TSTP Solution File: DAT034_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT034_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:03:44 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 148
% Syntax : Number of formulae : 468 ( 60 unt; 8 typ; 0 def)
% Number of atoms : 1292 ( 238 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1465 ( 633 ~; 685 |; 15 &)
% ( 129 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 1376 ( 268 atm; 389 fun; 225 num; 494 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 119 ( 115 usr; 115 prp; 0-2 aty)
% Number of functors : 12 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 638 ( 634 !; 4 ?; 638 :)
% 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(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f1615,plain,
$false,
inference(avatar_sat_refutation,[],[f90,f94,f98,f102,f107,f112,f116,f120,f124,f128,f132,f136,f141,f145,f149,f153,f163,f167,f182,f186,f190,f194,f198,f202,f206,f210,f248,f252,f256,f285,f289,f293,f297,f301,f318,f331,f335,f350,f354,f358,f362,f384,f407,f411,f430,f434,f438,f442,f505,f509,f513,f517,f521,f525,f544,f691,f695,f699,f765,f769,f773,f777,f781,f785,f847,f889,f893,f897,f901,f905,f909,f913,f921,f1129,f1134,f1138,f1142,f1146,f1150,f1221,f1229,f1233,f1264,f1292,f1296,f1314,f1337,f1346,f1369,f1390,f1396,f1400,f1413,f1420,f1428,f1439,f1443,f1489,f1494,f1498,f1502,f1506,f1565,f1570,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1605,f1609,f1614]) ).
tff(f1614,plain,
( ~ spl2_2
| ~ spl2_105 ),
inference(avatar_contradiction_clause,[],[f1610]) ).
tff(f1610,plain,
( $false
| ~ spl2_2
| ~ spl2_105 ),
inference(resolution,[],[f1569,f93]) ).
tff(f93,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f92]) ).
tff(f92,plain,
( spl2_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f1569,plain,
( $less(count(sK0),count(sK0))
| ~ spl2_105 ),
inference(avatar_component_clause,[],[f1567]) ).
tff(f1567,plain,
( spl2_105
<=> $less(count(sK0),count(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_105])]) ).
tff(f1609,plain,
( spl2_114
| ~ spl2_4
| ~ spl2_63 ),
inference(avatar_split_clause,[],[f876,f779,f100,f1607]) ).
tff(f1607,plain,
( spl2_114
<=> ! [X0: $int,X1: collection] : ~ $less($sum(1,count(remove(X0,X1))),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_114])]) ).
tff(f100,plain,
( spl2_4
<=> ! [X0: collection] : ~ $less(count(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f779,plain,
( spl2_63
<=> ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).
tff(f876,plain,
( ! [X0: $int,X1: collection] : ~ $less($sum(1,count(remove(X0,X1))),0)
| ~ spl2_4
| ~ spl2_63 ),
inference(superposition,[],[f101,f780]) ).
tff(f780,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) )
| ~ spl2_63 ),
inference(avatar_component_clause,[],[f779]) ).
tff(f101,plain,
( ! [X0: collection] : ~ $less(count(X0),0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f1605,plain,
( spl2_113
| ~ spl2_10
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f666,f523,f126,f1603]) ).
tff(f1603,plain,
( spl2_113
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_113])]) ).
tff(f126,plain,
( spl2_10
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f523,plain,
( spl2_54
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
tff(f666,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = X1 )
| ~ spl2_10
| ~ spl2_54 ),
inference(evaluation,[],[f603]) ).
tff(f603,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X1,X0)) = $sum(X1,0) )
| ~ spl2_10
| ~ spl2_54 ),
inference(superposition,[],[f524,f127]) ).
tff(f127,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f126]) ).
tff(f524,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f523]) ).
tff(f1601,plain,
( spl2_112
| ~ spl2_10
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f596,f519,f126,f1599]) ).
tff(f1599,plain,
( spl2_112
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_112])]) ).
tff(f519,plain,
( spl2_53
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
tff(f596,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X0),$sum(X0,X1)) = X1 )
| ~ spl2_10
| ~ spl2_53 ),
inference(evaluation,[],[f565]) ).
tff(f565,plain,
( ! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum($uminus(X0),$sum(X0,X1)) )
| ~ spl2_10
| ~ spl2_53 ),
inference(superposition,[],[f520,f127]) ).
tff(f520,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f519]) ).
tff(f1597,plain,
( spl2_111
| ~ spl2_39
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f464,f432,f352,f1595]) ).
tff(f1595,plain,
( spl2_111
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_111])]) ).
tff(f352,plain,
( spl2_39
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
tff(f432,plain,
( spl2_46
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
tff(f464,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,1)
| ~ $less(X1,$sum(X1,X0)) )
| ~ spl2_39
| ~ spl2_46 ),
inference(resolution,[],[f433,f353]) ).
tff(f353,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f352]) ).
tff(f433,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f432]) ).
tff(f1593,plain,
( spl2_110
| ~ spl2_39
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f402,f360,f352,f1591]) ).
tff(f1591,plain,
( spl2_110
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_110])]) ).
tff(f360,plain,
( spl2_41
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
tff(f402,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum(-1,X0),X1) )
| ~ spl2_39
| ~ spl2_41 ),
inference(evaluation,[],[f398]) ).
tff(f398,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less($sum($uminus(1),X0),X1) )
| ~ spl2_39
| ~ spl2_41 ),
inference(superposition,[],[f353,f361]) ).
tff(f361,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f360]) ).
tff(f1589,plain,
( spl2_109
| ~ spl2_38
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f401,f360,f348,f1587]) ).
tff(f1587,plain,
( spl2_109
<=> ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_109])]) ).
tff(f348,plain,
( spl2_38
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
tff(f401,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum(-1,X0),X1) )
| ~ spl2_38
| ~ spl2_41 ),
inference(evaluation,[],[f399]) ).
tff(f399,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less($sum($uminus(1),X0),X1) )
| ~ spl2_38
| ~ spl2_41 ),
inference(superposition,[],[f349,f361]) ).
tff(f349,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f348]) ).
tff(f1585,plain,
( spl2_108
| ~ spl2_11
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f391,f360,f130,f1583]) ).
tff(f1583,plain,
( spl2_108
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_108])]) ).
tff(f130,plain,
( spl2_11
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f391,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum(X1,$uminus(X0))) = X1 )
| ~ spl2_11
| ~ spl2_41 ),
inference(superposition,[],[f361,f131]) ).
