [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_76])]) ).
tff(f139,plain,
( spl8_10
<=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
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_10
| ~ spl8_46 ),
inference(resolution,[],[f390,f140]) ).
tff(f140,plain,
( ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5))
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f139]) ).
tff(f872,plain,
( spl8_75
| ~ spl8_17
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f387,f381,f169,f870]) ).
tff(f870,plain,
( spl8_75
<=> ! [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_75])]) ).
tff(f169,plain,
( spl8_17
<=> ! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
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(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,f170]) ).
tff(f170,plain,
( ! [X0: $int,X1: list] :
( ~ in(X0,X1)
| sP1(X0,X1) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f169]) ).
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(f766,plain,
( spl8_74
| ~ spl8_24
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f329,f294,f200,f764]) ).
tff(f764,plain,
( spl8_74
<=> ! [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_74])]) ).
tff(f329,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,[],[f201,f295]) ).
tff(f762,plain,
( spl8_73
| ~ spl8_20
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f315,f278,f184,f760]) ).
tff(f760,plain,
( spl8_73
<=> ! [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_73])]) ).
tff(f184,plain,
( spl8_20
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f278,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(f315,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,[],[f185,f279]) ).
tff(f279,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f278]) ).
tff(f185,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f758,plain,
( spl8_72
| ~ spl8_21
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f314,f278,f188,f756]) ).
tff(f756,plain,
( spl8_72
<=> ! [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_72])]) ).
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(f314,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,[],[f189,f279]) ).
tff(f189,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f743,plain,
( spl8_71
| ~ spl8_14
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f326,f290,f157,f741]) ).
tff(f741,plain,
( spl8_71
<=> ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
tff(f157,plain,
( spl8_14
<=> ! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f290,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(f326,plain,
( ! [X0: list,X1: $int] :
( ( nil = X0 )
| ~ sP0(X1,X0)
| sP0(X1,sK3(X1,X0)) )
| ~ spl8_14
| ~ spl8_35 ),
inference(resolution,[],[f291,f158]) ).
tff(f158,plain,
( ! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| sP0(X0,X1) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f291,plain,
( ! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f290]) ).
tff(f734,plain,
~ spl8_65,
inference(avatar_contradiction_clause,[],[f733]) ).
tff(f733,plain,
( $false
| ~ spl8_65 ),
inference(equality_resolution,[],[f640]) ).
tff(f640,plain,
( ! [X1: list] : ( nil != X1 )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f639]) ).
tff(f639,plain,
( spl8_65
<=> ! [X1: list] : ( nil != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
tff(f732,plain,
( spl8_70
| ~ spl8_20
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f227,f216,f184,f730]) ).
tff(f730,plain,
( spl8_70
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
tff(f216,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(f227,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl8_20
| ~ spl8_26 ),
inference(resolution,[],[f217,f185]) ).
tff(f217,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f216]) ).
tff(f658,plain,
( spl8_69
| ~ spl8_12
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f331,f294,f149,f656]) ).
tff(f656,plain,
( spl8_69
<=> ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
tff(f149,plain,
( spl8_12
<=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f331,plain,
( ! [X2: list,X0: $int,X1: list] : ( append(X1,X2) = tail(append(cons(X0,X1),X2)) )
| ~ spl8_12
| ~ spl8_36 ),
inference(superposition,[],[f150,f295]) ).
tff(f150,plain,
( ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f653,plain,
( spl8_68
| ~ spl8_11
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f306,f278,f145,f651]) ).
tff(f651,plain,
( spl8_68
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
tff(f145,plain,
( spl8_11
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f306,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl8_11
| ~ spl8_32 ),
inference(superposition,[],[f279,f146]) ).
tff(f146,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f145]) ).
tff(f649,plain,
( spl8_67
| ~ spl8_24
| ~ spl8_31 ),
inference(avatar_split_clause,[],[f274,f246,f200,f647]) ).
tff(f647,plain,
( spl8_67
<=> ! [X0: list,X1: $int] :
( sP1(X1,X0)
| ~ in(X1,tail(X0))
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
tff(f274,plain,
( ! [X0: list,X1: $int] :
( sP1(X1,X0)
| ~ in(X1,tail(X0))
| ( nil = X0 ) )
| ~ spl8_24
| ~ spl8_31 ),
inference(superposition,[],[f201,f247]) ).
tff(f645,plain,
( spl8_66
| ~ spl8_19
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f268,f242,f179,f643]) ).
tff(f643,plain,
( spl8_66
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
tff(f179,plain,
( spl8_19
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f268,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl8_19
| ~ spl8_30 ),
inference(superposition,[],[f243,f180]) ).
