TSTP Solution File: DAT041_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT041_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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:03:46 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 90
% Syntax : Number of formulae : 266 ( 59 unt; 6 typ; 0 def)
% Number of atoms : 633 ( 134 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 669 ( 296 ~; 282 |; 15 &)
% ( 74 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 693 ( 116 atm; 184 fun; 112 num; 281 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 65 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 11 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 384 ( 378 !; 6 ?; 384 :)
% 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(f745,plain,
$false,
inference(avatar_sat_refutation,[],[f87,f91,f95,f99,f104,f111,f115,f119,f123,f127,f131,f135,f139,f144,f148,f152,f156,f166,f170,f174,f192,f196,f200,f204,f208,f212,f216,f230,f255,f259,f263,f293,f297,f301,f305,f322,f334,f338,f369,f373,f377,f381,f385,f426,f430,f449,f453,f457,f461,f465,f524,f528,f532,f536,f540,f553,f730,f734,f738,f744]) ).
tff(f744,plain,
( ~ spl0_38
| ~ spl0_43
| ~ spl0_54 ),
inference(avatar_contradiction_clause,[],[f743]) ).
tff(f743,plain,
( $false
| ~ spl0_38
| ~ spl0_43
| ~ spl0_54 ),
inference(evaluation,[],[f742]) ).
tff(f742,plain,
( ~ $less(1,2)
| ~ spl0_38
| ~ spl0_43
| ~ spl0_54 ),
inference(forward_demodulation,[],[f741,f337]) ).
tff(f337,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f336]) ).
tff(f336,plain,
( spl0_38
<=> ! [X0: $int] : ( 1 = count(add(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f741,plain,
( ! [X0: $int] : ~ $less(count(add(X0,empty)),2)
| ~ spl0_43
| ~ spl0_54 ),
inference(superposition,[],[f384,f535]) ).
tff(f535,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f534]) ).
tff(f534,plain,
( spl0_54
<=> ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
tff(f384,plain,
( ! [X0: $int,X1: $int] : ~ $less(count(add(X1,add(X0,empty))),2)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f383]) ).
tff(f383,plain,
( spl0_43
<=> ! [X0: $int,X1: $int] : ~ $less(count(add(X1,add(X0,empty))),2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f738,plain,
( spl0_59
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f278,f253,f142,f736]) ).
tff(f736,plain,
( spl0_59
<=> ! [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_59])]) ).
tff(f142,plain,
( spl0_14
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f253,plain,
( spl0_29
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f278,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,$sum(X0,$sum(X1,1)))
| $less($sum(X0,X1),X2) )
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[],[f143,f254]) ).
tff(f254,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f253]) ).
tff(f143,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
tff(f734,plain,
( spl0_58
| ~ spl0_15
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f277,f253,f146,f732]) ).
tff(f732,plain,
( spl0_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,[spl0_58])]) ).
tff(f146,plain,
( spl0_15
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f277,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,$sum(X0,$sum(X1,1)))
| ~ $less($sum(X0,X1),X2) )
| ~ spl0_15
| ~ spl0_29 ),
inference(superposition,[],[f147,f254]) ).
tff(f147,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f146]) ).
tff(f730,plain,
( spl0_57
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f181,f168,f164,f728]) ).
tff(f728,plain,
( spl0_57
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
tff(f164,plain,
( spl0_18
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f168,plain,
( spl0_19
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f181,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| ( X0 = X1 )
| ~ $less(X2,X0)
| $less(X2,X1) )
| ~ spl0_18
| ~ spl0_19 ),
inference(resolution,[],[f169,f165]) ).
tff(f165,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f164]) ).
tff(f169,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f168]) ).
tff(f553,plain,
( spl0_56
| ~ spl0_12
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f270,f253,f133,f551]) ).
tff(f551,plain,
( spl0_56
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
tff(f133,plain,
( spl0_12
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f270,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl0_12
| ~ spl0_29 ),
inference(superposition,[],[f254,f134]) ).
tff(f134,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f540,plain,
( spl0_55
| ~ spl0_12
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f265,f253,f133,f538]) ).
tff(f538,plain,
( spl0_55
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
tff(f265,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl0_12
| ~ spl0_29 ),
inference(superposition,[],[f254,f134]) ).
tff(f536,plain,
( spl0_54
| ~ spl0_10
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f249,f210,f125,f534]) ).