tff(f131,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f1581,plain,
( spl2_107
| ~ spl2_21
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f371,f352,f188,f1579]) ).
tff(f1579,plain,
( spl2_107
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_107])]) ).
tff(f188,plain,
( spl2_21
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
tff(f371,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) )
| ~ spl2_21
| ~ spl2_39 ),
inference(resolution,[],[f353,f189]) ).
tff(f189,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f188]) ).
tff(f1577,plain,
( spl2_106
| ~ spl2_17
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f320,f316,f161,f1575]) ).
tff(f1575,plain,
( spl2_106
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_106])]) ).
tff(f161,plain,
( spl2_17
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f316,plain,
( spl2_35
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
tff(f320,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) )
| ~ spl2_17
| ~ spl2_35 ),
inference(resolution,[],[f317,f162]) ).
tff(f162,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f161]) ).
tff(f317,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f316]) ).
tff(f1570,plain,
( spl2_105
| ~ spl2_55
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f1375,f1362,f541,f1567]) ).
tff(f541,plain,
( spl2_55
<=> $less(count(sK0),count(add(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_55])]) ).
tff(f1362,plain,
( spl2_90
<=> ( count(sK0) = count(add(sK1,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
tff(f1375,plain,
( $less(count(sK0),count(sK0))
| ~ spl2_55
| ~ spl2_90 ),
inference(superposition,[],[f543,f1364]) ).
tff(f1364,plain,
( ( count(sK0) = count(add(sK1,sK0)) )
| ~ spl2_90 ),
inference(avatar_component_clause,[],[f1362]) ).
tff(f543,plain,
( $less(count(sK0),count(add(sK1,sK0)))
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f541]) ).
tff(f1565,plain,
( spl2_104
| ~ spl2_39
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f412,f405,f352,f1563]) ).
tff(f1563,plain,
( spl2_104
<=> ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_104])]) ).
tff(f405,plain,
( spl2_43
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
tff(f412,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| ~ $less($uminus(X0),0) )
| ~ spl2_39
| ~ spl2_43 ),
inference(resolution,[],[f406,f353]) ).
tff(f406,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f405]) ).
tff(f1506,plain,
( spl2_103
| ~ spl2_10
| ~ spl2_41
| ~ spl2_58 ),
inference(avatar_split_clause,[],[f757,f697,f360,f126,f1504]) ).
tff(f1504,plain,
( spl2_103
<=> ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_103])]) ).
tff(f697,plain,
( spl2_58
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).
tff(f757,plain,
( ! [X1: $int] :
( $less(0,X1)
| $less(X1,1) )
| ~ spl2_10
| ~ spl2_41
| ~ spl2_58 ),
inference(forward_demodulation,[],[f750,f127]) ).
tff(f750,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,1)
| $less($sum(X0,$uminus(X0)),X1) )
| ~ spl2_41
| ~ spl2_58 ),
inference(superposition,[],[f698,f361]) ).
tff(f698,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl2_58 ),
inference(avatar_component_clause,[],[f697]) ).
tff(f1502,plain,
( spl2_102
| ~ spl2_10
| ~ spl2_41
| ~ spl2_57 ),
inference(avatar_split_clause,[],[f732,f693,f360,f126,f1500]) ).
tff(f1500,plain,
( spl2_102
<=> ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_102])]) ).
tff(f693,plain,
( spl2_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,[spl2_57])]) ).
tff(f732,plain,
( ! [X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,1) )
| ~ spl2_10
| ~ spl2_41
| ~ spl2_57 ),
inference(forward_demodulation,[],[f724,f127]) ).
tff(f724,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,1)
| ~ $less($sum(X0,$uminus(X0)),X1) )
| ~ spl2_41
| ~ spl2_57 ),
inference(superposition,[],[f694,f361]) ).
tff(f694,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl2_57 ),
inference(avatar_component_clause,[],[f693]) ).
tff(f1498,plain,
( spl2_101
| ~ spl2_10
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f380,f352,f126,f1496]) ).
tff(f1496,plain,
( spl2_101
<=> ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_101])]) ).
tff(f380,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less(-1,X0) )
| ~ spl2_10
| ~ spl2_39 ),
inference(evaluation,[],[f377]) ).
tff(f377,plain,
( ! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) )
| ~ spl2_10
| ~ spl2_39 ),
inference(superposition,[],[f353,f127]) ).
tff(f1494,plain,
( spl2_100
| ~ spl2_10
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f370,f348,f126,f1492]) ).
tff(f1492,plain,
( spl2_100
<=> ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_100])]) ).
tff(f370,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) )
| ~ spl2_10
| ~ spl2_38 ),
inference(evaluation,[],[f367]) ).
tff(f367,plain,
( ! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) )
| ~ spl2_10
| ~ spl2_38 ),
inference(superposition,[],[f349,f127]) ).
tff(f1489,plain,
( spl2_99
| ~ spl2_19
| ~ spl2_59 ),
inference(avatar_split_clause,[],[f789,f763,f180,f1487]) ).
tff(f1487,plain,
( spl2_99
<=> ! [X0: $int] :
( ( $sum(X0,1) = $sum(1,count(sK0)) )
| ~ $less(X0,$sum(1,count(sK0)))
| $less($sum(X0,1),count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_99])]) ).
tff(f180,plain,
( spl2_19
<=> ! [X0: $int] :
( ~ $less(X0,$sum(1,count(sK0)))
| $less(X0,count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f763,plain,
( spl2_59
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_59])]) ).
tff(f789,plain,
( ! [X0: $int] :
( ( $sum(X0,1) = $sum(1,count(sK0)) )
| ~ $less(X0,$sum(1,count(sK0)))
| $less($sum(X0,1),count(add(sK1,sK0))) )
| ~ spl2_19
| ~ spl2_59 ),
inference(resolution,[],[f764,f181]) ).
tff(f181,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,count(sK0)))
| $less(X0,count(add(sK1,sK0))) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f180]) ).
tff(f764,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl2_59 ),
inference(avatar_component_clause,[],[f763]) ).
tff(f1443,plain,
( spl2_98
| ~ spl2_12
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f340,f329,f134,f1441]) ).
tff(f1441,plain,
( spl2_98
<=> ! [X0: $int] : ( empty = remove(X0,empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).