tff(f180,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f179]) ).
tff(f641,plain,
( spl8_64
| spl8_65
| ~ spl8_9
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f504,f451,f135,f639,f636]) ).
tff(f135,plain,
( spl8_9
<=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f451,plain,
( spl8_53
<=> ! [X2: $int,X0: $int,X1: list] :
( ( cons(X0,X1) = X1 )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
tff(f504,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( nil != X1 )
| ( X0 = X2 ) )
| ~ spl8_9
| ~ spl8_53 ),
inference(superposition,[],[f136,f452]) ).
tff(f452,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( cons(X0,X1) = X1 )
| ( X0 = X2 ) )
| ~ spl8_53 ),
inference(avatar_component_clause,[],[f451]) ).
tff(f136,plain,
( ! [X0: $int,X1: list] : ( cons(X0,X1) != nil )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f135]) ).
tff(f634,plain,
( spl8_63
| ~ spl8_19
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f264,f242,f179,f632]) ).
tff(f264,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl8_19
| ~ spl8_30 ),
inference(superposition,[],[f243,f180]) ).
tff(f630,plain,
( spl8_62
| ~ spl8_19
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f251,f238,f179,f628]) ).
tff(f628,plain,
( spl8_62
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
tff(f238,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(f251,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl8_19
| ~ spl8_29 ),
inference(superposition,[],[f239,f180]) ).
tff(f239,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f238]) ).
tff(f599,plain,
( spl8_61
| ~ spl8_8
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f327,f294,f131,f597]) ).
tff(f597,plain,
( spl8_61
<=> ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
tff(f131,plain,
( spl8_8
<=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f327,plain,
( ! [X0: list,X1: $int] : ( append(cons(X1,nil),X0) = cons(X1,X0) )
| ~ spl8_8
| ~ spl8_36 ),
inference(superposition,[],[f295,f132]) ).
tff(f132,plain,
( ! [X0: list] : ( append(nil,X0) = X0 )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f131]) ).
tff(f595,plain,
( spl8_60
| ~ spl8_11
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f267,f242,f145,f593]) ).
tff(f593,plain,
( spl8_60
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
tff(f267,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl8_11
| ~ spl8_30 ),
inference(superposition,[],[f243,f146]) ).
tff(f591,plain,
( spl8_59
| ~ spl8_11
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f263,f242,f145,f589]) ).
tff(f263,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl8_11
| ~ spl8_30 ),
inference(superposition,[],[f243,f146]) ).
tff(f480,plain,
( spl8_58
| ~ spl8_13
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f330,f294,f153,f478]) ).
tff(f478,plain,
( spl8_58
<=> ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
tff(f153,plain,
( spl8_13
<=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f330,plain,
( ! [X2: list,X0: $int,X1: list] : ( head(append(cons(X0,X1),X2)) = X0 )
| ~ spl8_13
| ~ spl8_36 ),
inference(superposition,[],[f154,f295]) ).
tff(f154,plain,
( ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f476,plain,
( spl8_57
| ~ spl8_11
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f316,f278,f145,f474]) ).
tff(f474,plain,
( spl8_57
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
tff(f316,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl8_11
| ~ spl8_32 ),
inference(evaluation,[],[f301]) ).
tff(f301,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl8_11
| ~ spl8_32 ),
inference(superposition,[],[f279,f146]) ).
tff(f472,plain,
( spl8_56
| ~ spl8_18
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f214,f200,f173,f470]) ).
tff(f470,plain,
( spl8_56
<=> ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
tff(f173,plain,
( spl8_18
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f214,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ~ in(X0,X1)
| in(X0,cons(X2,X1)) )
| ~ spl8_18
| ~ spl8_24 ),
inference(resolution,[],[f201,f174]) ).
tff(f174,plain,
( ! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| in(X0,X1) )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f173]) ).
tff(f468,plain,
( spl8_55
| ~ spl8_19
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f207,f188,f179,f466]) ).
tff(f207,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl8_19
| ~ spl8_21 ),
inference(superposition,[],[f189,f180]) ).
tff(f464,plain,
( spl8_54
| ~ spl8_19
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f204,f184,f179,f462]) ).
tff(f462,plain,
( spl8_54
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
tff(f204,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl8_19
| ~ spl8_20 ),
inference(superposition,[],[f185,f180]) ).
tff(f453,plain,
( spl8_53
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f419,f410,f451]) ).