tff(f125,plain,
( spl0_10
<=> ! [X0: $int,X1: collection] : in(X0,add(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f210,plain,
( spl0_26
<=> ! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f249,plain,
( ! [X0: $int,X1: collection] : ( count(add(X0,X1)) = count(add(X0,add(X0,X1))) )
| ~ spl0_10
| ~ spl0_26 ),
inference(resolution,[],[f211,f126]) ).
tff(f126,plain,
( ! [X0: $int,X1: collection] : in(X0,add(X0,X1))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f211,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(X1) = count(add(X0,X1)) ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f210]) ).
tff(f532,plain,
( spl0_53
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f245,f202,f121,f530]) ).
tff(f530,plain,
( spl0_53
<=> ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f121,plain,
( spl0_9
<=> ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f202,plain,
( spl0_24
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f245,plain,
( ! [X0: $int,X1: collection] : ( count(remove(X0,X1)) = count(remove(X0,remove(X0,X1))) )
| ~ spl0_9
| ~ spl0_24 ),
inference(resolution,[],[f203,f122]) ).
tff(f122,plain,
( ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f203,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) = count(X1) ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f202]) ).
tff(f528,plain,
( spl0_52
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f242,f198,f125,f526]) ).
tff(f526,plain,
( spl0_52
<=> ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f198,plain,
( spl0_23
<=> ! [X0: $int,X1: collection] :
( ( add(X0,remove(X0,X1)) = X1 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f242,plain,
( ! [X0: $int,X1: collection] : ( add(X0,X1) = add(X0,remove(X0,add(X0,X1))) )
| ~ spl0_10
| ~ spl0_23 ),
inference(resolution,[],[f199,f126]) ).
tff(f199,plain,
( ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( add(X0,remove(X0,X1)) = X1 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f198]) ).
tff(f524,plain,
( spl0_51
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f175,f164,f142,f522]) ).
tff(f522,plain,
( spl0_51
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f175,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl0_14
| ~ spl0_18 ),
inference(resolution,[],[f165,f143]) ).
tff(f465,plain,
( spl0_50
| ~ spl0_11
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f269,f253,f129,f463]) ).
tff(f463,plain,
( spl0_50
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f129,plain,
( spl0_11
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f269,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl0_11
| ~ spl0_29 ),
inference(superposition,[],[f254,f130]) ).
tff(f130,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f129]) ).
tff(f461,plain,
( spl0_49
| ~ spl0_12
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f239,f194,f133,f459]) ).
tff(f459,plain,
( spl0_49
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f194,plain,
( spl0_22
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f239,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f195,f134]) ).
tff(f195,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f457,plain,
( spl0_48
| ~ spl0_1
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f386,f367,f85,f455]) ).
tff(f455,plain,
( spl0_48
<=> ! [X0: collection,X1: $int] : $less(count(X0),count(add(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f85,plain,
( spl0_1
<=> ! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(1,count(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f367,plain,
( spl0_39
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f386,plain,
( ! [X0: collection,X1: $int] : $less(count(X0),count(add(X1,X0)))
| ~ spl0_1
| ~ spl0_39 ),
inference(resolution,[],[f368,f86]) ).
tff(f86,plain,
( ! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(1,count(X0)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f368,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f367]) ).
tff(f453,plain,
( spl0_47
| ~ spl0_12
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f235,f194,f133,f451]) ).
tff(f451,plain,
( spl0_47
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f235,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl0_12
| ~ spl0_22 ),
inference(superposition,[],[f195,f134]) ).
tff(f449,plain,
( spl0_46
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f218,f190,f133,f447]) ).
tff(f447,plain,
( spl0_46
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f190,plain,
( spl0_21
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f218,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f191,f134]) ).
tff(f191,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f430,plain,
( spl0_45
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f238,f194,f129,f428]) ).
tff(f428,plain,
( spl0_45
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f238,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f195,f130]) ).
tff(f426,plain,
( spl0_44
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f234,f194,f129,f424]) ).
tff(f424,plain,
( spl0_44
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f234,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[],[f195,f130]) ).
tff(f385,plain,
( spl0_43
| ~ spl0_1
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f359,f336,f85,f383]) ).
tff(f359,plain,
( ! [X0: $int,X1: $int] : ~ $less(count(add(X1,add(X0,empty))),2)
| ~ spl0_1
| ~ spl0_38 ),
inference(evaluation,[],[f358]) ).
tff(f358,plain,
( ! [X0: $int,X1: $int] : ~ $less(count(add(X1,add(X0,empty))),$sum(1,1))
| ~ spl0_1
| ~ spl0_38 ),
inference(superposition,[],[f86,f337]) ).
