TSTP Solution File: DAT047_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT047_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:51:09 EDT 2024
% Result : Theorem 0.24s 0.47s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 118
% Syntax : Number of formulae : 384 ( 57 unt; 6 typ; 0 def)
% Number of atoms : 1063 ( 248 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1198 ( 513 ~; 566 |; 15 &)
% ( 102 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 1132 ( 137 atm; 289 fun; 319 num; 387 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 92 ( 88 usr; 88 prp; 0-2 aty)
% Number of functors : 13 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 524 ( 524 !; 0 ?; 524 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f1427,plain,
$false,
inference(avatar_sat_refutation,[],[f86,f90,f94,f98,f103,f108,f112,f116,f120,f124,f128,f132,f137,f141,f145,f149,f159,f163,f177,f181,f185,f189,f193,f197,f201,f205,f244,f248,f252,f282,f286,f290,f294,f298,f315,f319,f339,f343,f347,f351,f394,f398,f402,f421,f425,f429,f433,f500,f504,f508,f512,f516,f520,f551,f686,f690,f694,f756,f776,f780,f784,f788,f792,f889,f900,f904,f908,f912,f916,f920,f924,f928,f1149,f1153,f1157,f1161,f1165,f1169,f1247,f1251,f1255,f1260,f1291,f1322,f1326,f1402,f1407,f1416,f1418]) ).
tff(f1418,plain,
( ~ spl0_39
| ~ spl0_87 ),
inference(avatar_contradiction_clause,[],[f1417]) ).
tff(f1417,plain,
( $false
| ~ spl0_39
| ~ spl0_87 ),
inference(evaluation,[],[f1412]) ).
tff(f1412,plain,
( $less(0,-1)
| ( 0 = -1 )
| ~ spl0_39
| ~ spl0_87 ),
inference(superposition,[],[f346,f1406]) ).
tff(f1406,plain,
( ( -1 = count(remove(5,remove(3,add(3,empty)))) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1404]) ).
tff(f1404,plain,
( spl0_87
<=> ( -1 = count(remove(5,remove(3,add(3,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
tff(f346,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f345]) ).
tff(f345,plain,
( spl0_39
<=> ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f1416,plain,
( ~ spl0_4
| ~ spl0_87 ),
inference(avatar_contradiction_clause,[],[f1415]) ).
tff(f1415,plain,
( $false
| ~ spl0_4
| ~ spl0_87 ),
inference(evaluation,[],[f1414]) ).
tff(f1414,plain,
( ~ $less(-1,0)
| ~ spl0_4
| ~ spl0_87 ),
inference(superposition,[],[f97,f1406]) ).
tff(f97,plain,
( ! [X0: collection] : ~ $less(count(X0),0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f96,plain,
( spl0_4
<=> ! [X0: collection] : ~ $less(count(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f1407,plain,
( spl0_87
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f1317,f1289,f790,f317,f83,f1404]) ).
tff(f83,plain,
( spl0_1
<=> ( 1 = count(add(5,remove(3,add(3,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f317,plain,
( spl0_36
<=> ! [X0: $int] : ( 1 = count(add(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f790,plain,
( spl0_63
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
tff(f1289,plain,
( spl0_83
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
tff(f1317,plain,
( ( -1 = count(remove(5,remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(evaluation,[],[f1316]) ).
tff(f1316,plain,
( ( count(remove(5,remove(3,add(3,empty)))) = $sum(-2,1) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(forward_demodulation,[],[f1315,f318]) ).
tff(f318,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f317]) ).
tff(f1315,plain,
( ( count(remove(5,remove(3,add(3,empty)))) = $sum(-2,count(add(3,empty))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(evaluation,[],[f1314]) ).
tff(f1314,plain,
( ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,$sum(-1,count(add(3,empty)))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(forward_demodulation,[],[f1313,f791]) ).
tff(f791,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f790]) ).
tff(f1313,plain,
( ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,count(remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(trivial_inequality_removal,[],[f1312]) ).
tff(f1312,plain,
( ( 1 != 1 )
| ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,count(remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_83 ),
inference(forward_demodulation,[],[f1311,f318]) ).
tff(f1311,plain,
( ( 1 != count(add(3,empty)) )
| ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,count(remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_63
| ~ spl0_83 ),
inference(evaluation,[],[f1310]) ).