tff(f134,plain,
( spl2_12
<=> ! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f329,plain,
( spl2_36
<=> ! [X0: $int] : ( 0 = count(remove(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
tff(f340,plain,
( ! [X0: $int] : ( empty = remove(X0,empty) )
| ~ spl2_12
| ~ spl2_36 ),
inference(trivial_inequality_removal,[],[f338]) ).
tff(f338,plain,
( ! [X0: $int] :
( ( 0 != 0 )
| ( empty = remove(X0,empty) ) )
| ~ spl2_12
| ~ spl2_36 ),
inference(superposition,[],[f135,f330]) ).
tff(f330,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f329]) ).
tff(f135,plain,
( ! [X0: collection] :
( ( 0 != count(X0) )
| ( empty = X0 ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f134]) ).
tff(f1439,plain,
( spl2_97
| ~ spl2_11
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f321,f316,f130,f1437]) ).
tff(f1437,plain,
( spl2_97
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).
tff(f321,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl2_11
| ~ spl2_35 ),
inference(superposition,[],[f317,f131]) ).
tff(f1428,plain,
( ~ spl2_2
| ~ spl2_91 ),
inference(avatar_contradiction_clause,[],[f1424]) ).
tff(f1424,plain,
( $false
| ~ spl2_2
| ~ spl2_91 ),
inference(resolution,[],[f1368,f93]) ).
tff(f1368,plain,
( $less($sum(1,count(sK0)),$sum(1,count(sK0)))
| ~ spl2_91 ),
inference(avatar_component_clause,[],[f1366]) ).
tff(f1366,plain,
( spl2_91
<=> $less($sum(1,count(sK0)),$sum(1,count(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).
tff(f1420,plain,
( spl2_96
| spl2_91
| ~ spl2_1
| ~ spl2_83 ),
inference(avatar_split_clause,[],[f1276,f1262,f87,f1366,f1417]) ).
tff(f1417,plain,
( spl2_96
<=> ( count(remove(sK1,sK0)) = $sum(-1,count(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
tff(f87,plain,
( spl2_1
<=> $less($sum(1,count(sK0)),count(add(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f1262,plain,
( spl2_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,[spl2_83])]) ).
tff(f1276,plain,
( $less($sum(1,count(sK0)),$sum(1,count(sK0)))
| ( count(remove(sK1,sK0)) = $sum(-1,count(sK0)) )
| ~ spl2_1
| ~ spl2_83 ),
inference(superposition,[],[f89,f1263]) ).
tff(f1263,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) )
| ~ spl2_83 ),
inference(avatar_component_clause,[],[f1262]) ).
tff(f89,plain,
( $less($sum(1,count(sK0)),count(add(sK1,sK0)))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f87]) ).
tff(f1413,plain,
( spl2_95
| ~ spl2_1
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f700,f689,f87,f1411]) ).
tff(f1411,plain,
( spl2_95
<=> ! [X0: $int] :
( ( count(add(sK1,sK0)) = X0 )
| $less(X0,count(add(sK1,sK0)))
| $less($sum(1,count(sK0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).
tff(f689,plain,
( spl2_56
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
tff(f700,plain,
( ! [X0: $int] :
( ( count(add(sK1,sK0)) = X0 )
| $less(X0,count(add(sK1,sK0)))
| $less($sum(1,count(sK0)),X0) )
| ~ spl2_1
| ~ spl2_56 ),
inference(resolution,[],[f690,f89]) ).
tff(f690,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| ( X0 = X1 )
| $less(X1,X0)
| $less(X2,X1) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f689]) ).
tff(f1400,plain,
( spl2_94
| ~ spl2_90
| ~ spl2_92 ),
inference(avatar_split_clause,[],[f1391,f1388,f1362,f1398]) ).
tff(f1398,plain,
( spl2_94
<=> ! [X0: $int] :
( $less(X0,count(sK0))
| $less($sum(1,count(sK0)),X0)
| ( $sum(1,count(sK0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).
tff(f1388,plain,
( spl2_92
<=> ! [X0: $int] :
( $less(X0,count(add(sK1,sK0)))
| $less($sum(1,count(sK0)),X0)
| ( $sum(1,count(sK0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).
tff(f1391,plain,
( ! [X0: $int] :
( $less(X0,count(sK0))
| $less($sum(1,count(sK0)),X0)
| ( $sum(1,count(sK0)) = X0 ) )
| ~ spl2_90
| ~ spl2_92 ),
inference(forward_demodulation,[],[f1389,f1364]) ).
tff(f1389,plain,
( ! [X0: $int] :
( $less(X0,count(add(sK1,sK0)))
| $less($sum(1,count(sK0)),X0)
| ( $sum(1,count(sK0)) = X0 ) )
| ~ spl2_92 ),
inference(avatar_component_clause,[],[f1388]) ).
tff(f1396,plain,
( spl2_93
| ~ spl2_26
| ~ spl2_90 ),
inference(avatar_split_clause,[],[f1386,f1362,f208,f1393]) ).
tff(f1393,plain,
( spl2_93
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).
tff(f208,plain,
( spl2_26
<=> ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
tff(f1386,plain,
( in(sK1,sK0)
| ~ spl2_26
| ~ spl2_90 ),
inference(trivial_inequality_removal,[],[f1382]) ).
tff(f1382,plain,
( ( count(sK0) != count(sK0) )
| in(sK1,sK0)
| ~ spl2_26
| ~ spl2_90 ),
inference(superposition,[],[f209,f1364]) ).
tff(f209,plain,
( ! [X0: $int,X1: collection] :
( ( count(X1) != count(add(X0,X1)) )
| in(X0,X1) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f208]) ).
tff(f1390,plain,
( spl2_92
| ~ spl2_18
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f235,f180,f165,f1388]) ).
tff(f165,plain,
( spl2_18
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f235,plain,
( ! [X0: $int] :
( $less(X0,count(add(sK1,sK0)))
| $less($sum(1,count(sK0)),X0)
| ( $sum(1,count(sK0)) = X0 ) )
| ~ spl2_18
| ~ spl2_19 ),
inference(resolution,[],[f181,f166]) ).
tff(f166,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f165]) ).
tff(f1369,plain,
( spl2_90
| spl2_91
| ~ spl2_1
| ~ spl2_74 ),
inference(avatar_split_clause,[],[f1160,f1127,f87,f1366,f1362]) ).
tff(f1127,plain,
( spl2_74
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).