tff(f381,plain,
( spl0_42
| ~ spl0_11
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f279,f253,f129,f379]) ).
tff(f379,plain,
( spl0_42
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f279,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl0_11
| ~ spl0_29 ),
inference(evaluation,[],[f264]) ).
tff(f264,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl0_11
| ~ spl0_29 ),
inference(superposition,[],[f254,f130]) ).
tff(f377,plain,
( spl0_41
| ~ spl0_4
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f177,f168,f97,f375]) ).
tff(f375,plain,
( spl0_41
<=> ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f97,plain,
( spl0_4
<=> ! [X0: collection] : ~ $less(count(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f177,plain,
( ! [X0: collection] :
( $less(0,count(X0))
| ( 0 = count(X0) ) )
| ~ spl0_4
| ~ spl0_19 ),
inference(resolution,[],[f169,f98]) ).
tff(f98,plain,
( ! [X0: collection] : ~ $less(count(X0),0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
tff(f373,plain,
( spl0_40
| ~ spl0_12
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f161,f146,f133,f371]) ).
tff(f371,plain,
( spl0_40
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f161,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f147,f134]) ).
tff(f369,plain,
( spl0_39
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f158,f142,f133,f367]) ).
tff(f158,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f143,f134]) ).
tff(f338,plain,
( spl0_38
| ~ spl0_3
| ~ spl0_5
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f313,f295,f101,f93,f336]) ).
tff(f93,plain,
( spl0_3
<=> ! [X0: $int] : ~ in(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f101,plain,
( spl0_5
<=> ( 0 = count(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f295,plain,
( spl0_33
<=> ! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f313,plain,
( ! [X0: $int] : ( 1 = count(add(X0,empty)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_33 ),
inference(evaluation,[],[f312]) ).
tff(f312,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,0) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_33 ),
inference(forward_demodulation,[],[f308,f103]) ).
tff(f103,plain,
( ( 0 = count(empty) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
tff(f308,plain,
( ! [X0: $int] : ( count(add(X0,empty)) = $sum(1,count(empty)) )
| ~ spl0_3
| ~ spl0_33 ),
inference(resolution,[],[f296,f94]) ).
tff(f94,plain,
( ! [X0: $int] : ~ in(X0,empty)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f93]) ).
tff(f296,plain,
( ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f295]) ).
tff(f334,plain,
( spl0_37
| ~ spl0_3
| ~ spl0_5
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f248,f202,f101,f93,f332]) ).
tff(f332,plain,
( spl0_37
<=> ! [X0: $int] : ( 0 = count(remove(X0,empty)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f248,plain,
( ! [X0: $int] : ( 0 = count(remove(X0,empty)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f244,f103]) ).
tff(f244,plain,
( ! [X0: $int] : ( count(empty) = count(remove(X0,empty)) )
| ~ spl0_3
| ~ spl0_24 ),
inference(resolution,[],[f203,f94]) ).
tff(f322,plain,
( spl0_36
| ~ spl0_1
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f176,f168,f85,f320]) ).
tff(f320,plain,
( spl0_36
<=> ! [X0: $int,X1: collection] :
( $less($sum(1,count(X1)),count(add(X0,X1)))
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f176,plain,
( ! [X0: $int,X1: collection] :
( $less($sum(1,count(X1)),count(add(X0,X1)))
| ( count(add(X0,X1)) = $sum(1,count(X1)) ) )
| ~ spl0_1
| ~ spl0_19 ),
inference(resolution,[],[f169,f86]) ).
tff(f305,plain,
spl0_35,
inference(avatar_split_clause,[],[f83,f303]) ).
tff(f303,plain,
( spl0_35
<=> ! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f83,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(-1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f77,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f77,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f66]) ).
tff(f66,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,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(f301,plain,
spl0_34,
inference(avatar_split_clause,[],[f82,f299]) ).
tff(f299,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(f82,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) != $sum(-1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f78,f18]) ).
tff(f78,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),-1) ) ),
inference(evaluation,[],[f67]) ).
tff(f67,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) ),
inference(cnf_transformation,[],[f47]) ).
tff(f297,plain,
spl0_33,
inference(avatar_split_clause,[],[f81,f295]) ).
tff(f81,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(1,count(X1)) )
| in(X0,X1) ),
inference(forward_demodulation,[],[f62,f18]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f45,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(f293,plain,
spl0_32,
inference(avatar_split_clause,[],[f80,f291]) ).
tff(f291,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(f80,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) != $sum(1,count(X1)) )
| ~ in(X0,X1) ),
inference(forward_demodulation,[],[f63,f18]) ).