tff(f1310,plain,
( ( 1 != $sum(1,$sum(-1,count(add(3,empty)))) )
| ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,count(remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_63
| ~ spl0_83 ),
inference(forward_demodulation,[],[f1298,f791]) ).
tff(f1298,plain,
( ( 1 != $sum(1,count(remove(3,add(3,empty)))) )
| ( count(remove(5,remove(3,add(3,empty)))) = $sum(-1,count(remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_83 ),
inference(superposition,[],[f85,f1290]) ).
tff(f1290,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1289]) ).
tff(f85,plain,
( ( 1 != count(add(5,remove(3,add(3,empty)))) )
| spl0_1 ),
inference(avatar_component_clause,[],[f83]) ).
tff(f1402,plain,
( spl0_86
| ~ spl0_26
| ~ spl0_36
| ~ spl0_63
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f1397,f1257,f790,f317,f203,f1399]) ).
tff(f1399,plain,
( spl0_86
<=> in(5,remove(3,add(3,empty))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
tff(f203,plain,
( spl0_26
<=> ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f1257,plain,
( spl0_82
<=> ( 0 = count(add(5,remove(3,add(3,empty)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
tff(f1397,plain,
( in(5,remove(3,add(3,empty)))
| ~ spl0_26
| ~ spl0_36
| ~ spl0_63
| ~ spl0_82 ),
inference(evaluation,[],[f1396]) ).
tff(f1396,plain,
( ( 0 != $sum(-1,1) )
| in(5,remove(3,add(3,empty)))
| ~ spl0_26
| ~ spl0_36
| ~ spl0_63
| ~ spl0_82 ),
inference(forward_demodulation,[],[f1395,f318]) ).
tff(f1395,plain,
( ( 0 != $sum(-1,count(add(3,empty))) )
| in(5,remove(3,add(3,empty)))
| ~ spl0_26
| ~ spl0_63
| ~ spl0_82 ),
inference(forward_demodulation,[],[f1358,f791]) ).
tff(f1358,plain,
( ( 0 != count(remove(3,add(3,empty))) )
| in(5,remove(3,add(3,empty)))
| ~ spl0_26
| ~ spl0_82 ),
inference(superposition,[],[f204,f1259]) ).
tff(f1259,plain,
( ( 0 = count(add(5,remove(3,add(3,empty)))) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1257]) ).
tff(f204,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f203]) ).
tff(f1326,plain,
( spl0_85
| ~ spl0_28
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f311,f296,f246,f1324]) ).
tff(f1324,plain,
( spl0_85
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X1 )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
tff(f246,plain,
( spl0_28
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f296,plain,
( spl0_34
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f311,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X1 )
| ~ in(X0,X2) )
| ~ spl0_28
| ~ spl0_34 ),
inference(resolution,[],[f297,f247]) ).
tff(f247,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f246]) ).
tff(f297,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f296]) ).
tff(f1322,plain,
( spl0_84
| ~ spl0_29
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f302,f288,f250,f1320]) ).
tff(f1320,plain,
( spl0_84
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| in(X0,X2)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
tff(f250,plain,
( spl0_29
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f288,plain,
( spl0_32
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f302,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| in(X0,X2)
| ( X0 = X1 ) )
| ~ spl0_29
| ~ spl0_32 ),
inference(resolution,[],[f289,f251]) ).
tff(f251,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f250]) ).
tff(f289,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f288]) ).
tff(f1291,plain,
( spl0_83
| ~ spl0_32
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f309,f296,f288,f1289]) ).
tff(f309,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl0_32
| ~ spl0_34 ),
inference(resolution,[],[f297,f289]) ).
tff(f1260,plain,
( spl0_82
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1194,f1147,f790,f317,f83,f1257]) ).
tff(f1147,plain,
( spl0_73
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
tff(f1194,plain,
( ( 0 = count(add(5,remove(3,add(3,empty)))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(evaluation,[],[f1193]) ).
tff(f1193,plain,
( ( count(add(5,remove(3,add(3,empty)))) = $sum(-1,1) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1192,f318]) ).
tff(f1192,plain,
( ( count(add(5,remove(3,add(3,empty)))) = $sum(-1,count(add(3,empty))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1191,f791]) ).
tff(f1191,plain,
( ( count(add(5,remove(3,add(3,empty)))) = count(remove(3,add(3,empty))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f1190]) ).