tff(f1160,plain,
( $less($sum(1,count(sK0)),$sum(1,count(sK0)))
| ( count(sK0) = count(add(sK1,sK0)) )
| ~ spl2_1
| ~ spl2_74 ),
inference(superposition,[],[f89,f1128]) ).
tff(f1128,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl2_74 ),
inference(avatar_component_clause,[],[f1127]) ).
tff(f1346,plain,
( spl2_88
| spl2_89
| ~ spl2_1
| ~ spl2_70 ),
inference(avatar_split_clause,[],[f960,f903,f87,f1343,f1339]) ).
tff(f1339,plain,
( spl2_88
<=> ( count(sK0) = count(remove(sK1,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).
tff(f1343,plain,
( spl2_89
<=> $less($sum(1,count(sK0)),count(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
tff(f903,plain,
( spl2_70
<=> ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
tff(f960,plain,
( $less($sum(1,count(sK0)),count(sK0))
| ( count(sK0) = count(remove(sK1,sK0)) )
| ~ spl2_1
| ~ spl2_70 ),
inference(superposition,[],[f89,f904]) ).
tff(f904,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) )
| ~ spl2_70 ),
inference(avatar_component_clause,[],[f903]) ).
tff(f1337,plain,
( spl2_87
| ~ spl2_1
| ~ spl2_49 ),
inference(avatar_split_clause,[],[f526,f503,f87,f1335]) ).
tff(f1335,plain,
( spl2_87
<=> ! [X0: $int] :
( $less($sum(1,count(sK0)),$sum(X0,1))
| $less(X0,count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
tff(f503,plain,
( spl2_49
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
tff(f526,plain,
( ! [X0: $int] :
( $less($sum(1,count(sK0)),$sum(X0,1))
| $less(X0,count(add(sK1,sK0))) )
| ~ spl2_1
| ~ spl2_49 ),
inference(resolution,[],[f504,f89]) ).
tff(f504,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl2_49 ),
inference(avatar_component_clause,[],[f503]) ).
tff(f1314,plain,
( spl2_86
| ~ spl2_19
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f483,f436,f180,f1312]) ).
tff(f1312,plain,
( spl2_86
<=> ! [X0: $int] :
( ~ $less(X0,count(sK0))
| $less($sum(X0,1),count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
tff(f436,plain,
( spl2_47
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
tff(f483,plain,
( ! [X0: $int] :
( ~ $less(X0,count(sK0))
| $less($sum(X0,1),count(add(sK1,sK0))) )
| ~ spl2_19
| ~ spl2_47 ),
inference(resolution,[],[f437,f181]) ).
tff(f437,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl2_47 ),
inference(avatar_component_clause,[],[f436]) ).
tff(f1296,plain,
( spl2_85
| ~ spl2_28
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f314,f299,f250,f1294]) ).
tff(f1294,plain,
( spl2_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,[spl2_85])]) ).
tff(f250,plain,
( spl2_28
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
tff(f299,plain,
( spl2_34
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
tff(f314,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = $sum(-1,count(remove(X1,X2))) )
| ( X0 = X1 )
| ~ in(X0,X2) )
| ~ spl2_28
| ~ spl2_34 ),
inference(resolution,[],[f300,f251]) ).
tff(f251,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f250]) ).
tff(f300,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) )
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f299]) ).
tff(f1292,plain,
( spl2_84
| ~ spl2_29
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f305,f291,f254,f1290]) ).
tff(f1290,plain,
( spl2_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,[spl2_84])]) ).
tff(f254,plain,
( spl2_29
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
tff(f291,plain,
( spl2_32
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
tff(f305,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,add(X1,X2))) = $sum(1,count(add(X1,X2))) )
| in(X0,X2)
| ( X0 = X1 ) )
| ~ spl2_29
| ~ spl2_32 ),
inference(resolution,[],[f292,f255]) ).
tff(f255,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,add(X2,X1))
| in(X0,X1)
| ( X0 = X2 ) )
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f254]) ).
tff(f292,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f291]) ).
tff(f1264,plain,
( spl2_83
| ~ spl2_32
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f312,f299,f291,f1262]) ).
tff(f312,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl2_32
| ~ spl2_34 ),
inference(resolution,[],[f300,f292]) ).
tff(f1233,plain,
( spl2_82
| ~ spl2_23
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f281,f254,f196,f1231]) ).
tff(f1231,plain,
( spl2_82
<=> ! [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,[spl2_82])]) ).
tff(f196,plain,
( spl2_23
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
tff(f281,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ( X0 = X2 )
| ( count(remove(X0,add(X2,X1))) = count(add(X2,X1)) ) )
| ~ spl2_23
| ~ spl2_29 ),
inference(resolution,[],[f255,f197]) ).
tff(f197,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f196]) ).
tff(f1229,plain,
( spl2_81
| ~ spl2_22
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f278,f250,f192,f1227]) ).
tff(f1227,plain,
( spl2_81
<=> ! [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,[spl2_81])]) ).
tff(f192,plain,
( spl2_22
<=> ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
tff(f278,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( remove(X1,X2) = add(X0,remove(X0,remove(X1,X2))) ) )
| ~ spl2_22
| ~ spl2_28 ),
inference(resolution,[],[f251,f193]) ).
tff(f193,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f192]) ).
tff(f1221,plain,
( spl2_80
| ~ spl2_25
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f277,f250,f204,f1219]) ).
tff(f1219,plain,
( spl2_80
<=> ! [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,[spl2_80])]) ).
tff(f204,plain,
( spl2_25
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
tff(f277,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ in(X0,X2)
| ( count(remove(X1,X2)) = count(add(X0,remove(X1,X2))) ) )
| ~ spl2_25
| ~ spl2_28 ),
inference(resolution,[],[f251,f205]) ).
tff(f205,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f204]) ).
tff(f1150,plain,
( spl2_79
| ~ spl2_23
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f313,f299,f196,f1148]) ).
tff(f1148,plain,
( spl2_79
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_79])]) ).
tff(f313,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl2_23
| ~ spl2_34 ),
inference(resolution,[],[f300,f197]) ).
tff(f1146,plain,
( spl2_78
| ~ spl2_16
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f311,f299,f151,f1144]) ).
tff(f1144,plain,
( spl2_78
<=> ! [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,[spl2_78])]) ).