tff(f63,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f263,plain,
spl0_31,
inference(avatar_split_clause,[],[f73,f261]) ).
tff(f261,plain,
( spl0_31
<=> ! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f73,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,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,[],[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(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(f259,plain,
spl0_30,
inference(avatar_split_clause,[],[f68,f257]) ).
tff(f257,plain,
( spl0_30
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f68,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,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,[],[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(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(f255,plain,
spl0_29,
inference(avatar_split_clause,[],[f19,f253]) ).
tff(f19,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f230,plain,
( spl0_28
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f178,f168,f117,f228]) ).
tff(f228,plain,
( spl0_28
<=> ! [X0: $int] :
( $less(1,count(add(X0,empty)))
| ( 1 = count(add(X0,empty)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f117,plain,
( spl0_8
<=> ! [X0: $int] : ~ $less(count(add(X0,empty)),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f178,plain,
( ! [X0: $int] :
( $less(1,count(add(X0,empty)))
| ( 1 = count(add(X0,empty)) ) )
| ~ spl0_8
| ~ spl0_19 ),
inference(resolution,[],[f169,f118]) ).
tff(f118,plain,
( ! [X0: $int] : ~ $less(count(add(X0,empty)),1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f216,plain,
spl0_27,
inference(avatar_split_clause,[],[f65,f214]) ).
tff(f214,plain,
( spl0_27
<=> ! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f65,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(X1) != count(add(X0,X1)) ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,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(f212,plain,
spl0_26,
inference(avatar_split_clause,[],[f64,f210]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(add(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f208,plain,
spl0_25,
inference(avatar_split_clause,[],[f61,f206]) ).
tff(f206,plain,
( spl0_25
<=> ! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f61,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(remove(X0,X1)) != count(X1) ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,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(f204,plain,
spl0_24,
inference(avatar_split_clause,[],[f60,f202]) ).
tff(f60,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = count(X1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f200,plain,
spl0_23,
inference(avatar_split_clause,[],[f59,f198]) ).
tff(f59,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(f196,plain,
spl0_22,
inference(avatar_split_clause,[],[f26,f194]) ).
tff(f26,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f192,plain,
spl0_21,
inference(avatar_split_clause,[],[f21,f190]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f174,plain,
( spl0_20
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f157,f142,f89,f172]) ).
tff(f172,plain,
( spl0_20
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f89,plain,
( spl0_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f157,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl0_2
| ~ spl0_14 ),
inference(resolution,[],[f143,f90]) ).
tff(f90,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f89]) ).
tff(f170,plain,
spl0_19,
inference(avatar_split_clause,[],[f25,f168]) ).
tff(f25,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f166,plain,
spl0_18,
inference(avatar_split_clause,[],[f24,f164]) ).
tff(f24,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f156,plain,
spl0_17,
inference(avatar_split_clause,[],[f71,f154]) ).
tff(f154,plain,
( spl0_17
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f71,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tff(f152,plain,
spl0_16,
inference(avatar_split_clause,[],[f69,f150]) ).
tff(f150,plain,
( spl0_16
<=> ! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f69,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,X1)
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f148,plain,
spl0_15,
inference(avatar_split_clause,[],[f29,f146]) ).
tff(f29,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f144,plain,
spl0_14,
inference(avatar_split_clause,[],[f27,f142]) ).
tff(f27,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f139,plain,
spl0_13,
inference(avatar_split_clause,[],[f56,f137]) ).
tff(f137,plain,
( spl0_13
<=> ! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f56,plain,
! [X0: collection] :
( ( empty = X0 )
| ( 0 != count(X0) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,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(f135,plain,
spl0_12,
inference(avatar_split_clause,[],[f18,f133]) ).
tff(f131,plain,
spl0_11,
inference(avatar_split_clause,[],[f22,f129]) ).
tff(f22,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f127,plain,
spl0_10,
inference(avatar_split_clause,[],[f58,f125]) ).
tff(f58,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(f123,plain,
spl0_9,
inference(avatar_split_clause,[],[f57,f121]) ).
tff(f57,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(f119,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f107,f101,f85,f117]) ).
tff(f107,plain,
( ! [X0: $int] : ~ $less(count(add(X0,empty)),1)
| ~ spl0_1
| ~ spl0_5 ),
inference(evaluation,[],[f106]) ).
tff(f106,plain,
( ! [X0: $int] : ~ $less(count(add(X0,empty)),$sum(1,0))
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f86,f103]) ).