tff(f410,plain,
( spl8_48
<=> ! [X0: $int,X3: list,X2: list,X1: $int] :
( ( count(X0,X2) != count(X0,X3) )
| ( cons(X1,X2) = X3 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
tff(f419,plain,
( ! [X2: $int,X0: $int,X1: list] :
( ( cons(X0,X1) = X1 )
| ( X0 = X2 ) )
| ~ spl8_48 ),
inference(equality_resolution,[],[f411]) ).
tff(f411,plain,
( ! [X2: list,X3: list,X0: $int,X1: $int] :
( ( count(X0,X2) != count(X0,X3) )
| ( cons(X1,X2) = X3 )
| ( X0 = X1 ) )
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f410]) ).
tff(f445,plain,
( spl8_52
| ~ spl8_9
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f333,f294,f135,f443]) ).
tff(f333,plain,
( ! [X2: list,X0: $int,X1: list] : ( nil != append(cons(X0,X1),X2) )
| ~ spl8_9
| ~ spl8_36 ),
inference(superposition,[],[f136,f295]) ).
tff(f441,plain,
( spl8_51
| ~ spl8_10
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f332,f294,f139,f439]) ).
tff(f332,plain,
( ! [X2: list,X0: $int,X1: list] : sP1(X0,append(cons(X0,X1),X2))
| ~ spl8_10
| ~ spl8_36 ),
inference(superposition,[],[f140,f295]) ).
tff(f437,plain,
( spl8_50
| ~ spl8_10
| ~ spl8_31 ),
inference(avatar_split_clause,[],[f275,f246,f139,f435]) ).
tff(f435,plain,
( spl8_50
<=> ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
tff(f275,plain,
( ! [X0: list] :
( sP1(head(X0),X0)
| ( nil = X0 ) )
| ~ spl8_10
| ~ spl8_31 ),
inference(superposition,[],[f140,f247]) ).
tff(f423,plain,
( spl8_49
| ~ spl8_2
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f203,f184,f106,f421]) ).
tff(f203,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl8_2
| ~ spl8_20 ),
inference(resolution,[],[f185,f107]) ).
tff(f412,plain,
( spl8_48
| ~ spl8_1
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f350,f341,f101,f410]) ).
tff(f101,plain,
( spl8_1
<=> ! [X2: $int,X0: list,X1: list] :
( ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f341,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(f350,plain,
( ! [X2: list,X3: list,X0: $int,X1: $int] :
( ( count(X0,X2) != count(X0,X3) )
| ( cons(X1,X2) = X3 )
| ( X0 = X1 ) )
| ~ spl8_1
| ~ spl8_39 ),
inference(superposition,[],[f102,f342]) ).
tff(f342,plain,
( ! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f341]) ).
tff(f102,plain,
( ! [X2: $int,X0: list,X1: list] :
( ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f101]) ).
tff(f397,plain,
( spl8_47
| ~ spl8_1
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f338,f298,f101,f395]) ).
tff(f395,plain,
( spl8_47
<=> ! [X2: list,X0: $int,X1: list] :
( ( count(X0,X2) != $sum(1,count(X0,X1)) )
| ( cons(X0,X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
tff(f298,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(f338,plain,
( ! [X2: list,X0: $int,X1: list] :
( ( count(X0,X2) != $sum(1,count(X0,X1)) )
| ( cons(X0,X1) = X2 ) )
| ~ spl8_1
| ~ spl8_37 ),
inference(superposition,[],[f102,f299]) ).
tff(f299,plain,
( ! [X2: list,X1: $int] : ( count(X1,cons(X1,X2)) = $sum(1,count(X1,X2)) )
| ~ spl8_37 ),
inference(avatar_component_clause,[],[f298]) ).
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(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(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
| ~ spl8_16
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f337,f298,f165,f363]) ).
tff(f363,plain,
( spl8_42
<=> ! [X0: $int,X1: list] :
( ( 0 != $sum(1,count(X0,X1)) )
| ( cons(X0,X1) = nil ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
tff(f165,plain,
( spl8_16
<=> ! [X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( nil = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f337,plain,
( ! [X0: $int,X1: list] :
( ( 0 != $sum(1,count(X0,X1)) )
| ( cons(X0,X1) = nil ) )
| ~ spl8_16
| ~ spl8_37 ),
inference(superposition,[],[f166,f299]) ).
tff(f166,plain,
( ! [X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( nil = X1 ) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f165]) ).
tff(f361,plain,
spl8_41,
inference(avatar_split_clause,[],[f93,f359]) ).
tff(f359,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(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(f355,plain,
spl8_40,
inference(avatar_split_clause,[],[f85,f353]) ).