tff(f1190,plain,
( ( 1 != 1 )
| ( count(add(5,remove(3,add(3,empty)))) = count(remove(3,add(3,empty))) )
| spl0_1
| ~ spl0_36
| ~ spl0_63
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1189,f318]) ).
tff(f1189,plain,
( ( 1 != count(add(3,empty)) )
| ( count(add(5,remove(3,add(3,empty)))) = count(remove(3,add(3,empty))) )
| spl0_1
| ~ spl0_63
| ~ spl0_73 ),
inference(evaluation,[],[f1188]) ).
tff(f1188,plain,
( ( 1 != $sum(1,$sum(-1,count(add(3,empty)))) )
| ( count(add(5,remove(3,add(3,empty)))) = count(remove(3,add(3,empty))) )
| spl0_1
| ~ spl0_63
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1175,f791]) ).
tff(f1175,plain,
( ( 1 != $sum(1,count(remove(3,add(3,empty)))) )
| ( count(add(5,remove(3,add(3,empty)))) = count(remove(3,add(3,empty))) )
| spl0_1
| ~ spl0_73 ),
inference(superposition,[],[f85,f1148]) ).
tff(f1148,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1147]) ).
tff(f1255,plain,
( spl0_81
| ~ spl0_23
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f278,f250,f191,f1253]) ).
tff(f1253,plain,
( spl0_81
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
tff(f191,plain,
( spl0_23
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f278,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) )
| ~ spl0_23
| ~ spl0_29 ),
inference(resolution,[],[f251,f192]) ).
tff(f192,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f191]) ).
tff(f1251,plain,
( spl0_80
| ~ spl0_22
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f275,f246,f187,f1249]) ).
tff(f1249,plain,
( spl0_80
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
tff(f187,plain,
( spl0_22
<=> ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f275,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) )
| ~ spl0_22
| ~ spl0_28 ),
inference(resolution,[],[f247,f188]) ).
tff(f188,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f187]) ).
tff(f1247,plain,
( spl0_79
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f274,f246,f199,f1245]) ).
tff(f1245,plain,
( spl0_79
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
tff(f199,plain,
( spl0_25
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f274,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) )
| ~ spl0_25
| ~ spl0_28 ),
inference(resolution,[],[f247,f200]) ).
tff(f200,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f199]) ).
tff(f1169,plain,
( spl0_78
| ~ spl0_23
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f310,f296,f191,f1167]) ).
tff(f1167,plain,
( spl0_78
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
tff(f310,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl0_23
| ~ spl0_34 ),
inference(resolution,[],[f297,f192]) ).
tff(f1165,plain,
( spl0_77
| ~ spl0_16
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f308,f296,f147,f1163]) ).
tff(f1163,plain,
( spl0_77
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
tff(f147,plain,
( spl0_16
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f308,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl0_16
| ~ spl0_34 ),
inference(resolution,[],[f297,f148]) ).
tff(f148,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f147]) ).
tff(f1161,plain,
( spl0_76
| ~ spl0_10
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f358,f337,f122,f1159]) ).
tff(f1159,plain,
( spl0_76
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
tff(f122,plain,
( spl0_10
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f337,plain,
( spl0_37
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f358,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl0_10
| ~ spl0_37 ),
inference(evaluation,[],[f355]) ).
tff(f355,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl0_10
| ~ spl0_37 ),
inference(superposition,[],[f338,f123]) ).
tff(f123,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f122]) ).
tff(f338,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f337]) ).
tff(f1157,plain,
( spl0_75
| ~ spl0_15
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f304,f288,f143,f1155]) ).
tff(f1155,plain,
( spl0_75
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
tff(f143,plain,
( spl0_15
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f304,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| in(X0,X2) )
| ~ spl0_15
| ~ spl0_32 ),
inference(resolution,[],[f289,f144]) ).
tff(f144,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f1153,plain,
( spl0_74
| ~ spl0_22
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f300,f288,f187,f1151]) ).
tff(f1151,plain,
( spl0_74
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
tff(f300,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl0_22
| ~ spl0_32 ),
inference(resolution,[],[f289,f188]) ).
tff(f1149,plain,
( spl0_73
| ~ spl0_25
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f299,f288,f199,f1147]) ).
tff(f299,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl0_25
| ~ spl0_32 ),
inference(resolution,[],[f289,f200]) ).