tff(f151,plain,
( spl2_16
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f311,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,add(X1,X2))) = $sum(-1,count(add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl2_16
| ~ spl2_34 ),
inference(resolution,[],[f300,f152]) ).
tff(f152,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f151]) ).
tff(f1142,plain,
( spl2_77
| ~ spl2_15
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f307,f291,f147,f1140]) ).
tff(f1140,plain,
( spl2_77
<=> ! [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,[spl2_77])]) ).
tff(f147,plain,
( spl2_15
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f307,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(add(X0,remove(X1,X2))) = $sum(1,count(remove(X1,X2))) )
| in(X0,X2) )
| ~ spl2_15
| ~ spl2_32 ),
inference(resolution,[],[f292,f148]) ).
tff(f148,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f147]) ).
tff(f1138,plain,
( spl2_76
| ~ spl2_22
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f303,f291,f192,f1136]) ).
tff(f1136,plain,
( spl2_76
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
tff(f303,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl2_22
| ~ spl2_32 ),
inference(resolution,[],[f292,f193]) ).
tff(f1134,plain,
( ~ spl2_75
| ~ spl2_2
| ~ spl2_65 ),
inference(avatar_split_clause,[],[f914,f845,f92,f1131]) ).
tff(f1131,plain,
( spl2_75
<=> $less(count(add(sK1,sK0)),count(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
tff(f845,plain,
( spl2_65
<=> ! [X0: $int] :
( ~ $less(X0,count(sK0))
| $less(X0,count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).
tff(f914,plain,
( ~ $less(count(add(sK1,sK0)),count(sK0))
| ~ spl2_2
| ~ spl2_65 ),
inference(resolution,[],[f846,f93]) ).
tff(f846,plain,
( ! [X0: $int] :
( $less(X0,count(add(sK1,sK0)))
| ~ $less(X0,count(sK0)) )
| ~ spl2_65 ),
inference(avatar_component_clause,[],[f845]) ).
tff(f1129,plain,
( spl2_74
| ~ spl2_25
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f302,f291,f204,f1127]) ).
tff(f302,plain,
( ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl2_25
| ~ spl2_32 ),
inference(resolution,[],[f292,f205]) ).
tff(f921,plain,
( spl2_73
| ~ spl2_21
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f267,f246,f188,f919]) ).
tff(f919,plain,
( spl2_73
<=> ! [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,[spl2_73])]) ).
tff(f246,plain,
( spl2_27
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
tff(f267,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X0,$sum(X1,X2)),$sum(X3,X2))
| ~ $less($sum(X0,X1),X3) )
| ~ spl2_21
| ~ spl2_27 ),
inference(superposition,[],[f189,f247]) ).
tff(f247,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f246]) ).
tff(f913,plain,
( spl2_72
| ~ spl2_21
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f266,f246,f188,f911]) ).
tff(f911,plain,
( spl2_72
<=> ! [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,[spl2_72])]) ).
tff(f266,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( $less($sum(X3,X2),$sum(X0,$sum(X1,X2)))
| ~ $less(X3,$sum(X0,X1)) )
| ~ spl2_21
| ~ spl2_27 ),
inference(superposition,[],[f189,f247]) ).
tff(f909,plain,
( spl2_71
| ~ spl2_20
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f260,f246,f184,f907]) ).
tff(f907,plain,
( spl2_71
<=> ! [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,[spl2_71])]) ).
tff(f184,plain,
( spl2_20
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
tff(f260,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum($uminus(X0),$sum($uminus(X1),X2)) = $sum($uminus($sum(X1,X0)),X2) )
| ~ spl2_20
| ~ spl2_27 ),
inference(superposition,[],[f247,f185]) ).
tff(f185,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f184]) ).
tff(f905,plain,
( spl2_70
| ~ spl2_23
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f244,f204,f196,f903]) ).
tff(f244,plain,
( ! [X0: collection,X1: $int] :
( ( count(X0) = count(add(X1,X0)) )
| ( count(X0) = count(remove(X1,X0)) ) )
| ~ spl2_23
| ~ spl2_25 ),
inference(resolution,[],[f205,f197]) ).
tff(f901,plain,
( spl2_69
| ~ spl2_16
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f243,f204,f151,f899]) ).
tff(f899,plain,
( spl2_69
<=> ! [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,[spl2_69])]) ).
tff(f243,plain,
( ! [X2: $int,X0: $int,X1: collection] :
( ( count(add(X0,X1)) = count(add(X2,add(X0,X1))) )
| ~ in(X2,X1) )
| ~ spl2_16
| ~ spl2_25 ),
inference(resolution,[],[f205,f152]) ).
tff(f897,plain,
( spl2_68
| ~ spl2_22
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f240,f196,f192,f895]) ).
tff(f895,plain,
( spl2_68
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
tff(f240,plain,
( ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl2_22
| ~ spl2_23 ),
inference(resolution,[],[f197,f193]) ).
tff(f893,plain,
( spl2_67
| ~ spl2_15
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f239,f196,f147,f891]) ).
tff(f891,plain,
( spl2_67
<=> ! [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,[spl2_67])]) ).
tff(f239,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( count(remove(X0,remove(X1,X2))) = count(remove(X1,X2)) )
| in(X0,X2) )
| ~ spl2_15
| ~ spl2_23 ),
inference(resolution,[],[f197,f148]) ).
tff(f889,plain,
( spl2_66
| ~ spl2_16
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f233,f192,f151,f887]) ).
tff(f887,plain,
( spl2_66
<=> ! [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,[spl2_66])]) ).
tff(f233,plain,
( ! [X2: collection,X0: $int,X1: $int] :
( ( add(X1,X2) = add(X0,remove(X0,add(X1,X2))) )
| ~ in(X0,X2) )
| ~ spl2_16
| ~ spl2_22 ),
inference(resolution,[],[f193,f152]) ).
tff(f847,plain,
( spl2_65
| ~ spl2_17
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f739,f541,f161,f845]) ).
tff(f739,plain,
( ! [X0: $int] :
( ~ $less(X0,count(sK0))
| $less(X0,count(add(sK1,sK0))) )
| ~ spl2_17
| ~ spl2_55 ),
inference(resolution,[],[f543,f162]) ).
tff(f785,plain,
( spl2_64
| ~ spl2_9
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f310,f299,f122,f783]) ).