tff(f115,plain,
spl0_7,
inference(avatar_split_clause,[],[f28,f113]) ).
tff(f113,plain,
( spl0_7
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f28,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f111,plain,
spl0_6,
inference(avatar_split_clause,[],[f20,f109]) ).
tff(f109,plain,
( spl0_6
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f20,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f104,plain,
spl0_5,
inference(avatar_split_clause,[],[f74,f101]) ).
tff(f74,plain,
0 = count(empty),
inference(equality_resolution,[],[f55]) ).
tff(f55,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f99,plain,
spl0_4,
inference(avatar_split_clause,[],[f54,f97]) ).
tff(f54,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(f95,plain,
spl0_3,
inference(avatar_split_clause,[],[f53,f93]) ).
tff(f53,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(f91,plain,
spl0_2,
inference(avatar_split_clause,[],[f23,f89]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f87,plain,
spl0_1,
inference(avatar_split_clause,[],[f79,f85]) ).
tff(f79,plain,
! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(1,count(X0))),
inference(forward_demodulation,[],[f52,f18]) ).
tff(f52,plain,
! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: collection,X1: $int] : ~ $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
~ ? [X0: collection,X1: $int] : $less(count(add(X1,X0)),$sum(count(X0),1)),
inference(theory_normalization,[],[f14]) ).
tff(f14,negated_conjecture,
~ ? [X0: collection,X1: $int] : $greater($sum(count(X0),1),count(add(X1,X0))),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
? [X0: collection,X1: $int] : $greater($sum(count(X0),1),count(add(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT041_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:16:13 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (6160)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (6164)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (6164)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (6164)Terminated due to inappropriate strategy.
% 0.15/0.37 % (6164)------------------------------
% 0.15/0.37 % (6164)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.37 % (6164)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (6164)Memory used [KB]: 765
% 0.15/0.37 % (6164)Time elapsed: 0.002 s
% 0.15/0.37 % (6164)Instructions burned: 3 (million)
% 0.15/0.37 % (6164)------------------------------
% 0.15/0.37 % (6164)------------------------------
% 0.15/0.37 % (6165)WARNING: value z3 for option sas not known
% 0.15/0.37 % (6163)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (6166)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (6167)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)
% 0.15/0.37 % (6165)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)
% 0.15/0.37 % (6169)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)
% 0.15/0.37 % (6168)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)
% 0.15/0.37 % (6163)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (6163)Terminated due to inappropriate strategy.
% 0.15/0.37 % (6163)------------------------------
% 0.15/0.37 % (6163)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.37 % (6163)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (6163)Memory used [KB]: 764
% 0.15/0.37 % (6163)Time elapsed: 0.002 s
% 0.15/0.37 % (6163)Instructions burned: 3 (million)
% 0.15/0.37 % (6163)------------------------------
% 0.15/0.37 % (6163)------------------------------
% 0.15/0.37 % (6166)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (6166)Terminated due to inappropriate strategy.
% 0.15/0.37 % (6166)------------------------------
% 0.15/0.37 % (6166)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.37 % (6166)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (6166)Memory used [KB]: 764
% 0.15/0.37 % (6166)Time elapsed: 0.002 s
% 0.15/0.37 % (6166)Instructions burned: 3 (million)
% 0.15/0.37 % (6166)------------------------------
% 0.15/0.37 % (6166)------------------------------
% 0.15/0.38 % (6175)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.38 % (6175)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (6175)Terminated due to inappropriate strategy.
% 0.15/0.38 % (6175)------------------------------
% 0.15/0.38 % (6175)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (6175)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (6175)Memory used [KB]: 764
% 0.15/0.38 % (6175)Time elapsed: 0.001 s
% 0.15/0.38 % (6175)Instructions burned: 3 (million)
% 0.15/0.38 % (6175)------------------------------
% 0.15/0.38 % (6175)------------------------------
% 0.15/0.39 % (6183)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)
% 0.15/0.39 % (6180)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)
% 0.15/0.39 % (6179)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.40 % (6167)First to succeed.
% 0.21/0.40 % (6167)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (6167)------------------------------
% 0.21/0.41 % (6167)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41 % (6167)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (6167)Memory used [KB]: 1176
% 0.21/0.41 % (6167)Time elapsed: 0.029 s
% 0.21/0.41 % (6167)Instructions burned: 44 (million)
% 0.21/0.41 % (6167)------------------------------
% 0.21/0.41 % (6167)------------------------------
% 0.21/0.41 % (6160)Success in time 0.044 s
%------------------------------------------------------------------------------