tff(f928,plain,
( spl0_72
| ~ spl0_21
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f263,f242,f183,f926]) ).
tff(f926,plain,
( spl0_72
<=> ! [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,[spl0_72])]) ).
tff(f183,plain,
( spl0_21
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f242,plain,
( spl0_27
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f263,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl0_21
| ~ spl0_27 ),
inference(superposition,[],[f184,f243]) ).
tff(f243,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f242]) ).
tff(f184,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f183]) ).
tff(f924,plain,
( spl0_71
| ~ spl0_21
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f262,f242,f183,f922]) ).
tff(f922,plain,
( spl0_71
<=> ! [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,[spl0_71])]) ).
tff(f262,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl0_21
| ~ spl0_27 ),
inference(superposition,[],[f184,f243]) ).
tff(f920,plain,
( spl0_70
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f256,f242,f179,f918]) ).
tff(f918,plain,
( spl0_70
<=> ! [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,[spl0_70])]) ).
tff(f179,plain,
( spl0_20
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f256,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f243,f180]) ).
tff(f180,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f179]) ).
tff(f916,plain,
( spl0_69
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f240,f199,f191,f914]) ).
tff(f914,plain,
( spl0_69
<=> ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
tff(f240,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) )
| ~ spl0_23
| ~ spl0_25 ),
inference(resolution,[],[f200,f192]) ).
tff(f912,plain,
( spl0_68
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f239,f199,f147,f910]) ).
tff(f910,plain,
( spl0_68
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ~ in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
tff(f239,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ~ in(X2,X1) )
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f200,f148]) ).
tff(f908,plain,
( spl0_67
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f236,f191,f187,f906]) ).
tff(f906,plain,
( spl0_67
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
tff(f236,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl0_22
| ~ spl0_23 ),
inference(resolution,[],[f192,f188]) ).
tff(f904,plain,
( spl0_66
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f235,f191,f143,f902]) ).
tff(f902,plain,
( spl0_66
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
tff(f235,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| in(X0,X2) )
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f192,f144]) ).
tff(f900,plain,
( spl0_65
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f228,f187,f147,f898]) ).
tff(f898,plain,
( spl0_65
<=> ! [X2: collection,X0: $int,X1: $int] :
( ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) )
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
tff(f228,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl0_16
| ~ spl0_22 ),
inference(resolution,[],[f188,f148]) ).
tff(f889,plain,
( spl0_64
| ~ spl0_11
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f764,f549,f126,f887]) ).
tff(f887,plain,
( spl0_64
<=> ! [X0: $int] : $less($sum(X0,-1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
tff(f126,plain,
( spl0_11
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f549,plain,
( spl0_54
<=> ! [X0: $int] : $less($sum(-1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
tff(f764,plain,
( ! [X0: $int] : $less($sum(X0,-1),X0)
| ~ spl0_11
| ~ spl0_54 ),
inference(superposition,[],[f550,f127]) ).
tff(f127,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f126]) ).
tff(f550,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f792,plain,
( spl0_63
| ~ spl0_9
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f307,f296,f118,f790]) ).
tff(f118,plain,
( spl0_9
<=> ! [X0: $int,X1: collection] : in(X0,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f307,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) )
| ~ spl0_9
| ~ spl0_34 ),
inference(resolution,[],[f297,f119]) ).
tff(f119,plain,
( ! [X0: $int,X1: collection] : in(X0,add(X0,X1))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f118]) ).
tff(f788,plain,
( spl0_62
| ~ spl0_8
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f303,f288,f114,f786]) ).
tff(f786,plain,
( spl0_62
<=> ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
tff(f114,plain,
( spl0_8
<=> ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f303,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) )
| ~ spl0_8
| ~ spl0_32 ),
inference(resolution,[],[f289,f115]) ).
tff(f115,plain,
( ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f114]) ).
tff(f784,plain,
( spl0_61
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f226,f183,f179,f782]) ).
tff(f782,plain,
( spl0_61
<=> ! [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,[spl0_61])]) ).
tff(f226,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f184,f180]) ).
tff(f780,plain,
( spl0_60
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f222,f183,f179,f778]) ).
tff(f778,plain,
( spl0_60
<=> ! [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,[spl0_60])]) ).
tff(f222,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f184,f180]) ).
tff(f776,plain,
( spl0_59
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f218,f183,f157,f774]) ).