tff(f783,plain,
( spl2_64
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
tff(f122,plain,
( spl2_9
<=> ! [X0: $int,X1: collection] : in(X0,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f310,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1))) )
| ~ spl2_9
| ~ spl2_34 ),
inference(resolution,[],[f300,f123]) ).
tff(f123,plain,
( ! [X0: $int,X1: collection] : in(X0,add(X0,X1))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f122]) ).
tff(f781,plain,
( spl2_63
| ~ spl2_8
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f306,f291,f118,f779]) ).
tff(f118,plain,
( spl2_8
<=> ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f306,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,remove(X0,X1))) = $sum(1,count(remove(X0,X1))) )
| ~ spl2_8
| ~ spl2_32 ),
inference(resolution,[],[f292,f119]) ).
tff(f119,plain,
( ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1))
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f118]) ).
tff(f777,plain,
( spl2_62
| ~ spl2_20
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f231,f188,f184,f775]) ).
tff(f775,plain,
( spl2_62
<=> ! [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,[spl2_62])]) ).
tff(f231,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,$uminus(X1)),$uminus($sum(X1,X0)))
| ~ $less(X2,$uminus(X0)) )
| ~ spl2_20
| ~ spl2_21 ),
inference(superposition,[],[f189,f185]) ).
tff(f773,plain,
( spl2_61
| ~ spl2_20
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f227,f188,f184,f771]) ).
tff(f771,plain,
( spl2_61
<=> ! [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,[spl2_61])]) ).
tff(f227,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($uminus($sum(X1,X0)),$sum(X2,$uminus(X1)))
| ~ $less($uminus(X0),X2) )
| ~ spl2_20
| ~ spl2_21 ),
inference(superposition,[],[f189,f185]) ).
tff(f769,plain,
( spl2_60
| ~ spl2_17
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f223,f188,f161,f767]) ).
tff(f767,plain,
( spl2_60
<=> ! [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,[spl2_60])]) ).
tff(f223,plain,
( ! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X2,$sum(X0,X3))
| $less(X2,$sum(X1,X3)) )
| ~ spl2_17
| ~ spl2_21 ),
inference(resolution,[],[f189,f162]) ).
tff(f765,plain,
( spl2_59
| ~ spl2_14
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f171,f165,f143,f763]) ).
tff(f143,plain,
( spl2_14
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f171,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,1),X0)
| ( $sum(X1,1) = X0 )
| ~ $less(X1,X0) )
| ~ spl2_14
| ~ spl2_18 ),
inference(resolution,[],[f166,f144]) ).
tff(f144,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f699,plain,
( spl2_58
| ~ spl2_13
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f271,f246,f139,f697]) ).
tff(f139,plain,
( spl2_13
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f271,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl2_13
| ~ spl2_27 ),
inference(superposition,[],[f140,f247]) ).
tff(f140,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f139]) ).
tff(f695,plain,
( spl2_57
| ~ spl2_14
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f270,f246,f143,f693]) ).
tff(f270,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl2_14
| ~ spl2_27 ),
inference(superposition,[],[f144,f247]) ).
tff(f691,plain,
( spl2_56
| ~ spl2_17
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f172,f165,f161,f689]) ).
tff(f172,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl2_17
| ~ spl2_18 ),
inference(resolution,[],[f166,f162]) ).
tff(f544,plain,
( spl2_55
| ~ spl2_2
| ~ spl2_42 ),
inference(avatar_split_clause,[],[f444,f382,f92,f541]) ).
tff(f382,plain,
( spl2_42
<=> ! [X0: $int] :
( $less(count(sK0),X0)
| $less(X0,count(add(sK1,sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
tff(f444,plain,
( $less(count(sK0),count(add(sK1,sK0)))
| ~ spl2_2
| ~ spl2_42 ),
inference(resolution,[],[f383,f93]) ).
tff(f383,plain,
( ! [X0: $int] :
( $less(X0,count(add(sK1,sK0)))
| $less(count(sK0),X0) )
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f382]) ).
tff(f525,plain,
( spl2_54
| ~ spl2_11
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f263,f246,f130,f523]) ).
tff(f263,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl2_11
| ~ spl2_27 ),
inference(superposition,[],[f247,f131]) ).
tff(f521,plain,
( spl2_53
| ~ spl2_11
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f258,f246,f130,f519]) ).
tff(f258,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl2_11
| ~ spl2_27 ),
inference(superposition,[],[f247,f131]) ).
tff(f517,plain,
( spl2_52
| ~ spl2_9
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f242,f204,f122,f515]) ).
tff(f515,plain,
( spl2_52
<=> ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
tff(f242,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl2_9
| ~ spl2_25 ),
inference(resolution,[],[f205,f123]) ).
tff(f513,plain,
( spl2_51
| ~ spl2_8
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f238,f196,f118,f511]) ).
tff(f511,plain,
( spl2_51
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
tff(f238,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) )
| ~ spl2_8
| ~ spl2_23 ),
inference(resolution,[],[f197,f119]) ).
tff(f509,plain,
( spl2_50
| ~ spl2_9
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f232,f192,f122,f507]) ).
tff(f507,plain,
( spl2_50
<=> ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
tff(f232,plain,
( ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) )
| ~ spl2_9
| ~ spl2_22 ),
inference(resolution,[],[f193,f123]) ).
tff(f505,plain,
( spl2_49
| ~ spl2_13
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f169,f161,f139,f503]) ).
tff(f169,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl2_13
| ~ spl2_17 ),
inference(resolution,[],[f162,f140]) ).
tff(f442,plain,
( spl2_48
| ~ spl2_10
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f262,f246,f126,f440]) ).
tff(f440,plain,
( spl2_48
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
tff(f262,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl2_10
| ~ spl2_27 ),
inference(superposition,[],[f247,f127]) ).
tff(f438,plain,
( spl2_47
| ~ spl2_11
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f229,f188,f130,f436]) ).
tff(f229,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl2_11
| ~ spl2_21 ),
inference(superposition,[],[f189,f131]) ).
tff(f434,plain,
( spl2_46
| ~ spl2_11
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f225,f188,f130,f432]) ).
tff(f225,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl2_11
| ~ spl2_21 ),
inference(superposition,[],[f189,f131]) ).
tff(f430,plain,
( spl2_45
| ~ spl2_11
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f212,f184,f130,f428]) ).
tff(f428,plain,
( spl2_45
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
tff(f212,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl2_11
| ~ spl2_20 ),
inference(superposition,[],[f185,f131]) ).