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(f85,plain,
! [X0: $int,X1: list] :
( in(X0,sK5(X0,X1))
| ( sK6(X0,X1) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f343,plain,
spl8_39,
inference(avatar_split_clause,[],[f91,f341]) ).
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(f322,plain,
( spl8_38
| ~ spl8_10
| ~ spl8_18 ),
inference(avatar_split_clause,[],[f177,f173,f139,f320]) ).
tff(f177,plain,
( ! [X0: $int,X1: list] : in(X0,cons(X0,X1))
| ~ spl8_10
| ~ spl8_18 ),
inference(resolution,[],[f174,f140]) ).
tff(f300,plain,
spl8_37,
inference(avatar_split_clause,[],[f99,f298]) ).
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(f296,plain,
spl8_36,
inference(avatar_split_clause,[],[f90,f294]) ).
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(f292,plain,
spl8_35,
inference(avatar_split_clause,[],[f75,f290]) ).
tff(f75,plain,
! [X0: $int,X1: list] :
( inRange(X0,sK3(X0,X1))
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f288,plain,
spl8_34,
inference(avatar_split_clause,[],[f74,f286]) ).
tff(f286,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(f74,plain,
! [X0: $int,X1: list] :
( $less(sK2(X0,X1),X0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f284,plain,
spl8_33,
inference(avatar_split_clause,[],[f73,f282]) ).
tff(f282,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(f73,plain,
! [X0: $int,X1: list] :
( ~ $less(sK2(X0,X1),0)
| ( nil = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f280,plain,
spl8_32,
inference(avatar_split_clause,[],[f20,f278]) ).
tff(f20,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f248,plain,
spl8_31,
inference(avatar_split_clause,[],[f67,f246]) ).
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(f244,plain,
spl8_30,
inference(avatar_split_clause,[],[f27,f242]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f240,plain,
spl8_29,
inference(avatar_split_clause,[],[f22,f238]) ).
tff(f22,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f226,plain,
spl8_28,
inference(avatar_split_clause,[],[f71,f224]) ).
tff(f224,plain,
( spl8_28
<=> ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
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(f222,plain,
spl8_27,
inference(avatar_split_clause,[],[f26,f220]) ).
tff(f220,plain,
( spl8_27
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f218,plain,
spl8_26,
inference(avatar_split_clause,[],[f25,f216]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f213,plain,
( spl8_25
| ~ spl8_3
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f176,f161,f110,f211]) ).
tff(f211,plain,
( spl8_25
<=> ! [X0: $int] : inRange(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f110,plain,
( spl8_3
<=> ! [X0: $int] : sP0(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f161,plain,
( spl8_15
<=> ! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
tff(f176,plain,
( ! [X0: $int] : inRange(X0,nil)
| ~ spl8_3
| ~ spl8_15 ),
inference(resolution,[],[f162,f111]) ).
tff(f111,plain,
( ! [X0: $int] : sP0(X0,nil)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f110]) ).
tff(f162,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| inRange(X0,X1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f161]) ).
tff(f202,plain,
spl8_24,
inference(avatar_split_clause,[],[f95,f200]) ).
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(f198,plain,
spl8_23,
inference(avatar_split_clause,[],[f81,f196]) ).
tff(f196,plain,
( spl8_23
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
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(f194,plain,
spl8_22,
inference(avatar_split_clause,[],[f80,f192]) ).
tff(f192,plain,
( spl8_22
<=> ! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
tff(f80,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tff(f190,plain,
spl8_21,
inference(avatar_split_clause,[],[f30,f188]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f186,plain,
spl8_20,
inference(avatar_split_clause,[],[f28,f184]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f181,plain,
spl8_19,
inference(avatar_split_clause,[],[f19,f179]) ).
tff(f175,plain,
spl8_18,
inference(avatar_split_clause,[],[f89,f173]) ).
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(f171,plain,
spl8_17,
inference(avatar_split_clause,[],[f88,f169]) ).
tff(f88,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f167,plain,
( spl8_16
| ~ spl8_1
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f142,f127,f101,f165]) ).
tff(f127,plain,
( spl8_7
<=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f142,plain,
( ! [X0: $int,X1: list] :
( ( 0 != count(X0,X1) )
| ( nil = X1 ) )
| ~ spl8_1
| ~ spl8_7 ),
inference(superposition,[],[f102,f128]) ).
tff(f128,plain,
( ! [X0: $int] : ( 0 = count(X0,nil) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f127]) ).
tff(f163,plain,
spl8_15,
inference(avatar_split_clause,[],[f79,f161]) ).