tff(f774,plain,
( spl0_59
<=> ! [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,[spl0_59])]) ).
tff(f157,plain,
( spl0_17
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f218,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl0_17
| ~ spl0_21 ),
inference(resolution,[],[f184,f158]) ).
tff(f158,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f756,plain,
( spl0_58
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f166,f161,f139,f754]) ).
tff(f754,plain,
( spl0_58
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
tff(f139,plain,
( spl0_14
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f161,plain,
( spl0_18
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f166,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl0_14
| ~ spl0_18 ),
inference(resolution,[],[f162,f140]) ).
tff(f140,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f139]) ).
tff(f162,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f161]) ).
tff(f694,plain,
( spl0_57
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f268,f242,f135,f692]) ).
tff(f692,plain,
( spl0_57
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
tff(f135,plain,
( spl0_13
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f268,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl0_13
| ~ spl0_27 ),
inference(superposition,[],[f136,f243]) ).
tff(f136,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f135]) ).
tff(f690,plain,
( spl0_56
| ~ spl0_14
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f267,f242,f139,f688]) ).
tff(f688,plain,
( spl0_56
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
tff(f267,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl0_14
| ~ spl0_27 ),
inference(superposition,[],[f140,f243]) ).
tff(f686,plain,
( spl0_55
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f167,f161,f157,f684]) ).
tff(f684,plain,
( spl0_55
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
tff(f167,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f162,f158]) ).
tff(f551,plain,
( spl0_54
| ~ spl0_30
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f387,f349,f280,f549]) ).
tff(f280,plain,
( spl0_30
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f349,plain,
( spl0_40
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f387,plain,
( ! [X0: $int] : $less($sum(-1,X0),X0)
| ~ spl0_30
| ~ spl0_40 ),
inference(evaluation,[],[f385]) ).
tff(f385,plain,
( ! [X0: $int] : $less($sum($uminus(1),X0),X0)
| ~ spl0_30
| ~ spl0_40 ),
inference(superposition,[],[f281,f350]) ).
tff(f350,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f349]) ).
tff(f281,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f280]) ).
tff(f520,plain,
( spl0_53
| ~ spl0_11
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f259,f242,f126,f518]) ).
tff(f518,plain,
( spl0_53
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f259,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl0_11
| ~ spl0_27 ),
inference(superposition,[],[f243,f127]) ).
tff(f516,plain,
( spl0_52
| ~ spl0_11
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f254,f242,f126,f514]) ).
tff(f514,plain,
( spl0_52
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f254,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl0_11
| ~ spl0_27 ),
inference(superposition,[],[f243,f127]) ).
tff(f512,plain,
( spl0_51
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f238,f199,f118,f510]) ).
tff(f510,plain,
( spl0_51
<=> ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f238,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl0_9
| ~ spl0_25 ),
inference(resolution,[],[f200,f119]) ).
tff(f508,plain,
( spl0_50
| ~ spl0_8
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f234,f191,f114,f506]) ).
tff(f506,plain,
( spl0_50
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f234,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) )
| ~ spl0_8
| ~ spl0_23 ),
inference(resolution,[],[f192,f115]) ).
tff(f504,plain,
( spl0_49
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f227,f187,f118,f502]) ).
tff(f502,plain,
( spl0_49
<=> ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f227,plain,
( ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) )
| ~ spl0_9
| ~ spl0_22 ),
inference(resolution,[],[f188,f119]) ).
tff(f500,plain,
( spl0_48
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f164,f157,f135,f498]) ).
tff(f498,plain,
( spl0_48
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f164,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f158,f136]) ).
tff(f433,plain,
( spl0_47
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f258,f242,f122,f431]) ).
tff(f431,plain,
( spl0_47
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f258,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[],[f243,f123]) ).
tff(f429,plain,
( spl0_46
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f224,f183,f126,f427]) ).
tff(f427,plain,
( spl0_46
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f224,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f184,f127]) ).
tff(f425,plain,
( spl0_45
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f220,f183,f126,f423]) ).
tff(f423,plain,
( spl0_45
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f220,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f184,f127]) ).
tff(f421,plain,
( spl0_44
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f207,f179,f126,f419]) ).
tff(f419,plain,
( spl0_44
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f207,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f180,f127]) ).
tff(f402,plain,
( spl0_43
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f223,f183,f122,f400]) ).