tff(f411,plain,
( spl2_44
| ~ spl2_10
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f228,f188,f126,f409]) ).
tff(f409,plain,
( spl2_44
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
tff(f228,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl2_10
| ~ spl2_21 ),
inference(superposition,[],[f189,f127]) ).
tff(f407,plain,
( spl2_43
| ~ spl2_10
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f224,f188,f126,f405]) ).
tff(f224,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl2_10
| ~ spl2_21 ),
inference(superposition,[],[f189,f127]) ).
tff(f384,plain,
( spl2_42
| ~ spl2_19
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f363,f348,f180,f382]) ).
tff(f363,plain,
( ! [X0: $int] :
( $less(count(sK0),X0)
| $less(X0,count(add(sK1,sK0))) )
| ~ spl2_19
| ~ spl2_38 ),
inference(resolution,[],[f349,f181]) ).
tff(f362,plain,
( spl2_41
| ~ spl2_10
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f272,f246,f126,f360]) ).
tff(f272,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl2_10
| ~ spl2_27 ),
inference(evaluation,[],[f257]) ).
tff(f257,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl2_10
| ~ spl2_27 ),
inference(superposition,[],[f247,f127]) ).
tff(f358,plain,
( spl2_40
| ~ spl2_4
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f173,f165,f100,f356]) ).
tff(f356,plain,
( spl2_40
<=> ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
tff(f173,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl2_4
| ~ spl2_18 ),
inference(resolution,[],[f166,f101]) ).
tff(f354,plain,
( spl2_39
| ~ spl2_11
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f158,f143,f130,f352]) ).
tff(f158,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl2_11
| ~ spl2_14 ),
inference(superposition,[],[f144,f131]) ).
tff(f350,plain,
( spl2_38
| ~ spl2_11
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f155,f139,f130,f348]) ).
tff(f155,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl2_11
| ~ spl2_13 ),
inference(superposition,[],[f140,f131]) ).
tff(f335,plain,
( spl2_37
| ~ spl2_3
| ~ spl2_5
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f309,f291,f104,f96,f333]) ).
tff(f333,plain,
( spl2_37
<=> ! [X0: $int] : ( 1 = count(add(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
tff(f96,plain,
( spl2_3
<=> ! [X0: $int] : ~ in(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f104,plain,
( spl2_5
<=> ( 0 = count(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f309,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl2_3
| ~ spl2_5
| ~ spl2_32 ),
inference(evaluation,[],[f308]) ).
tff(f308,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,0) )
| ~ spl2_3
| ~ spl2_5
| ~ spl2_32 ),
inference(forward_demodulation,[],[f304,f106]) ).
tff(f106,plain,
( ( 0 = count(empty) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f304,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) )
| ~ spl2_3
| ~ spl2_32 ),
inference(resolution,[],[f292,f97]) ).
tff(f97,plain,
( ! [X0: $int] : ~ in(X0,empty)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f331,plain,
( spl2_36
| ~ spl2_3
| ~ spl2_5
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f241,f196,f104,f96,f329]) ).
tff(f241,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl2_3
| ~ spl2_5
| ~ spl2_23 ),
inference(forward_demodulation,[],[f237,f106]) ).
tff(f237,plain,
( ! [X0: $int] : ( count(empty) = count(remove(X0,empty)) )
| ~ spl2_3
| ~ spl2_23 ),
inference(resolution,[],[f197,f97]) ).
tff(f318,plain,
( spl2_35
| ~ spl2_2
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f154,f139,f92,f316]) ).
tff(f154,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl2_2
| ~ spl2_13 ),
inference(resolution,[],[f140,f93]) ).
tff(f301,plain,
spl2_34,
inference(avatar_split_clause,[],[f85,f299]) ).
tff(f85,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f79,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f79,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f68]) ).
tff(f68,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,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,[],[f17]) ).
tff(f17,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(f297,plain,
spl2_33,
inference(avatar_split_clause,[],[f84,f295]) ).
tff(f295,plain,
( spl2_33
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
tff(f84,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f80,f18]) ).
tff(f80,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),-1) ) ),
inference(evaluation,[],[f69]) ).
tff(f69,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) ),
inference(cnf_transformation,[],[f49]) ).
tff(f293,plain,
spl2_32,
inference(avatar_split_clause,[],[f83,f291]) ).
tff(f83,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f64,f18]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,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(f289,plain,
spl2_31,
inference(avatar_split_clause,[],[f82,f287]) ).
tff(f287,plain,
( spl2_31
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
tff(f82,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f65,f18]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f285,plain,
( spl2_30
| ~ spl2_19
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f234,f188,f180,f283]) ).
tff(f283,plain,
( spl2_30
<=> ! [X0: $int] :
( $less($sum(X0,count(sK0)),count(add(sK1,sK0)))
| ~ $less(X0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
tff(f234,plain,
( ! [X0: $int] :
( $less($sum(X0,count(sK0)),count(add(sK1,sK0)))
| ~ $less(X0,1) )
| ~ spl2_19
| ~ spl2_21 ),
inference(resolution,[],[f181,f189]) ).
tff(f256,plain,
spl2_29,
inference(avatar_split_clause,[],[f75,f254]) ).
tff(f75,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,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,[],[f52]) ).
tff(f52,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(f252,plain,
spl2_28,
inference(avatar_split_clause,[],[f70,f250]) ).
tff(f70,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,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,[],[f50]) ).
tff(f50,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(f248,plain,
spl2_27,
inference(avatar_split_clause,[],[f19,f246]) ).
tff(f19,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f210,plain,
spl2_26,
inference(avatar_split_clause,[],[f67,f208]) ).
tff(f67,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,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(f206,plain,
spl2_25,
inference(avatar_split_clause,[],[f66,f204]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f202,plain,
spl2_24,
inference(avatar_split_clause,[],[f63,f200]) ).
tff(f200,plain,
( spl2_24
<=> ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
tff(f63,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,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(f198,plain,
spl2_23,
inference(avatar_split_clause,[],[f62,f196]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f194,plain,
spl2_22,
inference(avatar_split_clause,[],[f61,f192]) ).
tff(f61,plain,
! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,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(f190,plain,
spl2_21,
inference(avatar_split_clause,[],[f26,f188]) ).
tff(f26,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f186,plain,
spl2_20,
inference(avatar_split_clause,[],[f21,f184]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f182,plain,
( spl2_19
| ~ spl2_1
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f168,f161,f87,f180]) ).