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(f159,plain,
spl8_14,
inference(avatar_split_clause,[],[f78,f157]) ).
tff(f78,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f155,plain,
spl8_13,
inference(avatar_split_clause,[],[f70,f153]) ).
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(f151,plain,
spl8_12,
inference(avatar_split_clause,[],[f69,f149]) ).
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(f147,plain,
spl8_11,
inference(avatar_split_clause,[],[f23,f145]) ).
tff(f23,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f141,plain,
spl8_10,
inference(avatar_split_clause,[],[f97,f139]) ).
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(f137,plain,
spl8_9,
inference(avatar_split_clause,[],[f68,f135]) ).
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(f133,plain,
spl8_8,
inference(avatar_split_clause,[],[f66,f131]) ).
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(f129,plain,
spl8_7,
inference(avatar_split_clause,[],[f65,f127]) ).
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(f125,plain,
spl8_6,
inference(avatar_split_clause,[],[f29,f123]) ).
tff(f123,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(f121,plain,
spl8_5,
inference(avatar_split_clause,[],[f21,f119]) ).
tff(f119,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(f114,plain,
( spl8_4
<=> ( 0 = length(nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
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,
! [X2: $int,X0: list,X1: list] :
( ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: list,X1: list] :
( ! [X2: $int] : ( count(X2,X0) != count(X2,X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
~ ~ ! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ~ ! [X7: list,X8: list] :
( ( X7 != X8 )
=> ! [X5: $int] : ( count(X5,X7) != count(X5,X8) ) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
~ ! [X7: list,X8: list] :
( ( X7 != X8 )
=> ! [X5: $int] : ( count(X5,X7) != count(X5,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT091_1 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n008.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri May 3 13:00:27 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (26392)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (26395)WARNING: value z3 for option sas not known
% 0.14/0.39 % (26398)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 % (26394)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 % (26395)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 % (26397)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 % (26396)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (26399)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 % (26394)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (26394)Terminated due to inappropriate strategy.
% 0.14/0.39 % (26394)------------------------------
% 0.14/0.39 % (26394)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (26394)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (26394)Memory used [KB]: 803
% 0.14/0.39 % (26394)Time elapsed: 0.002 s
% 0.14/0.39 % (26394)Instructions burned: 3 (million)
% 0.14/0.39 % (26396)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (26394)------------------------------
% 0.14/0.39 % (26394)------------------------------
% 0.14/0.39 % (26396)Terminated due to inappropriate strategy.
% 0.14/0.39 % (26396)------------------------------
% 0.14/0.39 % (26396)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (26396)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (26396)Memory used [KB]: 803
% 0.14/0.39 % (26396)Time elapsed: 0.003 s
% 0.14/0.39 % (26396)Instructions burned: 3 (million)
% 0.14/0.39 % (26396)------------------------------
% 0.14/0.39 % (26396)------------------------------
% 0.14/0.40 % (26393)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (26393)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (26393)Terminated due to inappropriate strategy.
% 0.14/0.40 % (26393)------------------------------
% 0.14/0.40 % (26393)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (26393)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (26393)Memory used [KB]: 803
% 0.14/0.40 % (26393)Time elapsed: 0.003 s
% 0.14/0.40 % (26393)Instructions burned: 3 (million)
% 0.14/0.40 % (26393)------------------------------
% 0.14/0.40 % (26393)------------------------------
% 0.20/0.40 % (26400)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.40 % (26401)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)
% 0.20/0.40 % (26400)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.40 % (26400)Terminated due to inappropriate strategy.
% 0.20/0.40 % (26400)------------------------------
% 0.20/0.40 % (26400)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40 % (26400)Termination reason: Inappropriate
% 0.20/0.40
% 0.20/0.40 % (26400)Memory used [KB]: 804
% 0.20/0.40 % (26400)Time elapsed: 0.003 s
% 0.20/0.40 % (26400)Instructions burned: 3 (million)
% 0.20/0.41 % (26400)------------------------------
% 0.20/0.41 % (26400)------------------------------
% 0.20/0.41 % (26397)First to succeed.
% 0.20/0.41 % (26402)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)
% 0.20/0.42 % (26397)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26392"
% 0.20/0.42 % (26397)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Theorem for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.42 % (26397)------------------------------
% 0.20/0.42 % (26397)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.42 % (26397)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42 % (26397)Memory used [KB]: 1219
% 0.20/0.42 % (26397)Time elapsed: 0.033 s
% 0.20/0.42 % (26397)Instructions burned: 57 (million)
% 0.20/0.42 % (26392)Success in time 0.046 s
%------------------------------------------------------------------------------