tff(f400,plain,
( spl0_43
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f223,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f184,f123]) ).
tff(f398,plain,
( spl0_42
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f219,f183,f122,f396]) ).
tff(f396,plain,
( spl0_42
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f219,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f184,f123]) ).
tff(f394,plain,
( spl0_41
| ~ spl0_12
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f329,f313,f130,f392]) ).
tff(f392,plain,
( spl0_41
<=> ! [X0: $int] : ( empty = remove(X0,empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f130,plain,
( spl0_12
<=> ! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f313,plain,
( spl0_35
<=> ! [X0: $int] : ( 0 = count(remove(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f329,plain,
( ! [X0: $int] : ( empty = remove(X0,empty) )
| ~ spl0_12
| ~ spl0_35 ),
inference(trivial_inequality_removal,[],[f327]) ).
tff(f327,plain,
( ! [X0: $int] :
( ( 0 != 0 )
| ( empty = remove(X0,empty) ) )
| ~ spl0_12
| ~ spl0_35 ),
inference(superposition,[],[f131,f314]) ).
tff(f314,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f313]) ).
tff(f131,plain,
( ! [X0: collection] :
( ( 0 != count(X0) )
| ( empty = X0 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f351,plain,
( spl0_40
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f269,f242,f122,f349]) ).
tff(f269,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl0_10
| ~ spl0_27 ),
inference(evaluation,[],[f253]) ).
tff(f253,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[],[f243,f123]) ).
tff(f347,plain,
( spl0_39
| ~ spl0_4
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f168,f161,f96,f345]) ).
tff(f168,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl0_4
| ~ spl0_18 ),
inference(resolution,[],[f162,f97]) ).
tff(f343,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f154,f139,f126,f341]) ).
tff(f341,plain,
( spl0_38
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f154,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f140,f127]) ).
tff(f339,plain,
( spl0_37
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f151,f135,f126,f337]) ).
tff(f151,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f136,f127]) ).
tff(f319,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f306,f288,f100,f92,f317]) ).
tff(f92,plain,
( spl0_3
<=> ! [X0: $int] : ~ in(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f100,plain,
( spl0_5
<=> ( 0 = count(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f306,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32 ),
inference(evaluation,[],[f305]) ).
tff(f305,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,0) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_32 ),
inference(forward_demodulation,[],[f301,f102]) ).
tff(f102,plain,
( ( 0 = count(empty) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f301,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) )
| ~ spl0_3
| ~ spl0_32 ),
inference(resolution,[],[f289,f93]) ).
tff(f93,plain,
( ! [X0: $int] : ~ in(X0,empty)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f92]) ).
tff(f315,plain,
( spl0_35
| ~ spl0_3
| ~ spl0_5
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f237,f191,f100,f92,f313]) ).
tff(f237,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_demodulation,[],[f233,f102]) ).
tff(f233,plain,
( ! [X0: $int] : ( count(empty) = count(remove(X0,empty)) )
| ~ spl0_3
| ~ spl0_23 ),
inference(resolution,[],[f192,f93]) ).
tff(f298,plain,
spl0_34,
inference(avatar_split_clause,[],[f81,f296]) ).
tff(f81,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f76,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f76,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f65]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) )
& ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,plain,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f294,plain,
spl0_33,
inference(avatar_split_clause,[],[f80,f292]) ).
tff(f292,plain,
( spl0_33
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f80,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f77,f17]) ).
tff(f77,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),-1) ) ),
inference(evaluation,[],[f66]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f290,plain,
spl0_32,
inference(avatar_split_clause,[],[f79,f288]) ).
tff(f79,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f61,f17]) ).
tff(f61,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X13: $int,X14: collection] :
( ~ in(X13,X14)
<=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f286,plain,
spl0_31,
inference(avatar_split_clause,[],[f78,f284]) ).
tff(f284,plain,
( spl0_31
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f78,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f62,f17]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f282,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f231,f175,f126,f280]) ).
tff(f175,plain,
( spl0_19
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f231,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl0_11
| ~ spl0_19 ),
inference(superposition,[],[f176,f127]) ).
tff(f176,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f175]) ).
tff(f252,plain,
spl0_29,
inference(avatar_split_clause,[],[f72,f250]) ).
tff(f72,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f49]) ).
tff(f49,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f248,plain,
spl0_28,
inference(avatar_split_clause,[],[f67,f246]) ).