tff(f168,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,count(sK0)))
| $less(X0,count(add(sK1,sK0))) )
| ~ spl2_1
| ~ spl2_17 ),
inference(resolution,[],[f162,f89]) ).
tff(f167,plain,
spl2_18,
inference(avatar_split_clause,[],[f25,f165]) ).
tff(f25,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f163,plain,
spl2_17,
inference(avatar_split_clause,[],[f24,f161]) ).
tff(f24,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f153,plain,
spl2_16,
inference(avatar_split_clause,[],[f73,f151]) ).
tff(f73,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f149,plain,
spl2_15,
inference(avatar_split_clause,[],[f71,f147]) ).
tff(f71,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f145,plain,
spl2_14,
inference(avatar_split_clause,[],[f29,f143]) ).
tff(f29,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f141,plain,
spl2_13,
inference(avatar_split_clause,[],[f27,f139]) ).
tff(f27,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f136,plain,
spl2_12,
inference(avatar_split_clause,[],[f58,f134]) ).
tff(f58,plain,
! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,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(f132,plain,
spl2_11,
inference(avatar_split_clause,[],[f18,f130]) ).
tff(f128,plain,
spl2_10,
inference(avatar_split_clause,[],[f22,f126]) ).
tff(f22,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f124,plain,
spl2_9,
inference(avatar_split_clause,[],[f60,f122]) ).
tff(f60,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(f120,plain,
spl2_8,
inference(avatar_split_clause,[],[f59,f118]) ).
tff(f59,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(f116,plain,
spl2_7,
inference(avatar_split_clause,[],[f28,f114]) ).
tff(f114,plain,
( spl2_7
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f28,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f112,plain,
spl2_6,
inference(avatar_split_clause,[],[f20,f110]) ).
tff(f110,plain,
( spl2_6
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f20,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f107,plain,
spl2_5,
inference(avatar_split_clause,[],[f76,f104]) ).
tff(f76,plain,
0 = count(empty),
inference(equality_resolution,[],[f57]) ).
tff(f57,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f102,plain,
spl2_4,
inference(avatar_split_clause,[],[f56,f100]) ).
tff(f56,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: collection] : ~ $less(count(X0),0),
inference(rectify,[],[f16]) ).
tff(f16,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(f98,plain,
spl2_3,
inference(avatar_split_clause,[],[f55,f96]) ).
tff(f55,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(f94,plain,
spl2_2,
inference(avatar_split_clause,[],[f23,f92]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f90,plain,
spl2_1,
inference(avatar_split_clause,[],[f81,f87]) ).
tff(f81,plain,
$less($sum(1,count(sK0)),count(add(sK1,sK0))),
inference(forward_demodulation,[],[f54,f18]) ).
tff(f54,plain,
$less($sum(count(sK0),1),count(add(sK1,sK0))),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
$less($sum(count(sK0),1),count(add(sK1,sK0))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f43]) ).
tff(f43,plain,
( ? [X0: collection,X1: $int] : $less($sum(count(X0),1),count(add(X1,X0)))
=> $less($sum(count(sK0),1),count(add(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0: collection,X1: $int] : $less($sum(count(X0),1),count(add(X1,X0))),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
~ ! [X0: collection,X1: $int] : ~ $less($sum(count(X0),1),count(add(X1,X0))),
inference(theory_normalization,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection,X1: $int] : $greatereq($sum(count(X0),1),count(add(X1,X0))),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection,X1: $int] : $greatereq($sum(count(X0),1),count(add(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT034_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 22:18:55 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (12437)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (12440)WARNING: value z3 for option sas not known
% 0.15/0.38 % (12441)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (12439)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (12444)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)
% 0.15/0.38 % (12442)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)
% 0.15/0.38 % (12438)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (12443)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)
% 0.15/0.38 % (12440)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)
% 0.15/0.38 % (12438)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12439)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12439)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12439)------------------------------
% 0.15/0.38 % (12439)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12439)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (12441)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12439)Memory used [KB]: 766
% 0.15/0.38 % (12439)Time elapsed: 0.003 s
% 0.15/0.38 % (12439)Instructions burned: 3 (million)
% 0.15/0.38 % (12439)------------------------------
% 0.15/0.38 % (12439)------------------------------
% 0.15/0.38 % (12441)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12441)------------------------------
% 0.15/0.38 % (12441)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12441)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (12441)Memory used [KB]: 766
% 0.15/0.38 % (12441)Time elapsed: 0.003 s
% 0.15/0.38 % (12441)Instructions burned: 3 (million)
% 0.15/0.38 % (12441)------------------------------
% 0.15/0.38 % (12441)------------------------------
% 0.15/0.38 % (12438)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12438)------------------------------
% 0.15/0.38 % (12438)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12438)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (12438)Memory used [KB]: 766
% 0.15/0.38 % (12438)Time elapsed: 0.004 s
% 0.15/0.38 % (12438)Instructions burned: 3 (million)
% 0.15/0.38 % (12438)------------------------------
% 0.15/0.38 % (12438)------------------------------
% 0.15/0.40 % (12445)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.40 % (12446)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)
% 0.15/0.40 % (12445)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.40 % (12447)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)
% 0.15/0.40 % (12445)Terminated due to inappropriate strategy.
% 0.15/0.40 % (12445)------------------------------
% 0.15/0.40 % (12445)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (12445)Termination reason: Inappropriate
% 0.15/0.40
% 0.15/0.40 % (12445)Memory used [KB]: 765
% 0.15/0.40 % (12445)Time elapsed: 0.003 s
% 0.15/0.40 % (12445)Instructions burned: 3 (million)
% 0.15/0.40 % (12445)------------------------------
% 0.15/0.40 % (12445)------------------------------
% 0.21/0.42 % (12448)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.21/0.45 % (12442)First to succeed.
% 0.21/0.46 % (12442)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (12442)------------------------------
% 0.21/0.46 % (12442)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.46 % (12442)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (12442)Memory used [KB]: 1667
% 0.21/0.46 % (12442)Time elapsed: 0.076 s
% 0.21/0.46 % (12442)Instructions burned: 120 (million)
% 0.21/0.46 % (12442)------------------------------
% 0.21/0.46 % (12442)------------------------------
% 0.21/0.46 % (12437)Success in time 0.081 s
%------------------------------------------------------------------------------