tff(f67,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f244,plain,
spl0_27,
inference(avatar_split_clause,[],[f18,f242]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f205,plain,
spl0_26,
inference(avatar_split_clause,[],[f64,f203]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) )
& ( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(X1) = count(add(X0,X1)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X15: $int,X16: collection] :
( in(X15,X16)
<=> ( count(add(X15,X16)) = count(X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f201,plain,
spl0_25,
inference(avatar_split_clause,[],[f63,f199]) ).
tff(f63,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f197,plain,
spl0_24,
inference(avatar_split_clause,[],[f60,f195]) ).
tff(f195,plain,
( spl0_24
<=> ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f60,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) )
& ( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(remove(X0,X1)) = count(X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X19: $int,X20: collection] :
( ~ in(X19,X20)
<=> ( count(remove(X19,X20)) = count(X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
tff(f193,plain,
spl0_23,
inference(avatar_split_clause,[],[f59,f191]) ).
tff(f59,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tff(f189,plain,
spl0_22,
inference(avatar_split_clause,[],[f58,f187]) ).
tff(f58,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
=> ( add(X0,remove(X0,X1)) = X1 ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X21: $int,X22: collection] :
( in(X21,X22)
=> ( add(X21,remove(X21,X22)) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
tff(f185,plain,
spl0_21,
inference(avatar_split_clause,[],[f25,f183]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f181,plain,
spl0_20,
inference(avatar_split_clause,[],[f20,f179]) ).
tff(f20,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f177,plain,
( spl0_19
| ~ spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f150,f135,f88,f175]) ).
tff(f88,plain,
( spl0_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f150,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl0_2
| ~ spl0_13 ),
inference(resolution,[],[f136,f89]) ).
tff(f89,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f163,plain,
spl0_18,
inference(avatar_split_clause,[],[f24,f161]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f159,plain,
spl0_17,
inference(avatar_split_clause,[],[f23,f157]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f149,plain,
spl0_16,
inference(avatar_split_clause,[],[f70,f147]) ).
tff(f70,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tff(f145,plain,
spl0_15,
inference(avatar_split_clause,[],[f68,f143]) ).
tff(f68,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f48]) ).
tff(f141,plain,
spl0_14,
inference(avatar_split_clause,[],[f28,f139]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f137,plain,
spl0_13,
inference(avatar_split_clause,[],[f26,f135]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f132,plain,
spl0_12,
inference(avatar_split_clause,[],[f55,f130]) ).
tff(f55,plain,
! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: collection] :
( ( ( empty = X0 )
| ( 0 != count(X0) ) )
& ( ( 0 = count(X0) )
| ( empty != X0 ) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: collection] :
( ( empty = X0 )
<=> ( 0 = count(X0) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X12: collection] :
( ( empty = X12 )
<=> ( 0 = count(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f128,plain,
spl0_11,
inference(avatar_split_clause,[],[f17,f126]) ).
tff(f124,plain,
spl0_10,
inference(avatar_split_clause,[],[f21,f122]) ).
tff(f21,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f120,plain,
spl0_9,
inference(avatar_split_clause,[],[f57,f118]) ).
tff(f57,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f116,plain,
spl0_8,
inference(avatar_split_clause,[],[f56,f114]) ).
tff(f56,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f112,plain,
spl0_7,
inference(avatar_split_clause,[],[f27,f110]) ).
tff(f110,plain,
( spl0_7
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f27,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f108,plain,
spl0_6,
inference(avatar_split_clause,[],[f19,f106]) ).
tff(f106,plain,
( spl0_6
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f19,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f103,plain,
spl0_5,
inference(avatar_split_clause,[],[f73,f100]) ).
tff(f73,plain,
0 = count(empty),
inference(equality_resolution,[],[f54]) ).
tff(f54,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f98,plain,
spl0_4,
inference(avatar_split_clause,[],[f53,f96]) ).
tff(f53,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(rectify,[],[f15]) ).
tff(f15,plain,
! [X11: collection] : ~ $less(count(X11),0),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
! [X11: collection] : $greatereq(count(X11),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f94,plain,
spl0_3,
inference(avatar_split_clause,[],[f52,f92]) ).
tff(f52,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f90,plain,
spl0_2,
inference(avatar_split_clause,[],[f22,f88]) ).
tff(f22,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f86,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f51,f83]) ).
tff(f51,plain,
1 != count(add(5,remove(3,add(3,empty)))),
inference(cnf_transformation,[],[f29]) ).
tff(f29,plain,
1 != count(add(5,remove(3,add(3,empty)))),
inference(flattening,[],[f14]) ).
tff(f14,negated_conjecture,
( ~ 1 = count(add(5,remove(3,add(3,empty)))) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
1 = count(add(5,remove(3,add(3,empty)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : DAT047_1 : TPTP v8.2.0. Released v5.0.0.
% 0.07/0.18 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.18/0.38 % Computer : n013.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Sun May 19 23:40:08 EDT 2024
% 0.18/0.38 % CPUTime :
% 0.18/0.39 % (2295)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.40 % (2298)WARNING: value z3 for option sas not known
% 0.24/0.41 % (2298)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)
% 0.24/0.41 % (2297)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.41 % (2299)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.24/0.41 % (2302)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)
% 0.24/0.41 % (2301)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)
% 0.24/0.41 % (2300)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)
% 0.24/0.41 % (2299)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.24/0.41 % (2297)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.24/0.41 % (2297)Terminated due to inappropriate strategy.
% 0.24/0.41 % (2297)------------------------------
% 0.24/0.41 % (2297)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.41 % (2297)Termination reason: Inappropriate
% 0.24/0.41
% 0.24/0.41 % (2297)Memory used [KB]: 765
% 0.24/0.41 % (2297)Time elapsed: 0.003 s
% 0.24/0.41 % (2297)Instructions burned: 3 (million)
% 0.24/0.41 % (2299)Terminated due to inappropriate strategy.
% 0.24/0.41 % (2299)------------------------------
% 0.24/0.41 % (2299)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.41 % (2299)Termination reason: Inappropriate
% 0.24/0.41
% 0.24/0.41 % (2299)Memory used [KB]: 765
% 0.24/0.41 % (2299)Time elapsed: 0.003 s
% 0.24/0.41 % (2299)Instructions burned: 3 (million)
% 0.24/0.41 % (2297)------------------------------
% 0.24/0.41 % (2297)------------------------------
% 0.24/0.41 % (2299)------------------------------
% 0.24/0.41 % (2299)------------------------------
% 0.24/0.41 % (2296)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.24/0.41 % (2296)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.24/0.41 % (2296)Terminated due to inappropriate strategy.
% 0.24/0.41 % (2296)------------------------------
% 0.24/0.41 % (2296)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.41 % (2296)Termination reason: Inappropriate
% 0.24/0.41
% 0.24/0.41 % (2296)Memory used [KB]: 765
% 0.24/0.41 % (2296)Time elapsed: 0.004 s
% 0.24/0.41 % (2296)Instructions burned: 3 (million)
% 0.24/0.41 % (2296)------------------------------
% 0.24/0.41 % (2296)------------------------------
% 0.24/0.42 % (2303)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.24/0.42 % (2304)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)
% 0.24/0.42 % (2303)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.24/0.42 % (2303)Terminated due to inappropriate strategy.
% 0.24/0.42 % (2303)------------------------------
% 0.24/0.42 % (2303)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.42 % (2303)Termination reason: Inappropriate
% 0.24/0.42
% 0.24/0.42 % (2303)Memory used [KB]: 764
% 0.24/0.43 % (2303)Time elapsed: 0.003 s
% 0.24/0.43 % (2303)Instructions burned: 3 (million)
% 0.24/0.43 % (2303)------------------------------
% 0.24/0.43 % (2303)------------------------------
% 0.24/0.43 % (2305)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)
% 0.24/0.44 % (2306)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.24/0.46 % (2300)First to succeed.
% 0.24/0.47 % (2300)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2295"
% 0.24/0.47 % (2300)Refutation found. Thanks to Tanya!
% 0.24/0.47 % SZS status Theorem for theBenchmark
% 0.24/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.47 % (2300)------------------------------
% 0.24/0.47 % (2300)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.47 % (2300)Termination reason: Refutation
% 0.24/0.47
% 0.24/0.47 % (2300)Memory used [KB]: 1552
% 0.24/0.47 % (2300)Time elapsed: 0.063 s
% 0.24/0.47 % (2300)Instructions burned: 106 (million)
% 0.24/0.47 % (2295)Success in time 0.077 s
%------------------------------------------------------------------------------